New method of attack and security enhancement on an asymmetric cryptosystem based on equal modulus decomposition.

A recently proposed asymmetric cryptosystem based on coherent superposition and equal modulus decomposition has shown to be robust against a specific attack. In this paper, we have shown that it is vulnerable to a newly designed attack. With this attack, an intruder is able to access the exact private key and obtain precise attack results using a phase retrieval algorithm.

Improved method of attack on an asymmetric cryptosystem based on phase-truncated Fourier transform.

We propose an improved method of attack on an asymmetric cryptosystem based on a phase-truncated Fourier transform. With the proposed method of attack, an attacker is able to access the exact decryption keys and obtain precise attack results. The method is based on a novel median-filtering phase-retrieval algorithm.

Flexible structured-light-based three-dimensional profile reconstruction method considering lens projection-imaging distortion.

Structured-light profilometry is a powerful tool to reconstruct the three-dimensional (3D) profile of an object. Accurate profile acquisition is often hindered by not only the nonlinear response (i.e.

Surface profile measurement in white-light scanning interferometry using a three-chip color CCD.

White-light scanning interferometry (WLSI) is a useful technique to measure surface profile when a test object contains discontinuous structures or microstructures. A black and white CCD camera is usually utilized to capture interferograms, and a series of corresponding algorithms is used to achieve the profile measurement. However, the color information in the interferograms is lost.

Simultaneous measurement of translation and tilt using digital speckle photography.

A Michelson-type digital speckle photographic system has been proposed in which one light beam produces a Fourier transform and another beam produces an image at a recording plane, without interfering between themselves. Because the optical Fourier transform is insensitive to translation and the imaging technique is insensitive to tilt, the proposed system is able to simultaneously and independently determine both surface tilt and translation by two separate recordings, one before and another after the surface motion, without the need to obtain solutions for simultaneous equations. Experimental results are presented to verify the theoretical analysis.

Measurement of curvature and twist of a deformed object using digital holography.

Measurement of curvature and twist is an important aspect in the study of object deformation. In recent years, several methods have been proposed to determine curvature and twist of a deformed object using digital shearography. Here we propose a novel method to determine the curvature and twist of a deformed object using digital holography and a complex phasor.

Determination of three-dimensional displacement using two-dimensional digital image correlation.

A novel method that uses a two-dimensional (2D) digital image correlation (DIC) based on a single CCD camera to measure three-dimensional (3D) displacement and deformation is proposed. Rigid-body displacement in 3D space consists of both in-plane and out-of-plane components. The presence of an in-plane displacement component results in a shift of the center of the image displacement vector, while the slope of the image displacement vector is related to the out-of-plane displacement component.

Temporal phase retrieval from a complex field in digital holographic interferometry.

We describe a novel method of processing complex phasors in digital holographic interferometry (DHI). Unlike the commonly used digital phase subtraction method that operates on the phase itself, the proposed method operates on the complex phasor instead. Two temporal phase retrieval algorithms are developed in which the complex phasor of each pixel is measured and analyzed as a function of time.

Global and local coordinates in digital image correlation.

Digital image correlation (DIC) is commonly used to measure specimen displacements by correlating an image of a specimen in an undeformed or reference configuration and a second image under load. To establish the correlation between the images, numerical techniques are used to locate an initially square image subset in a reference image. In this process, choosing appropriate coordinates is of fundamental importance to ensure accurate results.

Carrier phase component removal: a generalized least-squares approach.

In fringe projection profilometry, an object shape is evaluated through phase distribution extracted from a projected fringe pattern. For parallel illumination geometry, the carrier phase component introduced by the fringes is spatially linear, whereas nonparallel illumination would lead to a nonlinear carrier. In this study, a general approach for the removal of a nonlinear-carrier phase component is proposed.

Determination of curvature and twist by digital shearography and wavelet transforms.

A new technique based on digital shearography for determining the transient curvature and twist of a continuously deforming object from a series of speckle patterns is presented. The intensity variation of each pixel is analyzed along the time axis by using a complex Morlet wavelet transform. The absolute sign of the phase variation is determined by introduction of a temporal carrier when the speckle patterns are captured by a high-speed camera.

Phase extraction from a single fringe pattern based on guidance of an extreme map.

A method for automatic phase extraction from a single fringe pattern based on the guidance of an extreme map is introduced. The method uses an adaptive weighted filter to reduce noise and enhance contrast and to locate the fringe extremes. Wrapped phase values are calculated by use of an arccosine function obtained from the extreme map.

