Enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm

Abstract

It is a challenge for Phase Measurement Profilometry (PMP) to measure objects with a large range of reflectivity variation across the surface. Saturated or dark pixels in the deformed fringe patterns captured by the camera will lead to phase fluctuations and errors. Jiang et al. proposed a high dynamic range real-time 3D shape measurement method without changing camera exposures. Three inverted phase-shifted fringe patterns are used to complement three regular phase-shifted fringe patterns for phase retrieval when any of the regular fringe patterns are saturated. But Jiang's method still has some drawbacks: (1) The phases in saturated pixels are respectively estimated by different formulas for different cases. It is shortage of an universal formula; (2) it cannot be extended to four-step phase-shifting algorithm because inverted fringe patterns are the repetition of regular fringe patterns; (3) only three unsaturated intensity values at every pixel of fringe patterns are chosen for phase demodulation, lying idle the other unsaturated ones. We proposed a method for enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm, which combines the complementary technique of inverted and regular fringe patterns with generalized phase-shifting algorithm. Firstly, two sets of complementary phase-shifted fringe patterns, namely regular and inverted fringe patterns are projected and collected. Then all unsaturated intensity values at the same camera pixel from two sets of fringe patterns are selected, and employed to retrieve the phase by generalized phase-shifting algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with Jiang's method, which demonstrate that the proposed method not only expands the scope of Jiang's method, but also improves the measurement accuracy. Keywordsphase-shifting algorithm; high dynamic range (HDR); phase measuring profilometry (PMP); fringe projection; least-square algorithm; phase error

Dynamic 3D shape measurement based on the phase-shifting moire algorithm

“…The software was programmed in Matlab with an i5-760 CPU at 2.80 GHz. We chose the object with a rough surface as the tested specimen, did not consider measuring objects with large reflectivity variations across their surface [34][35].…”

Three-dimensional measurement with reflection suppression based on high-dynamic range images

“…For reflective objects, there are overexposure and underexposure areas in the acquired images, and images contain different effective information under different exposure times. 12 Therefore, image exposure intensity factor B k ðx; yÞ is a key factor of image fusion. In order to assign larger fusion weights to the pixels with moderate exposure time in the image, and to assign smaller fusion weights to the pixels with excessive exposure time and insufficient exposure time, the Gauss equation is selected to assign fusion weights to each pixel in the image.…”

“…In this method, ϕ 0 1 ðx; yÞ and ϕ 0 2 ðx; yÞ can be directly obtained by Eq. (12), without needing to calculate synthetic phase. Thus it avoids the phase error produced in image fusion, reduces the error in phase unwrapping, and improves the quality of the 3-D point cloud data.…”

“…Then the mask image sequence is calculated, and finally each pixel of the edge image is generated by selecting the brightest within the setting range of the corresponding pixel from one set of fringe images. Jiang et al 12 fused the original fringe patterns acquired with different exposure times and illumination intensity to generate a synthetic fringe image. However, these methods rely on multiple exposures with different system configurations, which are mainly obtained through the offline calculation and cannot automatically adjust the configuration for different scenes.…”

Robust wrapping-free phase retrieval method based on weighted least squares method

“…Over the years, many phase demodulation methods have been proposed to retrieve phase from fringe patterns. Some of these methods determine the phase by evaluating the arctangent of the ratio of the intensity functions, such as phase-shifting algorithm [5][6][7], Fourier-based techniques [8,9], and spatial interferometry [10]. So that the obtained phase is usually restricted in (-π, π].…”