Development of speckle shearing interferometer error analysis as an aperture function of wavefront divergence

Increasing the confidence in whole-field speckle-based optical metrology transducers requires a detailed understanding of the error sources of the respective instruments. The analysis of error contributions to the optical phase output of a Michelson-based speckle shearing interferometer have been modelled. Specific attention has been paid to the effect of the aperture at the image plane, with respect to collimated and non-collimated object illumination. This modelling presents an advance on a previous modelled analytical relationship, which includes partial displacement derivative terms and components as a function of illumination geometries and, importantly, aperture effects. The work has identified a phase error contribution due to the aperture function of between 0.15% and 1.48%, dependent on the object distance, when considering a planar object undergoing predominantly surface to normal deformation.     

Carrier-modulated Object Step-loading Method of Automated Analysis in Digital Speckle Shearing Interferometry

Abstract

An object step-loading method has been recently reported to overcome the problems of phase unwrapping and decorrelation in digital speckle shearing interferometry. In this paper, a carrier modulation procedure is incorporated into the object step-loading method in order to improve the phase derivation accuracy. An added advantage with this approach is that the direction of deformation is also revealed.     

Multi-directional shearography based on multiplexed Mach–Zehnder interference system

ABSTRACT

Shearography is only sensitive to deformation in the shearing direction, and the deformation of object defects after loading may occur in multiple directions. This work reports a multi-direction shearography system that uses spatial phase-shift methods to detect the object from multi-shearing directions, effectively avoiding the missed detection of directional defects. A single laser is utilized to illuminate an object, and a single CCD camera records images in the multiplexed Mach–Zehnder interference system. First, the aperture stops in suitable size and location are set to produce different spatial carrier frequencies. Second, the shearing amount is independently adjusted by using different devices. Finally, the Fourier transform method is used to extract the phase information from the frequency domain. This system can be used for nondestructive testing of multi-directional defects and the feasibility of the method is verified by theoretical analysis and experiment.     

Spatial filtering in digital holographic microscopy

Abstract

An optical system based on digital holography suitable for microscopic investigations is described. A lensless digital hologram of the object under test is recorded on a CCD faceplate. The reference point source and the object are equidistant from the CCD. The point source for the illumination of the transparent microscopic object is located in another plane some millimetres behind the object. For digital reconstruction of the wavefronts the Sommerfeld propagation relation is used. The particular recording arrangement allows one to perform spatial filtering. Examples of amplitude filtering are presented.     

An illumination and highlights invariant colour model for image matching

Abstract

Colour can provide critical information for a variety of computer vision tasks such as image matching, object recognition and image retrieval. However, for it to be useful in practice, the colour model used to represent the intrinsic properties of the imaged objects must be insensitive of imaging conditions such as lighting geometry, illumination colour and highlights. In this paper, we present a colour model for image matching and object recognition that is invariant for illumination and highlights. The colour model is defined as the ratios of the colour differences between neighbouring pixels for each colour component. Based on the dichromatic reflection colour model, it is shown that the proposed colour model is invariant to lighting geometry, illumination colour, highlights and diffuse lighting. Experimental results show robust image matching using the proposed colour model on objects that are illuminated under different illumination colours and lighting geometry. The proposed colour model can be used as a prepossessing step for applications where limited or no constraints on the imaging process can be imposed.     

Interactive direct illumination in dynamic scenes using graphics APIS

Abstract

We present a progressive refinement system for rendering direct illumination at interactive rates for dynamic scenes using available graphics APIs. We achieve the progression by subdividing object surfaces using a quad‐tree approach. Integrating the visibility and illumination, we can render scenes with soft shadows, taking into account the BRDFs of the scene objects. Our system allows a user to specify the desired frame rates, and the system will achieve such rates with the available time budget. Our system can also render dynamic scenes where the system restores the initial meshes and calculates illumination, producing finer but accurate soft shadows during iterative refinements.     

