Methods, systems, and computer readable media for improved digital holography and display incorporating same

1. A method for digital holography, the method comprising:

modeling a hologram using a forward propagation model that models propagation of a light field from a hologram plane to an image plane;

computing the hologram as a solution to an optimization problem that is based on the model, wherein computing the hologram as a solution to an optimization problem includes evaluating holograms as potential solutions to the optimization problem by computing an approximation of a gradient of a penalty function with respect to amplitude of a complex wave field of a reconstructed image on the image plane using Wirtinger derivatives, wherein the penalty function quantifies a difference between the amplitude of the complex wave field of the reconstructed image on the image plane and an amplitude of a complex wave field of the target image on the image plane, adjusting a phase of a spatial light modulator based on the penalty function, wherein computing an approximation of the gradient of the penalty function using Wirtinger derivatives includes computing a scaled value of field intensity on the image plane;

configuring at least one spatial light modulator using the hologram; and

illuminating the spatial light modulator using a light source to create the reconstructed image.

2. The method of claim 1 wherein modeling the hologram using a forward propagation model includes modeling the hologram using an angular spectrum, Fourier, Fraunhofer, or Fresnel propagation model.

3. The method of claim 1 wherein modeling the hologram using a forward propagation model includes modeling the hologram as a spatially invariant convolution of the hologram and a lens phase function.

4. The method of claim 3 wherein the optimization problem uses a least squares optimization function.

5. The method of claim 4 wherein the least squares optimization function comprises:

minimize

H

⁢

⁢





H

*

L



2

-

I



2

2

,

where H is the hologram, L is the lens phase function, and I is the square of a target image intensity.

6. The method of claim 5 wherein the hologram comprises a phase hologram for a phase only spatial light modulator and the function

minimize

H

⁢

⁢





H

*

L



2

-

I



2

2

is approximated using the function:

arg

⁢

⁢

min

ϕ

⁢

⁢





H

*

L



2

-

I



2

2

,

where Φ is the phase angle of the hologram for a given object point.

7. The method of claim 6 wherein the function

arg

⁢

⁢

min

ϕ

⁢

⁢





H

*

L



2

-

I



2

2

is approximated using the following function:

arg

⁢

⁢

min

ϕ

⁢

⁢





F

H

⁡

(

FH

)

⁢

(

FL

)



2

-

I



2

2

,

where F is the Fourier transform operator and F H is the inverse Fourier transform operator.

8. The method of claim 7 wherein computing the hologram includes calculating a gradient of the function

arg

⁢

⁢

min

ϕ

⁢

⁢





F

H

⁡

(

FH

)

⁢

(

FL

)



2

-

I



2

2

.

9. The method of claim 1 wherein configuring at least one spatial light modulator includes configuring a single phase only spatial light modulator.

10. The method of claim 1 wherein configuring at least one spatial light modulator includes configuring each of a pair of cascaded phase only spatial light modulators.

11. The method of claim 1 wherein computing the hologram includes using the penalty function to quantify error between the reconstructed image produced by a hologram H and a target image.

12. The method of claim 11 wherein the penalty function is based on perceptual accuracy or a learned perceptual similarity metric.

13. The method of claim 11 wherein the hologram comprises a phase only hologram and computing the hologram as a solution to the optimization problem comprises determining a phase angle of the hologram H that minimizes the error.

14. A system for digital holography, the system comprising:

a display device comprising:

at least one processor;

a hologram calculator implemented by the at least one processor and configured for modeling a hologram using a forward propagation model that models propagation of a light field from a hologram plane to an image plane and computing the hologram as a solution to an optimization problem that is based on the model, wherein computing the hologram as a solution to an optimization problem includes evaluating holograms as potential solutions to the optimization problem by computing an approximation of a gradient of a penalty function with respect to a complex wave field of a reconstructed image on the image plane using Wirtinger derivatives, wherein the penalty function quantifies a difference between the amplitude of the complex wave field of the reconstructed image on the image plane and an amplitude of a complex wave field of the target image on the image plane, adjusting a phase of a spatial light modulator based on the penalty function, wherein computing an approximation of the gradient of the penalty function using Wirtinger derivatives includes computing a scaled value of field intensity on the image plane;

at least one spatial light modulator;

a spatial light modulator controller for configuring the at least one spatial light modulator using the hologram; and

a light source for illuminating the at least one spatial light modulator to create the reconstructed image.

15. The system of claim 14 wherein modeling the hologram using a forward propagation model includes modeling the hologram using an angular spectrum, Fourier, Fraunhofer, or Fresnel propagation model.

16. The system of claim 14 wherein modeling the hologram using a forward propagation model includes modeling the hologram as a spatially invariant convolution of the hologram and a lens phase function.

17. The system of claim 16 wherein the optimization problem uses a least squares optimization function.

18. The system of claim 17 wherein the least squares optimization function comprises:

minimize

H

⁢

⁢





H

*

L



2

-

I



2

2

where H is the hologram, L is the lens phase function, and r is the square of a target image intensity.

19. The system of claim 18 wherein the hologram comprises a phase hologram for a phase only spatial light modulator and the function

minimize

H

⁢

⁢





H

*

L



2

-

I



2

2

is approximated using the function:

arg

⁢

⁢

min

ϕ

⁢

⁢





H

*

L



2

-

I



2

2

,

where Φ is the phase angle of the hologram for a given object point.

20. The system of claim 19 wherein the function

arg

⁢

⁢

min

ϕ

⁢

⁢





H

*

L



2

-

I



2

2

is approximated using the following function:

arg

⁢

⁢

min

ϕ

⁢

⁢





F

H

⁡

(

FH

)

⁢

(

FL

)



2

-

I



2

2

,

where F is the Fourier transform operator and F H is the inverse Fourier transform operator.

21. The system of claim 20 wherein computing the hologram includes calculating a gradient of the function

arg

⁢

⁢

min

ϕ

⁢

⁢





F

H

⁡

(

FH

)

⁢

(

FL

)



2

-

I



2

2

.

22. The system of claim 14 wherein computing the hologram includes using the penalty function to quantify error between the reconstructed image produced by a hologram H and a target image.

23. The system of claim 22 wherein the hologram comprises a phase only hologram and computing the hologram as a solution to the optimization problem comprises determining a phase angle of the hologram H that minimizes the error.

24. The system of claim 22 wherein the penalty function is based on perceptual accuracy or a learned perceptual similarity metric.

25. The system of claim 14 wherein the at least one spatial light modulator comprises a single phase only spatial light modulator.

26. The system of claim 14 wherein the at least one spatial light modulator comprises a pair of cascaded phase only spatial light modulators.

27. A non-transitory computer readable medium having stored thereon executable instructions that when executed by a processor of a computer control the computer to perform steps comprising:

modeling a hologram using a forward propagation model that models propagation of a light field from a hologram plane to an image plane;

computing the hologram as a solution to an optimization problem that is based on the model, wherein computing the hologram as a solution to an optimization problem includes evaluating holograms as potential solutions to the optimization problem by computing an approximation of a gradient of a penalty function with respect to a complex wave field of a reconstructed image on the image plane using Wirtinger derivatives, wherein the penalty function quantifies a difference between the amplitude of the complex wave field of the reconstructed image on the image plane and an amplitude of a complex wave field of the target image on the image plane, adjusting a phase of a spatial light modulator based on the penalty function, wherein computing an approximation of the gradient of the penalty function using Wirtinger derivatives computing a scaled value of field intensity on the image plane;

configuring at least one spatial light modulator using the hologram; and

illuminating the spatial light modulator using a light source to create the reconstructed image.