# Classification and reconstruction of spatially overlapping phase images using diffractive optical networks

arXiv: https://arxiv.org/abs/2108.07977 · HTML: https://mlsanity.com/paper/2108.07977/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 18 Aug 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit](https://mlsanity.com/paper/2008.11659/) (2020)
- [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)
- [Design of Task-Specific Optical Systems Using Broadband Diffractive Neural Networks](https://mlsanity.com/paper/1909.06553/) (2019)
- [Ensemble learning of diffractive optical networks](https://mlsanity.com/paper/2009.06869/) (2020)
- [Computational Imaging Without a Computer: Seeing Through Random Diffusers at the Speed of Light](https://mlsanity.com/paper/2107.06586/) (2021)
- [An Optical Frontend for a Convolutional Neural Network](https://mlsanity.com/paper/1901.03661/) (2018)
- [Class-specific Differential Detection in Diffractive Optical Neural Networks Improves Inference Accuracy](https://mlsanity.com/paper/1906.03417/) (2019)
- [Scale-, shift- and rotation-invariant diffractive optical networks](https://mlsanity.com/paper/2010.12747/) (2020)
- [Computer-free, all-optical reconstruction of holograms using diffractive networks](https://mlsanity.com/paper/2107.08177/) (2021)
- [Optical machine learning with incoherent light and a single-pixel detector](https://mlsanity.com/paper/1904.10851/) (2019)
- [Photonic convolutional neural networks using integrated diffractive optics](https://mlsanity.com/paper/2003.12015/) (2020)

## Built on by (most cited first, 5 of 5)

- [Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network](https://mlsanity.com/paper/2203.13482/) (2022)
- [All-optical image classification through unknown random diffusers using a single-pixel diffractive network](https://mlsanity.com/paper/2208.03968/) (2022)
- [Differentiable Microscopy Designs an All Optical Phase Retrieval Microscope](https://mlsanity.com/paper/2203.14944/) (2022)
- [Coherence Awareness in Diffractive Neural Networks](https://mlsanity.com/paper/2408.06681/) (2024)
- [SP2RINT: Spatially-Decoupled Physics-Inspired Progressive Inverse Optimization for Scalable, PDE-Constrained Meta-Optical Neural Network Training](https://mlsanity.com/paper/2505.18377/) (2025)

## Abstract (arXiv)

Diffractive optical networks unify wave optics and deep learning to all-optically compute a given machine learning or computational imaging task as the light propagates from the input to the output plane. Here, we report the design of diffractive optical networks for the classification and reconstruction of spatially overlapping, phase-encoded objects. When two different phase-only objects spatially overlap, the individual object functions are perturbed since their phase patterns are summed up. The retrieval of the underlying phase images from solely the overlapping phase distribution presents a challenging problem, the solution of which is generally not unique. We show that through a task-specific training process, passive diffractive networks composed of successive transmissive layers can all-optically and simultaneously classify two different randomly-selected, spatially overlapping phase images at the input. After trained with ~550 million unique combinations of phase-encoded handwritten digits from the MNIST dataset, our blind testing results reveal that the diffractive network achieves an accuracy of >85.8% for all-optical classification of two overlapping phase images of new handwritten digits. In addition to all-optical classification of overlapping phase objects, we also demonstrate the reconstruction of these phase images based on a shallow electronic neural network that uses the highly compressed output of the diffractive network as its input (with e.g., ~20-65 times less number of pixels) to rapidly reconstruct both of the phase images, despite their spatial overlap and related phase ambiguity. The presented phase image classification and reconstruction framework might find applications in e.g., computational imaging, microscopy and quantitative phase imaging fields.