Fig. 1. Experiment flow for programming optical propagation for a computational task. The SLM modulates the laser pulses with the data sample overlaid with a fixed programming pattern calculated by the programming patterns. The beam is coupled to an MMF; the pattern after propagation is recorded with a camera. A trainable output classification layer calculates the task accuracy, which is fed back to the surrogate optimization algorithm. The algorithm improves the task performance by exploring different PPs and refining potential solutions.

Fig. 2. Programming the MMF propagation for higher classification performance on Fashion-MNIST dataset. (a) Training accuracy during the progress of the programming procedure. The horizontal line labeled “without programming” shows the accuracy level when PPs are set to zero and “with programming” indicates the level when the PPs found by the programming algorithm are used. The colors of circles indicate their sequence in the training. (b) Relation between wavefront shaping parameters and training accuracy. Forty-six different wavefront shaping parameters are shown in two dimensions by means of random projection into two dimensions for visibility. (c) Peak power of pulses during the programming procedure. (d) Change of the diffraction angle on the SLM in horizontal and vertical directions (Δϕ and Δθ). (e) Shift of image on the SLM in horizontal and vertical directions (Δx and Δy). (f) Confusion matrix and average accuracy on the test set, without and with the programming of the transform (Video 1, MP4, 2.31 MB [URL: https://doi.org/10.1117/1.AP.6.1.016002.s1]).

Fig. 3. Programming procedure for all-optical classification of chest radiographs. (a) The schematic of the experiment, the data, and the control pattern are sent together to the SLM, and the fiber output pattern is imaged onto a camera. (b), (c) Distribution of the beam center locations and corresponding confusion matrices for the test set, without and with the programming of the transform. (d) Distribution of training accuracies with respect to the selection of wavefront shaping parameters. (e) Selected power levels for each iteration of the programming procedure. (f) Progression of training accuracy during training. The color map relates the color of circles to their sequence in the training, and it applies to (d)–(f) (Video 2, MP4, 4.17 MB [URL: https://doi.org/10.1117/1.AP.6.1.016002.s2]).

Fig. 4. Programming the optical transform using (a) phase addition and amplitude modulation, (e) multiplication with phase, and (i), (m) convolution. (b), (f), (j), (n) Example of programmed patterns on the SLM and recorded intensity patterns after the propagation inside the optical fiber for the given input pattern; for (f), (j), and (n), the intensity is not modulated. (c), (g), (k), (o) depict the progression of training accuracies during programming iterations. The confusion matrices on (d), (h), (l), (p) illustrate the classification performance of the programmed optical transform with different methods.

Fig. 5. Using previously dedicated parameters on a new dataset with corrective programming. (a) Procedure for transferring the PPs. (b)–(d), (h), (i) The experiment when the PPs are fully programmed without any prior knowledge. (e)–(g), (j), (k) Corrective programming of parameters. (b), (e) Relation between wavefront shaping parameters projected to two dimensions and the training accuracy. (c), (f) Peak power of pulses at the fiber entrance. (d), (g) Color bar for coding the iteration number related to each data point on (b), (c), (h) and (e), (f), (j). (h), (j) Training accuracy during the progress of the programming procedure. (i), (k) Confusion matrix and average accuracy on the test set.

Fig. 6. Dependency of the training accuracy on the CelebA gender classification task, diffracted beam shape, and spectrum on the optical intensity level, with all other PPs set to zero. (a) Camera images for the same input image and the task accuracy for different pulse peak powers. (b) Optical spectrum after propagating in the fiber at different power levels for the same sample from the dataset.

Fig. 7. Power efficiency and speed comparison between different computational approaches. The possible optimization refers to incorporating a digital micromirror device, a resonant mirror, and an optical phase mask in the optical computer.

Fig. 8. Flowchart of the programming procedure.