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DISPLAY DEVICE WITH TOTAL INTERNAL REFLECTIONCROSS REFERENCE TO RELATED APPLICATIONS[0001] This application claims benefit of commonly invented and assigned United StatesProvisional Patent Applications No. 62/105,905, filed on 2 1 January 2015 for "ImmersiveCompact Display Glasses", and No. 62/208,235, filed on 2 1 August 2015 for "Opticalapparatus." Both of those applications are incorporated herein by reference in their entirety.This application contains subject matter related to commonly assigned WO 2015/077718 Al(PCT/US 2014/067149) with inventors in common, for "Immersive compact display glasses,"referred to herein as "PCT1," which is incorporated herein by reference in its entirety.FIELD OF THE INVENTION [0002] The application relates to visual displays, and especially to head-mounted displaytechnology. BACKGROUND [0003] 1. References cited[0004] WO 2015/077718 of Benitez et al. ("PCT1")[0005] U.S. Pat. 4,924,215 to Nelson[0006] U.S. Pat. 5,390,047 to Mizukawa[0007] U.S. Pat. 5,699,194 to Takahashi[0008] U.S. Pat. 5,701,202 to Takahashi[0009] U.S. Pat. 5,706,136 to Okuyama & Takahashi[0010] U.S. Pat. 7,689,1 16 to Ho Sik You et al.[0011] U.S. Pat. 8,605,008 to Prest et al.[0012] U.S. Pat. App. 2010/0277575 Al of Ismael et al.[0013] U.S. Pat. App. 2012/0081800 of Cheng et al.[0014] D. Cheng, et al., "Design of a wide-angle, lightweight head-mounted display usingfree-form optics tiling," Opt. Lett. 36, 2098-2100 (2011)[0015] http:/ / 201005 19223434_Toshiba_Develops_High_Speed_High_Contrast_Active_Shutter_3D_Glasses.html ("Shilov2010")[0016] D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J . Brug, and R. G. Beausoleil, "Amulti-directional backlightfor a wide-angle, glasses-free three-dimensional display " Nature,vol. 495, 7441, pp 348-351, 2013. DOI: 10.1038/naturel 1972. ("Fattal 2013")[0017] H. Hoshi, N. Taniguchi, H. Morishima, T. Akiyama, S. Yamazaki, and A. Okuyama,"Off-axial HMD optical system consisting of aspherical surfaces without rotationalsymmetry;' Proc. SPIE 2653, 234-242 (1996).[0018] Inoguchi et al. "Fabrication and evaluation of HMD optical system consisting ofaspherical mirrors without rotation symmetry " Japan Optics '95, Extended Abstracts,20pB06, pp. 19-20, 1995).[0019] J.J. Kerr, Visual resolution in the periphery, Perception & Psychophysics, Vol. 9 (3),1971[0020] J.E. Melzer, "Overcoming the Field of View: Resolution Invariant in Head MountedDisplays", SPIE Vol. 3362, 1998[0021] H. Morishima, T. Akiyama, N. Nanba, and T. Tanaka, "The design of off-axialoptical system consisting of aspherical mirrors without rotational symmetry " in 20th OpticalSymposium, Extended Abstracts (1995), Vol. 21, pp. 53-56.[0022] 2. Definitionscluster Set of active opixels that illuminates the pupil range through a given lenslet.The number of clusters is equal to the number of lenslets.display Component that modulates the light spatially to form an image. Currentlyavailable displays are mostly electronically operated, and are "digital"displays that generate an array of distinct pixels. The display can be selfemitting,such as an OLED display, or externally illuminated by a front or abacklight system, such as an LCD or an LCOS. The displays may be of thetype called Light Field Displays (Huang 2015) implemented by stacked(transmissive) LCDs. Particularly interesting because of its thickness is thecase of just 2 stacked LCDs with a separator between them. Light FieldDisplays support focus cues which together with the rest of the device help tosolve the vergence-accommodation conflict at a reasonable cost and volume.eye pupil Image of the interior iris edge through the eye cornea seen from the exteriorof the eye. In visual optics, it is referenced to as the input pupil of the opticalsystem of the eye. Its boundary is typically a circle from 3 to 7 mm diameterdepending on the illumination level.eye sphere Sphere centered at the approximate center of the eye rotations and withradius the average distance of the eye pupil to that center (typically 13 mm).field of view Field defined by horizontal and vertical full angles subtended by the virtualscreen from the eye pupil center when the two eyes rest looking frontwards.fixation point Point of the scene that is imaged by the eye at center of the fovea, which isthe highest resolution area of the retina and typically has a diameter of 1.5mm.gaze vector Unit vector of the direction linking the center of the eye pupil and thefixation point.gazed region Region of the virtual screen containing the fixation points for all positions ofof virtual the eye pupil within the union of the pupil ranges. It contains all the ipixelsscreen that can be gazed.guard Corridor between adjacent clusters of the digital display that contains noactive opixels. The guard avoids optical cross-talk while guaranteeing acertain tolerance for the optics positioning.human Minimum angle subtended by two point sources which are distinguishable byangular an average perfect-vision human eye. The angular resolution is a function ofresolution the peripheral angle and of the illumination level.inactive area Region of the digital display in which the opixels are inactive.ipixel Virtual image of the opixels belonging to the same web. Preferably, thisvirtual image is formed at a certain distance from the eye (from 2 m toinfinity). It can also be considered as the pixel of the virtual screen seen bythe eye.lenslet Each one of the individual optical devices of the optics array, which collectslight from the digital display and projects it to the eye sphere. The lenslet isdesigned to form a continuous image of opixels into ipixels. Each lenslet maybe formed by one or more optical surfaces, either refractive or reflective.There is one lenslet per cluster and, in time multiplexing, one shutter (orequivalent) per cluster In time multiplexing, cluster whose lenslet has the shutter open. When thereis no time multiplexing any cluster is an open lenslet In time multiplexing, lenslet whose shutter is open. When there is no timemultiplexing any lenslet is an open lenslet.opixel Physical pixel of the digital display. There are active opixels, which are lit tocontribute to the displayed image, and inactive opixels, which are never lit.An inactive opixel can be physically nonexistent, for instance, because thedisplay lacks at that opixel position at least one necessary hardware element(OLED material, electrical connection) to make it functional, or it can beunaddressed by software. The use of inactive opixels reduces the powerconsumption and the amount of information to be managed.optical Undesired situation in which one opixel is imaged into more than one ipixel.cross-talkouter region Region of the virtual screen formed by the ipixels that do not belong to theof virtual gazed region of virtual screen, i.e., it is formed by ipixels that can be seenscreen only at peripheral angles greater than zero.peripheral Angle formed by a certain direction and the gaze vector.anglepupil range 1. Region of the eye sphere illuminated by a single cluster through itscorresponding lenslet. When the eye pupil intersects the pupil range of agiven lenslet, then the image corresponding to its corresponding cluster isprojected on the retina. For a practical immersive design, a pupil rangecomprising a circle of 15 degrees full angle on the eye sphere is sufficient. 2.The union of all pupil ranges corresponding to all lenslets of the array. It is aspherical shell to a good approximation. If all accessible eye pupil positionsfor an average human are considered, the boundary of the union of eye pupilranges is approximately an ellipse with angular horizontal semi-axis of 60degrees and vertical semi-axis of 45 degrees relative to the front direction.subframe slot A time slot into which the frame period is divided. Subframe slots are calledby an ordinal, i.e. first subframe slot, second, etc.virtual screen Surface containing the ipixels, preferably being a region of the surface of asphere concentric with the eye and with radius in the range from 2 m toinfinity.web Set of active opixels displaying information of the same ipixel during asubframe slot.RXIR lenslet Portion of the optical device in which light rays undergo (when going fromthe digital display towards the eye) at least four deflections in the followingsequence: refraction, reflection, total internal reflection (TIR) and refraction.The first refraction and the total internal reflection may be performed by thesame surface. The third deflection may be at a surface that is partly a TIRreflector and partly an opaque (e.g. metallized) mirror.[0023] 3. State of the art[0024] Head mounted display (HMD) technology is a rapidly developing area. One aspect ofhead mounted display technology provides a full immersive visual environment (which canbe described as virtual reality), such that the user only observes the images provided by oneor more displays, while the outside environment is visually blocked. These devices haveapplication in areas such as entertainment, gaming, military, medicine and industry. In US2010/0277575 Al there is a description of one of such devices. The basic optical function ofa HMD is that of a stereoviewer such as the one described in US Pat 5,390,047.[0025] A head mounted display consists typically in one or two displays, their correspondingoptical systems, which image the displays into a virtual screen to be visualized by the user'seye, and a helmet that visually blocks the external environment and provides structuralsupport to the mentioned components. The display may also have a pupil tracker and/or ahead tracker, such that the image provided by the display changes according to the user'smovement.[0026] An ideal head mounted display combines a high resolution, a large field of view, alow and well-distributed weight, and a structure with small dimensions. Although sometechnologies successfully achieve these desired features individually, so far mosttechnologies have been unable to combine all of them. That results in an incomplete or evenuncomfortable experience for the user. Problems may include a low degree of realism andeye strain (due to low resolution or to poor optics imaging quality), failure to create animmersive environment (small field of view), or excessive pressure on the user's head(excessive weight).[0027] First, PCT1 discloses concepts that are related to the present application, as clusters,opixels and ipixels. FIG. 1 of the present application, which was Fig. 3 in PCT1, shows asimple example with only four clusters 104t, 104b, 105t and 105b, which form the compoundimage created by opixels on the digital display 107. The opixels are projected in PCT1 by alenslet array optics to form the image of ipixels on the virtual screen 108 (which forsimplicity has been drawn here flat with a rectangular contour). Therefore, every opixelbelongs to a single cluster and the intersection of any two clusters is the empty set and theunion of all clusters is the whole digital display.[0028] Each cluster displays a portion of the image on the virtual screen. Adjacent clustersdisplay portions of the image with a certain shift that coincides in the neighboring regions. Inorder to explain why this is necessary, a two-dimensional schematic drawing has been addedat the top of FIG. 1. It shows the relevant rays to define the edges of the mapping betweenopixels and ipixels. In this drawing, the virtual screen with the ipixels is placed at infinity, sothe direction of rays 100a, 101a, 102a and 103a indicates the ipixel positions on the virtualscreen. The drawing is two-dimensional for simplicity, but the actual device that projects theimage on the bottom left in FIG. 1 is three-dimensional and contains four lenslets, two aboveand two below, and not only the two shown as 104 and 105 in the schematic drawing on thetop of FIG. 1. The two-dimensional scheme is used to explain the horizontal coordinates ofthe mapping between opixels and ipixels, and an analogous reasoning applies to the verticalcoordinates.[0029] The horizontal extent of the virtual screen extends from 100a to 103a. The portion ofthe image represented in the left clusters 104t and 104b is given by the edge rays 100a and102a reaching the edges of the pupil range 106, which define the vertical lines 100a and 102aon the virtual screen 108. Analogously, the portion of the image of represented in the rightclusters 105t and 105b is given by the edge rays 101a and 103a, which define two verticallines on the virtual screen 108. Therefore, the portion of the virtual screen 108 between 101aand 102a will be displayed in both left clusters and right clusters. Specifically, lenslet 104maps edge rays 100a and 102a of the virtual screen onto 100b and 102b on the digital display107. Analogously, lenslet 105 maps edge rays 101a and 103a onto 101b and 103b on thedigital display 107. The optical design aims to guarantee that the clusters do not overlap,which is achieved with maximum use of the digital display when 101b and 102b coincide.The analogous alignment of top clusters 104t, 105t with bottom clusters 104b, 105b, isapparent from FIG. 1.