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1. (WO1997015898) ASTIGMATISM MEASUREMENT APPARATUS AND METHOD
Note: Text based on automatic Optical Character Recognition processes. Please use the PDF version for legal matters

CLAIMS
1. A method for evaluating a condition of an optical system comprising the steps of:
(a) acquiring a plurality of images of a test pattern at different focus positions (85,

89) ;
(b) processing the plurality of images to compute a plurality of center of gravity vectors, one center of gravity vector for each one of the plurality of images (86) ;
(c) computing a focal plane separation from the plurality of center of gravity vectors (88) ;
and
(d) relating the condition of the optical system to the focal plane separation (88) .

2. The method of claim 1 further comprising the step of calculating an eccentricity of a point spread function from the plurality of center of gravity vectors (118) .

3. The method of claim 2 further comprising the steps of:
(a) calculating a first parameter, r_C0G_norm

(125) , by dividing a value of one of the plurality of center of gravity vectors, r_C0G, for each image in a Z panning sequence by a mean resolution, mean_res, for that image to yield a normalized value for eccentricity according to
r_COG_norm = r_C0G / mean_res;
(b) calculating a second parameter,

Sum_r_COG_norm (127), as a summation of r_COG_norm over all images in the Z panning sequence according to Sum_r_COG_norm = ∑ r_COG_norm(z); and

(c) relating a high value of Sum_r_COG_norm to eccentricity in the point spread function

(129) .
4. The method of claim 3 further comprising the step of computing a PASS/FAIL threshold for

Sum_r_COG_norm by measuring astigmatism of lens systems with known astigmatism (129) .

5. The method of claim 1 further including the step of finding a focus range comprising the steps of: (a) determining vertical motion limits for a Z panning sequence through a Z panning range by obtaining a plurality of focus images (83); (b) computing a resolution measure for each of the plurality of focus images (83) ; and
(c) determining a vertical position yielding a best overall resolution for a middle position of the Z panning range (83) .

6. The method of claim 1, wherein the optical system includes a stage, wherein the step of acquiring a plurality of images further comprises the step of acquiring the plurality of images (91) , beginning at a lower limit of the stage elevation, passing through a plane of best focus, and extending to an upper limit of the stage elevation (90) .

7. The method of claim 1 further comprising the steps of:
(a) edge enhancing the plurality of images in a first direction (92); and
(b) lowpass filtering the plurality of images in a second direction wherein the first direction is orthogonal to the second direction to substantially equalize the plurality of images (93) .

8. The method of claim 1 wherein the step of computing a focal plane separation comprises the steps of:
(a) computing a first derivative of one of the plurality of images to convey a location and a sharpness of boundaries in one of the plurality of images (132) ;
(b) summing derivative values for each pixel belonging to a given boundary and placing a resultant summation into an array indexed by boundary angle, so as to build the array indexed by boundary angle with a plurality of summed derivatives (112) ; and
(c) using the summed derivatives from the array to compute a center of gravity vector (118) .

9. The method of claim 1 wherein the step of computing a focal plane separation from the plurality of filtered test pattern images (124) further comprises the steps of :
(a) summing the magnitude of the center of gravity vector over the set of images from the Z panning sequence (127) ; and
(b) comparing the summation of the magnitude of the center of gravity vector against a threshold as a first estimate of the severity of astigmatism (129) .

10. The method of claim 9 wherein the threshold is an empirically derived fraction of the mean residue values integrated over all boundaries in the plurality of images in the Z panning sequence (116, 117) .

11. The method of claim 1 wherein the step of measuring a focal plane separation further comprises the steps of :
(a) finding a first dominant angle for a first focal plane (128) ;
(b) finding a second dominant angle for a second focal plane (128) ;
(c) computing the focal plane separation of the first focal plane from the second focal plane to generate a focal plane separation (134) .

12. The method of claim 11 wherein the steps of finding the first and second dominant angles (128) comprises :
(a) locating a plane of least confusion by finding an image in the Z panning sequence yielding the least value of the magnitude of the center of gravity vector (128);
(b) reading the angle of the center of gravity vector for an image offset below the plane of least confusion to yield the first dominant angle (128) ; and
(c) reading the angle of the center of gravity vector for an image offset above the plane of least confusion to yield the second dominant angle (128) .

13. The method of claim 12 wherein the step of finding the separation of focal planes (134) comprises the steps of :
(a) finding a first Z panning position with the highest resolution for the first dominant angle (134) ;
(b) finding a second Z panning position with the highest resolution for the second angle (134) ; and
(c) computing the absolute value of the difference between the first Z panning position and the second Z panning position

(134) .

14. The method of claim 5 wherein the step of determining a magnitude of a center of gravity vector for the plurality of images further comprises the steps of :
(a) initially centering the test pattern (84); (b) finding an exact center of the test pattern to align test pattern objects with preassigned bins (84);
(c) computing a plurality of X-Gradients and a plurality of Y-Gradients for each filtered test pattern image to produce a plurality of gradient image pixels (104);
(d) sorting the plurality of gradient image pixels into bins by boundary angle (106) ;
(e) rejecting each one of the plurality of gradient image pixels outside a predetermined region (108) ;
(f) rejecting each one of the plurality of gradient image pixels with low gradient scores (110) ;
(g) squaring each one of the plurality of gradient image pixels to produce a plurality of squared gradient values (112) ;
(h) summing the squares of the plurality of X_gradients and the plurality of Y gradients to produce a sum of squares (127) ;
(i) checking the sum of squares against a threshold (129) ;
(j) adding the squared gradient values to a bin for each gradient image pixel ' s boundary angle, if threshold requirement is met (129) ; (k) computing a mean residue for each boundary angle to produce a result (114) ;
(1) normalizing the result by dividing by the average number of pixels per bin (116) ;
(m) computing a third array by taking a quadratic sum of the two gradients; and
(n) computing the magnitude of the center of gravity vector from the third array (118) .

