Single Exposure Quantitative Phase Imaging with a Conventional Microscope using Diffusion Models

TL;DR

This work tackles the practical limitation of Transport-of-Intensity Equation (TIE) phase retrieval requiring through-focus acquisitions by exploiting chromatic aberrations in a conventional RGB microscope to synthesize a defocus stack from a single white-light exposure. It introduces a physics-based synthetic data pipeline and two diffusion-based approaches, Conditional Variational Diffusion Models (CVDM) and Zero-Mean Diffusion (ZMD), to perform robust, quantitative phase retrieval under polychromatic illumination. Empirical results on synthetic and clinical urine datasets show that polychromatic single-exposure phase reconstructions with ZMD achieve higher image fidelity (MS-SSIM) and lower error (MAE) than traditional 2-shot TIE and baseline predictions, recovering fine cellular morphologies including red blood cell rings. The method leverages readily available hardware, suggesting strong potential for real-world clinical adoption and motivating future integration with Physics-Informed Neural Networks and standardized QPI benchmarks.

Abstract

Phase imaging is gaining importance due to its applications in fields like biomedical imaging and material characterization. In biomedical applications, it can provide quantitative information missing in label-free microscopy modalities. One of the most prominent methods in phase quantification is the Transport-of-Intensity Equation (TIE). TIE often requires multiple acquisitions at different defocus distances, which is not always feasible in a clinical setting. To address this issue, we propose to use chromatic aberrations to induce the required through-focus images with a single exposure, effectively generating a through-focus stack. Since the defocus distance induced by the aberrations is small, conventional TIE solvers are insufficient to address the resulting artifacts. We propose Zero-Mean Diffusion, a modified version of diffusion models designed for quantitative image prediction, and train it with synthetic data to ensure robust phase retrieval. Our contributions offer an alternative TIE approach that leverages chromatic aberrations, achieving accurate single-exposure phase measurement with white light and thus improving the efficiency of phase imaging. Moreover, we present a new class of diffusion models that are well-suited for quantitative data and have a sound theoretical basis. To validate our approach, we employ a widespread brightfield microscope equipped with a commercially available color camera. We apply our model to clinical microscopy of patients' urine, obtaining accurate phase measurements.

Figures (12)

• Figure 1: Example of optical system. The defocus distance $\Delta f$ induced by chromatic aberration depends on the focal lengths $f_1$ and $f_2$. The resulting $\Delta f$ for a specific wavelength $\lambda$ corresponds to variable $z$ in (\ref{['eq:fresnel-k']}).
• Figure 2: QPI methods assessed using synthetic images from HCOCO.
• Figure 3: QPI methods assessed using clinical microscopy images depicting two overlapping (two upper rows) and an individual (two lower rows) epithelial cells. Scale bar (upper leftmost image) is 50 $\mu$m.
• Figure 4: Urine sample with red blood cells. From left to right: US TIE phase reconstruction, Mean Prediction, and Zero-Mean Diffusion prediction. Regions of the image are enlarged to better show reconstruction details. Phase reconstructions are quantitative, with values between 0 and 2.5 radians. Scale bar is 200 $\mu$m.
• Figure 5: Phase quantification performed on clinical images. Regions of the images are enlarged to better show the objects in the image (epithelial cells). Scale bar (upper leftmost image) is 200 $\mu$m.

Theorems & Definitions (13)

• proposition 1
• Theorem 1
• lemma 1
• proof
• proof : Proof of Proposition \ref{['prop:zero-mean-sde']}
• lemma 2
• proof
• lemma 3
• proof
• lemma 4