Transversal observation of the light-induced color-center concentration in photochromic glasses in stationary state.

The aim of the present work is to study the dependence of the light-induced optical density, i.e., the color-center concentration, as a function of the distance traveled inside a photochromic glass body in stationary state. We propose an experimental setup that allows the direct observation of that concentration from a transversal view. In particular, we will see that for activating intensities much higher than certain threshold, the photochromic material saturates between the surface and an inflection point that happens at a constant normalized concentration of 2/3. The width of this region depends logarithmically on the activating light intensity. This fact will allow us to determine one of the photochemical constants of the material. Validation experiments are presented.

Robust interferometer with external phase-shift control.

We describe a robust interferometer with external phase-shift control that does not require moving parts. The optical architecture resembles a common-path device in which the interfering waves propagate together in one collimated beam passing through the test sample. The collimated beam is incident on a calcite plate, which produces a polarization selective lateral translation and superposition of the reference and test waves. The characteristic features of the proposed interferometer, i.e. one-beam single-element scheme combined with external phase-shift control without moving parts, make a highly vibration insensitive device. Validation experiments are presented.

Three-dimensional shape profiling by out-of-focus projection of colored pulse width modulation fringe patterns.

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.

Generalized phase-shifting algorithms: error analysis and minimization of noise propagation: erratum.

There are a couple of typos in our recent paper Appl. Opt.55(6), 1461-1469 (2016)APOPAI0003-693510.1364/AO.55.001461.

Image segmentation by nonlinear filtering of optical Hough transform.

The identification and extraction (i.e., segmentation) of geometrical features is crucial in many tasks requiring image analysis. We present a method for the optical segmentation of features of interest from an edge enhanced image. The proposed method is based on the nonlinear filtering (implemented by the use of a spatial light modulator) of the generalized optical Hough transform and is capable of discriminating features by shape and by size. The robustness of the method against noise in the input, low contrast, or overlapping of geometrical features is assessed, and experimental validation of the working principle is presented.

Reconstruction of perspective shifts and refocusing of a three-dimensional scene from a multi-focus image stack.

The convergence of optical imaging acquisition and image processing algorithms is a fast-evolving interdisciplinary research field focused on the reconstruction of images with novel features of interest. We propose a method for post-capture perspective shift reconstruction (in the x, y, and z directions) of a three-dimensional scene as well as refocusing with apertures of arbitrary shapes and sizes from an optimal multi-focus image stack. The approach is based on the reorganization of the acquired visual information considering a depth-variant point-spread function, which allows it to be applied to strongly defocused multi-focus image stacks. Our method is performed without estimating the depth map or segmenting the in-focus regions. A conventional camera combined with an electrically tunable lens is used for image acquisition and does not require scale transformation or registration between the acquired images. Experimental results for both real and synthetic data images are provided and compared to state-of-the-art schemes.

Generalized phase-shifting algorithms: error analysis and minimization of noise propagation.

Phase shifting is a technique for phase retrieval that requires a series of intensity measurements with certain phase steps. The purpose of the present work is threefold: first we present a new method for generating general phase-shifting algorithms with arbitrarily spaced phase steps. Second, we study the conditions for which the phase-retrieval error due to phase-shift miscalibration can be minimized. Third, we study the phase extraction from interferograms with additive random noise, and deduce the conditions to be satisfied for minimizing the phase-retrieval error. Algorithms with unevenly spaced phase steps are discussed under linear phase-shift errors and additive Gaussian noise, and simulations are presented.

Color-fringe pattern profilometry using a generalized phase-shifting algorithm.

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.

Optical implementation of the generalized Hough transform with totally incoherent light.

The generalized Hough transform is a well-established technique for detecting complex shapes in images containing noisy or missing data. We present an efficient optical implementation of this transform using an electrical lens with variable focal length and a rotating pupil mask matching the pattern to be found. The proposed setup works under fully (i.e., both spatially and temporally) incoherent illumination and can handle orientation changes or scale variations in the pattern. Validation experiments showing its real-time application are presented.

