Robust real-time estimation of non-uniform angular velocity and sub-pixel jitter in images captured with resonant scanners.

Images captured with resonant scanners are affected by angular velocity fluctuations that result in image distortion and by poor synchronization between scanning and light detection that creates jitter between image rows. We previously demonstrated that both problems can be mitigated in post-processing by recording the scanner orientation in synchrony with the image capture, followed by data resampling [Opt. Express30, 112 (2022)10.1364/OE.446162]. Here we introduce more robust algorithms for estimation of both angular velocity fluctuation and jitter in the presence of random and deterministic noise. We also show linearization of the scanner oscillation model to reduce calculation times by two orders of magnitude, reaching 65,000 jitter estimations per second when using 2,800 samples per image row, and 500,000 when using only 500 samples, easily supporting real-time generation of jitter-corrected images.

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.

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.

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.

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.

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.

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.

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.

Incoherent optical processor for nondirectional edge enhancement of color images.

We present an optical method for nondirectional edge extraction/enhancement in color images. The method is based on the capability of twisted-nematic LCDs to traduce the image information in changes of the state of polarization of light, which allows us to generate simultaneously two replicas of the digital image displayed on the LCD: a true-color ("positive") image and a complementary-color ("negative") one. In our setup the imaging system consists of a lens plus a pupil mask formed with concentric apertures and orthogonal polarizers. This layout allows us to simultaneously image a well-focused positive replica (due to the circular aperture) superimposed to a slightly defocused negative one (due to the annular aperture). It is not difficult to demonstrate that this generates a nondirectional (Laplacian) edge enhancement. Unlike Fourier, our proposal works with incoherent illumination and does not require precise alignment, and thus, it could be a useful tool for edge extraction/enhancement in large images in real-time applications. Validation experiments are presented.

Optical processing of color images with incoherent illumination: orientation-selective edge enhancement using a modified liquid-crystal display.

We present a novel optical method for edge enhancement in color images based on the polarization properties of liquid-crystal displays (LCD). In principle, a LCD generates simultaneously two color-complementary, orthogonally polarized replicas of the digital image used as input. The currently viewed image in standard LCD monitors and cell phone's screens -which we will refer as the "positive image or true-color image"- is the one obtained by placing an analyzer in front of the LCD, in cross configuration to the back polarizer of the display. The orthogonally polarized replica of this image -the "negative image or complementary-color image"- is absorbed by the front polarizer. In order to generate the positive and negative replica with a slight displacement between them, we used a LCD monitor whose analyzer (originally a linear polarizer) was replaced by a calcite crystal acting as beam displacer. When both images are superimposed laterally displaced across the image plane, one obtains an image with enhanced first-order derivatives along a specific direction. The proposed technique works under incoherent illumination and does not require precise alignment, and thus, it could be potentially useful for processing large color images in real-time applications. Validation experiments are presented.

Optimal pulse-width modulation for sinusoidal fringe generation with projector defocusing: comment.

We comment on a recent Letter [Opt. Lett. 35, 4121 (2010)], in which the authors discuss an optimal pulse-width modulation (OPWM) method for sinusoidal fringe generation. We consider that the comparison of the squared binary method (SBM) and the sinusoidal pulse-width modulation (SPWM) method has considerable deficiencies.

Three-dimensional profiling with binary fringes using phase-shifting interferometry algorithms.

Three-dimensional shape measurements by sinusoidal fringe projection using phase-shifting interferometry algorithms are distorted by the nonlinear response in intensity of commercial video projectors and digital cameras. To solve the problem, we present a method that consists in projecting and acquiring a temporal sequence of strictly binary patterns, whose (adequately weighted) average leads to a sinusoidal fringe pattern with the required number of bits. Since binary patterns consist of "ones" and "zeros"--and no half-tones are involved--the nonlinear response of the projector and the camera will not play a role, and a nearly unit contrast gray-level sinusoidal fringe pattern is obtained. Validation experiments are presented.

Pulse-width modulation in defocused three-dimensional fringe projection.

Shape measurements by fringe projection methods require high-quality sinusoidal fringes. We present a sinusoidal fringe generation technique that utilizes slightly defocused binary fringe projection. The proposed method is a spatial version of the well-known pulse-width modulation (PWM) technique of electrical engineering. PWM is easy to implement using off-the-shelf projectors, and it allows us to overcome the gamma problem (i.e., the nonlinear projector response) in the output light intensity. We will demonstrate that, with a small defocusing level--lower than with other techniques proposed in the literature--a high-quality sinusoidal pattern is obtained. Validation experiments using a commercial video projector are presented.