Monte Carlo based techniques of two-stage phase shifting algorithms

Miranda, Marta; Dorrio, Benito Vasquez

doi:10.1016/j.optlaseng.2010.11.014

Cited by 7 publications

(5 citation statements)

References 28 publications

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“…We can conclude that the main differences between the present analysis and the works reported in [1][2][3] are (a) the possibility of working with two different reference frequencies and nonequally spaced shifts, and (b) a methodological proposal based on the work in [17] to design two-stage algorithms with insensitivity to detuning and harmonics. These last two approaches increase the scope of the two-stage PSI techniques similarly to the way the generalized PSI algorithms increase the scope of the equally spaced PSI algorithms.…”

Section: Discussionmentioning

confidence: 71%

“…Moreover, these mathematical expressions allow us to obtain the weight factors of phase-shifting algorithms in a simple fashion. This fact can be noticed in the development of the present study by focusing in the design of the TSPS algorithms [1][2][3]. In this work, we have proposed a way to compensate the two-stage PSI algorithms to cope with detuning and harmonics by analyzing their 2D frequency sampling functions (differential spectra).…”

Section: Discussionmentioning

confidence: 95%

“…Another difference of this study, in comparison of the works reported in [1][2][3], is the possibility to generalize the TSPS algorithms if it was necessary to consider nonequally spaced shifts for the sets of interferograms fμ 1;k g, fμ 2;p g. The generalized phase-shifting algorithms [18][19][20] emerge from the problem of estimating erratic phase shifts from the intensity patterns. If the phase shifts can be estimated with sufficient precision, then a generalized phase-shifting algorithm could be applied to obtain a better estimation of the objective function, the phase.…”

Section: Discussionmentioning

confidence: 99%

“…The design and analysis in the Fourier domain of two-stage phase-shifting (TSPS) algorithms induce an interesting field of study that has been considered in some publications [1][2][3][4][5]. Interferometric applications described in [6][7][8] require adequate phase-shifting equations that can compensate error sources as deviated shifts due to linear (detuning) [9,10] or nonlinear miscalibration [11,12], the presence of harmonics in the intensity patterns [13,14], or the presence of noise, etc.…”

Section: Introductionmentioning

confidence: 99%

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Compensation of the two-stage phase-shifting algorithms in the presence of detuning and harmonics

2013

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The Fourier analysis of two-stage phase-shifting (TSPS) algorithms is growing in interest as a research topic, specifically, the algorithm's insensitivity properties to various error sources. The main motivation of this paper is to propose TSPS algorithms that perform well in the face of detuning and harmonics for each of the two sets of interferograms with different or equal reference frequencies. TSPS algorithms based on the development of generalized equations consider both the frequency sampling functions that represent them and nonconstant phase shifts.

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Section: Discussionmentioning

confidence: 71%

Section: Discussionmentioning

confidence: 95%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Compensation of the two-stage phase-shifting algorithms in the presence of detuning and harmonics

2013

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“…Amato et al [3] presented the indirect measurement of angles and evaluation of uncertainty using CMM. A Monte Carlo simulation method was used for error analysis by many investigators [4], [5] and [6]. Gyula Hermann [7] developed an algorithm for geometric error correction in coordinate measurement.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Uncertainty in Angle Measurement performed on a Coordinate Measuring Machine

Rajamani¹,

Vignesh²,

Mouliprasanth³

2021

Proceedings of the First International Conference on Combinatorial and Optimization, ICCAP 2021, December 7-8 2021, Chennai, In

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Coordinate Measuring Machine (CMM) is a universally accepted instrument that is widely used for inspection in industries and laboratories. Evaluation of uncertainty in dimensional measurement is very important for any measurement process. The components and the parts of the mechanical systems must have the accurate dimensions to meet the functional requirements. The environmental conditions and measurement methodhighly influence the accuracy of measurement process.This paper focuses on estimating the uncertaintyin angle measurementscarried out using CMM. In this study, anglegauge blocks are used as the reference materials for assessing the uncertainty in measurement using a CMM. An uncertainty estimation is carried out according to the guide to the expression of uncertainty in measurement (GUM). The influence of position accuracy, environment temperature, vibration, measurement and probing strategies are analysed and uncertainty in angle measurement is estimated as 40 arc seconds.

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