Nonplanar fiber-optic sensing head for the compensation of bending-induced birefringence in Faraday current sensors.

We demonstrate the compensation of bending-induced linear birefringence in single-mode fibers coiled in a nonplanar path by alternating orthogonal bending planes. This effect can be applied for the construction of birefringence-free fiber coils in Faraday sensor heads (e.g., in current sensors) to improve their sensitivity. Validation experiments are presented.

Wrapping-free phase retrieval with applications to interferometry, 3D-shape profiling, and deflectometry.

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.

All-in-focus image reconstruction under severe defocus.

Limited depth-of-focus is a problem in many fields of optics, e.g., microscopy and macro-photography. We propose a new physically based method with a space variant point spread function (PSF) to accomplish all-in-focus reconstruction (image fusion) from a multi-focus image sequence in order to extend the depth-of-field. The proposed method works well under strong defocus conditions for color image stacks of arbitrary length. Experimental results are provided to demonstrate that our method outperforms state-of-the-art image fusion algorithms for strong defocus on both synthetic as well as real data images.

Real-time pattern recognition using an optical generalized Hough transform.

We present some pattern recognition applications of a generalized optical Hough transform and the temporal multiplexing strategies for dynamic scale and orientation-variant detection. Unlike computer-based implementations of the Hough transform, in principle its optical implementation does not impose restrictions on the execution time or on the resolution of the images or frame rate of the videos to be processed, which is potentially useful for real-time applications. Validation experiments are presented.

Generation of phase-shifting algorithms with N arbitrarily spaced phase-steps.

Phase-shifting (PS) is an important technique for phase retrieval in interferometry (and three-dimensional profiling by fringe projection) that requires a series of intensity measurements with known phase-steps. Usual PS algorithms are based on the assumption that the phase-steps are evenly spaced. In practice, however, this assumption is often not satisfied exactly, which leads to errors in the recovered phase. In this work we present a systematic algebraic approach for generating general PS algorithms with N arbitrarily spaced phase-steps, which present advantages (e.g., the PS error can be avoided) over known algorithms that assume equally spaced phase-steps. Simulations are presented.

Phase retrieval from one partial derivative.

Phase objects can be characterized using well-known methods such as shear interferometry and deflectometry, which provide information on the partial derivatives of the phase. It is often believed that for phase retrieval it is strictly necessary to have knowledge of two partial derivatives in orthogonal directions. In the praxis, this implies that the measurements have to be performed along two dimensions, which often requires a rotation of the object or rotation of the shear direction. This is time consuming and errors can be easily generated from the process of rotation, especially for image registration in the axial direction. In the present Letter, we will demonstrate that only one partial derivative often suffices to recover the phase, and we will discuss under which conditions that is possible. Simulations and validation experiments are presented.

One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns.

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.

Gradient field microscopy of unstained specimens: comment.

We comment on a recent paper by Kim et al. [Opt. Exp. 20(6) 6737-6745 (2012)], in which the authors claimed to present a new method for first-order differentiation of phase objects called gradient field microscopy (GFM). We consider that the method does not substantially differ from well-known Fourier methods discussed in textbooks. Also, we discuss some deficiencies of the paper.

Binary coded triangular fringes for 3-D surface-shape measurement.

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.

Edge enhancement of color images using a digital micromirror device.

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.

Color encoding of binary fringes for gamma correction in 3-D profiling.

Three-dimensional profiling by sinusoidal fringe projection using PSI-algorithms are distorted by the nonlinear response of digital cameras and commercial video projectors. To solve the problem, we present a fringe generation technique that consists of projecting and acquiring a temporal sequence of strictly binary color patterns, whose (adequately weighted) average leads to sinusoidal fringe patterns with the required number of bits, which allows for a reliable three-dimensional profile using a PSI-algorithm. Validation experiments are presented.