Variance and Error in One-Step Phase-Retrieval

TL;DR

This paper develops statistical models to analyze how time multiplexing in One-Step Phase-Retrieval affects image quality, revealing that variance decreases with more frames but MSE and SSIM approach non-zero limits.

Contribution

It introduces new models for MSE and SSIM behavior in OSPR, enhancing understanding of image quality impacts in high frame-rate holography.

Findings

Variance converges to zero as frame rate increases

MSE converges to a non-zero value with more frames

SSIM approaches a non-unitary value quadratically

Abstract

Time multiplexed approaches for high frame-rate holographic displays have been around since the invention of One-Step Phase-Retrieval (OSPR) in the early 2000s. When discovered, formulations were created for variance reduction but other image quality metrics were ignored. This work sets out statistical models for the mean squared error (MSE) and structural similarity index (SSIM) behaviour of OSPR for a range of image types in order to better understand the effect of time multiplexing on visible images. This finds that while observed variances converges to zero as the number of frames per second increases, MSE converges to a non-zero value while SSIM converges quadratically to a non-unitary value.