SYSTEMS AND METHODS FOR WAVEFRONT RECONSTRUCTION FOR APERTURE WITH ARBITRARY SHAPE

Abstract

Systems, methods, and devices for determining an aberration in an optical tissue system of an eye are provided. Techniques include inputting optical data from the optical tissue system of the eye, where the optical data includes set of local gradients corresponding to a non-circular shaped aperture, processing the optical data with an iterative Fourier transform to obtain a set of Fourier coefficients, converting the set of Fourier coefficients to a set of modified Zernike coefficients that are orthogonal over the non-circular shaped aperture, and determining the aberration in the optical tissue system of the eye based on the set of modified Zernike coefficients.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a laser ablation system according to an embodiment of the present invention.

FIG. 2 illustrates a simplified computer system according to an embodiment of the present invention.

FIG. 3 illustrates a wavefront measurement system according to an embodiment of the present invention.

FIG. 3A illustrates another wavefront measurement system according to another embodiment of the present invention.

FIG. 4 schematically illustrates a simplified set of modules that carry out one method of the present invention.

FIG. 5 is a flow chart that schematically illustrates a method of using a Fourier transform algorithm to determine a corneal ablation treatment program according to one embodiment of the present invention.

FIG. 6 schematically illustrates a comparison of a direct integration reconstruction, a 6th order Zernike polynomial reconstruction, a 10th order Zernike polynomial reconstruction, and a Fourier transform reconstruction for a surface having a +2 ablation on a 6 mm pupil according to one embodiment of the present invention.

FIG. 7 schematically illustrates a comparison of a direct integration reconstruction, a 6th order Zernike polynomial reconstruction, a 10th order Zernike polynomial reconstruction, and a Fourier transform reconstruction for a presbyopia surface according to one embodiment of the present invention.

FIG. 8 schematically illustrates a comparison of a direct integration reconstruction, a 6th order Zernike polynomial reconstruction, a 10th order Zernike polynomial reconstruction, and a Fourier transform reconstruction for another presbyopia surface according to one embodiment of the present invention.

FIG. 9 illustrates a difference in a gradient field calculated from a reconstructed wavefront from a Fourier transform reconstruction algorithm (F Gradient), Zernike polynomial reconstruction algorithm (Z Gradient), a direct integration reconstruction algorithm (D Gradient) and a directly measured wavefront according to one embodiment of the present invention.

FIG. 10 illustrates intensity plots of reconstructed wavefronts for Fourier, 10th Order Zernike and Direct Integration reconstructions according to one embodiment of the present invention.

FIG. 11 illustrates intensity plots of reconstructed wavefronts for Fourier, 6th Order Zernike and Direct Integration reconstructions according to one embodiment of the present invention.

FIG. 12 illustrates an algorithm flow chart according to one embodiment of the present invention.

FIG. 13 illustrates surface plots of wavefront reconstruction according to one embodiment of the present invention.

FIG. 14 illustrates surface plots of wavefront reconstruction according to one embodiment of the present invention.

FIG. 15 illustrates a comparison of wavefront maps with or without missing data according to one embodiment of the present invention.

FIG. 16 illustrates a Zernike pyramid that displays the first four orders of Zernike polynomials according to one embodiment of the present invention.

FIG. 17 illustrates a Fourier pyramid corresponding to the first two orders of Fourier series according to one embodiment of the present invention.

FIG. 19 illustrates a Taylor pyramid that contains the first four orders of Taylor monomials according to one embodiment of the present invention.

FIG. 20 illustrates a comparison between an input wave-front contour map and the calculated or wave-front Zernike coefficients from a random wavefront sample according to one embodiment of the present invention.

FIG. 21 illustrates input and calculated output 6^th order Zernike coefficients using 2000 discrete points in a reconstruction with Fourier transform according to one embodiment of the present invention.

FIG. 22 illustrates speed comparisons between various algorithms according to one embodiment of the present invention.

FIG. 23 illustrates an RMS reconstruction error as a function of dk according to one embodiment of the present invention.

FIG. 24 illustrates an exemplary Fourier to Zernike Process for wavefront reconstruction using an iterative Fourier approach according to one embodiment of the present invention.

FIG. 25 illustrates an exemplary Fourier to Zernike subprocess according to one embodiment of the present invention.

