Ternary Gray code-based phase unwrapping for 3D measurement using binary patterns with projector defocusing

Abstract

The three-dimensional measurement technique using binary pattern projection with projector defocusing has become increasingly important due to its high speed and high accuracy. To obtain even faster speed without sacrificing accuracy, a ternary Gray code-based phase-unwrapping method is proposed by using even fewer binary patterns, which makes it possible to efficiently and accurately unwrap the phase. Theoretical analysis, simulations, and experiments are presented to validate the proposed method's efficiency and robustness.

Period-Wise Phase Unwrapping Method With Two Gray Level Coding Patterns

“…Binary coding methods including simple coding [17] and gray code [19] at least require 2 log M patterns to generate M codewords, which are inefficient in time-critical measurements. To this end, Zheng et al [24] used three intensity levels to develop a ternary gray-code method, and it needs 3 log M patterns to generate M periods. Subsequently, He et al [25] proposed a quaternary gray-code method to further reduce the number of patterns.…”

Temporal phase unwrapping towards high-accuracy and high-speed fringe projection profilometry

“…The binary defocusing technique [45], [77] is an effective and widely used method to reduce the projection time for each pattern. To reduce the number of the required patterns for different TPU methods, many new methods, such as ternary gray code phase unwrapping [78], two-plus-one phase-shifting algorithm [79]- [81], geometry [81], [82] and continuity [83], [84] constrained SPU, have been proposed.…”

“…For a typical value of = 64 , ⌈log 2 64⌉ = 6 binary GC patterns are required for phase unwrapping. To enhance the measurement speed, a ternary GC (TGC) method phase unwrapping methods is proposed [78], by which the number of required GC patterns is reduced to ⌈log 3 64⌉. In TGC, a one-dimensional binary pattern generation method is used, in which the repeated patches of 00, 10, and 11 are used to represent three different gray levels (black, gray, and white), after defocusing.…”

“…The most widely used gray code is binary, which can be quickly generated and projected by a DMD projector, but the binary GC method requires = ⌈log 2 ⌉ patterns to uniquely encode periods [86]. Recently, an interesting TGC method has been proposed, where the projected pattern is still binary, but it will become ternary after defocusing [78]. As a result, is reduced to ⌈log 3 ⌉.…”

“…The ternary GC (TGC) phase unwrapping ( = 3) [78] intuitively represents represent three different gray levels (black, gray, and white) with repeated patches of 00, 10, and 11 and extract the gray code from the captured binary defocused patterns by thresholding.…”