Contouring by Electronic Speckle Pattern Interferometry Employing Divergent Dual Beam Illumination

Abstract

For contouring of large object surfaces by means of electronic speckle pattern interferometry divergent illuminations were used. A method to shift dual illumination beams was employed to obtain contour fringes. The relationship between the fringes and object depth does not have the same form as in the case of collimated illuminations. It shows that the original measurement data can be corrected. Theoretical analysis and experimental results are presented which are in agreement with each other.     

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.     

Sampling error analysis of Shack–Hartmann wavefront sensor with variable subaperture pixels

Abstract

The sampling error of a Shack–Hartmann wavefront sensor with variable subaperture pixels is analysed under the consideration of various threshold values and detecting dynamic ranges. A generalized expression, which is used for fitting the sampling error of a Shack-Hartmann wavefront sensor with variable subaperture pixels, is presented. The computational results of the sampling error of a Shack–Hartmann wavefront sensor with different pixel numbers per subaperture, different detecting dynamic ranges, different atmospheric coherence length, different extended degree of the object and the different threshold values are also given. The results indicate that the sampling error of the Shack–Hartmann wavefront sensor is sensitive to the dynamic range of the subaperture, the pixel numbers per subaperture, the extended degree of the object and the coherent length of atmosphere, but not sensitive to the threshold value.     

Investigating occupant safety through simulating the interaction between side curtain airbag deployment and an out-of-position occupant

The objective of this research is to elucidate the effect of side curtain airbag deployment on occupant injuries and safety when the occupant is either in-position or out-of-position (OOP). We used side impact vehicle collision simulations with a 1996 Dodge Neon model, which was further modified to include a side curtain airbag, a seatbelt, and a 50th percentile Hybrid III dummy. The airbag used in the study was inflated using both the uniform pressure (UP) and smooth particle hydrodynamics (SPH) methods. In-position and OOP simulations were performed to assess and establish guidelines for airbag aggressivity thresholds and occupant position versus risk of injury. Three different OOP scenarios (OOP1, OOP2, OOP3) were initially setup following the work of Lund (2003), then modified such that the dummy's head was closer to the airbag, increasing the chance of injury caused by the airbag. The resultant head acceleration as a function of time for in-position and OOP simulations shows that both UP and SPH methods produce similar peak accelerations in cases where the airbag is fully inflated prior to impact. In all cases, the head peak accelerations and the head injury criteria for simulations with an airbag were significantly lower when compared with the no airbag case, which would typically indicate that the use of an airbag results in improved occupant protection during side impact. However, in the case of OOP2 and OOP3, the neck flexion forces actually increase significantly when compared with the no airbag case. This finding indicates that the HIC and neck flexion forces criterion are in conflict and that there may be a tradeoff in terms of occupant injury/safety with a side curtain airbag that is strongly correlated to the occupant position. Consequently, this study shows that safety devices result in a significant effect on occupant injury/safety when the occupant is in OOP conditions. Moreover, in some cases, simulation results show that the side curtain airbag may not make the occupant safer. This study requires further investigation of the vehicle-specific airbag and its interaction with an occupant in various OOP conditions.     

Turbulence-induced zernike aberrations of optical wavefronts in partial adaptive compensation

Abstract

The residual phase error after correction for turbulence-induced phase aberrations by a partially compensating adaptive optics system with a laser guide star (LGS) as reference is computed by using the phase expansion on the Zernike polynomials. To get the most from the compensation, the limitation due to the actuator spacing of a deformable mirror, temporal lag and angular separation between the object and the LGS (anisoplanatism effect) have been analysed in this paper. If Fried's parameter r₀ is 10.7 cm, the temporal lag should be less than 2ms for a sodium LGS. Also the higher the aberration radial degree is, the less the actuator spacing is required. To correct for aberration of radial degree higher than 4 (if r₀ is 10.7 cm), the actuator spacing should be less than 300mm.     

