Digital fringe projection profilometry utilizes a digital video projector as a structured light source and thus gains great flexibility. However, the gamma nonlinearity of the video projector inevitably decreases the accuracy and resolution of the measurement. We propose a gamma-correction technique based on statistical analysis of the fringe images. The technique allows one to estimate the value of gamma from the normalized cumulative histogram of the fringe images. By iterating the two steps, gamma estimation and phase evaluation, the actual gamma value can be calculated. At the same time the phase distribution of the fringe pattern can be solved with higher accuracy. In so doing, neither photometric calibration nor knowledge of the device is required. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.

Gamma correction for digital fringe projection profilometry.

We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.

/pdf/complex-wave-retrieval-from-a-single-off-axis-hologram-4xkjxab0oj.pdf

Complex-wave retrieval from a single off-axis hologram.

Many optical measurement techniques provide fringe patterns as their results. The decodification processes that employ one or several fringe patterns to automatically retrieve the phase are generally designated as phase-evaluation methods. In this work, an overview of these methods will be schematically presented. Their particular performances will be compared, stressing their main advantages and drawbacks. An important group of these methods employs the well-known phase-shifting algorithms as a tool for calculating the phase. In the general form of these algorithms, the principal value of the optical phase is computed by an inverse trigonometric function whose argument is a combination of phase-shifted intensity values, provided by the modulation of one or several fringe patterns. These algorithms will be also studied in the general context of the phase-evaluation methods.

https://iopscience.iop.org/article/10.1088/0957-0233/10/3/005/pdf

Phase-evaluation methods in whole-field optical measurement techniques

Interferogram Analysis For Optical Testing, Second Edition

The grid method is a technique suitable for the measurement of in-plane displacement and strain components on specimens undergoing a small deformation. It relies on a regular marking of the surfaces under investigation. Various techniques are proposed in the literature to retrieve these sought quantities from images of regular markings, but recent advances show that techniques developed initially to process fringe patterns lead to the best results. The grid method features a good compromise between measurement resolution and spatial resolution, thus making it an efficient tool to characterise strain gradients. Another advantage of this technique is the ability to establish closed-form expressions between its main metrological characteristics, thus enabling to predict them within certain limits. In this context, the objective of this paper is to give the state of the art in the grid method, the information being currently spread out in the literature. We propose first to recall various techniques that were used in the past to process grid images, to focus progressively on the one that is the most used in recent examples: the windowed Fourier transform. From a practical point of view, surfaces under investigation must be marked with grids, so the techniques available to mark specimens with grids are presented. Then we gather the information available in the recent literature to synthesise the connection between three important characteristics of full-field measurement techniques: the spatial resolution, the measurement resolution and the measurement bias. Some practical information is then offered to help the readers who discover this technique to start using it. In particular, programmes used here to process the grid images are offered to the readers on a dedicated website. We finally present some recent examples available in the literature to highlight the effectiveness of the grid method for in-plane displacement and strain measurement in real situations.

/pdf/the-grid-method-for-in-plane-displacement-and-strain-19w07norsx.pdf

The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

Various interferometric and fringe projection techniques may result in crossed and closed fringe patterns with the information about the phenomena tested Recent applications require the analysis on the basis of a single fringe pattern Here, we address two problems: simultaneous analysis of the information about two events, and analysis of fringe pattern with high phase gradients in both x and y directions The analysis of a fringe pattern is performed by the spatial-carrier phase-shifting method used sequentially for x and y sampling directions The error analysis of the method in reference to both problems is presented

Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns

Two-directional spatial-carrier phase shifting method was proposed for analysis of crossed and closed fringe patterns. This paper focuses on the major limitations for phase calculation by the standard 5-point algorithm used sequentially for x and y sampling directions. These limitations include the influence of improper carrier frequencies, nonequally spaced fringes, nonlinearities in the detection system, variations in the contrast and background intensity functions and interaction between the component fringe patterns. Computer simulation reveals the character and magnitude of these major errors.

Errors in two-directional spatial-carrier phase-shifting method

Modified procedure for automatic surface topography

Two-directional method was proposed for analysis of crossed or closed fringe paUerns. This paper focuses on the analysis of
closed fringe pauern and the major limitations for the N-point algorithms (standard five-point, modified five- and threepoint
algorithms).The limitations include the influence of the tilt of fringes, variations in the background intensity and
contrast functions, the nonlinearities in a detection system, random noise. Computer simulation reveal the character and the
magnitude of the major errors for all algorithms tested. The comparison of the results obtained is given and the advantages
ofusing the modified five- and three-point algorithm are described.

Errors in two-directional spatial-carrier phase shifting method for closed fringe patterns analysis

The new approach to the shape measurement system by implementations of adaptive and feed-back elements for an automated fringe projection system is proposed. Specifically the fringe pattern evaluation module based on the assessment of fringe pattern parameters performed by Fourier analysis and new version of spatial-carrier phase shifting method based on sampling in two directions are presented. The functioning of the system in the calibration and operational modes is shown on a representative example.

Maria Pirga

Papers

Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns

Errors in two-directional spatial-carrier phase-shifting method

Modified procedure for automatic surface topography

Errors in two-directional spatial-carrier phase shifting method for closed fringe patterns analysis

Adaptive automatic shape measurement system