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Journal ArticleDOI

Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

Song Zhang1
01 Oct 2009-Optical Engineering (International Society for Optics and Photonics)-Vol. 48, Iss: 10, pp 105601
TL;DR: A framework to reduce the unwrapping errors of the measurement system using a digital multiple-wavelength phase- shifting algorithm and significantly alleviated the measurement errors caused by the phase noise.
Abstract: We address a framework to reduce the unwrapping errors of the measurement system using a digital multiple-wavelength phase- shifting algorithm. In particular, the following framework is proposed: 1 smooth the raw phase by smoothing the sine and cosine images of the phase computation of the inverse tangent function; 2 locate and re- move the incorrectly unwrapped points by the monotonicity condition of the phase map; 3 obtain the unwrapped phase map for the shortest wavelength without smoothing; 4 detect holes and fill them to preserve as much useful information as possible. Experiments demonstrated that the proposed framework significantly alleviated the measurement errors caused by the phase noise. © 2009 Society of Photo-Optical Instrumentation

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Citations
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Journal ArticleDOI
TL;DR: The results show that the multi-frequency temporal phase unwrapping provides the best unwrapped reliability, while the multi -wavelength approach is the most susceptible to noise-induced unwrappers errors.

598 citations


Cites methods from "Phase unwrapping error reduction fr..."

  • ...For example, complex domain Gaussian filtering [90,109], modulation consistency [90], and absolute phase monotonicity [109–112] can be used to identify the fringe order error and refine the final continuous phase map....

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Journal ArticleDOI
Song Zhang1
TL;DR: Two conventional absolute phase unwrapping methods are presented: multi-frequency or -wavelength phase-shifting methods, and hybrid binary coding and phase-Shifting methods; and some non-conventional methods that are specific for DFP systems are introduced.

262 citations

Journal ArticleDOI
TL;DR: An effective method using an adaptive median filter is proposed to effectively remove unwrapping errors and simultaneously preserve step-heights and both simulations and experiments can demonstrate its effectiveness.
Abstract: Phase-shifting profilometry combined with Gray-code patterns projection has been widely used for 3D measurement. In this technique, a phase-shifting algorithm is used to calculate the wrapped phase, and a set of Gray-code binary patterns is used to determine the unwrapped phase. In the real measurement, the captured Gray-code patterns are no longer binary, resulting in phase unwrapping errors at a large number of erroneous pixels. Although this problem has been attended and well resolved by a few methods, it remains challenging when a measured object has step-heights and the captured patterns contain invalid pixels. To effectively remove unwrapping errors and simultaneously preserve step-heights, in this paper, an effective method using an adaptive median filter is proposed. Both simulations and experiments can demonstrate its effectiveness.

115 citations

Journal ArticleDOI
TL;DR: A novel structured light approach for direct measurement of shiny target so as to skip the coating preprocedure is presented and an improved zero-crossing feature detector that has subpixel accuracy is proposed for strip-edge localization.
Abstract: Three-dimensional measurement of shiny or reflective surface is a challenging issue for optical-based instrumentations. In this paper, we present a novel structured light approach for direct measurement of shiny target so as to skip the coating preprocedure. In comparison with traditional image-intensity-based structured light coding strategies like sinusoidal and line patterns, strip edges not raw image intensities are encoded in the illuminated patterns. With strip edges generally better preserved than individual image intensity in the image data in the presence of surface reflections, such a coding strategy is more robust. To remove the periodic ambiguity within strip patterns, traditional Gray code patterns are adopted. To localize the strip edges more precisely, both positive and negative strip patterns are used. An improved zero-crossing feature detector that has subpixel accuracy is proposed for strip-edge localization. The experimental setup is configured with merely an off-the-shelf pico-projector and a camera. Extensive experiments including accuracy evaluation, comparison with previous structured light algorithms, and the reconstruction of some real shiny objects are shown to demonstrate the system's accuracy and endurance against reflective nature of surfaces.

