Depth Error and Noise Analysis in Multi-frequency Indirect Time-of-Flight Imaging

Abstract

Compendi d'articles, Doctorat industrialThis PhD thesis investigates the fundamental limitations and performance factors of indirect Time-of-Flight (iToF) camera systems, with a focus on improving phase estimation accuracy and depth reliability. The global objective is to enhance the understanding of error sources in iToF systems and to develop models and methodologies that improve their robustness and precision in both academic and industrial contexts. The research is structured around three main contributions. First, a multi-objective optimization framework is proposed for selecting modulation frequencies in multi-frequency iToF systems. This model simultaneously minimizes phase unwrapping errors and maximizes depth precision, while incorporating constraints such as maximum unambiguous range and frequency limits, adapting to specific application requirements. Thanks to this multi-objective formulation, the proposed optimization model improves the performance over existing methods. Second, the thesis presents a generalized shot noise model for traditional sampling architectures. This model accounts for key system parameters including modulation frequency, signal amplitude, background illumination, integration time and the number of points in the Discrete Fourier Transform. It provides a deeper understanding of noise behaviour. A second order-order error propagation is modelled to get a more accurate phase variance estimation. Third, the analysis is extended to the differential sampling architecture used in commercial sensors, such as those developed by Analog Devices Inc (ADI). This architecture simplifies the analog front-end and removes the DC component of the received light, optimizing the use of the dynamic range of the Analog to Digital Converter. A new shot noise model is derived, showing that phase error is inversely proportional to signal amplitude and directly proportional to background illumination, while remaining independent of the number of points in the Discrete Fourier Transform. Together, these contributions form a unified framework that links frequency design and noise modelling, offering practical tools for optimizing iToF systems. The proposed methodologies have been validated through extensive simulations and experimental data, and have been integrated into the development of next-generation iToF modules at ADI. This work lays the foundation for future research in adaptive frequency selection strategies and enhanced noise mitigation, particularly in environments affected by multipath interference and dynamic scene conditions.Programa de Doctorat en Informàtic