Jorge Luis Flores

Optical metrology and interferometry are widely known disciplines that study and develop techniques to measure physical quantities such as dimensions, force, temperature, stress, etc. A key part of these disciplines is the processing of interferograms, also called fringe patterns. Owing that this kind of images contains the information of interest in a codified form, processing them is of main relevance and has been a widely studied topic for many years. Several mathematical tools have been used to analyze fringe patterns, from the classic Fourier analysis to regularization methods. Some methods based on wavelet theory have been proposed for this purpose in the last years and have evidenced virtues to consider them as a good alternative for fringe pattern analysis. In this chapter, we resume the theoretical basis of fringe pattern image formation and processing, and some of the most relevant applications of the 2D continuous wavelet transform (CWT) in fringe pattern analysis.

Three-dimensional (3D) shape profiling by sinusoidal phase-shifting methods is affected by the non-linearity of the projector. To overcome this problem, the defocusing technique has become an important alternative to generate sinusoidal fringe patterns. The precision of this method depends on the binary pattern used and on the defocusing applied. To improve the defocusing technique, we propose the implementation of a color-based binary fringe patterns. The proposed technique involves the generation of colored pulse width modulation (PWM) fringe patterns, which are generated with different frequencies at the carrier signal. From an adequate selection of these frequencies, the colored PWM fringe patterns will lead to amplitude harmonics lower than the conventional PWM fringe patterns. Hence, the defocusing can decrease, and the 3D shape profiling can be more accurate. Numerical simulations and experimental results are presented as validation.

In order to overcome the limitations of the sequential phase-shifting fringe pattern profilometry for dynamic measurements, a color-channel-based approach is presented. The proposed technique consists of projecting and acquiring a colored image formed by three sinusoidal phase-shifted patterns. Therefore, by using the conventional three-step phase-shifting algorithm, only one color image is required for phase retrieval each time. However, the use of colored fringe patterns leads to a major problem, the color crosstalk, which introduces phase errors when conventional phase-shifting algorithms with fixed phase-shift values are utilized to retrieve the phase. To overcome the crosstalk issue, we propose the use of a generalized phase-shifting algorithm with arbitrary phase-shift values. The simulations and experimental results show that the proposed algorithm can significantly reduce the influence of the color crosstalk.

Phase unwrapping is probably the most challenging step in the phase retrieval process in phase-shifting and spatial-carrier interferometry. Likewise, phase unwrapping is required in 3D-shape profiling and deflectometry. In this paper, we present a novel phase retrieval method that completely sidesteps the phase unwrapping process, significantly eliminating the guessing in phase reconstruction and thus decreasing the time data processing. The proposed wrapping-free method is based on the direct integration of the spatial derivatives of the interference patterns under the single assumption that the phase is continuous. This assumption is valid in most physical applications. Validation experiments are presented confirming the robustness of the proposed method.

Deflectometry is a well-known method to characterize pure phase objects by measuring the deformation of fringes. In principle, the retrieved magnitude is the partial derivative of the phase along the coordinate orthogonal to the fringes. In order to recover the phase it is necessary to know the derivatives in two orthogonal directions, which is usually achieved by rotating 90° the original fringes and acquiring a new deformed pattern. This “time-multiplexed” two-dimensional deflectometry is a time-consuming operation if the goal is to characterize phase objects in real time. In the present paper we propose a kind of two-dimensional deflectometry that allows acquisition of fringe patterns in two orthogonal directions in a single frame. The proposed procedure utilizes a two-dimensional (“additive”) fringe pattern that allows the application of Takeda’s method to each coordinate independently. The advantage of the method (with respect to the traditional one) is that it simplifies the setup and reduces the acquisition time. Validation experiments are presented.

We present a method for synthesizing triangular intensity fringes as a way to solve the problems caused by projector/camera gamma nonlinearity in triangular-pattern phase-shifting profilometry. The fringe generation technique consists of projecting and acquiring a temporal sequence of strictly binary color patterns (code gray), whose (adequately weighted) average leads to triangular fringe patterns with the required number of bits, which allows a reliable three-dimensional profile reconstruction using these methods. Validation experiments are presented.

A method for orientation-selective enhancement of edges in color images is proposed. The method utilizes the capacity of digital micromirror devices to generate a positive and a negative color replica of the image used as input. When both images are slightly displaced and imagined together, one obtains an image with enhanced edges. The proposed technique does not require a coherent light source or precise alignment. The proposed method could be potentially useful for processing large image sequences in real time. Validation experiments are presented.