Absolute Depth Measurement Using Multiphase Normalized Cross-Correlation for Precise Optical Profilometry

Abstract

In a multifrequency phase-shifting (MFPS) algorithm, the temporal phase unwrapping algorithm can extend the unambiguous phase range by transforming the measurement range from a short fringe pitch into an extended synthetic pitch of two different frequencies. However, this undesirably amplifies the uncertainty of measurement, with each single-frequency phase map retaining its measurement uncertainty, which is carried over to the final unwrapped phase maps in fringe-order calculations. This article analyzes possible causes and proposes a new absolute depth measurement algorithm to minimize the propagation of measurement uncertainty. Developed from normalized cross-correlation (NCC), the proposed algorithm can minimize wrong fringe-order calculations in the MFPS algorithm. The experimental results demonstrated that the proposed measurement method could effectively calibrate the wrong fringe order. Moreover, some extremely low signal-to-noise ratio (SNR) regions of a captured image could be correctly reconstructed (for surface profiles). The present findings confirmed measurement precision at one standard deviation below 5.4 µm, with an absolute distance measurement of 16 mm. The measurement accuracy of the absolute depth could be significantly improved from an unacceptable level of measured errors down to 0.5% of the overall measuring range. Additionally, the proposed algorithm was capable of extracting the absolute phase map in other optical measurement applications, such as distance measurements using interferometry.

The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

“…The systolic array's total adder number is ranged from 2L − 2 to 2L + N − 3, and its multiplier number is 5. (3), a 1 (2)+a 2 (2)=f(2)+f (3), (3), a 3 (0)+a 4 (0)=f (2) 0, 0, 0…”

“…Normalized cross-correlation (NCC) is an important mathematical tool in signal and image processing for feature matching, similarity analysis, motion tracking, object recognition, and so on [1][2][3]. In order to improve its real-time and efficient performance, digital NCC has been suggested to be implemented by some fast algorithms and hardware structures, due to its high computational complexity [4,5].…”

“…, and the module A using 0 adders when { g(i) } = { 2, 4, 6, 8 } inFigure 9b. From Figures 7-9, it can be obtained the adder number of the module A is from 0 to N − 1, and the latency T A is from 0 to log 2 N. +a2 (3)=f(3), a 1 (2)+a 2 (2)=f(2)+f(3), a 1 (1)+a 2 (1)=f(1)+f(2), a 1 (0)+a 2 (0)=f(0)+f(1) a 3 (3)+a 4 (3)=0, a 3 (2)+a 4 (2)=0, a 3 (1)+a 4 (1)=f(3), a 3 (0)+a 4 (0)=f(2)+f(The module A for { g(i) } = {1, 2, 3, 4}. +a 2 (3)=f(3), a 1 (2)+a 2 (2)=f(2)+f(3), a 1 (1)+a 2 (1)=f(1)+f(2), a 1 (0)+a 2 (0)=f(0)+f(1)+f(3)a 3 (3)+a 4 (3)=0, a 3 (2)+a 4 (2)=0, a 3 (1)+a 4 (1)=f(3), a 3 (0)+a 4 (0)=f(2The module A for { g(i) } = {2, 1, 4, 2}.…”