Feature-specific structured imaging

We present a feature-specific imaging system based on the use of structured light. Feature measurements are obtained by projecting spatially structured illumination onto an object and collecting all the reflected light onto a single photodetector. Principal component features are used to define the illumination patterns. The optimal linear minimum mean-square error (LMMSE) operator is used to generate object estimates from the measured features. We study the optimal allocation of illumination energy into each feature measurement in the presence of additive white Gaussian detector noise and optical blur. We demonstrate that this new imaging approach reduces imager complexity and provides improved image quality in high noise environments. Compared to the optimal LMMSE postprocessing of a conventional image, feature-specific structured imaging provides a 38% rms error reduction and requires 400 times fewer measurements for a noise standard deviation of sigma = 2 x 10(-3). Experimental results validate these theoretical predictions.     

Interferometric fidelity of self-pumped phase conjugation in BaTiO3 and a four-wave mixing set-up with Bi12SiO20 using nanosecond pulses

Abstract

The fidelity of a self-pumped phase conjugating mirror (SPPCM) in the so-called cat configuration is studied with an interferometric method for a cobalt-doped barium titanate crystal (BaTiO₃:Co) under pulse illumination (8 ns, 532 nm). With this SPPCM a phase conjugating four-wave mixing set-up using the sillenite-type crystal Bi₁₂SiO₂₀ (BSO) was realized. It is shown that the fidelity of both phase conjugating processes under pulse illumination nearly reaches the fidelity of continuous-wave experiments.     

Object oriented matrix classes for use in a finite element code using C++

This paper presents a new method of writing finite element programs using the programming approach known as object oriented programming (OOP). More specifically, the C++ language is used to illustrate the key OOP concepts. In addition to the OOP finite element examples, a detailed discussion of OOP techniques in the creation of a generalized matrix library is presented. The C++ language is used in this paper because it is more suited to numerical programs than a pure OOP language such as Smalltalk. The efficiency, flexibility and maintainability of the C++ program are shown to be superior to a comparable version written in a non-OOP language, such as FORTRAN. The matrix library contains a number of matrix objects that are useful for specific types of matrix related problems. Different sparse storage schemes are implemented for each different type of matrix. A large number of functions are provided for each matrix type in order to implement many common matrix operations. In applications, the OOP paradigm allows the functions to be used in a very simple way that is common to all the matrix types. The sample finite element code included in this paper is primarily intended to illustrate the key concepts of OOP style. This paper explains how to set up a finite element hierarchy, material hierarchy and how to integrate this with the matrix hierarchy (library). Thus, a completely object oriented finite element program can be written.     

Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth

Abstract

Recording of holographic volume diffraction gratings in Du Pont's photopolymer HRS-150 is studied theoretically and experimentally. Particular attention is paid to the dynamics of the recording process. The temporal evolution of holographic gratings is monitored for a range of illumination intensities in two ways: (i) by means of a multiple-exposure approach when intensity profiles of recording beams are uniform, many holographic exposures are necessary and each exposure is carried out for a particular value of the total illumination intensity; (ii) by means of a single-exposure approach when intensity profiles of recording beams are strongly Gaussian and a volume grating with spatially distributed diffraction efficiency arises, depending on a local (average) value of the total illumination intensity. The second approach proves to be a useful tool providing us very quickly with qualitative information about the dynamics of the recording process while the first one, which is much more time-consuming, is more reliable for quantitative evaluations. The grating evolution is analysed theoretically by means of the well known photopolymerization-diffusion model. Discrepancies are found between the model and experimental results for low illumination intensities while qualitative agreement is found for higher intensities. For a given grating period, the discrepancies are interpreted in terms of insufficient change of the refractive index due to photopolymerization for low illumination intensities.     

A freeform optics design with limited data for extended LED light sources

Abstract

This paper proposes an optimization method for designing a freeform lens which can produce a good uniform circular illumination distribution and obtain high efficiency on the target plane. The initial surface profile of the freeform lens is calculated based on the laws of reflection and the energy conservation law, and then is fitted using the non-uniform rational basis spline (NURBS) method. The control points and weights are applied to parameterize the shape of freeform lens. The merit function for the optimization is defined as relative standard deviation (RSD) of the simulated illumination from the desired illumination and the efficiency of the lens. The simulation results indicate that the RSD is shown to be lower than 0.157, and maximum efficiency can be as high as 83.9%. In addition, it is demonstrated that this algorithm can obtain high uniform illumination distribution on the target plane with less variables. Compared with the conventional method, the simulation results show that the modified algorithm converges with less variables, good uniformity and high efficiency. Moreover, a freeform lens with different lighting patterns and non-rotational symmetry can be produced by the proposed method.     

