Adaptable phase retrieval for coherent transition radiation spectroscopy based on differentiable physics information

2026-04-28

AI Summary

Reconstructing the longitudinal profile of a relativistic electron beam from coherent transition radiation (CTR) spectra constitutes an ill-posed phase retrieval problem, which traditional methods struggle to address due to complex forward models. This work proposes a differentiable physics-informed gradient optimization framework, termed GD-Phase, which updates only the phase in the Fourier domain while strictly enforcing agreement with the measured spectral amplitude and incorporating real-space physical priors. By uniquely integrating a differentiable forward model with phase retrieval, the method enables seamless embedding of arbitrary differentiable experimental effects, establishing a general foundation for multi-diagnostic fusion and uncertainty quantification. On both multi-peak and strongly modulated synthetic spectra, GD-Phase achieves reconstruction fidelity comparable to conventional approaches while demonstrating superior adaptability and extensibility, making it well-suited for high-dimensional, multimodal, and uncertainty-aware diagnostic scenarios.

Abstract

Coherent transition radiation (CTR) spectroscopy is a critical diagnostic for characterizing the longitudinal structure of relativistic electron bunches in laser-plasma and conventional accelerators. In practice, recovering the bunch profile from a measured CTR spectrum is an ill-posed phase-retrieval problem. Traditionally, this is addressed using Gerchberg-Saxton (GS)-type iterative algorithms. However, these implementations often rely on explicit inverse propagators, making them difficult to adapt to sophisticated experimental forward models. In this work, we introduce a flexible gradient-based framework for CTR phase retrieval. By leveraging a differentiable forward model, we propose a phase-only gradient descent (GD-Phase) approach that enforces the measured spectral amplitude as a hard constraint while optimizing the Fourier phase under physical real-space priors. Using synthetic CTR spectra spanning multi-peaked and strongly modulated profiles, we benchmark GD-Phase against traditional GS and a real-space amplitude-parametrized gradient descent (GD-Amp) algorithm. Unlike traditional methods, this formulation allows for the seamless inclusion of arbitrary differentiable experimental effects into the reconstruction loop. We demonstrate that this physics-informed approach not only reproduces the fidelity of GS methods but also establishes a robust baseline for incorporating multi-diagnostic constraints and uncertainty quantification. This enables the systematic extension to higher-dimensional, multimodal, and uncertainty-aware diagnostics, facilitating fast and scalable phase retrieval in realistic experimental settings.

Problem

• phase retrieval
• coherent transition radiation
• electron bunch characterization
• ill-posed problem
• spectroscopy

Innovation

• differentiable physics
• phase retrieval
• coherent transition radiation
• gradient descent
• physics-informed optimization