Compressive sensing optical design and simulation tool

1. A computer implemented method for designing optical systems comprising:

generating a mathematical model of an imaging system;

tracing, using a computer, a plurality of light rays from a source through the model of the imaging system in a forward direction or a backward direction incident upon an arbitrarily defined detector location;

calculating, using the computer, total light rays incident upon the arbitrarily defined detector location in response to the plurality of light rays;

tracing, using the computer, a series of calibration images through a computational imaging system mathematical model or a compressive imaging system mathematical model using the total light rays incident upon the arbitrarily defined detector location;

calculating, using the computer, an output set of parameters based on a plurality of detected rays or calibration images at the arbitrarily defined detector location;

storing the output set of parameters in memory;

determining, using the computer, a system transfer function used to design an optical system using the output set of parameters; and

designing, using the computer, a computational imaging or a compressive imaging optical system using the determined system transfer function.

2. The method of claim 1 , further comprising processing a plurality of simulated test images.

3. The method of claim 2 , further comprising applying the model of the imaging system to the plurality of simulated test images;

tracing the plurality of simulated test images via the mathematical model;

storing the simulated set of test images in memory;

applying the system transfer function to a plurality of simulated test images output from the tracing step; and

reconstructing the plurality of simulated test images.

4. The method of claim 1 , further comprising processing the plurality of reconstructed simulated test images to create at least one performance metric.

5. The method of claim 1 , wherein the at least one performance metric provides a quantitative evaluation of the performance of the computational imaging system or compressive imaging system.

6. The method of claim 1 , wherein the imaging system comprises a computational imaging system.

7. The method of claim 1 , wherein the imaging system comprises a compressive imaging system.

8. The method of claim 1 , wherein the step of generating comprises simulating a source of emitted photons, or rays.

9. The method of claim 8 , wherein the step of generating further comprises defining the computational imaging system mathematical model or compressive imaging system mathematical model.

10. The method of claim 1 , wherein the source is a photon source comprising one of: a flat plane of parallel rays; converging rays; diverging rays; and a complex lightfield representative of a scene of interest.

11. The method of claim 1 , wherein the calibration images comprise one of: a Hadamard pseudo-random pattern, a random binary patterns, and a raster scanned single pixels.

12. A computer implemented method for designing optical systems comprising:

generating a mathematical model of an imaging system;

tracing, using a computer, a plurality of light rays from a source through the model of the imaging system in a forward direction and a backward direction incident upon an arbitrarily defined detector location;

calculating, using the computer, total light rays incident upon the arbitrarily defined detector location in response to the plurality of light rays;

tracing, using the computer, a series of calibration images through a computational imaging system mathematical model or a compressive imaging system mathematical model;

calculating, using the computer, an output set of parameters based on a plurality of detected rays or calibration images at the arbitrarily defined detector location;

storing the output set of parameters in memory;

determining, using the computer, a system transfer function;

processing, using the computer, a plurality of simulated test images;

applying, using the computer, the model of the imaging system to the plurality of simulated test images;

tracing, using the computer, the plurality of simulated test images via the mathematical model;

storing the simulated set of test images in memory;

applying, using the computer, the system transfer function to a plurality of simulated test images output from the tracing step;

reconstructing, using the computer, the plurality of simulated test images to design an optical system; and

designing, using the computer, a computational imaging or a compressive imaging optical system using the reconstructed plurality of simulated test images.

13. The method of claim 12 , further comprising applying a mathematical solver to a plurality of calibration inputs and the measured calibration outputs to determine the transfer function.

14. The method of claim 13 , wherein the model comprises physical surface models.

15. The method of claim 14 wherein the physical surface models comprise models utilized in a random scatterer.

16. The method of claim 13 wherein the physical surface model comprises a mathematically defined parametric optical system.

17. The method of claim 16 wherein the optical system is selected from the group consisting of: a spherical lens, a parabolic lens, a spherical mirror, a parabolic mirror, a refracting element, a reflecting element, a diffracting element, a spatially variant absorbing element, a polarization element, a non-linear element, a spatially varying retardance element, a stochastically defined scattering element, and a fluorescence element.

18. A non-transitory computer-readable storage medium having stored thereon instructions which, when executed by one or more processing units in a computer, cause the one or more processing units to perform a method for designing a computational imaging or a compressive imaging optical system, comprising:

generating a mathematical model of an imaging system;

tracing a plurality of light rays from a source through the model of the imaging system in a forward direction and a backward direction incident upon an arbitrarily defined detector location;

calculating the total light rays incident upon the arbitrarily defined detector location in response to the plurality of light rays;

tracing a series of calibration images through a computational imaging system mathematical model or a compressive imaging system mathematical model;

calculating an output set of parameters based on a plurality of detected rays or calibration images at the defined detector location;

storing the output set of parameters in memory;

determining a system transfer function; and

developing a merit function from one or more user defined features; and

designing a computational imagine or a compressive image optical system using the system transfer function and merit function.

19. The medium of claim 18 , further comprising searching for a computational imaging system or a compressive imaging system that maximizes performance of the merit function, and basing the merit function on a set of predetermined metrics and an optimization algorithm.

20. The medium of claim 19 , further comprising: the optimization algorithm utilizing least-squares minimization or simulated annealing.