High-speed impact of electromagnetically sensitive fabric and induced projectile spin

This work deals with the dynamic contact of a rigid body with a deformable electromagnetically sensitive fabric structure, represented by a network model. Of particular interest are the electromagnetically induced forces generated on the fabric, which are proportional to the external electric field (E ^EXT ) and the velocity crossed with the external magnetic field (v × B ^EXT ). These forces transmit reactions to the rigid contacting object, which can induce rotational motion. Modeling and simulation of this effect can be useful in ballistic shielding applications, because the rotation of an incoming, ogival, projectile allows it to be more easily impeded. A modular formulation for the deformation of impacted fabric structures, represented by a network model, is developed in this paper, characterized by (1) stretching of interconnected yarn networks, described by simple constitutive relations, including yarn damage, (2) interaction with impacting objects, incorporating contact with friction and (3) electromagnetic sensitivity and actuation, demonstrating how the Lorentz force can be harnessed to break symmetric deformation patterns in order to induce spin onto an incoming object, whether that object is electromagnetically sensitive or not.     

Gate‐Tunable and Multidirection‐Switchable Memristive Phenomena in a Van Der Waals Ferroelectric

Memristive devices have been extensively demonstrated for applications in nonvolatile memory, computer logic, and biological synapses. Precise control of the conducting paths associated with the resistance switching in memristive devices is critical for optimizing their performances including ON/OFF ratios. Here, gate tunability and multidirectional switching can be implemented in memristors for modulating the conducting paths using hexagonal α‐In₂Se₃, a semiconducting van der Waals ferroelectric material. The planar memristor based on in‐plane (IP) polarization of α‐In₂Se₃ exhibits a pronounced switchable photocurrent, as well as gate tunability of the channel conductance, ferroelectric polarization, and resistance‐switching ratio. The integration of vertical α‐In₂Se₃ memristors based on out‐of‐plane (OOP) polarization is demonstrated with a device density of 7.1 × 10⁹ in.^?2 and a resistance‐switching ratio of well over 10³. A multidirectionally operated α‐In₂Se₃ memristor is also proposed, enabling the control of the OOP (or IP) resistance state directly by an IP (or OOP) programming pulse, which has not been achieved in other reported memristors. The remarkable behavior and diverse functionalities of these ferroelectric α‐In₂Se₃ memristors suggest opportunities for future logic circuits and complex neuromorphic computing.     

Accurate Linewidth Measurements in Aperture Limited In-line Fraunhofer Holography

Abstract

Methods for accurate width analysis of line objects in aperture limited in-line Fraunhofer holography are described. One approach involves size correction utilizing the nature of the error commonly introduced. The other technique used involves measuring the width at a certain normalized intensity and not at the apparent edge. The general background is discussed in detail using an opaque object model.     

Hybrid retinal image registration using phase correlation

Abstract

This paper deals with registration of retinal images, which were taken by high-resolution digital colour fundus cameras. The proposed method describes successful application of phase correlation method. It combines several basic steps — global correction of shift, rotation and scaling, detection of landmarks, their correspondences and finally image registration using second-order polynomial model. The method is tested on two sets of images. The first set contains images from the diabetic patients where many retinal pathologies can disturb the registration process. The second set contains images from healthy subjects, which were acquired by different illumination conditions. The method was evaluated using four different criteria - tree objective and one subjective. These criteria are also compared. The achieved registration accuracy of the landmarks position error is 1·13 and 0·93 pixels for respective image sets. Finally, the simple scheme for retinal pathology visualisation of registered fundus pairs is presented.