[0030] Because of the partial coincidence of the information on the clusters, ipixel ipl isformed by the projection of four opixels, opl 1, op 12, op 13 and op 14. This set of opixels isreferred to as the "web" of ipixel ipl. Webs of ipixels located in the center of the virtualscreen, such as ipl, contain four opixels each. However, webs of ipixels close to theboundaries of the virtual screen may have fewer opixels. For instance, the web of ipixel ip2contains only two opixels, op21 and op22, and the web of ip3 contains only op31.[0031] The devices disclosed herein do not use only refractive lenslets as the embodimentsdisclosed in PCT1, but a wedge-shaped prism optics with total internal reflection that allowsrather long focal lengths (from 0 mm to 80 mm) while keeping the HMD with smalldimensions.[0032] Prior art using a wedge-shaped prism optics for HMDs has been proposed in the past,and multiple patents reflect it, although all of them share the same principle. Since thepioneer work was first presented by Morishima et al. in 1995, we will refer to all of them asMorishima's wedge-shaped prism optics. The fabrication and evaluation method wereexplored by Inoguchi. Following these pioneering efforts, many attempts have been made todesign HMDs using free-form surfaces, particularly designs based on a wedge-shaped prism(U.S. Pat. Nos. 5,699,194, 5,701,202, 5,706,136. D. Cheng, et al., "Design of a lightweightand wide field-of-view HMD system with free form surface prism," Infrared and LaserEngineering, Vol. 36, 3 (2007).). For instance, Hoshi et al. presented a freeform prismoffering a field of view of 34° and a thickness of 15 mm; and Yamazaki et al. described a 51°HMD design with optical-see though capability consisting of a wedge-shaped prism and anauxiliary lens attached to the wedge-shaped prism. More recently, US Pat. 8,605,008 to Prestet al. includes a similar wedge-shaped prism optics. There are also several commerciallyavailable HMD products based on the wedge-shaped prism optics concept. For instance,Olympus released their Eye-Trek series of HMDs based on free-form prisms. Emagin carriedZ800 with the optical module WF05, Daeyang carried i-Visor FX series (GEOMC module,A3 prism) products; Rockwell Collins announced the ProView SL40 using the prismtechnology of OEM display optics. US 2012/0081800 A "Optical see-through free-formhead-mounted display" by D. Cheng et al., also proposes a novel optical design for HMDapplications, where particularly is presented a see-through free-form head-mounted displayincluding a wedge-shaped prism-lens having free-form surfaces and low F-number.[0033] The working principle of Morishima's wedge-shaped prism optics is shown in FIG. 3(taken from US Pat. 8,605,008 to Prest et al.), where 301 represents the eye, 302 is the digitaldisplay, and 303 is the lens. Rays 304 emitted by the digital display are first refracted bysurface 305, then reflected by total internal reflection on surface 306, then reflected bymirrored surface 307 and finally refracted by surface 306 towards the eye.[0034] However, Prest's lens is totally different from our embodiments since the order of thedeflections is not the same. For instance, consider the case shown in FIG. 6 where the raysemitted by the digital display 608 undergo a refraction on surface 601, then a reflection onmirrored surface 602, a total internal reflection on surface 601 (or a reflection on the mirroredsurface area 607), and finally a refraction on surface 603 to be sent to the eye 610. Thisdifferent sequence of incidences allows the digital display of FIG. 8 to be placed in a rathervertical position in FIG. 6, while Morishima's wedge-shaped prism needs the display to beallocated rather horizontally (as shown in FIG. 3).[0035] Another important difference between the embodiments disclosed herein and thepreviously mentioned prior art is that ours provides a very wide field of view (> 60 degrees)even with a single display per eye, while the prior art achieves much smaller fields of view (<50 degrees) for a single display. One approach used in the prior art to increase the field ofview is tiling, i.e., using multiple displays per eye arranged in a mosaic pattern, and not in thesame plane. That approach is presented in D. Cheng et al., "Design of a wide-angle,lightweight head-mounted display using free-form optics tiling," Opt. Lett. 36, 2098-2100(201 1) and it is as shown in FIG. 4 (in which only a 2D vertical cross-section is presented,but in the real design, there are a total of up to 6 digital displays placed around the eye, asshown in Fig. 4c of Cheng). In contrast to that prior system which uses non-coplanar multipledisplays per eye, in the presently disclosed devices, we use either a single display for botheyes, or a single display per eye, or several displays per eye but all them can lay in the sameplane for easier mounting in a common PCB.[0036] Other related prior art is disclosed in US patent 7,689,1 16 to You et al., whichconsists in an optical design composed of a two-lenslet optics. This patent, applicable to amobile camera, presents an optical lens system which divides the field of view into two usingtwo separate symmetric off-axis refractive-reflective systems, thereby achieving a thinnermobile camera optical lens system.[0037] FIG. 5 explains the basis of US patent 7,689, 116. In FIG. 5, the light emitted by theobject (in the example, the flower 501) is transmitted through the optical system andimpinges on the image plane, where a light sensor is placed 502. The light corresponding tothe top half of the field of view enters the system through refractive surface 503, while thebottom half of the field of view enters the system through refractive surface 504. Both halvesof the optical system are symmetrical, as shown in FIG. 5. The rays belonging to the top halfare deflected successively by four different surfaces: first refracted on surface 503, thenreflected on surface 507, again reflected on surface 508, then refracted by surface 509, andfinally impinge on the top half of the image plane 502. Due to the particular opticalarchitecture used in this device, each half of the image obtained on the image plane isinverted 505. This situation is corrected electronically, in order to finally obtain the desiredimage on the sensor 506.[0038] Even though You's design is related with the embodiments disclosed herein as theone shown in FIG. 12, there are several important differences, which will be made clear bythe disclosure in the detailed description below. First, the present embodiments are for adifferent purpose, i.e. head-mounted displays, while You's invention, shown in FIG. 5, is fora mobile camera optical lens. That requires a very different geometry. Second, You's realobject (which is the scene to take the picture of) is located far from the lens, while ourequivalent element (the digital display with opixels) is at a very short distance from the lens,even touching it. Third, You's image (projected onto the camera sensor) is real and is locatedvery close to the lens, while our equivalent element (the virtual screen with ipixels) is virtualand is located far from the lens. Fourth, the output pupil in our case shown in FIG. 12 is real,is located on the exit side of the lens and is defined as the pupil range to allow for eyemovements, while in You the equivalent pupil (which is the exit pupil) is virtual and islocated at the entrance side of the lens. Fifth, the clear apertures of the two surfaces 503 and508 in FIG. 5 are separated (no intersection between them), while in our case they areoverlapped, actually being the same surface 1201 in FIG. 12 with two regions: a mirroredregion, and a region that works by total internal reflection and refraction. Sixth, in You'ssystem, (unlike the present embodiments), the mapping of ipixel to opixel is univocal, i.e.there are no webs, which is common to the multiaperture camera appearing in the state of theart of PCT1 (Figure 1 and Figure 2 of PCT1). And seventh, in You's system every raygenerated by one pixel of the object goes to its corresponding one pixel of the image througha single lenslet, while in our case, there are many ipixels whose light comes from rayspassing through more than one lenslet. SUMMARY [0039] In one aspect, a device for immersive virtual reality applications based on opticaldesign has one or more lenslets to project the display light to the eye. There is at least onelenslet such that the light rays undergo at least four deflections on freeform surfaces in thefollowing sequence in the direction of propagation from the display towards the eye:refraction, reflection, total internal or metallic reflection and refraction. The first refractionand the total internal reflection are performed by the same surface. This lenslet is calledRXIR type herein. When multiple lenslets are used, the set of object pixels (opixels) of thedigital display that are imaged onto image pixel (ipixels) of the virtual image through any onelenslet is called the cluster of that lenslet. In general, the opixel to ipixel assignation is notbijective, since several opixels belonging to different clusters may be mapped to the sameipixel of the virtual image.[0040] There are multiple possible configurations of these embodiments depending on thenumber and type of lenslets. Preferred embodiments have either one, two or four RXIRlenslets, which can be alone or combined with refractive lenslets. These embodiments can bedesigned to be used with a single digital display for both eyes, one display per eye, or twodisplays per eye, and the digital display can be either flat or curved. The two RXIR lensletembodiment can easily accommodate an eye tracking system using a small camera.[0041] In an embodiment, the optical design is done using two or more freeform surfaces bymultiparameter optimization of the coefficients of a polynomial expansion, preferably usingan orthogonal basis. The design requirements are adapted to the human eye resolution forbest utilization of the available degrees of freeform. This adaptation implies that the imagequality of every ipixel should be a maximum when eye is gazing at or near to that ipixel (sothe peripheral angle is small), since that ipixel will be imaged by the eye on the fovea, while- l ithe image quality is gradually relaxed when increasing the peripheral angles, where the eyeresolving power decreases.[0042] The addition of a time multiplexing technique allows increasing the number of ipixelsby representing the image in several consecutive parts within the frame period and using allthe available opixels for any of these image parts.[0043] In an embodiment, the contrast of those embodiments is improved by includingabsorbers in several selected positions or with the help of a half-wave plate when polarizedlight is used (as in the case of an LCD digital display).[0044] In another aspect, a display device comprises a display, operable to generate a realimage. An optical system, comprising one or more lenslets, is arranged to generate a virtualsub-image from a respective partial real image on the display, by each lenslet projecting lightfrom the display to an eye position. The sub-images combine to form a virtual imageviewable from the eye position. At least one of the lenslets is such that the light rays from thedisplay to the eye position are deflected sequentially at least four times by a refraction (R), areflection (X), a total internal or metallic reflection (I), and a refraction (R) in that order(RXIR lenslet).[0045] The display device may further comprise a display driver operative to receive aninput image, and to generate the respective partial real images such that the resulting virtualsub-images align to form a virtual image of said input image as said viewable virtual image.[0046] The first refraction (R) and the total internal or metallic reflection (I) may beperformed by the same surface with non-coincident overlapping clear apertures. The regionof overlap is then usually a region of both refraction and total internal reflection. Anotherregion of the same surface that is outside the region of the first refraction may be metalized.[0047] The one or more lenslets may comprise at least two of the RXIR lenslets, which maybe superposable or different.[0048] The one or more lenslets may comprise at least one of the RXIR lenslets and at leastone lenslet that is a non-RXIR lenslet.[0049] The at least one RXIR lenslet may then generate its virtual sub-image at a centralportion of the viewable virtual image, and the at least one non-RXIR lenslet may thengenerate its virtual sub-image at a portion of the virtual image nearer to a periphery of theviewable virtual image. The RXIR lenslet(s),which typically provide the better imagingquality, are then used for the parts of the virtual image that are most likely to be viewed withthe fovea.[0050] At least two lenslets may be non-superposable.[0051] The display device may be arranged to produce partial virtual images each of whichcontains a part projected by an eye onto a 1.5 mm region representing the fovea of the eyewhen the eye is represented by an imaginary sphere at the eye position of the display devicewith its pupil within the pupil range, the fovea part of each viewable virtual image having ahigher resolution than a peripheral part of the viewable virtual image.[0052] The optics may be placed at a distance from the imaginary eye sphere between 5 and40 mm, the at least one lenslet forming an array of lenslets subtending a solid angle from theclosest point of the imaginary sphere comprising a cone with 40 degrees whole angle,wherein the display is on a side of the optics remote from the imaginary sphere, at a distancefrom the optics of no more than 80 mm.