Spectral pre-modulation of training examples enhances the spatial resolution of the Phase Extraction Neural Network (PhENN)

TL;DR

This paper introduces a spectral pre-modulation technique that improves the spatial resolution of the PhENN neural network for phase retrieval, effectively doubling its resolution by addressing the frequency content of training data.

Contribution

The study proposes a spectral pre-modulation method to enhance PhENN's resolution, addressing the limitation caused by sparse high-frequency content in training data.

Findings

Spectral pre-modulation doubles PhENN's spatial resolution.

Training data spectral flattening improves fine feature reconstruction.

Method effective for natural scene-like phase objects.

Abstract

The Phase Extraction Neural Network (PhENN) is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through examples consisting of pairs of true phase objects and their corresponding intensity diffraction patterns; thereafter, given a test raw intensity pattern PhENN is capable of reconstructing the original phase object robustly, in many cases even for objects outside the database where the training examples were drawn from. Here, we show that the spatial frequency content of the training examples is an important factor limiting PhENN's spatial frequency response. For example, if the training database is relatively sparse in high spatial frequencies, as most natural scenes are, PhENN's ability to resolve fine spatial features in test patterns will be correspondingly limited. To combat this issue, we propose "flattening" the power spectral density of the training examples before presenting them to PhENN. For phase objects following the statistics of natural scenes, we demonstrate experimentally that the spectral pre-modulation method enhances the spatial resolution of PhENN by a factor of 2.