# All-optical complex field imaging using diffractive processors

arXiv: https://arxiv.org/abs/2401.16779 · HTML: https://mlsanity.com/paper/2401.16779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 81 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 25 of 25)

- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Lensless computational imaging through deep learning](https://mlsanity.com/paper/1702.08516/) (2017)
- [Misalignment Resilient Diffractive Optical Networks](https://mlsanity.com/paper/2005.11464/) (2020)
- [Analysis of Diffractive Optical Neural Networks and Their Integration with Electronic Neural Networks](https://mlsanity.com/paper/1810.01916/) (2018)
- [All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces](https://mlsanity.com/paper/2108.09833/) (2021)
- [Diffractive all-optical computing for quantitative phase imaging](https://mlsanity.com/paper/2201.08964/) (2022)
- [To image, or not to image: Class-specific diffractive cameras with all-optical erasure of undesired objects](https://mlsanity.com/paper/2205.13122/) (2022)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Fourier Imager Network (FIN): A deep neural network for hologram reconstruction with superior external generalization](https://mlsanity.com/paper/2204.10533/) (2022)
- [Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors](https://mlsanity.com/paper/2303.13037/) (2023)
- [Data class-specific all-optical transformations and encryption](https://mlsanity.com/paper/2212.12873/) (2022)
- [Self-supervised learning of hologram reconstruction using physics consistency](https://mlsanity.com/paper/2209.08288/) (2022)
- [Early-detection and classification of live bacteria using time-lapse coherent imaging and deep learning](https://mlsanity.com/paper/2001.10695/) (2020)
- [Super-resolution image display using diffractive decoders](https://mlsanity.com/paper/2206.07281/) (2022)
- [Unidirectional Imaging using Deep Learning-Designed Materials](https://mlsanity.com/paper/2212.02025/) (2022)
- [Quantitative phase imaging (QPI) through random diffusers using a diffractive optical network](https://mlsanity.com/paper/2301.07908/) (2023)
- [Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2308.02952/) (2023)
- [Cascadable all-optical NAND gates using diffractive networks](https://mlsanity.com/paper/2111.01404/) (2021)
- [Universal Polarization Transformations: Spatial programming of polarization scattering matrices using a deep learning-designed diffractive polarization transformer](https://mlsanity.com/paper/2304.05724/) (2023)
- [All-Optical Phase Conjugation Using Diffractive Wavefront Processing](https://mlsanity.com/paper/2311.04473/) (2023)
- [Learning Diffractive Optical Communication Around Arbitrary Opaque Occlusions](https://mlsanity.com/paper/2304.10087/) (2023)
- [Quantitative phase imaging through an ultra-thin lensless fiber endoscope](https://mlsanity.com/paper/2112.12055/) (2021)
- [Deep Learning-enabled Detection and Classification of Bacterial Colonies using a Thin Film Transistor (TFT) Image Sensor](https://mlsanity.com/paper/2205.03549/) (2022)

## Built on by (most cited first, 2 of 2)

- [Integration of Programmable Diffraction with Digital Neural Networks](https://mlsanity.com/paper/2406.10688/) (2024)
- [Beyond the Thin-Layer Limit: Differentiable Volumetric Training for Visible-Range Diffractive Neural Networks](https://mlsanity.com/paper/2606.07896/) (2026)

## Abstract (arXiv)

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.