[0053] The respective partial real images on the display may comprise at least two partialreal images that overlap on a same portion of the display and that are activated duringdifferent time periods, and wherein different lenslets image said same portion of the displayto different sub-images at different positions of the virtual image.[0054] The display device may further comprise a stray-light control system that removeslight not contributing to the virtual sub-images.[0055] The stray-light control system may comprise light-absorbent material in a part of thedisplay device not crossed by light rays contributing to the virtual sub-images.[0056] The stray-light control system may comprise a polarizer and a half-wave rotatorarranged to absorb light reflected back towards the display.[0057] An embodiment of a headgear comprises any of the above-mentioned aspects and/orembodiments of a display device, with a mount for positioning the display device on a humanhead with the eye position of the display device coinciding with an eye of the human.[0058] The headgear may further comprise a second display device, mounted with the eyeposition of the second display device coinciding with a second eye of the human.[0059] The displays of the first and second display devices may be parts of a single physicaldisplay.[0060] In an embodiment, the RXIR deflections take place at surfaces of a solid transparentbody that is longer in a direction towards and away from the eye position, or in a directiontowards and away from the exit surface at which the second R refraction occurs, than in adirection perpendicular or transverse to that. As explained in an embodiment below, the solidbody may be a pair of bodies, or one of a pair of bodies, that are separated only by a narrowlow-refractive-index gap.BRIEF DESCRIPTION OF DRAWINGS [0061] The above and other aspects, features and advantages will be apparent from thefollowing more particular description of certain embodiments, presented in conjunction withthe following drawings. In the drawings:[0062] FIG. 1 is a schematic view of ipixels to opixels mapping (prior art).[0063] FIG. 2 shows the angular resolution of a typical human eye as a function of theperipheral angle.[0064] FIG. 3 is a cross-sectional view of a wedge-prism optics (prior art).[0065] FIG. 4 is a cross-sectional view of a tiled system with non-coplanar displays (priorart).[0066] FIG. 5 is cross-sectional view of a compact camera optics design for mobile phones(prior art).[0067] FIG. 6 is a cross section of a single RXIR lenslet embodiment for a large area digitaldisplay.[0068] FIG. 7 is a perspective view of a single RXIR lenslet device with a single large areadigital display for both eyes.[0069] FIG. 8 is a cross section of a single-lenslet RXIR embodiment for a smallmicrodisplay.[0070] FIG. 9A is a top view of a single-lenslet RXIR embodiment with a singlemicrodisplay for both eyes.[0071] FIG. 9B is a horizontal cross-sectional view of a single-lenslet RXIR embodimentwith a large area curved digital display.[0072] FIG. 10 is the cross sectional view of an embodiment with RXIR and RXR lenslets.[0073] FIG. 11 is the cross sectional view of an embodiment with RXIR and RR lenslets.[0074] FIG. 12 is a cross sectional view and a perspective view of a 2-fold embodiment withtwo RXIR lenslets.[0075] FIG. 13 is a schematic diagram of the added camera for eye-tracking.[0076] FIG. 14 is a perspective view of an embodiment with two RXIR lenslets per eye anda single digital display for both eyes.[0077] FIG. 5 is a cross section of an embodiment in which the two RXIR lenslets aremanufactured as separate pieces.[0078] FIG. 16 is a cross section of an embodiment with one central RR lenslet and twoperipheral RXIR lenslets.[0079] FIG. 7 shows a variation of the design in FIG. 6 in which a lens has been added tothe RR lenslet.[0080] FIG. 8 shows perspective views of the embodiment of FIG. 16 and of a 4-fold RXIRembodiment.[0081] FIG. 9 is a perspective view of another 4-fold embodiment.[0082] FIG. 20 shows the embodiment in FIG. 19 applied to a single digital display for botheyes.[0083] FIG. 1 is a cross-sectional view of an embodiment with an additional lens close tothe display.[0084] FIG. 22 is a cross-sectional view of an embodiment using a flat mirror decoupledfrom the dielectric piece.[0085] FIG. 23 shows cross sectional views of an embodiment with an additional lens closeto the eye.[0086] FIG. 24 is a cross sectional view of another embodiment with two central RXIRlenslets and two peripheral RR lenslets.[0087] FIG. 25 is a cross-sectional view of an embodiment which uses a low index gap togain compactness.[0088] FIG. 26 is a cross-sectional view of an embodiment that substitutes the mirror of theRXIR by two mirrors.[0089] FIG. 27 is a cross-sectional view of a non-superposable embodiment with two RXIRchannels for a tilted flat display per eye.[0090] FIG. 28 is the top view of a non-superposable embodiment with two RXIR channelsfor a curved display.[0091] FIG. 29 is a perspective view of two 4-fold designs for a single display for both eyes.[0092] FIG. 30 shows the radial and sagittal focal lengths along the diagonal line of onelenslet in FIG. 29.[0093] FIG. 31A shows several characteristic lines of ipixels to opixels mapping on thedigital display.[0094] FIG. B is a diagram for defining several angles.[0095] FIG. 32 describes the local coordinate system used to represent the surfaces of thedetailed design.[0096] FIG. 33 is the cross-sectional view of the detailed design showing somecharacteristics rays.[0097] FIG. 34 is another cross-sectional view of the same design in FIG. 33.[0098] FIG. 35 is a time multiplexing embodiment using one flat shutter per lenslet.[0099] FIG. 36 shows the digital display utilization in three time multiplexing designs.[0100] FIG. 37 is an alternative time multiplexing embodiment using coplanar shutters.[0101] FIG. 38 is a cross-sectional view of the embodiment to minimize stray light using ahalf-wave retarder.[0102] FIG. 39 is a perspective view of the same embodiment as in FIG. 38.[0103] FIG. 40 shows the location of an absorber to reduce other stray light generationmechanisms.[0104] FIG. 4 shows the location of an alternative absorber to reduce other stray lightgeneration mechanisms.[0105] DETAILED DESCRIPTION [0106] The embodiments in the present invention include an optical device (per eye) thattransmits the light from one or several digital displays to the area of the pupil range of the eyethrough one or more optical lenslets, where at least one of the lenslets is an RXIR lenslet,defined in the sense that the light rays of interest suffer (when going from the digital displayto the eye) at least four deflections in the following sequence: refraction (R), reflection (X),total internal or metallic reflection (I) and refraction (R), whereas the first refraction (R) andthe total internal or metallic reflection (I) are performed by the same surface with noncoincidentoverlapping clear apertures. (We call herein "surface" to a surface with first ordercontinuity, that is, continuity of the slope, or higher). These embodiments use severalfreeform optical surfaces, which mean that they are surfaces which do not have the classicalrotational or linear symmetries. Their design is done according to the detailed descriptiongiven in section 8.[0107] Embodiments of the present optical designs are unbalanced to optimize their degreesof freedom to image better the opixels whose image will be directly gazed by the eye (whichwill be focused on the fovea, where the human angular resolution is much higher), while theimage quality corresponding to our peripheral vision is relaxed.[0108] 4. Embodiments with a single RXIR ens et[0109] FIG. 6 shows the 2D lateral cross-section of a device with a single lenslet of theRXIR type, indicating the positions of the user's eye 610 and nose 609. The digital display608 may be placed in a tilted position. This position of the digital display allows for a bettermechanical coupling of the whole device to the user's face, especially adapted to the noseshape. As shown in FIG. 6, rays 604, 605 and 606 emitted by the digital display 608 undergoa refraction on surface 601, then are reflected on mirrored surface 602, again reflected, partlyby total internal reflection on surface 601 and partly by metallic reflection at surface 607,where surfaces 601 and 607 form optically a single mirror, and finally refracted by surface603 and directed towards the center of the eye sphere 6 11. These rays are therefore parallel tothe gaze vector when the eye gazes its corresponding ipixel, and therefore the design is doneto guarantee that the image quality for those ipixels is the highest. The rays 612 and 613emitted from the edges of the display reach center of the eye pupil when it is restingfrontwards, which delimits the edges of the field of view. A region of surface 601, indicatedby 607, is metallized in order to perform the reflection of those rays not satisfying the totalinternal reflection condition, as for example ray 604 in FIG. 6. Of course this region,although it is part of surface 601, is not available as an entrance for rays coming from thedigital display 608. Therefore, the clear aperture of surface 601 for the refraction and for thereflection overlap but they do not coincide. All three surfaces 601, 602 and 603 are preferablyfreeform, because breaking the classical rotational symmetry constraints provides moredegrees of freedom in the optical design to guarantee the adequate image quality in the wholeimmersive field of view.[0110] This design allows for using a single large digital display for both eyes or two halfsizedigital displays, i.e. one per eye. FIG. 7 shows the particular case of a single largedisplay 703 for both eyes, where there are two lenses 702, one lens 702 for each eye 701. Thedigital display 703 is represented frontwards and, as explained in FIG. 6, it is tilted to have abetter coupling with the user's face. This configuration is especially attractive for commercialdigital displays made with low cost backplane technology of about 5 to 6 inches (125 to 150mm) in diagonal, because this size implies that the longest side length is close to double theaverage human interpupil distance, which is about 63 mm.[0111] This kind of lens, where there are one total internal reflection, two refractions andone reflection, can also be used in combination with one digital display per eye, instead ofone large display for both eyes. This alternative decreases the digital display area and,consequently, the whole device cost. If we further reduce the size of the digital display, highcost backplane technology (as crystalline silicon ones of OLED-on-silicon, LCOS or DMD's)can be used cost-effectively. This is illustrated in FIG. 8.[0112] The design shown in FIG. 8 is for one lens and one digital display per eye.Nevertheless, a similar lens design, where there are two lenses but a single digital display forboth eyes, can be obtained, and an example is shown in FIG. 9A, with a view of the wholedevice and both eyes from above. As shown in FIG. 9A, both lenses are similar to that inFIG. 8, but they are rotated in order to obtain the desired direction of the input/output rays.The digital display 905 emits rays, which are refracted by surface 901, reflected by surface902, reflected by total internal reflection on 90 1 and finally refracted by 903 towards the lefteye. The same behavior of the rays is shown in the right eye. Line 904 indicates onesymmetry plane of the digital display and splits it into two regions: the left one, that sendslight towards the left eye; and the right one, that sends light towards the right eye. In thisway, this configuration can be designed for a 16:9 digital display, hence having two separatedregions with 8:9 aspect ratio, one region corresponding to each eye. In the plane of symmetry904, a flat absorbent surface can be added in order to avoid rays crossing the plane ofsymmetry and sending information to the wrong eye. When an LCD display is used as digitaldisplay, the backlight unit can be designed to emit directionally so the flat absorbent shield904 is not needed. Analogously, a digital mirror device (DMD) can be used, and itsillumination can be adjusted so the light is reflected in the desired directions.[0113] FIG. 9B shows another variation of the same device 906 through 2D cross sectionsseen from above. The digital display 907 is designed to present a cylindrical configurationaround the user's head. This alternative allows for an ergonomic and compact device, sincethe lateral parts of the digital display are closer to the face.