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This paper introduces a gradient-based phase retrieval framework (GD-Phase) for coherent transition radiation (CTR) spectroscopy, a technique used to characterize relativistic electron bunches. By employing a differentiable forward model and optimizing the Fourier phase with real-space priors, the method overcomes limitations of traditional Gerchberg-Saxton (GS) algorithms, which struggle with complex experimental setups. Benchmarking against GS and GD-Amp using synthetic CTR spectra, GD-Phase demonstrates comparable fidelity while offering the flexibility to incorporate arbitrary differentiable experimental effects and multi-diagnostic constraints.
Differentiable physics unlocks adaptable and scalable phase retrieval for coherent transition radiation spectroscopy, outperforming traditional methods by seamlessly incorporating complex experimental effects.
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.