15. The method of claim 10 wherein the step of computing the magnitude of the center of gravity vector (118) further comprises the operators,
π
Mx = Σ IcosQ-®) *MAG(ø)] ,

Mγ = [sin(2ø) *MAG(ø)] , and
ø=0



where MAG(ø) is the residue value.
16. The method of claim 10 wherein the steps of computing a plurality of X_Gradients and Y_Gradients (104) summing the squares of the gradients, and sorting into boundary angle bins (106) comprise the operators
Gradx[i,j] = ABS (A [i+1] fj ] - A[i] [j]), and
Gradγ[i,j] = ABS (A [i] [j+1] - A[i] [j]),

where pixels [i,J] lie on the boundary at angle ø

SUMy[ø] = ∑ Grady

where pixels [i,j] lie on the boundary at angle 0.

17. The method of claim 5 wherein the computation of the angle of the center of gravity vector (88) comprises the operator



18. The method of claim 1 wherein the test pattern image is initially centered during system calibration and an initial center location of the test pattern is stored (Fig. 5A-5F) .

19. The method of claim 17 wherein the exact center of the test pattern is found from the initial center of the test pattern by morphological operations (158) .

20. A method for qualifying an optical system for compliance with a standard for low astigmatism, comprising the steps of :
(a) finding a best focus position for an image of a test pattern (83) ;
(b) centering the test pattern (84);
(c) acquiring a set of images of the test pattern (90, 91) ;
(d) determining vertical motion limits for a Z panning sequence through a Z panning range by obtaining a series of images on the test pattern and examining them for overall resolution (83);
(e) determining a vertical position yielding a best overall resolution for the middle of the z -panning range (83) ;
(f) acquiring the set of images, beginning at a lower limit of the stage elevation, passing through a plane of best focus, and extending to an upper limit of the stage elevation (85,

89) ;
(g) filtering the set of images to generate a set of filtered test pattern images (93);
(h) computing an estimate of the sharpness of each of a set of boundaries disposed at various angles (114) ;
(i) finding the angle of highest resolution for each image in a z -panning sequence (114) ;
(j) computing an estimate of the severity of eccentricity of the point spread function for each image in a Z panning sequence (118) ;
(k) finding the two angles of best resolution, called the dominant angles, displaced above and below the plane of least confusion (128) ; (1) measuring a focal plane separation based on the z -dependent resolution for boundaries at the two dominant angles (130); and
(m) applying test criteria to the outcome of the astigmatism measurement (136) .

21. The method of claim 19 wherein the step of applying test criteria comprises the steps of :
(a) comparing the sum of the magnitude of the normalized center of gravity vector computed over the set of images in the z -panning sequence with a threshold, the threshold having been determined empirically as a small fraction of the mean residue values integrated over all boundaries in all images in the z -panning sequence (129) ; and
(b) comparing the focal plane separation with a threshold, the threshold having been determined empirically from the depth of field of the optical system under test and the particular requirements of the application of the optical system (136) .

22. An apparatus for measurement of astigmatism of an optical system (22, 24) comprising:
(a) means for focusing the optical system on a test pattern having a focus control input

(20) ;
(b) means for obtaining a digital representation

(26) of the test pattern image (18) through the optical system, wherein the image gathering means has a digital image output;
and
(c) means for measuring astigmatism (30) in the optical system (22, 24) connected to the digital image output, wherein the means for measuring astigmatism (30) further has a focus control output connected to the focus control input.

23. The apparatus of claim 21 wherein the means for measuring astigmatism (30) in the optical system (22, 24) further comprises a digital computer

(30) .

24. The apparatus of claim 21 wherein the test pattern (18) further comprises a star test pattern (Fig. 5B) .

25. The apparatus of claim 21 wherein the optical system (22, 24) further comprises a microscope.

26. The apparatus of claim 21 wherein the optical system (22, 24) further comprises the optical components of a camera.

27. The apparatus of claim 21 wherein the image gathering means (26) further comprises a charge coupled device array.

28. An astigmatism measurement apparatus for measuring of astigmatism in an optical train having an objective lens, the apparatus comprising:
(a) an optical mount to hold the optical train (22, 24) ;
(b) an optical stage (16) to hold a test pattern (18) in view of the objective lens (22) wherein the objective lens (22) receives an image of the test pattern (18) and transmits a test pattern image;
(c) a stage drive (20) attached to move the optical stage (16) , wherein the optical stage drive (20) has a focus control input;
(d) a computer processor (34) connected to control the stage drive (20) ;
(e) a test pattern illuminator (12) disposed to illuminate the test pattern (18);
(f) a video camera (26) for viewing the test pattern image through the optical train (22, 24) and generating a video signal;
(g) image acquisition electronics (28) connected to the video signal, having a digital image output ; and
(h) an image analysis computer (30) connected to receive the digital image output including means for analyzing a plurality of test pattern images to measure astigmatism of the optical train (22, 24) .

29. The apparatus of claim 28 wherein the test pattern illuminator (12, 14) further comprises a light (12) and a condenser lens (14) .

30. The apparatus of claim 28 further comprising a microscope in the optical train (22, 24), the microscope including an output converted to an electronically stored image.

31. The apparatus of claim 28 wherein the test pattern (18) is a star pattern (Fig. 5B) .

32. The apparatus of claim 28 further comprising the integration of an image interpretation system (30) with a computer driven microscope.