[0114] FIG. 10 shows a 2D vertical cross-section of another variant of the previouslydescribed embodiment. This one is formed by two lenslets, one of them RXIR-type, whichcan be recognized in FIG. 0 by the slope discontinuities of two of the surfaces (labeled with1004 and 1006). With a multi-lenslet configuration such as this one, we may obtain morecompact devices, in general at the expense of slightly smaller resolution because some imagepixels (ipixels) are seen in more than one lenslet. Each lenslet images a certain part of theobject. Often these image parts overlap. The object pixels (opixels) to image pixels (ipixels)mapping for a given lenslet is continuous but there is in general no such continuity betweenmappings of different lensiets. In order to get the complete continuous image on the retina,the digital display must then show a discontinuous picture, which, once imaged by thedifferent lensiets, forms a continuous picture on the retina. In FIG. 10, rays labeled with 1007and 1008 emitted by the digital display undergo a refraction on surface 1002, then reflectionon metallized surface 1003, then once more these rays deflect on surface 1002 suffering totalinternal reflection and finally they are refracted on the upper lenslet of surface 1006 anddirected towards the eye 1012. There are thus a total of 4 deflections through this lenslet,which is of the RXIR type mentioned before. Rays that belong to the other lenslet areillustrated in FIG. 10 with rays labeled as 1009 and 1010. These rays are refracted on surface1002, then ray 1009 suffers total internal reflection on surface 1004 and ray 1010 is reflectedon the metalized part of surface 1004 labeled as 1005, and afterwards both rays are refractedon the lower lenslet surface 1013 and directed towards the eye 1012, totaling threedeflections, which could be labeled as RXR. Thus these two lensiets do not have the sameoptical configuration. All surfaces 1002, 1003, 1004, 1005 and 1006 are preferably freeform.[0115] Alternatively, the device in FIG. 10 can be rotated 90 degrees with respect to an axispassing through the center of the eye and pointing frontwards, so the displays of the two eyeswill be positioned generally vertically, one on each side of the head.[0116] FIG. 11 shows a top view of a horizontal cross section of another 2-lensletconfiguration. User's nose 1 7 and eye 1 8 are shown for orientation purposes. Innerlenslet 1111 is RXIR-type and has front and back metallized parts labeled as 108 and 1107,respectively. Outer lenslet 112 is a lens that consists of 2 refractive surfaces (which could betherefore called RR with the same nomenclature) labeled as 120 and 1110. Thisconfiguration works with the tilted display 1101 to provide a better ergonomics, and then ituses two interdependent digital displays, one per eye (e.g. digital display diagonal <2.2" (55mm)). The inner lenslet 1111 is similar to that described in FIG. 6, while the outer lens 1 12is designed similarly to the lenslet designs described in Section 6.6 of PCT1. The digitaldisplay area that works with the outer lens lenslet 12 is smaller in comparison with theinner digital display area that works with the inner lenslet. This is the case as the inner lenslet11 is designed for a wider fraction of the horizontal FoV and higher focal lengths.[0117] Rays 11 3 and 114 that exit inner part of digital display 0 1 shown in FIG. arerefracted at entrance surface 1106, reflected on back mirror surface 107, totally internallyreflected on the entrance surface 106 (or reflected on the metallized part 1108 of surface1106), refracted at surface 1109, and directed towards the eye 1118. Optical cross-talkbetween lenslets needs to be avoided. Therefore, ray 1114 starts its path in the inner cluster atthe edge 1119 between the inner cluster and the outer cluster, propagates through lenslet 1 1and ends its path on the inner edge of the pupil range 1104. Ray 1115 starts its path in theouter cluster at the same edge 1 19, propagates through lenslet 1 1 12 and concludes its pathon the outer edge of the pupil range 1105. Ray 1 1 13 determines the inner border of thehorizontal monocular field of view, it deflects near the inner border of exit surface 1109 andwhen traced backwards it ends near the inner border of digital display 1101. Ray 1 1 16determines the outer edge of the monocular horizontal field of view. It deflects near the outeredge of the exit surface 1120 and when traced backwards it ends near the outer border ofdigital display 1101. Rays 15 and 116 that exit outer cluster and suffer only twodeflections - they refract on surface , refract on surface 0 before reaching the eye.[0118] For simplicity, a 2-lenslet configuration was chosen to be shown in FIGS. 0 and 1,although the number of lenslets may be substantially bigger. Particularly interesting is a 2x2configuration such that the two top lenslets are RXIR type and the two bottom lenslets areRXR and RR for FIG. 0 and FIG. 1, respectively. These options include more than oneRXIR lenslet, and therefore could be consider embodiments belonging to the next sections.[0119] 5. Embodiments with multiple superposable RXIR lenslets[0120] Another preferred embodiment, shown in FIG. 12, is a variation of the design shownin FIG. 6 with two superposable RXIR lenslets instead of one. "Superposable" here meansthat a rigid motion (rotation, reflection, and/or translation) of a lenslet can make it identical tothe active area of another lenslet. The principles disclosed here do not require such symmetry,as will be disclosed in the next section, but symmetry or superposability simplifies the design,manufacturing, mounting and testing.[0121] FIG. 1 shows the cross section of a 2-fold design with a top view of the device andthe user's head, indicating the position of the nose 1209. In this 2-fold configuration, the longside digital display 1208 is placed in a rather vertical position, unlike the tilted position of thedigital display in FIG. 6. The design usually requires the digital display 1208 to be dividedinto two clusters, one for each of the upper and lower lenslets in FIG. 12. The physicaldisplay 1208 can then be divided into two separate displays, one per cluster, preferably butnot necessarily coplanar, which adds degrees of freedom to the design. Rays 1204, 1205 and1206 undergo a refraction on surface 1201, then a reflection on mirrored surface 1202, areflection on surface 1201, and finally a refraction on surface 1203 to be directed towards theeye. While the second reflection is performed by total internal reflection in the case of ray1204, in the cases of rays 1205 and 1206 it is performed by the mirrored portion of surface1207. Again, these surfaces are freeform.[0122] Optical cross-talk needs to be avoided by the definition of a pupil range (as was donein PCT1) so the edge ray 1210 of the pupil range impinging at the edge of surface 1201 issent as 1206 to the cluster edge. The need for the pupil range to be included in the edgeregion of each partial virtual image requires the virtual images to overlap slightly. Therefore,the region of overlap must be duplicated in both clusters on the digital display. Therefore, theoverall display resolution is slightly reduced compared to what is theoretically available witha single lenslet using the whole digital display as a single cluster. The optimization of thefreeform profiles of this 2-fold symmetric design (as detailed below in section 8, "Detailedexample of a 2-fold superposable optics") tends to lead to a refractive surface 1203 which isconvex in the direction perpendicular to the plane shown in FIG. 12.[0123] FIG. 3 shows how a system to track the eye pupil position can be added. An eyepupil tracking system is able to detect the eye pupil position, which allows the display deviceto modify dynamically the information displayed on the digital display, showing informationto the user related to the part of the field of view towards which the user is gazing.Additionally, the clusters are real-time adjustable in order to avoid optical cross-talk amongdifferent lenslets, while reducing the overlap needed between the different partial images. Acamera 1306, preferably based on a small CMOS sensor, gets an image of at least the pupilrange through a small pin-hole 1313 placed in the intersection of the two lenslets close to theedge of surface 1302. The pinhole 1313 is small enough (about 1mm diameter) to make itnot noticeable to the user. Camera wires (and, if needed, holder) can be located perpendicularto the plane of FIG. 13, using the volume that is not crossed by any ray in this design. On theleft side of FIG. 13, the gaze vector direction is pointing frontwards, showing the digitaldisplay 1301, the first refraction of the rays on surface 1302, then reflection on mirroredsurface 1303, then reflection on surface 1302 and finally refraction on surface 1304. FIG. 13shows the extreme reversed rays coming from the edges of the eye pupil 1305. On the rightside of FIG. 13, we show the eye pupil 1308 at the extreme of the pupil range and reversedrays 1309 and 1310 are the edge rays of the eye pupil. In both situations (eye lookingfrontwards and maximally rotated) none of the rays are blocked by the camera 1306, which ishidden behind the metallized region of surface 1302, and the separation between the clusterschanges from 1311 to 1312 when the pupil moves from one situation to the other.[0124] FIG. 14 shows a device similar to the one in FIG. 12, but rotated 90° with respect toan axis pointing frontwards passing through the center of each eye sphere. This orientation ofthe lens allows for a configuration where both lenses work with a single standard 5.7" (145mm) diagonal display, as shown in FIG. 14. Light emitted from the digital display 1402 isdeflected by surfaces 1403, 1404 and 1405 of the lenses, and finally arrive to the eyes 1401 .[0125] FIG. 15 shows another possible configuration which consists in a 2-fold lens designwith a cusp 1512 on exit surface 1504 (thus creating two exit surfaces, one for each lenslet).This configuration is interesting to manufacture two lenslets independently and make themoperate without the optical cross-talk. This design principle may be applied to k-fold lensconfigurations, where k > 1. FIG. 5 shows a top view of the device's horizontal crosssectionand the user's head, indicating the position of user's nose 1509 and eye 1517. Theprofile shown in FIG. 15 is similar to the 2D profile shown in FIG. 12, with a difference thatthe FIG. 15 embodiment consists of 2 pieces that meet along the face 1518. The digitaldisplay 1501 is placed for this 2-fold configuration in the same position as in FIG. 12. Rays1506 and 1507 undergo a refraction on surface 1502, then reflection on mirrored surface1503, total internal reflection in case of ray 1506 or reflection in case of rays 1507 onmetalized part 1505 of surface 1502, and finally refraction on surface 1504 to be directedtowards the eye 1517 (similarly for the ray 1508). Surfaces 1502, 1503 and 1504 arefreeform. A difference from the design without cusp in FIG. 12 appears on the exit surface atthe point of the trajectory of the extreme ray 1507 that defines a pupil range, since opticalcross-talk needs to be avoided. Ray 1507 comes from the cluster edge, and after refraction onthe inner border of the refracting part of surface 1502 and after reflections on edges ofsurfaces 1503 and 1505, it is reflected parallel to the optical axis 151 1, refracted on the cuspedge of exit surface 1504 and directed towards the pupil range edge labeled as 1510. This isthe extreme ray of the pupil range.[0126] FIG. 6 shows the 2D cross section of a 5 lenslet device, where the section onlyshows 3 lenslets, separated by dashed lines (FIG. 16 is valid for a 3-fold configuration aswell). The extreme lenslets are analogous to those shown in FIG. 12, and in this way, ray1604 behaves in a similar way to ray 1204. On the other hand, the rays going through thecentral lenslet, e.g. ray 1603, undergo a refraction on surface 1601 and another refraction onsurface 1602, and the profiles of the central lenslet can be rotationally symmetric. In theembodiment shown in FIG. 16, the outer lenslets may be superposable by rotation about thecentral axis, but that is not required in the more general case. As before in the 2 lenslet case,optical cross talk needs to be avoided by the definition of a pupil range as was disclosed inPCT1.[0127] FIG. 17 shows a variation of the design shown in FIG. 16, in which an extrarefractive lens 1703 is introduced to deflect rays transmitted through the central lenslet. Thisextra lens allows the output surface of central lenslet 04 to be flat, hence also allowing thesurface closest to the eye to be continuous and differentiable (with no cusp) along the threelenslets. We now have three design surfaces for the central lenslet, thus being able to havegood image formation and to control the focal length of the optical design (at the same timethat we do not have cusps on the surface near the eye).[0128] FIG. shows 3-lenslet (left) and 4-lenslet (right) designs in 3D. In both sides ofFIG. 18, a single eye is plotted on the background, as 1801 and 1802, respectively. On theother hand, the digital display has been plotted frontwards with dashed lines, and isrepresented by 1803 and 1804 respectively. Notice that the 3 lenslet design is more suitablefor rectangular digital displays, e.g. 16:9 ratio, while 4-lenslet designs are more suitable forsquare-shaped digital displays. The 3-lenslet design presents two different lenslets, from theoptical design point of view: one design for the central lenslet 1805, and one design for thetwo outer lenslets 1806. On the other hand, the 4 lenslet design presents only one kind of[MM] 8 7. 