FIG. 26 illustrates an exemplary iterative approach for determining an i^th Zernike polynomial according to one embodiment of the present invention.

FIG. 27 depicts wavefront reconstruction data according to one embodiment of the present invention.

FIG. 28 depicts wavefront reconstruction data according to one embodiment of the present invention.

FIG. 29 shows a coordinate system for a hexagonal pupil according to one embodiment of the present invention.

FIG. 30 illustrates isometric, interferometric, and PSF plots of orthonormal hexagonal and circle polynomials according to one embodiment of the present invention.

FIG. 31 provides an exemplary data flow chart according to one embodiment of the present invention.

FIG. 32 depicts wavefront reconstruction data according to one embodiment of the present invention.

Claims

1. A method of determining an aberration in an optical tissue system of an eye, the method comprising: inputting optical data from the optical tissue system of the eye, the optical data comprising a set of local gradients corresponding to a non-circular shaped aperture;processing the optical data with an iterative Fourier transform to obtain a set of Fourier coefficients;converting the set of Fourier coefficients to a set of modified Zernike coefficients that are orthogonal over the non-circular shaped aperture; anddetermining the aberration in the optical tissue system of the eye based on the set of modified Zernike coefficients.

2. The method of claim 1, comprising establishing a prescription shape for the eye based on the aberration.

3. The method of claim 1, wherein the non-circular shaped aperture comprises a hexagonal aperture.

4. The method of claim 1, wherein the non-circular shaped aperture comprises an elliptical aperture.

5. The method of claim 1, wherein the non-circular shaped aperture comprises an annular aperture.

6. The method of claim 1, wherein the optical data comprises Hartmann-Shack wavefront sensor data.

7. The method of claim 1, wherein the step of converting the set of Fourier coefficients to a set of modified Zernike coefficients comprises a Gram-Schmidt orthogonalization process.

8. A system for determining an aberration in an optical tissue system of an eye, the system comprising: a light source for transmitting an image through the optical tissue system;a sensor oriented for determining a set of local gradients for the optical tissue system by detecting the transmitted image, the set of local gradients corresponding to a non-circular shaped aperture;a processor coupled with the sensor; anda memory coupled with the processor, the memory configured to store a plurality of code modules for execution by the processor, the plurality of code modules comprising: a module for inputting optical data from the optical tissue system of the eye, the optical data comprising the set of local gradients;a module for processing the optical data with an iterative Fourier transform to obtain a set of Fourier coefficients;a module for converting the set of Fourier coefficients to a set of modified Zernike coefficients that are orthogonal over the non-circular shaped aperture; anda module for determining the aberration in the optical tissue system of the eye based on the set of modified Zernike coefficients.

9. The system of claim 8, further comprising a module for establishing a prescription shape for the eye based on the aberration.

10. The system of claim 8, wherein the non-circular shaped aperture comprises a hexagonal aperture.

11. The system of claim 8, wherein the non-circular shaped aperture comprises an elliptical aperture.

12. The system of claim 8, wherein the non-circular shaped aperture comprises an annular aperture.

13. The system of claim 1, wherein the optical data comprises Hartmann-Shack wavefront sensor data.

14. The system of claim 1, wherein the module for converting the set of Fourier coefficients to a set of modified Zernike coefficients comprises a Gram-Schmidt orthogonalization module.

15. A method of determining an optical surface model for an optical tissue system of an eye, the method comprising: inputting optical data from the optical tissue system of the eye, the optical data comprising a set of local gradients corresponding to a non-circular shaped aperture;processing the optical data with an iterative Fourier transform to obtain a set of Fourier coefficients;deriving a reconstructed surface based on the set of Fourier coefficients; anddetermining the optical surface model based on the reconstructed surface.

16. The system of claim 15, comprising establishing a prescription shape for the eye based on the optical surface model.

17. The method of claim 15, wherein the non-circular shaped aperture comprises a hexagonal aperture.

18. The method of claim 15, wherein the non-circular shaped aperture comprises an elliptical aperture.

19. The method of claim 15, wherein the non-circular shaped aperture comprises an annular aperture.

20. The method of claim 15, wherein the optical data comprises Hartmann-Shack wavefront sensor data.