What Are Optimal Coding Functions for Time-of-Flight Imaging?

Abstract

The depth resolution achieved by a continuous wave time-of-ight (C-ToF) imaging system is determined by the coding (modulation and demodulation) functions that it uses. Almost all current C-ToF systems use sinusoid or square coding functions, resulting in a limited depth resolution. In this paper, we present a mathematical framework for exploring and characterizing the space of C-ToF coding functions in a geometrically intuitive space. Using this framework, we design families of novel coding functions that are based on Hamiltonian cycles on hypercube graphs. Given a xed total source power and acquisition time, the new Hamiltonian coding scheme can achieve up to an order of magnitude higher resolution as compared to the current state-of-the art methods, especially in low SNR settings. We also develop a comprehensive physically-motivated simulator for C-ToF cameras that can be used to evaluate various coding schemes prior to a real hardware implementation. Since most o -the-shelf C-ToF sensors use sinusoid or square functions, we develop a hardware prototype that can implement a wide range of coding functions. Using this prototype and our software simulator, we demonstrate the performance advantages of the proposed Hamiltonian coding functions in a wide range of imaging settings.

Phase disambiguation using spatio-temporally modulated illumination in depth sensing

“…Figure 4 shows the depth resolution of ToF and phase shifting along with the depth according to Eqs. (25) and (26). The resolution of ToF is constant at any depth while the resolution of phase shifting is proportional to the square of the depth.…”

“…According to Eqs. (25) and (26), the resolution of ToF is constant (blue) and the resolution of phase shifting is proportional to the square of the depth (orange). The depth d cross is the depth where the lines of the resolution of ToF and the resolution of the phase shifting is crossed.…”

“…To obtain fine resolution, Gupta et al [26] proposes the optimal code for ToF modulation. Gutierrez-Barragan et al [27] proposes an optimization approach for designing practical coding functions under hardware constraints.…”

A Parallel-Phase Demodulation-Based Distance-Measurement Method Using Dual-Frequency Modulation

“…Likewise, the demodulation signal is also generated using two frequencies simultaneously. The demodulation signal can be expressed as (20) where M 1 and M 2 represent the amplitude of the f 1 component of the demodulation signal and the amplitude of the f 2 component of the demodulation signal, respectively. f e is the effective frequency, which is identical to the greatest common division of f 1 and f 2 .…”

Realization of Multitone Continuous Wave Lidar

“…Very recently, frequency combs are utilized to achieve >THz bandwidth with μm resolutions in shorter ranges, as well [33]. On the other hand, some frequency domain Lidars previously employed the multiple-wavelength techniques such as continuous time-of-flight measurements [34], multi-wavelength super-heterodyning [35], [36] and multi-frequency demodulation via CMOS photonic mixer devices [37], which were used for short-range and high precision imaging and ranging. However, it is important to note that these efforts are mainly targeted for short-range measurements in applications such as Microsoft Kinect.…”