9 shows a perspective view of the device 1910 for one eye, which is a 4 lensletvariant of the 2 lenslet device in FIG. 12. We use this configuration to prevent excessivechromatic aberration for a given field of view caused by convex curving of surface (2005),which may result from the freeform surface optimization. This 4 lenslet configuration may bebased on the 2 lenslets with cusp previously described with reference to FIG. 15 as well. Fourlenslets of device 1910 are shown and labeled as 1905, 1906, 1907 and 1908. Half of thedigital display 1901 that works with lens 1910 is shown. FIG. 19 shows dash dot lines 1903and 1904 along which the first derivatives (slopes) of the closest surfaces to the eye and tothe displays, respectively, are discontinuous (these lines separate surfaces that belong todifferent lenslets). The optical cross talk between each two adjacent lenslets is avoided inboth cross-sections shown in FIG. 19.[0130] FIG. 20 shows a 3D illustration of the same configuration as in FIG. 19 with two 4-lenslet devices (one per eye, metallized parts are omitted for drawing clarity) that work with asingle standard digital display (preferably 16:9) labeled as 2001. We may appreciate clearlyfrom FIG. 20 that the device placed in front of each of the two eyes 2002 has 4 lenslets, eachlenslet consists of refractive surface 2003 closest to digital display 2001, reflective surface2004 and refractive surface 2005 closest to eye 2002. The digital display 2001 sends light,which is refracted by surface 2003, reflected by surface 2004, totally internally reflectedagain on surface 2003, refracted on surface 2005, and finally reaches the eye 2002. Eachlenslet is individually not symmetric, but the lenslets are symmetric with each other withrespect to reflection in the planes that separate the lenslets when the digital display 1901 isflat. When a cylindrical display is used, so the short side of the display 2001 in FIG. 20 iscurved, such symmetry would still be preserved.[0131] FIG. 2 1 illustrates another embodiment with superposable lenslets showing thehorizontal cross-section of the device. The user's eye and nose are also shown labeled as2 111 and 2 117, respectively. This device consists of two separate dielectric pieces 2102 and2108 separated by an air gap, or alternatively filled with a low index material, for example, afluoropolymer like fluorinated ethylene propylene (FEP). This new lens 2102 placed in frontof digital display 2101 provides one more optical surface to design and so provides additionaldegrees of freedom. Exemplary ray 2 112 emitted by digital display 2101 is refracted on theentrance surface 2103, and on surface 2104 where it enters the low index gap 2 115. Ray 2 112is refracted on surface 2105 where it leaves the low index gap and enters another lens piece2108. Then ray 2 1 2 is reflected on metallized surface 2106, deflected by total internalreflection (or metallic reflection) on surface 2105 that is used for second time, refracted onexit surface 2107 and finally reaches the eye 2 11. Rays 2 113 and 2114 have similartrajectories. Ray 2112 starts its path on the cluster edge 2 16 and concludes its path on theborder of the pupil range 2 10. Ray 2 13 forms a small exit angle with the optical axis 2109and ends in the eye sphere center. Ray 2 1 4 exits digital display 2101 near the border of thedisplay and after passing through lenses 2102, 2108 points towards the eye sphere center,passing through the border of the pupil range. In this configuration, surface 2105 and itssymmetric counterpart are used twice (by refraction and by total internal reflection).[0132] The use of either a single large digital display for both eyes, or two separated digitaldisplays, i.e. one per eye, is also possible in the embodiment of FIG. 21.[0133] A vertical cross-section of another device configuration is illustrated in FIG. 22,where human eye is 2210 and nose is 221 1. In this design, instead of the back mirrored lenssurface we use a separated mirror 2205 for each lenslet behind the back lens surface 2204. Inthis way, we avoid back surface metallization and we may use separate flat or freeformmirrors. Rays 2208 and 2209 emitted by digital display 2201 are refracted on the entrancesurface 2203, then they exit the dielectric piece 2202 after refraction at the back surface 2204,pass through the air gap and are reflected on the flat mirror 2205. Then rays re-enter lens2202 by refraction at the same back surface 2204, they reflect on metallized part 2206 or arereflected by total internal reflection on surface 2205, refract at exit surface 2207 and finallyreach the eye 2210. The surface 2204 can be anti-reflection (AR) coated to avoid doubleimages caused by Fresnel reflections. Exemplary ray 2208 starts its path on the digital display2201 cluster edge and concludes its path on the border of the pupil range. Exemplary ray2209 exits digital display 2201 near the border and exits the lens near the border of exitsurface 2207 after which it passes through the border of the pupil range in a direction towardsthe eye sphere center. FIG. 22 shows an example of a 2-lenslet configuration, but may beextrapolated to a design with k lenslets, k > 2. Another variant of this configuration is 90°rotation around the dashed line axis 2212.[0134] Next configuration in FIG. 23 includes also two separate optical pieces, with a thinlens 2303 such as a thin Fresnel lens placed between a device 2302 similar to that in FIG. 12and user's eye. In order to solve the issue of excessive convex curving of surface 1203 of12 in the direction perpendicular to the plane of FIG. 12, FIG. 23 includes a lens 2303 withpositive optical power in that direction between the optical device 2302 and the human eye2306. In FIG. 23, this lens 2303 is a Fresnel lens, which is a thin lens so it will notsignificantly increase the overall system thickness. FIG. 23 right shows a top view of ahorizontal cross-section of this configuration and FIG. 23 left shows a side view of thevertical cross-section of the same configuration. FIG. 23 shows a user's eye 2306 and nose2307 for orientation purposes. A digital display 2301 is placed in a vertical position. The useof either a single large digital display for both eyes, or two separated digital displays, i.e. oneper eye, is allowed in this design.[0135] Different lenses 2303 can be designed for a given device 2302 to correct the user'svision defects (for example, myopia, hypermetropia or astigmatism) by changingcorrespondingly the virtual screen in the design. Thus, only lens 2303 needs to bereassembled to accommodate different users.[0136] Rays in this configuration suffer two additional refractions in comparison with thesystems that consist of lens 2302 alone. Rays exiting lens 2302 suffer one refraction onfaceted surface 2304 of Fresnel lens 2303 and the other refraction on plane exit surface 2305.As shown in FIG. 23, surface 2304 has facets only in one direction (see left side of FIG. 23),i.e., the grooves may have cylindrical symmetry along the vertical direction, which makes foreasier manufacturing. This is why the facets are not seen in the right side of FIG. 23. Fresnellens 2303 placed at the exit of lens 2302 concentrates rays 2308 and 2309 when they exit thelens 2302 towards the eye sphere center 23 10.[0137] As mentioned above, Fresnel lens 2303 may be substituted with another lens, eitherlinear symmetric, rotationally symmetric or freeform.[0138] FIG. 24 shows a top view of a horizontal cross section of another device. User's nose2413 and eye 2414 are shown for orientation purposes. This design has four lenslets: two ofthem are RXIR type and the other two are refractive RR type, and allow for a shorter displayto eye distance than the embodiment in FIG. 12. Therefore, this device has four clusters ofopixels in the digital display. The inner lenslet in each pair of lenslets preferably covers thepupil range where the eye usually gazes, for instance, the horizontal angular range from 0° to20° measured at the eye sphere center 2416 relative to the front direction 2415, which it istherefore the region where we need higher image quality. Rays that belong to the innerlenslets suffer 4 deflections. The outer lenslet consists of two refractive surfaces 2406 and2407 where rays suffer only two deflections. This lenslet covers a narrower angular range, forinstance, from 20° to 30° measured at the eye sphere center 2416 relative to the frontdirection 2415; and this range is rarely gazed by the eye. We illustrate the working principleof this embodiment in FIG. 24. This device can work with the vertical display 2401, so wemay have one large digital display for both eyes or two smaller digital displays per eye (i.e.,digital display diagonal < 2.5" (60 mm) approximately).[0139] FIG. 24 shows different surfaces. The refractive entrance surface 2402 (and itsmirrored portion 2403), the mirrored surface 2404 and the refractive exit surface 2405 belongto the inner lenslet. The refractive surfaces 2406 and 2407 belong to the outer lenslet. Theexit surfaces 2406 and 2405 of the same side are usually separated by a small slopediscontinuity. Focal distances are preferably distributed in order to have a maximum in afrontward direction along axis 2415, and then they gradually decrease when moving awayfrom the center of the virtual screen, as discussed in detail below in the next section 7. Theouter cluster of the digital display (which extends from point 2417b to the display outer edge)that works with the outer RR lenslet is smaller than the cluster (which extends from point2417a to 2417b) that operates with the inner RXIR lenslet because the inner cluster covers awider angular range and has higher focal lengths.[0140] Ray 2408 exiting the digital display is refracted on surface 2402, reflected on backmirror surface 2404, totally internally reflected on the entrance surface 2402 (or reflected onthe mirrored part 2403 of surface 2402), refracted on surface 2405 and directed towards theeye 2414, undergoing a total of 4 deflections. Rays 2409 and 2410 suffer the samedeflections. Ray 2409 starts its path on the inner edge 2417a of the cluster extending frompoint 2417a to 2417b and ends on the outer edge of the pupil range 2412a. Ray 241 1 workswith the outer RR lenslet, it exits digital display inside the outer cluster and suffers twodeflections, one refraction on surface 2407 and another one on surface 2406, after which it isdirected towards the eye in the gaze vector direction (i.e., approximately to the eye spherecenter 2416). Ray 2410 exits the outer edge of the cluster from 2417a to 2417b and suffersfour deflections, exits the outer RXIR lenslet near the derivative discontinuity with outer RRlenslet of the lens and is directed towards the border of the pupil range 2412b. The design ofthe outer lenslet is similar to the lenslet designs described in Section 6.6 of PCT1.[0141] A top view of a horizontal cross section of another configuration is shown in FIG. 25,with the vertical digital display 2501, and the user's nose 2520 and eye 2521 drawn fororientation purposes. This configuration consists of four lenslets whose working principlesare different. It does not require any mirror coatings and allows a shorter display to eyedistance than the device in FIG. 12. The device of FIG. 25 has a total four opixels clusters pereye in the digital display 2501. One lenslet is formed by pieces 2503 and 2504 and covers thepupil range where the eye usually gazes, i.e. a conical angular range of about 0°-20°measured from the eye sphere center, which is the region where we need higher imageThe rays that belong to this lenslet of the optical system suffer 6 deflections in 2 separate lenspieces. Alternatively, the air gap between the two pieces 2504 and 2503 (between surfaces2508 and 2509) can be filled with a low index material such as a fluoropolymer like FEP. Thesame piece 2503 and a separate thin lens 2502 form another lenslet whose virtual imagecovers a narrower angular range of about 10° starting where the first conical range ends(approximately from 20°-30°) measured from the eye sphere center, which is rarely gazed bythe eye. In this lenslet the rays suffer 5 deflections in 2 separate lens pieces. The central piece2503 is used in both types of lenslet, but the ray path is different for different lenslets. Weillustrate working principle of this embodiment in FIG. 25.[0142] FIG. 25 shows 4 lenslets in two pairs separated with a dashed line (central axis orplane of symmetry) and 3 separate optical lens pieces 2502, 2503 and 2504 per pair oflenslets. Lens 2503 may be either a single lens piece shared between the upper and lowerlenslets, as illustrated in FIG. 25, or it can be made in several separate pieces. This secondoption is feasible as the thickness of piece 2503 along the optical axis is small and theinfluence of optical cross-talk described with reference to FIG. 15 is negligible.[0143] Rays 2513 and 2517 exit the edges of one of the peripheral clusters of digital display2501 as shown in FIG. 25, suffer refraction on entrance surface 251 1, total internal reflectionon back surface 25 12, refractions on surfaces 2509 and 2508 at the gap between lens pieces2504 and 2503, total internal reflection on front surface 2507, refraction on exit surface 2510and conclude their path through the system (after 6 deflections) at the edges of the pupilrange as 2514 and 2519, respectively. The optical cross-talk is thus avoided.