Computer-Generated Holography

Our lab develops advanced techniques for 3D Light sculpting. We recently published DeepCGH, a new algorithm computes holograms much faster and with greater accuracy than existing algorithms using deep learning (Check out our Paper and the open source DeepCGH code).

Computer Generated Holography (CGH) aims to create custom 3D illumination patterns by shaping the phase of a laser beam, typically with a spatial light modulator (SLM). The goal of CGH algorithms is to identify a digital phase mask, f(x,y), that must be applied on the SLM to render the desired illumination pattern. This is a nonlinear, nonconvex, and multidimensional inverse problem for which there is generally no exact solution.

Fourier Holography Setup for Computer Generated Holography

Experimental setup for 3D Computer Generated Hologrpahy with a Spatial Light Modulator in the Fourier plane of an imaging system.

The common approach to solve CGH problems relies on iterative algorithms. The simplest and most popular approach is an iterative search with the Gerchberg-Saxton  algorithm [1] (Check out our introduction to holography lecture). When better computational capabilities became available, new algorithms such as NOVO-CGH [2] have been developed that can improve hologram quality with direct optimization methods. However, in all these approaches, the accuracy of holograms improves with the number of steps but requires longer computation time.

Fourier Holography Setup for Computer Generated Holography

Left: With traditional CGH algorithms, hologram accuracy increases with the number of iterations, but computation takes more time. DeepCGH yields holograms in fixed time. Right: The accuracy is a measure of mismatch between the target intensity distribution and the Hologram that can be synthesized.

The algorithm we developed, DeepCGH [3], pushes the envelope with both greater speed and accuracy. To accelerate computation, we rely on a trained convolutional neural network (CNN) that yields holograms without iterations. The computation time is fixed and only depends on hologram dimensions and CNN model size. Gains in speed and accuracy are also made possible with a task-driven CNN model design. First, our model includes an interleaving step that reorganizes the input data to reduce the CNN size. This maximizes speed and allows for the computation of large holograms (~10M Voxels) in milliseconds.

Fourier Holography Setup for Computer Generated Holography

Interleaving reorganizes the input data to reduce the CNN model size by gathering voxels into parallel channels

To maximize accuracy, the CNN estimates the complex field in real space, and the output undergoes a Fourier transform to yield phase at the SLM plane. This ensures that the input and output of the CNN share spatial features, and best leverages the CNN's capabilities for nonlinear mapping.

Fourier Holography Setup for Computer Generated Holography

During operation, DeepCGH estimates the complex field in the image plane. An inverse Fourier Transform (iFT) then yields the desired output. This architecture optimizes the CNN's computationl capabilities for nonlinear maping of spatial features. 

Since no algorithm can calculate optimal CGH solutions, Matched I/O training datasets for supervised learning are not an option. Instead, DeepCGH is trained unsupervised, by comparing the input image to a simulated propagation of the estimated solution. An explicit loss function (e.g. accuracy) compares input and simulation and updates the CNN parameters to minimize errors.

Fourier Holography Setup for Computer Generated Holography

DeepCGH is trained unsupervised. For this, we implement a forward model that simulates the synhesis of the hologram. An explicit cost function compares the rendered hologram to the target illumination. Since all these opertions are differentiable with repsect to the CNN parameters, unsupervised learning becomes possible.

Unsupervised learning allows DeepCGH to explore potential solutions without restrictions on hologram feasibility. As a result, DeepCGH can identify solutions that are more accurate than state-of-the-art CGH methods, including some of our prior work. Improving accuracy is a major advantage for multiphoton holography, because with the same amount of laser power it is possible to yield larger amounts of two-photon absorption.

Fourier Holography Setup for Computer Generated Holography

We compared our method, to holograms synthesized with GS and NOVOCGH  in a multiphoton microscope. Left: while all three methods yield about the same amount of light under the microscope objective, we observed significantly more two-photon fluorescence with DeepCGH.   

For holographic optogenetics, this result indicates that DeepCGH can activate more neurons with the same amount of IR light below brain heating and photo-damage thresholds.

Fourier Holography Setup for Computer Generated Holography

3D renderings of fluorescence induced by two-photon absorption. The three holograms here have idnetical target intensity distributions and are recorded with the same amount of excitation laser power. The hologram computed with DeepCGH has greater accuracy and places more photons into the targets.

This work has been made possible by Hossein Eybposh (Ph.D. student), Nicholas Caira (Postdoc), Mathew Atisa (UNC Computer Sciences Major), and Praneeth Chakravarthula (Ph.D. Student) The team received generous support from the Burroughs Wellcome Fund (Career Award at the Scientific Interface, PI: N.Pegard), and the Nvidia GPU research grant program.

Hossein Eybposh received an OSA Student Paper Award for this work at the 2020 OSA Biophotonics congress).

Mathew Atisa received a first poster prize for his contributions at the 2020 Duke Research Computing Symnposium.

  1. R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures”, Optik 35, 237–246 (1972).
  2. J. Zhang, N. Pegard, J. Zhong, H. Adesnik, and L. Waller, “3d computer-generated holography by non-convex optimization”, Optica 4, 1306–1313 (2017).
  3. M. Hossein Eybposh, Nicholas W. Caira, Mathew Atisa, Praneeth Chakravarthula, and Nicolas C. Pégard, "DeepCGH: 3D computer-generated holography using deep learning," Opt. Express 28, 26636-26650 (2020)