High-speed computer generated holography using convolutional neural networks
The goal of computer generated holography (CGH) is to synthesize custom illumination patterns by shaping the wavefront of a coherent light beam. Existing algorithms for CGH rely on iterative optimization with a fundamental trade-off between hologram fidelity and computation speed, making them inadequate for high-speed holography applications such as optogenetic photostimulation, optical trapping, or virtual reality displays. We propose a new algorithm, DeepCGH, that relies on a convolutional neural network to eliminate iterative exploration and rapidly synthesize high resolution holograms with fixed computational complexity. DeepCGH is an unsupervised model which can be tailored for specific tasks with customizable training data sets and an explicit cost function. Results show that our method computes 3D holograms at record speeds and with better accuracy than existing techniques.
1. A method for computer-generated holography, the method comprising:
providing a target holographic image illumination distribution as input to a trained convolutional neural network (CNN);
generating, using the trained CNN, a predicted complex optical field in an image plane located downstream along an optical axis from a spatial light modulator;
back propagating the complex optical field to a spatial light modulator plane to yield a predicted spatial light modulator phase mask;
configuring the spatial light modulator using the predicted spatial light modulator phase mask; and
passing incident light through the configured spatial light modulator to produce a holographic image.
2. The method of claim 1 wherein the target holographic image illumination distribution comprises a three dimensional (3D) illumination distribution and wherein the holographic image comprises a 3D holographic image.
3. The method of claim 1 wherein the target holographic image illumination distribution comprises a two dimensional (2D) illumination distribution and wherein the holographic image comprises a 2D holographic image.
4. The method of claim 1 wherein providing the target holographic image illumination distribution as input to the trained CNN includes interleaving different target holographic images and providing the interleaved images as input to the trained CNN.
5. The method of claim 1 wherein generating the predicted complex optical field in the image plane located downstream from the spatial light modulator includes generating the predicted complex optical field in an image plane located within a target image volume.
6. The method of claim 1 wherein back propagating the complex optical field to the spatial light modulator plane includes computing a near field wave propagation of the complex optical field.
7. The method of claim 6 wherein computing the near field wave propagation includes computing the near field wave propagation using the following equation for Fresnel wave propagation:
P
z
(
x
,
y
)
=
∫
∫
P
0
(
x
′
,
y
′
)
i
λ
z
exp
[
i
π
(
(
x
-
x
′
)
2
+
(
y
-
y
′
)
2
)
λ
z
]
dx
′
dy
′
,
where P z (x,y) is the complex optical field at any location z along the optical axis, x and y are dimensions of the complex optical field along axes transverse to the optical axis, P 0 (x′, y′) is the complex optical field at the image plane in z=0, x′ and y′ are dimensions of the complex optical field along the axes transverse to an optical path in the image plane, λ is a wavelength of the incident light.
8. The method of claim 1 wherein the CNN is trained using target holographic image illumination distributions as input to produce estimated complex optical fields as output.
9. The method of claim of claim 1 the CNN is trained using a user-specified cost function that measures dissimilarity between target holographic image illumination distributions and simulation results.
10. A method for training a convolutional neural network for computer generated holography, the method comprising:
providing a target holographic image illumination distribution as input to a convolutional neural network (CNN);
generating, using the CNN, a predicted complex optical field in an image plane located downstream along optical axis from a spatial light modulator (SLM);
back propagating the predicted complex optical field to spatial light modulator plane to yield predicted spatial light modulator phase mask;
simulating forward propagation of a simulated light field through a simulated SLM configured with the predicted SLM phase mask and simulated optics to produce reconstructed target image distribution;
evaluating the predicted SLM phase mask using a cost function that generates values based on a comparison between the reconstructed target image distribution and the target holographic image illumination distribution input to the CNN; and
providing the values of the cost function and different desired target holographic image illumination distributions as feedback to the CNN, wherein the CNN adjusts its parameters to achieve a desired value or range of values of the cost function.
11. A system for computer-generated holography, the system comprising:
a configurable spatial light modulator (SLM) for modulating an incident light beam;
a trained convolutional neural network (CNN) for receiving, as input, a target holographic image illumination distribution and for generating a predicted complex optical field in an image plane located downstream along an optical axis from the SLM;
an optical field back propagation module for back propagating the complex optical field to a spatial light modulator plane to yield a predicted spatial light modulator phase mask; and
an SLM configuration module for configuring the spatial light modulator using the phase mask to modulate the incident light beam and produce a holographic image.
12. The system of claim 11 wherein the target holographic image illumination distribution comprises a three dimensional (3D) holographic image illumination distribution and wherein the holographic image comprises a 3D holographic image.
13. The system of claim 11 wherein the target holographic image illumination distribution comprises a two dimensional (2D) holographic image illumination distribution and wherein the holographic image comprises a 2D holographic image.
14. The system of claim 11 wherein the CNN is configured to receive interleaved target holographic image illumination distributions.
15. The system of claim 11 wherein the CNN is configured to generate the predicted complex optical field in an image plane located within a target image volume.
16. The system of claim 11 wherein the back propagation module is configured to compute a near field wave propagation of the complex optical field.
17. The system of claim 16 wherein the back propagation module is configured to compute the near field wave propagation of the complex optical field using the following equation for Fresnel propagation:
P
z
(
x
,
y
)
=
∫
∫
P
0
(
x
′
,
y
′
)
i
λ
z
exp
[
i
π
(
(
x
-
x
′
)
2
+
(
y
-
y
′
)
2
)
λ
z
]
dx
′
dy
′
,
where P z (x,y) is the complex optical field at any location z along the optical axis, x and y are dimensions of the complex optical field along axes transverse to the optical axis, P 0 (x′, y′) is the complex optical field at the image plane, x′ and y′ are dimensions of the complex optical field along the axes transverse to the optical path in the image plane, λ is a wavelength of the incident light.
18. The system of claim 11 wherein the CNN is trained using target holographic image illumination distributions as input to produce estimated complex optical fields as output.
19. The system of claim 11 the CNN is trained using a user-specified cost function that measures dissimilarity between target holographic image illumination distributions and simulation results.
20. 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:
providing a target holographic image illumination distribution as input to a trained convolutional neural network (CNN);
generating, using the trained CNN, a predicted complex optical field in an image plane located downstream along an optical axis from a spatial light modulator;
back propagating the complex optical field to a spatial light modulator plane to yield a predicted spatial light modulator phase mask; and
configuring the spatial light modulator using the phase mask so that the spatial light modulator will modulate incident light using the phase mask and produce a holographic image.
21. 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:
providing a target holographic image illumination distribution as input to convolutional neural network (CNN);
generating, using the CNN, a predicted complex optical field in an image plane located downstream along optical axis from a spatial light modulator (SLM);
back propagating the predicted complex optical field to spatial light modulator plane to yield predicted spatial light modulator phase mask;
simulating forward propagation of a simulated light field through a simulated SLM configured with the predicted SLM phase mask and simulated optics to produce reconstructed target image distribution;
evaluating the predicted SLM phase mask using a cost function that generates values based on a comparison between the reconstructed target image distribution and the target holographic image illumination distribution input to the CNN; and
providing the values of the cost function and different desired target holographic image illumination distributions as inputs to the CNN, wherein the CNN adjusts its parameters to achieve a desired value or range of values of the cost function.