[0144] Rays 2515 and 2516 exit the edges of one of the central clusters, refract on surfaces2505 and 2506 of lens 2502, refract on front surface 2507 of lens 2503, totally internallyreflect on surface 2508 at the gap with lens piece 2504, refract on surface 25 10, and then ray2515 is directed towards the pupil range edge 2514 meanwhile ray 2516 is directed towardsthe eye pupil position when eye rests looking forward.[0145] Thus, in the configuration of FIG. 25, the opixel clusters corresponding to the outerparts of the final image are at the middle of the digital display 2501, and the opixel clusterscorresponding to the central parts of the final image are at the outer edges of the digitaldisplay 2501. That is taken into account in generating the partial real images for each cluster.[0146] FIG. 26 shows a top view of a horizontal cross section of another 2-lensletconfiguration. User's eye 2610 and nose 2614 are shown for orientation purposes. Eachlenslet of the lens 2609 has two metallized surfaces 2603 and 2604 that form a groove at theouter corner of the lenslet. Rays 2606 and 2607 exiting display 2601 are refracted at entrancesurface 2602, then reflected on each groove's side - first reflection on back surface 2604 andsecond reflection on side surface 2603, then totally internally reflected on entrance surface2602 and finally refracted on exit surface 2605 and directed towards the eye 2610. The samedeflections happen for ray 2608. Ray 2606 coming from the opixel near the digital displayedge is directed preferably towards the edge of pupil range 261 1 reflecting off cusp 2612 atthe central axis of lens 2609 between the entrance surfaces 2602 of the two lenslets. Ray2608 emitted from the opixel cluster edge near the center of digital display 2615 is preferablydeflected towards the border of pupil range 261 1 passing through the exit's edge point 2613.The optical cross-talk needs to be avoided by a proper definition of a pupil range exactly inthe same way as disclosed in patent PCTl. Maximum image quality is designed for rays suchas 2607, which starts its path on the interior of one of the two clusters and reaches the eyepointing towards the eye sphere center, so it is close to the gaze vector direction.[0147] 6. Embodiments with non-superposable RXIR lenslets[0148] It is obvious that the lens and displays in FIG. 12 can be rotated outboard through anangle with respect a vertical axis passing through the eye sphere center, for instance, about 5to 15°. This makes the whole HMD present better ergonomics, and increases the horizontalfield of view by twice the angle of rotation of each lens and display. As a consequence, thebinocular portion of the field of view is also reduced by twice the angle of rotation. However,better designs can be achieved for such rotated displays by breaking the symmetry of thesuperposable lenslets in FIG. 12, as follows.[0149] FIG. 27 shows a top view of a horizontal cross section of another 2-lensletconfiguration. User's nose 2717 and eye 2716 are drawn for orientation purposes. Thisconfiguration loses the symmetry between the two lenslets (and their corresponding opixelclusters) allowing the two lenslets to have different optical performance and size. Thisconfiguration works with a tilted digital display 2701 to provide better ergonomics, and thenit uses two independent digital displays, one per eye, e.g. digital display diagonal < 2.5" (60mm).[0150] The inner, larger lenslet 2714 of the lens embodiment shown in FIG. 27 is designedfor covering a wider fraction of the horizontal field of view (FOV) than the outer lensletsince the cusp at the outer edge of surface 2705 is no longer located at the front-viewdirection (given by the dashed line passing through 2702) but on the dashed line 2718, whichforms an angle that could be about 5° to 15° with the centerline to 2702 at the center 2703 ofthe eye 2716. Focal distances are preferably distributed in order to have a maximum in 0°direction where the eye pupil rests looking forward (as along the axis to point 2702), and thengradually decrease when moving away from the center of the virtual screen (as shown in FIG.2). The digital display area that works with the outer lenslet 2713 is smaller than the digitaldisplay area that works with the inner lenslet 2714, the point 271 5 being at the borderbetween the two clusters. This is the case as the inner lenslet 27 is designed for a widerfraction of the horizontal FOV and also for higher focal lengths.[0151] Rays 2709 and 2710 that exit digital display at the edges of the inner cluster arerefracted at entrance surface 2705, reflected on back mirror surface 2706, totally internallyreflected on the entrance surface 2705 (or reflected from the metallized part 2707 of surface2705), refracted at exit surface 2708, and directed towards the eye 2716. Ray 271 1 from theouter cluster has the same deflections. Ray 2710 starts its path on the edge 2715 in the innercluster through the inner lenslet 2714 and ends on the border of the pupil range 2712. Ray271 is emitted at the edge 2715 in the outer cluster and thus propagates through the outerlenslet 2713. Ray 2709 determines the inner border of the horizontal monocular field of view,it refracts on inner border of the exit surface 2708 and it is emitted approximately at the innerborder of digital display 2701. Analogously, ray 27 determines the outer border of thehorizontal monocular field of view, it refracts on outer border of the exit surface 2708 and itis emitted approximately at the outer border of digital display 2701 .[0152] FIG. 28 illustrates a horizontal cross-section of two similar 2-lenslet lenses similar tothat of FIG. 27, one for each eye, sharing a common curved digital display 2801.Alternatively, two separate curved displays could be used. Rays exiting the cylindrical digitaldisplay 2801 suffer four deflections on their way from the digital display to the eye in thefollowing sequence: refraction, reflection, total internal reflection and refraction. Dashedlines 2804 indicate virtual rays from the virtual screen to the eye sphere 2805. On the left areshown virtual rays for an eye looking straight ahead, and on the right are shown virtual raysfor the extreme sides of the field of view. Continuous lines 2803 represent rays traveling fromthe digital display 2801 to the eye sphere 2805. In general, the two lenslets 2802 of each lensare not symmetric one respect the other, although each lenslet may have a horizontal plane ofsymmetry. Another configuration is got when these devices are rotated 90 degrees around anaxis passing through the center of the eye and pointing frontwards. In this latter case, the twolenslets may be symmetric one respect to the other, but each lenslet may then have no planeof symmetry.[0153] 7. Adapting the design to the human eye resolution[0154] FIG. 2 shows the angular resolution of a typical human eye as a function of theperipheral angle (according to J.J. Kerr, "Visual resolution in the periphery", Perception &Psychophysics, Vol. 9 (3), 1971). Since the human eye resolution is much smaller inperipheral vision than close to the gazing direction, we can adjust the design conditions ofany of the embodiments in this specification to make the ipixels smaller in size on the gazedregion of the virtual screen and larger in the outer region of the virtual screen. For thispurpose we are going to assume that the optical systems are reasonably anastigmatic so wecan define a mapping between the object and the image. Let p, ) be the polar coordinates ofa point r on the digital display and let ¾ f be the polar and azimuthal angles, respectively, ofthe spherical coordinates o the virtual screen. The coordinates are defined so that Q= 0 is thefrontward axis, Qis the angle away from that axis, f is the azimuth around the Q= 0 axis, andthe directions f =0 and f = p are horizontal. The function, = , q,f , , 5 ,f ) is called the mapping function. The inversemapping function is given by (6 =( r), r)) .[0155] We call radial focal lengthf ra at the virtual screewe will write as |¾| . We call sagittal focal length to f sag =different than radial or sagittal, the focal length is given by f a = |r cosa + r sin /sinwhere is the angle formed by the radial direction and the direction along which the focaldistance is calculated. The focal length informs about the expansion or shrinking of themapping in a particular direction. When the mapping between the object and the image isconformal, then f a is independent of , which is equivalent to saying that the mappingexpansion or shrinking is isotropic. The angular extent of an ipixel along the direction canbe calculated as the corresponding opixel diameter divided by the focal length, i.e., D f(for simplicity, circular opixels are considered herein, but the reasoning is easily extended tothe usual square opixels). When there is more than one opixel for a given ipixel we may havedifferent ratios if the optical system is not properly designed. The human eye resolutiondepends on the peripheral angle but is to a good approximation not dependent on thedirection along which the resolution is evaluated. Then it is desirable that the angularextension of the ipixels be independent of (otherwise the resolution will be given by thegreatest angular diameter). Since the diameter of the opixels is in general quite constant withthen an f a independent of is in general desirable.[0156] The idea of an optical design whose resolution changes across the field of view and isadapted to that of human vision was introduced in PCT1, section 6.8. Human visionresolution peaks on the part of the scene imaged at the fovea and decreases as we move fromthat part. Assume the eye is gazing at front direction (0=0). Hence, longer radial focal lengths(leading to smaller ipixel angular size and hence higher optical resolution) should be used forlow values of Q where higher resolution is needed while, in the case of high values of Q(peripheral view), shorter focal lengths are acceptable since the eye resolution is lower forthose angles.[0157] FIG. 29 shows a 4-lenslet embodiment 2904. The surfaces of each lenslet have aplane of symmetry coinciding with the diagonal direction of the half of the display. Thus, themapping function f (q, f ) for one lenslet fulfills that f q, f= \ ° = 45°. This device hasvariable focal length. In particular, the radial focal length f d = decreases along thef - constant lines as Q increases. The focal length in the transverse directionfsag - designed to be essentially equal to f md order to give an optimal use ofthe display active area. FIG. 30, FIG. 3 1A, and FIG. 3IB show the results obtained for thedesign of FIG. 29 regarding the focal length distribution.[0158] FIG. 29 shows a display 2901 with aspect ratio close to 2:1 (for example, the 16:9aspect ratio that is a current standard) placed in a plane perpendicular to the floor with itslongest dimension parallel to the floor. FIG. 29 also shows two 4-lenslet devices 2904 (oneper eye) in front of the digital display, each one in front of the respective half display that it isimaging, similar to the lens 1807 disclosed in FIG. 18 but with a 45 degree rotation about anaxis normal to the display. Therefore, the 4-fold device is placed so the diagonal 2903 alongthe center of one of the lenslets 2902 is generally parallel to the diagonal of the half digitaldisplay as shown in FIG. 29.[01 5 FIG. 30 shows the radial and sagittal focal lengths as function of the angle Qalongthe line f = 45 deg. This illustration is done for one lenslet 2902 of the 4-lenslet device 2904of FIG. 29. Radial focal length is marked with full line 3001, and the sagittal one 3002 withdashed line. Both focal length distributions have the maximum value close to = 0°, and theygradually decrease for greater angles q , particularly beyond 20 degrees. We may observe thatboth focal lengths (radial and sagittal) are balanced at each value of angle Qalong thediagonal line f = 45 degrees in both radial and sagittal directions.[0160] FIG. 31A shows the portion of the display 2901 (in FIG. 29) which illuminatesthrough lenslet 2902 the eye pupil when this pupil has 4 mm diameter and the eye is gazingfrontwards. This half display is divided into 4 square clusters, each working with one lenslet2902 of the 4-lenslet device 2904. The direction = 0 is imaged on the digital display at thepoint p = 0, (3102) i.e. (x,y )= , in FIG. 31A. As is shown in FIG. 31B, we define as theangle 3112 between the projection 3 111 on the xz-plane of the direction 3109 of a pixel underconsideration and the z-axis, and we define g as the angle 3 114 between the projection 3 113on 3109 and the z-axis. The angle Q(3 110) can be expressed asin terms of c and g, which can be expressed as functions of andas c = arctan(cos) and ^=arctan(sin^tan6') . Full lines shown in FIG. 31A insideof the square section of the display represent the curves c - g = const, and c + g = const,mapped by the lenslet 2902 (FIG. 29) onto the digital display, for 2.5 degree increments ofthose constants. Line 3101 represents the curve for c - g = 0 i.e., for f = 45 degrees whoseradial and sagittal focal lengths as function of the angle Qare shown in FIG. 30. With thisfocal length distribution paired in two perpendicular directions an observer seesapproximately a square ipixel area if the original opixels are also squares. The radial andsagittal focal lengths in the neighborhood of the point 3102 are 23.5 and 22.8 mm,respectively. Additionally, near the point 3103 at the center of FIG. 31A the focal lengths are17.3 and 16.2 mm and along the isocurve 3104 c + g = 20 deg.) the radial and sagittal focallengths are maintained substantially constant, so in the neighborhood of the point 3108 wehave 17.6 and 18.0 mm, respectively. For higher values of the angle Q, e.g. in theneighborhood of the point 3 105, focal lengths are 1 .5 and 12.2 mm. At the point 3 107,which is in the same isocurve c + g = const.) 