95 citations

Journal ArticleDOI
TL;DR: The novel phase coding method can be used for absolute phase retrieval with high frequency and six additional fringe images can generate more than 64(2(6) unique codewords for correctabsolute phase retrieval.
Abstract: A recently proposed phase coding method for absolute phase retrieval performs well because its codeword is embedded into phase domain rather than intensity. Then, the codeword can determine the fringe order for the phase unwrapping. However, for absolute phase retrieval with a large number of codewords, the traditional phase coding method becomes not so reliable. In this paper, we present a novel phase coding method to tackle this problem. Six additional fringe images can generate more than 64(2(6)) unique codewords for correct absolute phase retrieval. The novel phase coding method can be used for absolute phase retrieval with high frequency. Experiment results demonstrate the proposed method is effective.

86 citations

References
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Book
28 Apr 1998
TL;DR: Methods for Phase Unwrapping, Phase Data, Quality Maps, Masks, and Filters, and Minimum-Norm Methods.
Abstract: Introduction to Phase Unwrapping. Line Integrals, Residues, and 2-D Phase Unwrapping. Phase Data, Quality Maps, Masks, and Filters. Path-Following Methods. Minimum-Norm Methods. Comparisons and Conclusion. Appendices. Index.

1,575 citations

Journal ArticleDOI
TL;DR: An alternative approach based on one-dimensional unwrapping along the time axis is proposed, applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest.
Abstract: A new algorithm is proposed for unwrapping interferometric phase maps. Existing algorithms search the two-dimensional spatial domain for 2π discontinuities: only one phase map is required, but phase errors can propagate outward from regions of high noise, corrupting the rest of the image. An alternative approach based on one-dimensional unwrapping along the time axis is proposed. It is applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest. A particular example is quasi-static deformation analysis. The main advantages are (i) it is inherently simple, (ii) phase errors are constrained within the high-noise regions, and (iii) phase maps containing global discontinuities are unwrapped correctly, provided the positions of the discontinuities remain fixed with time. The possibility of real-time phase unwrapping is also discussed.

691 citations

01 Jan 1984
TL;DR: A technique that combines ideas of phase shifting interferometry (PSI) and two-wavelength interferometer (TWLI) to extend the phase measurement range of conventional single-wa wavelength PSI is described.
Abstract: This paper describes a technique that combines ideas of phase shifting interferometry (PSI) and two-wavelength interferometry (TWLI) to extend the phase measurement range of conventional single-wavelength PSI. To verify theoretical predictions, experiments have been performed using a solid-state linear detector array to measure 1-D surface heights. Problems associated with TWLPSI and the experimental setup are discussed. To test the capability of the TWLPSI, a very fine fringe pattern was used to illuminate a 1024 element detector array. Without temporal averaging, the repeatability of measuring a surface having a sag of ~100 μm is better than 25-A (0.0025%) rms.

376 citations

Journal ArticleDOI
TL;DR: In this article, a technique that combines ideas of phase shifting interferometry (PSI) and two-wavelength interference (TWLI) to extend the phase measurement range of conventional singlewavelength PSI is described.
Abstract: This paper describes a technique that combines ideas of phase shifting interferometry (PSI) and two-wavelength interferometry (TWLI) to extend the phase measurement range of conventional single-wavelength PSI. To verify theoretical predictions, experiments have been performed using a solid-state linear detector array to measure 1-D surface heights. Problems associated with TWLPSI and the experimental setup are discussed. To test the capability of the TWLPSI, a very fine fringe pattern was used to illuminate a 1024 element detector array. Without temporal averaging, the repeatability of measuring a surface having a sag of ~100 μm is better than 25-A (0.0025%) rms.

365 citations

Journal ArticleDOI
TL;DR: The recently proposed technique of temporal phase unwrapping has been used to analyze the phase maps from a projected-fringe phase-shifting surface profilometer, showing the error in height is shown to decrease inversely with the number of phase maps used.
Abstract: The recently proposed technique of temporal phase unwrapping has been used to analyze the phase maps from a projected-fringe phase-shifting surface profilometer. A sequence of maps is acquired while the fringe pitch is changed; the phase at each pixel is then unwrapped over time independently of the other pixels in the image to provide an absolute measure of surface height. The main advantage is that objects containing height discontinuities are profiled as easily as smooth ones. This contrasts with the conventional spatial phase-unwrapping approach for which the phase jump across a height discontinuity is indeterminate to an integral multiple of 2π. The error in height is shown to decrease inversely with the number of phase maps used.

311 citations