Profiling of objects with height steps by wavelet analysis of shadow moiré fringes.

A temporal wavelet analysis algorithm is proposed for shadow-moiré-based three-dimensional surface profiling on objects having discontinuous height steps. A grating is positioned close to an object, and its shadow is observed through the grating. The moiré fringe patterns vary when the grating is in-plane rotating.

Surface profiling of a transparent object by use of phase-shifting Talbot interferometry.

Talbot interferometry is used to study the surface profile of a transparent object. Periodic patterns are produced by illuminating a grating with a collimated laser beam. The object is placed on the self-image plane of the grating.

Fringe-density estimation by continuous wavelet transform.

For many phase extraction algorithms, a priori knowledge of a fringe-pattern density distribution is beneficial for later processing. A fringe-density estimation method based on a continuous wavelet transform (CWT) is proposed. For a one-dimensional signal the instantaneous frequency detected at the CWT ridge is directly adopted as a measure of the local fringe density.

Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift.

A three-frame phase-shifting algorithm with a constant but unknown phase shift is proposed. The algorithm is based on background-intensity removal prior to phase retrieval to eliminate an undetermined factor in a fringe pattern. The proposed method is validated on three-dimensional profilometry by fringe projection and on deformation measurement by means of digital speckle shearing interferometry.

Grating projection system for surface contour measurement.

A grating projection system is a low-cost surface contour measurement technique that can be applied to a wide range of applications. There has been a resurgence of interest in the technique in recent years because of developments in computer hardware and image processing algorithms. We describe a method that projects a phase-shifted grating through a lens on an object surface.

Wavelet analysis of speckle patterns with a temporal carrier.

A novel temporal phase-analysis technique that is based on wavelet analysis and a temporal carrier is presented. To measure displacement on a vibrating object by using electronic speckle pattern interferometry, one captures a series of speckle patterns, using a high-speed CCD camera. To avoid ambiguity in phase estimation, a temporal carrier is generated by a piezoelectric transducer stage in the reference beam of the interferometer.

Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis.

A temporal wavelet analysis method is proposed for velocity, displacement, and three-dimensional surface-profile measurement of a continuously deforming object by use of the shadow moiré technique. A grating is placed close to a deforming object, and its shadow is observed through the grating. The moiré fringe patterns, generated by the interference of the grating lines and their shadows, are captured by a high-speed CCD camera with a telecentric gauging lens.

Measurement of a fiber-end surface profile by use of phase-shifting laser interferometry.

We describe a laser interferometric system in which two objectives are used to measure surface profile on a connectorized fiber-end surface. By the use of the proposed illumination design a He-Ne laser as a point light source is transformed to an extended light source, which is beneficial to localize interference fringe pattern near the test surface. To obtain an optimal contrast of the interference fringe pattern, the flat mirror with an adjustable reflection ratio is used to suit different test surfaces.

Spatial-fringe-modulation-based quality map for phase unwrapping.

The quality-guided algorithm is a method widely used in phase unwrapping. The algorithm uses a quality map to guide its unwrapping process, and its validity depends on whether the quality map can truly reflect phase quality. In fringe projection surface profilometry, discontinuous surface structure, low surface reflectivity, and saturation of the image-recording system are sources of unreliable phase data.

Height measurement of microchip connecting pins by use of stereovision.

A stereovision method for estimating the height of connecting pins on a microchip is described. The technique uses a centroidal method to simplify the calculation. A few seconds are required for a Pentium 586 PC to calculate the heights of 300 connecting pins on a 50 mm x 50 mm microchip.

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting.

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique.

Development of a laser-scattering-based probe for on-line measurement of surface roughness.

The design and properties of an optical probe for on-line measurement of surface roughness are discussed. Based on light scattering, a probe that consists of a laser diode, a measuring lens, and a linear photodiode array was designed to detect surface roughness, in which the light scattered from a test surface at a relatively large scattering angle phi (=28 degrees) can be collected to enhance measuring range and repeatability. A coaxial design that incorporates a dual-laser probe and compressed air makes the proposed system insensitive to the position of the test surface and to surface conditions such as the presence of debris, vibration, and lubricants that result from machining.

Proposed algorithm for phase unwrapping.

A new, to our knowledge, two-dimensional phase-unwrapping algorithm is proposed. The algorithm, which is based on the global continuity of physical information (e.g.