3106 as the point 3105, the focal lengths are12.5 and 12.9 mm. From those exemplary values, we may see how focal distance values arebalanced in two perpendicular directions, highest in the central region of display and howthey gradually decrease going towards the display edge.[0161] 8. Detailed example of a 2-fold superposable optics[0162] This section describes in detail the optical design for the configuration previouslydescribed. This configuration consists of one thin freeform lens where rays suffer tworefractions and another lens where rays suffer 4 deflections on 3 freeform surfaces ( 1 opticalsurface is used twice). The optical design is done by multiparameter optimization of thecoefficients of a polynomial expansion, preferably using an orthogonal basis. In theembodiments described herein, surfaces are described with the following equation:where Pm(x,y) is the 10 order polynomial, i.e. =10, are the optimized surfacecoefficients listed in Table 1 below, and P2i x- xm +Xm 2 /xm ax and Pj((y-( m x + mi y m ) e Legendre polynomials that are orthogonal inside of the area restrictedwith xmin and xmax, y min and y max in x and y directions, respectively. All surfaces have planesymmetry in the -p ane, i.e., the plane x=0 (plane of the drawing shown in FIG. 32) soLegendre polynomial P2i x - xm x+ Xm ) ' x has only pair order monomials.[0163] Explicit representation of Legendre polynomiawhere the latter expresses the Legendre polynomials by simple monomials and involves themultiplicative formula of the binomial coefficient, and wherek n ~ k ) '[0164] FIG. 32 shows local coordinate system of each surface polynomial description in -plane, x=0 (where the z-axis points left and the y-axis points up). The eye sphere center islabeled with 3201 and we use it as the center of the global coordinate system (x,y,z)=(0,0,0).Eye sphere is labeled as 3202. The local coordinate system origin 3203 used for the display3204 has coordinates (x,y,z)=(0, 0, 44.00). Surface 1 is labeled as 3206 and its localcoordinate origin 3205 is placed at x,y,z)= , 0, 29.04540). Surface 2 is labeled as 3208 andits local coordinate origin 3207 is placed at (x,y,å) ( , 15.5041, 27.85875). Surface 3 islabeled as 3210 and its local coordinate origin 3209 is placed at (x,y,z)=(0, 0, 25.00). Surface4 is labeled as 3212 and its local coordinate origin 321 1 is placed at (x,y,z)=(0, 0, 24.50).Surface 5 is labeled as 3214 and its local coordinate origin 3213 is placed at(x,y,z)=(0, 0, 24.00). Coordinates are given in mm. Coefficients of all surfaces' polynomialsare listed in Table 1. The first four rows are CI: xmin, C2: xmax, C3: y min and C4: y max thatdescribe a rectangular area between xmin and xmax in the x-direction, and y m„ and ymax in theperpendiculars-direction where each polynomial is orthogonal. The next rows C5 to C97 ofTable 1 are coefficients of 10th order Legendre polynomial Pm{x,y) for each surface we havedesigned. Surfaces 3, 4, and 5 have plane symmetries in both x= and y= planes. Thecoefficients that do not appear in Table 1 are equal to zero.Table 1Parameter surface 1 surface 2 surface 3 surface 4 surface 5CI . -14.5 -18 -12.5 -10.5 -10.5C2 14.5 18 12.5 10.5 10.53. -5 -4 -15 -15 -15C4. ymax 26 13 15 15 15C5: cOO 7.74826817 9.48685118 1.98441208 -0.03714411 -1.01185865C6: cOl 9.9901003 15.9891329 0 0 0C7: c02 -2.17415555 1.84212394 -1.02213907 -0.18904498 -0.39442517C8: c03 0.26992555 1.37861982 0 0 0C9: c04 0.07323412 1.32413174 0.21297795 -0.97463799 -0.56541986C10: c05 0.07232204 0.62427156 0 0 0Cl l : c06 0.07046191 0.37600442 -0.25925897 -0.1 1307267 -0.03753875C12: c07 0.01669641 0.19622519 0 0 0C13: c08 0.00564396 0.08847943 0.01571654 0.02814461 -0.05840282Parameter surface 1 surface 2 surface 3 surface 4 surface 5C14: c09 0 0.02943414 0 0 0C15: cOlO 0 -0.00486727 0.02433397 0.01892424 -0.01243578C27: c20 2.90274519 10.1007194 3.00674917 -0.27538838 1.22293126C28: c21 0.92173438 11.1935568 0 0 0C29: c22 -0.03224471 4.7809068 1.01919509 3.63663724 1.51062622C30: c23 0.51128187 3.66039714 0 0 0C31: c24 0.39628668 2.42170405 1.38578164 -0.18246823 -1.12598721C32: c25 0.30566662 1.98779412 0 0 0C33: c26 0.13709387 0.4712952 0.15831457 -0.00439278 -0.12677413C34: c27 0.02746642 0.2983583 0 0 0C35: c28 -0.01 145297 -0.02158365 -0.12161842 -0.17362037 -0.03418757C36: c29 0.00482329 -0.00669569 0 0 0C49: c40 0.10779636 1.841 16064 0.1079878 0.5172034 0.33745174C50: c41 0.04121436 2.16314619 0 0 0C51: c42 0.0693218 -0.21 160035 -0.10957435 1.05534915 0.55827464C52: c43 0.04130056 0.33742766 0 0 0C53: c44 -0.02768964 0.27471767 0.48922576 0.82583368 0.24898517C54: c45 0.03481823 0.38273918 0 0 0C55: c46 0.01519245 -0.1269211 0.32196795 0.44845829 -0.04187352C56: c47 0.00134877 -0.00406391 0 0 0C57: c48 0 0 0.086918 0.16666561 0.03091233C71: c60 -0.07007249 0.28370224 -0.05702479 0.02249273 0.02618387C72: c61 0.13503468 0.59377583 0 0 0C73: c62 0.12422693 -0.11686878 -0.09428408 0.05765244 0.096821C74: c63 -0.09692662 0.06321373 0 0 0Parameter surface 1 surface 2 surface 3 surface 4 surface 5C75: c64 -0.03198063 0.05192254 -0.2357585 0.05293862 0.0681094C76: c65 0.03040448 0.19384503 0 0 0C77: c66 0.00864096 -0.04787574 -0.24718492 -0.04115771 0.04880808C78: c67 0 0.00360285 0 0 0C79: c68 0 0 -0.12242551 -0.04221036 0C93: c80 -0.00354415 0.07247046 0.01092137 -0.0058482 -0.006173C94: c81 -0.00500629 0.07485071 0 0 0C95: c82 0.01760391 -0.01 142592 0.06069702 0.03417736 0.01 180534C96: c83 -0.00071029 0.00071433 0 0 0C97: c84 0 0 -0.00740858 -0.00163364 0.00492729[0165] FIG. 33 illustrates the x = 0 plane of a lenslet belonging to a 2-lenslet design such asthe one shown in FIG. 23 (using a continuous freeform lens 331 1 instead of a Fresnel lens).Half of the display is labeled as 3301 and user's eye is 3302. The complete design would beobtained with a irror image of the shown lenses 3310 and 3311 with respect the y=0 planethat contains axis 3308. In FIG. 33 we may examine design rays trajectories. Reverse ray3304 comes from the border of the pupil range 3303, impinges at the cusp of surface 1(surface 3206 of FIG. 32) and it is sent to the cluster edge 3309. The reverse ray 3305 exitsthe eye parallel to the z axis. The reverse ray 3306 comes from the eye sphere center, itimpinges on the border of surface 5 (surface 32 4 of FIG. 32) and it impinges on the display.The reverse ray 3307 fixes one end of the field of view as it is the border peripheral ray thatimpinges on the border of surface 5 from the eye pupil position when the eye rests lookingforward.[0166] FIG. 34 is the cross section at the plane y = 0 of one lenslet belonging to the 2-lensletconfiguration also shown in FIG. 33. This section is perpendicular to the section shown inFIG. 33. The display is 3401 and the user's eye is 3402. Lenses 3404 and 3405 correspond to3310 and 331 1 in FIG. 33, respectively. The reverse ray 3403 exits the eye pupil when thiseye pupil gazes near the border of pupil range.[0167] Table 2 and Table 3 show the root-mean-square (RMS) diameters of thepolychromatic spots for some selected fields of the design in FIG. 33 using a pupil diameterof 4 mm. This design has a focal length about 26 mm for the front direction and the focallength gradually decreases towards the edge of the field of view to be adapted to the eyeresolution. The horizontal field of view is 108 degrees and vertical field of view is 93 degreesfor a 2.1" (55 mm) diagonal 16:9 display. Angles^ and y in the table have the samedefinitions as in FIG. 3 IB.[0168] Table 2 corresponds to the situation when the eye is gazing the said field, so theperipheral angle for the human eye perception is 0 for all the fields, and thus the opticalresolution should be the maximum for this field. Table 2 shows that opixels as small as 20-30microns can be resolved well, although the RMS diameter increases significantly for thehighest values of the angle x(deg). This is caused by chromatic aberration, which can beeasily corrected by adding a diffractive kinoform, preferably in one of the surfaces 3210,3212 or 3214 in FIG. 32. For easier manufacturability, these kinoforms should be added on anon freeform surface. The case when the vertices of the kinoform facets are contained inplanes parallel to the plane of FIG. 32 is of special interest.[0169] Table 3 corresponds to the situation when the eye is gazing frontwards, so theperipheral angle for the human eye perception is not zero, but equal to Q. Therefore, theoptical resolution can be lower without affecting the human perception of optical quality.This design is adapted to the human eye resolution of FIG. 2. For this reason, the RMS valuesare much higher in Table 3 than in Table 2 for the same fields.Table 2X (deg) (deg) RMS (m i ) (deg) (deg) RMS (m i )0 0 19.1 4 20 24.80 2 19.2 4 22 25.90 4 14.4 4 24 30. 10 6 16.3 4 26 35. 10 8 18.7 4 28 53.00 10 19.2 4 30 96. 10 12 16.4 6 0 28.50 14 13.2 6 2 29.20 16 17.8 6 4 25.50 18 22.3 6 6 25.70 20 22.7 6 8 26. 10 22 24.0 6 10 26.20 24 28.6 6 12 25.00 26 32.9 6 14 23.20 28 40.0 6 16 26.50 30 76.8 6 18 28.82 0 20.3 6 20 27. 12 2 20.7 6 22 28.42 4 16.0 6 24 32.52 6 7.6 6 26 37.22 8 19.8 6 28 65.72 10 20.5 6 30 117.02 12 17.7 8 0 33.02 14 14.8 8 2 34.22 16 19.1 8 4 29.72 18 23.3 8 6 29.22 20 23.2 8 8 29.92 22 24.8 8 10 30.32 24 28.9 8 12 29.62 26 33.9 8 14 29. 12 28 43.3 8 16 3 1.12 30 81.4 8 18 32.74 0 23.9 8 20 3 1.54 2 24.4 8 22 32.94 4 20.4 8 24 36.24 6 20.9 8 26 39.74 8 22.5 8 28 83 .34 10 22.6 8 30 139.74 12 19.9 10 0 38.34 14 18.2 10 2 39.54 16 22.4 10 4 36.74 18 25.6 10 6 35.6(deg) RMS (mhi) X (deg) r(deg) RMS (mhi )2 0 10 64.0 2 0 16 65.720 12 66.2 2 0 18 7 1.520 14 66.7X (deg) RMS (m h ) ( e ) (deg) RMS (m i i )12 0 83.9 16 18 38.612 3 63.8 16 2 1 40.212 6 45.8 16 24 47.612 9 44.0 16 27 7 1.912 12 44.7 16 30 110.312 15 44.2 16 33 156.312 8 45.8 16 36 2 10.112 2 1 48. 1 16 39 264.812 24 50.0 16 42 301 .312 27 57.8 16 45 306.812 30 82.8 16 48 569.512 33 12 1.6 19 0 123.412 36 169.6 19 3 105.612 39 2 17.9 19 6 79.612 42 251.8 19 9 55.412 45 278.3 19 12 42.512 48 255.0 19 15 39.412 51 348.9 19 18 42.615 0 103.6 19 2 1 48. 115 3 83.5 19 24 62.715 6 6 1.0 19 27 96.115 9 48.2 19 30 14 1.115 12 42.3 19 33 192.515 15 39.8 19 36 253. 115 18 39.8 19 39 3 14.615 2 1 4 1.5 19 42 35 1.515 24 46.2 19 45 390.815 27 66.6 19 48 1197.615 30 102.0 22 0 124. 115 33 146.2 22 3 110.515 36 198.3 22 6 88.615 39 251.2 22 9 65.715 42 287.6 22 12 56.415 45 297.2 22 15 58.315 48 4 18.7 22 18 65.415 5 1 730.6 22 2 1 75.316 0 109.7 22 24 94.516 3 89.9 22 27 13 1.116 6 66. 1 22 30 179.516 9 49.8 22 33 237.216 12 4 1.4 22 36 308.516 15 38.7 22 39 380.3X (deg) RMS (mhi) (deg) ( eg) RMS (mi )22 42 436.0 29 2 1 193.922 45 693.6 29 24 213.822 4 8 2 119.8 29 27 238.423 0 120.2 29 30 282.323 3 109.1 29 33 363.323 6 90.9 29 36 492.323 9 71.7 29 39 688.423 12 64.7 29 42 1097.023 15 68.7 29 45 2344.323 18 76.7 32 0 83.123 2 1 87.8 32 3 103.923 24 108.0 32 6 126.823 27 144.8 32 9 148.423 30 193.6 32 12 174.923 33 254.4 32 15 206.123 36 329.7 32 18 237.623 39 407.1 32 2 1 263.723 42 476.3 32 24 280.323 45 865.7 32 27 292.726 0 99.4 32 30 329.326 3 99.8 32 33 434.926 6 101.3 32 36 666.726 9 97.9 35 0 122.726 12 100.8 35 3 141.026 15 109.0 35 6 150.026 18 120.0 35 9 161.826 2 1 134.5 35 12 196.126 24 155.7 35 15 246.626 27 190.6 35 18 298.326 30 236.4 35 2 1 335.426 33 307.5 35 24 348.626 36 401.4 35 27 350.626 39 510.6 38 0 208.726 42 683.4 38 3 171.826 4 5 1572.7 38 6 167.829 0 80.6 38 9 175.129 3 93.3 38 12 213.529 6 115.9 38 15 280.02 9 9 128.5 38 18 350.729 12 141.5 38 2 1 396.529 15 157.2 38 24 409.629 18 175.0 38 27 502.2[0170] 9. Embodiments with time division multiplexing[0171] The idea behind time multiplexing is increasing the number of ipixels byrepresenting the image in several consecutive parts within the frame period and using allthe available opixels for any of these image parts. Obviously the success of such strategydepends on the availability of digital displays with high switching rate such as OLED,transmissive or reflective FLC or DMD digital displays. This is illustrated in FIG. 35through a 2-lenslet example where the digital display 3501 is shown on the left side ofFIG. 35, and two active shutters are placed between the digital display and the 2-lensletdevice. The digital display emits rays 3504 and 3505 for the top lenslet of FIG. 35. Theserays are received by the eye only when the top shutter, i.e. 3502, is opened. Thisembodiment may use a fast ferroelectric light crystal display (FLCD) acting as a shutter.They work as a classical half-wave plate whose optic axis can be reoriented by an appliedfield. Benefits of FLCDs are their high resolution and very quick switching time (lessthan 100 m ) . In US 4,924,215 to Nelson, these FLCD are also used as shutters.According to the reference Shilov 2010, Toshiba's active-shutter stereo 3D glasses have0.1 ms (open to close/decay) and 1.8 ms (close to open/rise) response speed, whereasmany competing solutions declare 0.3 ms and 3.7 ms speeds respectively, or even 2 ms"typical" response time.