Shape Measurements on Large Surfaces by Fringe Projection

Fringe 2013, 2014

The ancestral roots of the Fringe conference are in the automatic processing of fringe patterns. When we think of patterns, an image comes to mind of flowing lines beautifully wrapped around surface contours. But automatic processing of fringes is not limited to this kind of pattern: The fringes may be laid out along a line of sight as the time history of an object displacement, captured by a detector and processed to tell us something about how the object has moved, or more generally, where the object is with respect to a reference point in space.

Applied Optics, 1998

A fringe-formation theory for a dual-beam illumination configuration that leads to a twofold increase in sensitivity for the measurement of in-plane displacement is described. Here we have taken into account all four beams simultaneously that are generated at the image plane owing to two-beam illumination and their cross-interference terms for fringe formation. We show that the sensitivity obtainable is the usual interferometric sensitivity when we take into account all four beams simultaneously and doubles only when the retroreflected beams are observed. A detailed theory and an experimental demonstration of the method are presented.

To date, no fringe analysis technique has the capability to provide simultaneous and direct estimation of the continuous distributions corresponding to the interference phase and its first and second-order derivatives within the framework of a single interferometric configuration. Achieving this task would provide a significant advancement in the field of optical metrology as it allows for the measurement of displacement, strain, and curvature of a deformed object and avoids the necessity of using filtering and unwrapping procedures, multiple analysis techniques, and multiple interferometric configurations. Developing such a spatial fringe analysis method with the added advantage of having less computational complexity would open up avenues for making real-time measurements such as in the study of temporal evolution of deformation and/or strain. This thesis presents a novel approach based on piecewise polynomial phase approximation as an elegant all-in-one solution to the problems mentioned above. This approach has given birth to several advanced fringe analysis methods such as discrete-chirp-Fourier transform method, high-order instantaneous moments method, and cubic-phase function method. Significant advancements brought in the field by these methods are made evident by both theoretical analysis (simulation results) and by experimental demonstrations such as the measurement of displacement, strain and curvature in digital holographic interferometry and the measurement of 3D shape, temporal evolution of deformation and/or strain in fringe projection techniques.

Optics and Lasers in Engineering, 2010

a b s t r a c t As technologies evolve, there have been high demands for the three-dimensional (3D) shape measurement techniques to posses the following combined technical features: high accuracy, fast speed, easy implementation, capability of measuring multiple objects as well as measuring complex shapes. Generally, the existing techniques can satisfy some of the requirements, but not all of them. This paper presents four practical considerations in fringe projection profilometry (FPP) based 3D shape measurements, along with simple but robust solutions, including gamma correction of digital projection, arbitrary setup of system components, phase unwrapping with multi-frequency fringes, and system calibration with a least-squares inverse approach. The validity and practicability of the FPPbased 3D shape measurement technique using the four corresponding technical approaches have been verified by experiments. The presented technique is capable of satisfying the various critical demands in enormous scientific and engineering applications.

Optics Communications, 2009

We report a sinusoidal fringe projection system based on superluminiscent diode (SLD) as a broad-band light source in conjunction with an acousto-optic tunable filter (AOTF) as frequency tuning device for three-dimensional shape measurement. The present system is based on a compact low-coherence Michelson interferometer system. The conventional interferometric system was modified in which one side of the beam splitter was coated with aluminum oxide which is used as reference mirror. With this modified version, interference fringes can easily be obtained by simply placing the external mirror in contact on the other side of beam splitter. Sinusoidal fringes with multiple spatial-carrier frequency can be generated in real-time using the present system by means of changing the radio-frequency signal to AOTF electronically without mechanically moving any component in the system. The present system was tested by projecting the sinusoidal fringes on a step-like object and 3D shape of the object was reconstructed using Fourier transform fringe analysis technique. The main advantages of the proposed system are completely non-mechanical scanning, easy to align, high stability because of its nearly common-path geometry and compactness.

Optics Communications, 2009

We report a sinusoidal fringe projection system based on superluminiscent diode (SLD) as a broad-band light source in conjunction with an acousto-optic tunable filter (AOTF) as frequency tuning device for three-dimensional shape measurement. The present system is based on a compact low-coherence Michelson interferometer system. The conventional interferometric system was modified in which one side of the beam splitter was coated with aluminum oxide which is used as reference mirror. With this modified version, interference fringes can easily be obtained by simply placing the external mirror in contact on the other side of beam splitter. Sinusoidal fringes with multiple spatial-carrier frequency can be generated in real-time using the present system by means of changing the radio-frequency signal to AOTF electronically without mechanically moving any component in the system. The present system was tested by projecting the sinusoidal fringes on a step-like object and 3D shape of the object was reconstructed using Fourier transform fringe analysis technique. The main advantages of the proposed system are completely non-mechanical scanning, easy to align, high stability because of its nearly common-path geometry and compactness.

Optical Engineering, 2003

We present a method to obtain profilometry of a suitable object by fringe projection. The method is appropriate to the case of large objects as compared to the distance from the illuminating source, that is, a nonconstant equivalent wavelength. We develop an experiment to laterally displace a set of fringes on a sphere and obtain quantitative results. There are several orientation parameters involved in the method, and a minimization algorithm is developed to adjust the values of some of them. A series of numerical experiments are performed on this method to test its accuracy under various circumstances. We show that the method can currently attain precisions of Ϸ eq /80 ( eq stands for equivalent wavelength) and identify possible sources of error.

Applied Optics, 1978

A technique is described for obtaining a linear readout of fringe shift from a high resolution Fabry-Perot interferometer. One mirror of the interferometer is mounted on a piezoelectric crystal driven by a high frequency sinusoidal voltage. A signal proportional to the mirror displacement is displayed on the Y axis of an oscilloscope, while the X axis is swept with time. Each time the interferometer passes through a transmission maximum, a pulse is produced which is fed to the Z axis ofthe oscilloscope, producing an intensified dot. The displacement of the resultant row of dots from its ambient position is linearly proportional to the fringe shift occurring within the interferometer, has no sign of ambiguity, and is independent of the finesse. All the circuits required for producing the readout were realized using the internal circuitry of a standard laboratory oscilloscope.

Applied Optics, 1998

Theoretical background along with experimental results are given for a simple method for in-plane fringe enhancement in dual-beam illumination holographic interferometry. In this method, the fringes representing in-plane displacements arise as a moiré pattern between two interferograms. To distinguish the in-plane displacement, a sequence of images is recorded while the reference mirror is continuously tilted at random. The in-plane fringes are then found as the maximum contrast of the out-of-plane fringes in the image sequence. The resulting fringe quality is close to the quality of the out-of-plane fringes.