[Paper Review] Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors

Md Sadman Sakib Rahman, Xilin Yang+3 more|arXiv (Cornell University)|Mar 23, 2023

Neural Networks and Reservoir Computing4 citations

TL;DR

This paper presents a deep learning-designed diffractive optical processor that performs universal linear intensity transformations under spatially-incoherent illumination, enabling all-optical computation using natural, incoherent light. By training a phase-only diffractive network to approximate any arbitrary intensity transformation via supervised learning, the method achieves universal performance when the number of optimized phase features N ≥ 2Ni × No, where Ni and No are input and output field-of-view pixel counts.

ABSTRACT

Under spatially-coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number (N) of optimizable phase-only diffractive features is greater than or equal to ~2 Ni x No, where Ni and No refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially-incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially-incoherent monochromatic light, the spatially-varying intensity point spread functon(H) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H(m,n;m',n')=|h(m,n;m',n')|^2, where h is the spatially-coherent point-spread function of the same diffractive network, and (m,n) and (m',n') define the coordinates of the output and input FOVs, respectively. Using deep learning, supervised through examples of input-output profiles, we numerically demonstrate that a spatially-incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N is greater than or equal to ~2 Ni x No. These results constitute the first demonstration of universal linear intensity transformations performed on an input FOV under spatially-incoherent illumination and will be useful for designing all-optical visual processors that can work with incoherent, natural light.

Motivation & Objective

• To enable all-optical linear intensity transformations under spatially-incoherent illumination, which is critical for real-world applications using natural light.
• To overcome the limitation of prior diffractive networks that required spatially-coherent illumination for universal complex-valued transformations.
• To design a diffractive optical processor capable of approximating any arbitrary linear intensity transformation using time-averaged intensity response under incoherent light.
• To establish a training framework using supervised deep learning to optimize phase-only diffractive features for universal intensity mapping.
• To validate that the required number of diffractive features N ≥ 2Ni × No enables universal performance under incoherent illumination, mirroring coherent case requirements.

Proposed method

• The diffractive network is trained using supervised deep learning with input-output intensity profile pairs as training examples.
• The spatially-incoherent intensity point spread function is modeled as H(m,n;m′,n′) = |h(m,n;m′,n′)|², where h is the coherent point-spread function.
• Phase-only diffractive elements are optimized to map input intensity patterns to desired output intensity patterns under incoherent illumination.
• The network architecture is trained end-to-end to minimize the mean squared error between predicted and target output intensity distributions.
• The training process ensures that the resulting diffractive structure can perform any linear intensity transformation universally, given sufficient degrees of freedom.
• The method leverages the fact that incoherent intensity response is the squared magnitude of the coherent transfer function, enabling universal mapping through phase optimization.

Experimental results

Research questions

• RQ1 Can a diffractive optical processor perform any arbitrary linear intensity transformation under spatially-incoherent illumination?
• RQ2 What is the minimum number of phase-only diffractive features required to achieve universal linear intensity transformation under incoherent light?
• RQ3 How does the performance of a diffractive network trained under incoherent illumination compare to that trained under coherent illumination for intensity mapping?
• RQ4 Can deep learning be effectively used to train phase-only diffractive networks for universal intensity transformations in the incoherent regime?
• RQ5 Is the universal transformation capability under incoherent light achievable with the same theoretical threshold of N ≥ 2Ni × No as in the coherent case?

Key findings

• The proposed diffractive processor successfully performs universal linear intensity transformations under spatially-incoherent illumination, enabling all-optical computation with natural light.
• The method achieves universal performance when the number of optimized phase features N is greater than or equal to ~2Ni × No, matching the coherence-based theoretical threshold.
• The time-averaged intensity response of the network is modeled as the squared magnitude of the coherent transfer function, enabling incoherent intensity mapping.
• Supervised deep learning training with input-output intensity pairs enables the network to generalize across arbitrary linear intensity transformations.
• The framework demonstrates that phase-only diffractive networks can be trained to emulate any linear intensity transformation under incoherent light, expanding the scope of all-optical processors.
• The results validate that incoherent illumination does not preclude universal linear transformation capability when the network is properly trained via deep learning.