[0172] In the situation illustrated in FIG. 35, the bottom shutter 3503 is closed, hence theeye only receives light from the top lenslet. When the top shutter 3502 is closed, then thebottom shutter 3503 is opened and the eye receives information only through the bottomlenslet of the lens. As shown in FIG. 35, each lenslet corresponds to a different region ofthe whole field of view, so the top lenslet transmits the top half of the whole field ofwhile the bottom lenslet transmits the bottom half of the whole field of view. These arethe 2 sub-images which together fill completely the virtual screen. Strictly speaking, thetwo sub-images overlap since they must allow for the eye moving within the pupil range(and also because of the non-zero diameter of the human pupil), as in most of the multilensletdesigns disclose herein. In this configuration, each frame period is divided in twosubframe slots. In the first subframe slot the digital display shows the informationcorresponding to the top sub-image, while in the second subframe slot the digital displayshows the information of the bottom sub-image. If the transition between these twodifferent situations is performed fast enough, then the eye will perceive a globaloverlapped image coming from both lenslets, i.e. it will perceive a total field of view withalmost double the number of pixels that we initially had in the vertical direction. This isthe same effect happening in a traditional Cathode Ray Tube (CRT) where the combinedpersistence of the phosphor of the screen and persistence of our retina creates the illusionof a steady image from a single scanning point (only one point is being drawn at a time)when the cathode beam scans the phosphor screen.[0173] When using a 16:9 digital display for each eye, then the digital display ispreferably placed in a horizontal position (i.e. with its longest dimension parallel to thefloor). In this orientation, the profile of the digital display shown in FIG. 35 is its shortestside, and the time-multiplexing device will generates a rather 1:1 aspect ratio (i.e., similarvertical and horizontal fields of view). The explanation of how the vertical field of viewis almost doubled can be seen in FIG. 36A, which represents the virtual screen 3601 forthis design. The dotted rectangle 3602 represents the top sub-image of the virtual screen,generated by the top lenslet, while the dashed rectangle 3603 represents the bottom subimageof the virtual screen, generated by the bottom lenslet. The addition of the two subimages,as explained above, generates a larger square-shaped total field of view. The subimagesoverlap in the central region, as shown in FIG. 36, to allow for the eyemovements within the pupil range.[0174] An alternative configuration uses a single standard 16:9 digital display for botheyes, instead of a digital display per eye as above. In this case, the lens is rotated 90°being placed in horizontal position, so the two halves of the shutter are aligned left-right,similarly to the design in FIG. 20. This alternative configuration leads to an elongatedfield of view, with a larger field of view in the horizontal direction. FIG. 36B shows thegeneration of the virtual screen 3604 for this design. The dotted square 3605 representsthe left section of the virtual screen, generated by the left lenslet, while the dashed square3606 represents the right section of the virtual screen, generated by the right lenslet,resulting in a larger rectangle-shaped total field of view.[0175] Time division multiplexing (TDM) idea can also be applied to 4-lensletconfigurations, as suggested in FIG. 37, which shows the diagonal 2D cross-section ofthe device, showing as well the diagonal profile of the digital display 3701. Theexplanation of how the rays are alternatively blocked by the shutters is analogous.Obviously, in this situation we will have four shutters (one per lenslet) instead of two.FIG. 37 shows the diagonal section of two shutters, 3702 and 3703, and the extreme rays3704 and 3705 of top lenslet in FIG. 3 . The shutters shown here are all coplanar, whichis easier to implement than those shown in FIG. 35. The 2-lenslet device in FIG. 35 canbe slightly modified to also allow for coplanar shutters. The 4-lenslet design shown inFIG. 37 is also compatible for working with a single 16:9 digital display for both eyes butit is not restricted to a single display. Hence, the top left lenslet of the lens generates thetop left section of the virtual screen, the top right lenslet generates the top right section ofthe virtual screen, and so on. This is represented by FIG. 36C, where the two dottedsquares represent the section of the virtual screen generated by the top left and bottomright lenslets, while the dashed squares 3608 and 3609 represent the section of the virtualscreen generated by the top right and bottom left lenslets, while the dashed squares 3610and 361 1 represent the section of the virtual screen generated by the top right and bottomleft lenslets, resulting in a larger total field of view with aspect ratio about 1:1, i.e. withsimilar horizontal and vertical fields of view.[0176] In the case of LCD digital displays (either transmissive or reflective) steerablecollimated backlight for can be used as an energy efficient alternative (Fattal 2013), or acombination of such backlight with shutters. If a DMD digital display is used, selectionof the lenslets to illuminate can be done with a proper design of the DMD illuminatorsinstead of using shutters. In the DMD option, there is an illumination set per lens section.This illumination set is only ON when the DMD is showing the part of the imagecorresponding to that Jens section. The illumination set can be realized with LEDs plus anoptical system that illuminates the DMD evenly and in such directions that the light, oncereflected by the DMD micromirrors in one of its stable states, reaches only thecorresponding lenslet.[0177] 10. Control of stray-light[0178] Stray-light is defined as light emitted by the digital display that reaches the pupilrange through a path different from that considered in the optical design of the surfaces.This light should be avoided. Some of this stray-light emitted by the display may bedeflected by the device towards the display again and once reflected there it may reachthe pupil range through the design path creating ghost images.[0179] There are several different configurations with different strategies for blockingthe stray-light or deflecting it outside the pupil range.[0180] FIG. 38 shows a horizontal cross-section (top view) of one of the stray lightcontrol configurations illustrated in the example of a 2 lenslet optical element 3804.User's nose 381 1 and eye 3812 are shown in FIG. 38 for orientation purposes. FIG. 38shows the working principle of a particular stray light control: following the ray 3808trajectory we see that light emitted by the digital display 3801 passes through the linearpolarizer 3802 and afterwards through a half-wave retarder 3803 whose fast axis forms anangle of 22.5° with the input plane of polarization. A half-wave retarder 3803 rotateslinearly polarized input light by twice the angle between the retarder fast axis and theinput plane of polarization. Afterwards, the ray is refracted on the surface 3805 of thelens, reflected on the mirrored surface 3806, reflected once more on the mirrored surface3809 and refracted on the surface 3810 towards the display. The light ray then passes forthe second time through the half-wave retarder. Now, the angle between the retarder' sfast axis and the input plane of polarization is - 1 12.5° (-90°-22.5°). (We adopt thedirection of rotation from the half-wave retarder' s fast axis towards its slow axis as the"positive" direction.) Light is rotated 225° around the retarder's fast axis and itspolarization direction is changed 90° in total. As a result, the light ray is absorbed by thepolarizer 3802. A more detailed illustration of this optical isolation strategy is shown inFIG. 39.[0181] FIG. 39 represents a 3D view of the previously mentioned configuration thatincludes an absorbing linear polarizer 3902, a half-wave retarder 3903 and a 2-lensletlens 3914. The digital display is not shown for reasons of drawing clarity. Fast axis ofhalf-wave retarder is labeled as 3906 and its slow axis as 3907. Ray 3901 emitted fromthe digital display passes through the horizontally aligned polarizer 3902. Horizontal lightpolarization of the light exiting the polarizer 3902 is illustrated with bold arrow labeled as3909. Horizontally polarized light falls on a half-wave plate 3903 whose fast axis 3906and the input polarization direction 3910 form the angle of 22.5°. Rotating the half-waveplate with respect to the input light polarization direction causes input light polarizationto rotate twice the angle of the half-wave plate's fast axis with the polarization plane (2 x22.5° = 45° illustrated with the arc 3908). We obtain at the half-wave plate's exit a linearpolarization of -22.5° with respect to the fast axis labeled as 391 1. After two mirrorreflections on back mirrors 3904 and 3905 of the lens 3914, the light polarization willchange approximately 90° with respect to the initial direction (assuming that thereflections on both reflectors are at 45 degrees incidence angle), so we will have apolarization illustrated with bold arrow 3912. Now light impinges on the half-waveretarder 3903 for the second time. The angle between retarder's fast axis and input planeof polarization is - 112.5°(-90 -22.5°). Light polarization is rotated twice the angle of thehalf wave plate's fast axis with the polarization plane, i.e. 225°, around retarder's fastaxis as illustrated with arc 39 1 . As a result, the polarization direction 3913 is changed90° in total respect to the initial direction 3909. Angle between resulting lightpolarization direction and the half-wave retarder's fast axis is 112.5°. We have obtainedlight polarization illustrated with 3913 that is perpendicular to the initial polarizationdirection 3909 and is absorbed by polarizer 3902. Optionally, polarizer 3902 may be ARcoated in order to reduce more undesired light reflections.[0182] Alternatively, the two part configuration in FIG. 15 can be used, placing a blackabsorber on the surface 1518 where the two lenslets are joined together, and so withoutthe need of retarders. Such black absorber also allows making the 2-part design in FIG.15 without the slope discontinuity 1512 (that is, its exit surface 1504 coincides with theexit surface 1203 of the design in FIG. 12) since the absorber will prevent rays thatattempt to cross the surface 1518 from reaching the pupil range.[0183] FIG. 40 shows another possible configuration for stray light control. A blackabsorbing solid piece may be added in the central part of the system to shield fromundesired light reaching the digital display. FIG. 40 shows the working principle of thisproposal on the 2 lenslet example. Light ray 4006 emitted by a digital display 4001passes through the matt layer on the digital display or diffusor 4002 that we mayoptionally add in order to reduce reflection, then it refracts on the surface 4003 of thelenslet 4008, it reflects on the mirror surface 4004, and it refracts once more on thesurface 4003. We add a black piece 4005 that absorbs the light ray 4006 on its pathtowards the digital display. The black piece 4005 may serve as a lens support or lensholder. In most embodiments, the central part of the lens surface 4003 is metallizedbecause the total internal reflection condition is generally not fulfilled in this area, so noadditional light shadowing is introduced with this opaque piece.[0184] Another proposal for stray light control is shown in FIG. 41. A central exteriorpart 4104 of the 2 lenslet optical element 4107 is painted black in order to absorbundesired stray light coming from the digital display. Following the light path illustratedwith the ray 4105, we may see how it works. Ray 4105 is emitted from the digital display4101, then instead being reflected towards the digital display following the path 4106drawn with dashed line, it is absorbed by the black painted part of the lens 4104. As thisinner part of the lens surface 4104 is usually metalized, by painting it black we may alsoprotect the metallization and block light coming from other directions.[0185] Although specific embodiments have been described, the preceding description ofpresently contemplated modes of practicing the invention is not to be taken in a limitingsense, but is made merely for the purpose of describing certain general principles of theinvention. Variations are possible from the specific embodiments described. For example,the patents and applications cross-referenced above describe systems and methods thatmay advantageously be combined with the teachings of the present application. Althoughspecific embodiments have been described, the skilled person will understand howfeatures of different embodiments may be combined.[0186] The full scope of the invention should be determined with reference to the claims,and features of any two or more of the claims may be combined.