Least-squares gamma estimation in fringe projection profilometry

Muñoz, Antonio; Flores, Jorge L.; Parra-Escamilla, Geliztle A.; Morales, Luis; Ordoñes, Sotero; Servı́n, Manuel

doi:10.1364/ao.415056

Cited by 17 publications

(6 citation statements)

References 18 publications

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“…Before starting our description of our proposal for phase demodulation, we would like to indicate that we considered that the so-called gamma distortion was previously overcome. For a detailed description of this matter, the reader is referred to [24][25][26][27] . Moreover, we consider that the projected fringe pattern has the same fringe pitch through the working region, so the height sensitivity of our system is spatially independent.…”

Section: Digital Moiré Profilementioning

confidence: 99%

“…( 6), it is considered that the color is neglectable since the chromatic spectral overlapping between red and blue channels has been seen as a minimum. 9,15 We have also considered that the acquired patterns do not have any gamma distortion or instead, it was corrected previously; please refer to papers 11,24,25 for a detailed discussion about gamma distortion, and how it can be overcome. Under these considerations, we can remove the background illumination or DC term straightforwardly by subtracting IR-IB, resulting…”

Section: Digital Moiré Profilementioning

confidence: 99%

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Colored digital Moire technique for self-occluding shading in fringe projection profilometry

Flores Nuñez,

Ordoñes,

Parra Escamilla

2023

Infrared Remote Sensing and Instrumentation XXXI

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In this work, we presented a phase demodulation technique for fringe analysis in fringe projection profilometry based on digital moiré and the co-phase technique. The approach involves the use of stereo illumination and the simultaneous projection and acquisition of two 𝜋 -shifted sinusoidal patterns from each projector. By taking advantage of color multiplexing, we code the sinusoidal patterns in the red and blue channels of the RGB images, so we need to project and acquire one image for each digital light projector. The phase demodulation consists of two steps: first, digitally generating the moiré pattern for each RGB image utilizing the spatial phase carrier; second, computing the analytic signals for the two moiré patterns via a third-order, low-pass Butterworth filter in the frequency domain; third, calculate the final phase by merging the two analytic signals using the co-phasing technique.

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Section: Digital Moiré Profilementioning

confidence: 99%

Section: Digital Moiré Profilementioning

confidence: 99%

Colored digital Moire technique for self-occluding shading in fringe projection profilometry

Flores Nuñez,

Ordoñes,

Parra Escamilla

2023

Infrared Remote Sensing and Instrumentation XXXI

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“…However, the method requires at least six fringe patterns, which greatly increases the measurement time. Mu˜noz et al [20] indirectly determines the gamma factor by obtaining the estimated phase of the reference plane through the least-squares method. Li and Chen [21] proposes a mathematical model-based doublefive-step algorithm in combination with the cross-grid phaseshifting contouring technique to suppress nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

The optimal algorithm for eliminating nonlinear error in phase measurement profilometry based on global statistical phase feature function

Zhu,

Xu,

Long

et al. 2024

Meas. Sci. Technol.

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In a digital stripe projection structured light system, the nonlinear phase error is generated by the gamma effect of both the projector, camera, and other electronic devices. One of the existing nonlinear correction methods is active correction by projecting ideal fringes as far as possible, and the other is passive compensation after capturing aberrant fringes. The former has higher accuracy but needs to capture a large number of fringe patterns, while the latter does not need many fringe patterns, but is not only greatly affected by random noise and out-of-focus effects, but also has poor accuracy. In this paper, an optimal algorithm for eliminating nonlinear error based on global statistical phase feature function (GSPF) is proposed. The phase distribution can be estimated from the difference between the global cumulative distribution function and the normalized cumulative distribution function. For an ideal fringe pattern without nonlinear error and a fringe pattern with nonlinear error, the region wrapped by the x-axis normalized cumulative distribution function is much smaller than the region wrapped by the x-axis global cumulative distribution function, and the larger the nonlinear error is, the larger the difference between the two is. Therefore, the global statistical phase feature function can be used for nonlinear error correction. Then the optimal nonlinear error correction is performed based on the minimum difference between the compensated phase entropy and the ideal phase entropy. The method does not require too many steps of phase-shifting, and only three fringe patterns are needed to realize accurate and robust correction. Experimental results show that the method is fast, highly accurate and robust. Using this technique, high accuracy measurements can be achieved with the traditional three-step phase-shifting algorithm.

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“…Researchers have deeply studied a variety of methods to suppress the nonlinear effects of the FPP system [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. These methods can be classified into two categories: active methods and passive methods.…”

Section: Introductionmentioning

confidence: 99%

Online nonlinearity elimination for fringe projection profilometry using slope intensity coding

Wan,

Tang,

et al. 2024

J. Opt.

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The nonlinearity effect in the system of fringe projection profilometry (FPP) will cause the non-sinusoidal deviation of the fringe patterns, inducing ripple-like phase errors and further affecting the measurement accuracy. This paper presents an online nonlinearity elimination method based on slope intensity coding. Two sequences of sinusoidal phase-shifting fringe patterns with different frequencies, and one slope intensity pattern with one uniform intensity pattern are projected. The equations of the nonlinearity response are established using the defined mean and modulation parameters, the captured uniform intensity and two extracted background intensities. The nonlinearity response coefficients determined by solving the equations are used for pixel-wise nonlinearity correction on the captured images, which are employed for computing the wrapped phase, and further obtaining continuous phase by the multi-frequency phase unwrapping method. Experimental results demonstrated that the proposed method could eliminate the nonlinearity-induced phase error online by using fewer images, and maintain the reliability of phase unwrapping in the measurement of isolated objects with complex surface.

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Least-squares gamma estimation in fringe projection profilometry

Cited by 17 publications

References 18 publications

Colored digital Moire technique for self-occluding shading in fringe projection profilometry

Colored digital Moire technique for self-occluding shading in fringe projection profilometry

The optimal algorithm for eliminating nonlinear error in phase measurement profilometry based on global statistical phase feature function

Online nonlinearity elimination for fringe projection profilometry using slope intensity coding

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