End-to-end design of electro-optic imaging systems using the nonequidistant discrete Fourier transform
A unified design strategy takes into account different subsystems within an overall electro-optic imaging system. In one implementation, the design methodology predicts end-to-end imaging performance using a spatial model for the source and models for the optical subsystem, the detector subsystem and the digital image processing subsystem. The optical subsystem and digital image processing subsystems are jointly designed taking into account the entire system. Unconventional techniques such as the nonequidistant DFT (nDFT) are used to accelerate the design process.
1. A method for designing an electro-optic imaging system for imaging a source, the electro-optic imaging system including an optical subsystem, a detector subsystem and a digital image processing subsystem, the method comprising:
modeling propagation of the source through the optical subsystem, the detector subsystem and the digital image processing subsystem, said modeling comprising:
calculating a pupil function G for the optical subsystem, the pupil function sampled on a non-rectangular grid;
calculating a post-processing performance metric that is a function of the modeled propagation, the performance metric accounting for a contrast capability of the optical subsystem and for noise from the detector subsystem and/or the digital image processing subsystem; and
jointly designing the optical subsystem and the digital image processing subsystem based directly on the performance metric.
2. The method of claim 1 wherein calculating a pupil function for the optical subsystem comprises:
tracing rays through the optical subsystem, the rays sampling a pupil of the optical subsystem on the non-rectangular grid, wherein the pupil function is calculated from the traced rays.
3. The method of claim 2 wherein the rays sample the pupil of the optical subsystem on a polar grid.
4. The method of claim 2 wherein the rays sample the pupil of the optical subsystem on a linogram grid.
5. The method of claim 2 wherein the rays sample the pupil of the optical subsystem along radially extending arms, the rays distributed evenly with respect to distance along each arm.
6. The method of claim 2 wherein the rays sample the pupil of the optical subsystem along radially extending arms, the rays distributed evenly with respect to distance squared along each arm.
7. The method of claim 2 wherein fewer than 250 rays are traced for each sampling of the pupil, and the ray trace is sufficient to estimate a wavefront error function with an accuracy of better than λ/10.
8. The method of claim 2 wherein a sufficient number of rays are traced to estimate a wavefront error function with an accuracy of better than λ/10.
9. The method of claim 2 wherein calculating a pupil function for the optical subsystem further comprises:
calculating the pupil function sampled on a square grid, by interpolating from the non-rectangular grid to the square grid.
10. The method of claim 1 wherein modeling propagation of the source further comprises:
applying an nDFT to the pupil function to calculate a complex-amplitude point spread function U.
11. The method of claim 1 wherein modeling propagation of the source further comprises:
applying an nDFT to an intensity point spread function PSF to calculate an optical transfer function OTF.
12. The method of claim 1 wherein the post-processing performance metric is defined as an integral of an error metric that is a function of the modeled propagation and that accounts for a contrast capability of the optical subsystem and for noise from the detector subsystem and/or the digital image processing subsystem, and the integral is evaluated using a quadrature-type numerical integration.
13. The method of claim 1 wherein the post-processing performance metric is a Wiener filter-based mean square error (MSE).
14. The method of claim 13 wherein:
the steps of modeling propagation of the source through the optical subsystem, the detector subsystem and the digital image processing subsystem and calculating a post-processing performance metric consist essentially of:
tracing rays through the optical subsystem, the rays sampling a pupil of the optical subsystem on an L×K non-rectangular grid;
calculating a pupil function G sampled on an N×N square grid, based on the ray trace sampled on the non-rectangular grid, said calculating including interpolating from the non-rectangular grid to the square grid;
applying an nFFT to the pupil function G to calculate a complex-amplitude point spread function U sampled on an N*×N* square grid;
calculating an intensity point spread function PSF from the complex-amplitude point spread function U;
applying an nFFT to the intensity point spread function PSF to calculate an optical transfer function OTF sampled at nodes of a quadrature function;
calculating a digital image error spectral density S e from the optical transfer function OTF; and
calculating the Wiener filter-based MSE by numerically integrating the digital image error spectral density S e using a quadrature-type numerical integration; and
the step of jointly designing the optical subsystem and the digital image processing subsystem comprises:
iteratively designing the optical subsystem to minimize the Wiener filter-based MSE.
15. The method of claim 14 further comprising:
in response to user input, varying values of L, K, N and/or N* for different iterations.
16. The method of claim 14 further comprising:
automatically varying values of L, K, N and/or N* for different iterations.
17. The method of claim 14 further comprising:
increasing values of L, K, N and/or N* for later iterations.
18. A non-transitory computer readable storage medium containing instructions to cause a processor to design an optical subsystem of an electro-optic imaging system by executing the following steps:
modeling propagation of the source through the optical subsystem, the detector subsystem and the digital image processing subsystem, said modeling comprising:
calculating a pupil function for the optical subsystem, the pupil function sampled on a non-rectangular grid;
calculating a post-processing performance metric that is a function of the modeled propagation, the performance metric accounting for a contrast capability of the optical subsystem and for noise from the detector subsystem and/or the digital image processing subsystem; and
jointly designing the optical subsystem and the digital image processing subsystem based directly on the performance metric.
19. The non-transitory computer readable storage medium of claim 18 wherein:
the post-processing performance metric is a Wiener filter-based mean square error (MSE);
the steps of modeling propagation of the source through the optical subsystem, the detector subsystem and the digital image processing subsystem and calculating a post-processing performance metric consist essentially of:
tracing rays through the optical subsystem, the rays sampling a pupil of the optical subsystem on an L×K non-rectangular grid;
calculating a pupil function G sampled on an N×N square grid, based on the ray trace sampled on the non-rectangular grid, said calculating including interpolating from the non-rectangular grid to the square grid;
applying an nFFT to the pupil function G to calculate a complex-amplitude point spread function U sampled on an N*×N* square grid;
calculating an intensity point spread function PSF from the complex-amplitude point spread function U;
applying an nFFT to the intensity point spread function PSF to calculate an optical transfer function OTF sampled at nodes of a quadrature function;
calculating a digital image error spectral density S e from the optical transfer function OTF; and
calculating the Wiener filter-based MSE by numerically integrating the digital image error spectral density S e using a quadrature-type numerical integration; and
the step of jointly designing the optical subsystem and the digital image processing subsystem comprises:
iteratively designing the optical subsystem to minimize the Wiener filter-based MSE.
20. The non-transitory computer readable storage medium of claim 19 wherein the step of iteratively designing the optical subsystem comprises:
varying values of L, K, N and/or N* for different iterations.