A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Phase unwrapping is an ill-posed classical problem in many practical applications of significance such as 3D profiling through fringe projection, synthetic aperture radar and magnetic resonance imaging. Conventional phase unwrapping techniques estimate the phase either by integrating through the confined path (referred to as path-following methods) or by minimizing the energy function between the wrapped phase and the approximated true phase (referred to as minimum-norm approaches). However, these conventional methods have some critical challenges like error accumulation and high computational time and often fail under low SNR conditions. To address these problems, this paper proposes a novel deep learning framework for unwrapping the phase and is referred to as “PhaseNet 2.0”. The phase unwrapping problem is formulated as a dense classification problem and a fully convolutional DenseNet based neural network is trained to predict the wrap-count at each pixel from the wrapped phase maps. To train this network, we simulate arbitrary shapes and propose new loss function that integrates the residues by minimizing the difference of gradients and also uses $L_{1}$ loss to overcome class imbalance problem. The proposed method, unlike our previous approach PhaseNet, does not require post-processing, highly robust to noise, accurately unwraps the phase even at the severe noise level of −5 dB, and can unwrap the phase maps even at relatively high dynamic ranges. Simulation results from the proposed framework are compared with different classes of existing phase unwrapping methods for varying SNR values and discontinuity, and these evaluations demonstrate the advantages of the proposed framework. We also demonstrate the generality of the proposed method on 3D reconstruction of synthetic CAD models that have diverse structures and finer geometric variations. Finally, the proposed method is applied to real-data for 3D profiling of objects using fringe projection technique and digital holographic interferometry. The proposed framework achieves significant improvements over existing methods while being highly efficient with interactive frame-rates on modern GPUs.

PhaseNet 2.0: Phase Unwrapping of Noisy Data Based on Deep Learning Approach

We describe a new mode of optical lithography called absorbance-modulation optical lithography (AMOL) in which a thin film of photochromic material is placed on top of a conventional photoresist and illuminated simultaneously by a focal spot of wavelength lambda1 and a ring-shaped illumination of wavelength lambda2. The lambda1 radiation converts the photochromic material from an opaque to a transparent configuration, thereby enabling exposure of the photoresist, while the lambda2 radiation reverses the transformation. As a result of these competing effects, the point-spread function that exposes the resist is strongly compressed, resulting in higher photolithographic resolution and information density. We show by modeling that the point-spread-function compression achieved via AMOL depends only on the absorbance distribution in the photostationary state. In this respect, absorbance modulation represents an optical nonlinearity that depends on the intensity ratio of lambda1 and lambda2 and not on the absolute intensity of either one alone. By inserting material parameters into the model, a lithographic resolution corresponding to lambda1/13 is predicted.

/pdf/absorbance-modulation-optical-lithography-3k3l1xhxw2.pdf

Absorbance-modulation optical lithography

We present a study of orbital angular momentum transfer from pump to down-converted beams in a type-II optical parametric oscillator. Cavity and anisotropy effects are investigated and demonstrated to play a central role in the transverse mode dynamics. While the idler beam can oscillate in a Laguerre-Gauss mode, the crystal birefringence induces an astigmatic effect in the signal beam that prevents the resonance of such a mode.

/pdf/orbital-angular-momentum-exchange-in-an-optical-parametric-30tswqr9pf.pdf

Orbital angular momentum exchange in an optical parametric oscillator

Quality-based 2D phase unwrapping algorithms provide one of the best tradeoffs between speed and quality of results. Their robustness depends on a quality map, which is used to build a path that visits the most reliable pixels first. Unwrapping then proceeds along this path, delaying unwrapping of noisy and inconsistent areas until the end, so that the unwrapping errors remain local. We propose a novel quality measure that is consistent, technically sound, effective, fast to compute, and immune to the presence of a carrier signal. The new measure combines the benefits of both the quality-guided and the residue-based phase unwrapping approaches. The quality map is justified from the two different theoretical points of view. Exhaustive tests on a variety of artificially generated and real 2D wrapped phase signals illustrate its potential usefulness in the field of fringe projection profilometry.

A Robust and Simple Measure for Quality-Guided 2D Phase Unwrapping Algorithms

In this Letter, a proposal addressing the problem of two-dimensional phase unwrapping based on the theory of residues is presented. Here, wrapped phase maps with shifted phase jumps are used to balance residue charges. With this approach, we seek to minimize processing time and residue connection, which is essential in the development of branch-cut algorithms. Finally, a phase-unwrapping algorithm is applied to these wrapped maps, generated by Fourier transform profilometry to obtain three-dimensional profiles of objects illuminated by photorefractive moire-like patterns generated in an experiment of real-time dynamic holography, and by fringe patterns generated with a Michelson interferometer.

Branch-cut algorithm for optical phase unwrapping

Hurst exponent determination for digital speckle patterns in roughness control of metallic surfaces

We present a study of spatial structures created by superposition of spiral zone plates used for generating optical beams with phase singularities. Moire fringes are observed that show topological defects similar to those appearing in interference patterns of optical vortices. A brief theoretical discussion is included that supports the similarities between the two phenomena. Our results may lead to interesting applications to digital information processing by optical means.

P. A. M. dos Santos

Papers

Branch-cut algorithm for optical phase unwrapping

Hurst exponent determination for digital speckle patterns in roughness control of metallic surfaces

Topological defects in moiré fringes with spiral zone plates

Moiré-like patterns as a spatial beat frequency in photorefractive sinusoidal phase gratings superposition

Optical activity measurements in the photorefractive Bi12TiO20 single crystal fibers