Paraxial speckle-based metrology systems with an aperture

It has been shown that complex paraxial optical systems, consisting of various lens and distances of free space propagation, can be described using the Linear Canonical Transform (LCT). Indeed it can be shown that many well know optical transforms such as the Optical Fourier Transform (OFT), Optical Fractional Fourier Transform (OFRT), the effect of a lens or Chirp Modulation Transform (CMT) are all subsets of the more general LCT. Using the <i>ABCD</i> Collins matrix formula it is possible to represent these integral transforms in a simpler form, which facilitates system analysis and design. Speckle Photography (SP) in combination with an optical LCT can be used to measure surface motion of an optically rough body. It has previously been shown that Optical FRT's (OFRT) can be used in speckle based metrology systems to vary the range and sensitivity of a metrology system and also to determine both, the magnitude and direction, of tilting (rotation) and translation motion simultaneously, provided that the motion is captured in two separate OFRT domains. In this paper we extend the OFRT analysis to more general LCT systems and demonstrate how simultaneous tilt and translation measurements can be discerned from the speckle images captured prior to, and after motion. A spherical wavefront can be conveniently described using the Collin's matrix notation. By changing the wavefront of the illuminating light we show that we effectively change the domain of the LCT system without changing the bulk elements in the optical system. Thus the complete motion (in-plane translation and small surface tilting) of a rigid body can be determined using one optical LCT system and illuminating fields of varying curvature.

It has been shown that complex paraxial optical systems, consisting of various lens and distances of free space propagation, can be described using the linear canonical transform (LCT). Indeed it can be shown that many well know optical transforms such as the optical fourier transform (OFT), optical fractional fourier transform (OFRT), the effect of a lens or chirp modulation transform (CMT) are all subsets of the more general LCT. Using the ABCD Collins matrix formula it is possible to represent these integral transforms in a simpler form, which facilitates system analysis and design. Speckle Photography (SP) in combination with an optical LCT can be used to measure surface motion of an optically rough body. It has previously been shown that Optical FRT&apos;s (OFRT) can be used in speckle based metrology systems to vary the range and sensitivity of a metrology system and also to determine both, the magnitude and direction, of tilting (rotation) and translation motion simultaneously, provided that the motion is captured in two separate OFRT domains. In this paper we extend the OFRT analysis to more general LCT systems and demonstrate how simultaneous tilt and translation measurements can be discerned from the speckle images captured prior to, and after motion. A spherical wavefront can be conveniently described using the Collin&apos;s matrix notation. By changing the wavefront of the illuminating light we show that we effectively change the domain of the LCT system without changing the bulk elements in the optical system. Thus the complete motion (in-plane translation and small surface tilting) of a rigid body can be determined using one optical LCT system and illuminating holds of varying curvature.

As a new time-frequency transformation, linear canonical ambiguity function (AFL) which combined the inherent peculiarities of the linear canonical transform (LCT) with the ambiguity function (AF) can estimate the signal with cubic phase effectively. In this paper, a new method based on the time delay cancellation of the AFL to detect the weak moving target with cubic phase in sea clutter is proposed. The theoretical analysis and simulations show the correctness and effectiveness of the proposed method.

It has been shown that the method of digital dynamic speckle photography is an efficient method of quantitative and qualitative diagnostics in orthopedic stomatology for optimization of the constructions of cermet dentures by evaluating their stressed-strained state. Determination of the stressed-strained state of cermet dentures by the method of digital laser speckle photography at the stages of their manufacture makes it possible to most reliably investigate the quality of manufactured constructions, which diminishes the number of complications and improves the efficiency of treatment in orthopedic stomatology,

The availability of high quality Spatial Light Modulators (SLMs) and high-resolution cameras have made it technologically feasible to perform many optical signal-processing functions in a relatively inexpensive manner. Furthermore, recent fast algorithms have been proposed to compute Linear Canonical Transforms (LCTs), which may be used to simulate paraxial optical systems. Optical Encryption offers the possibility of high-speed parallel encryption of image data. Such encryption/decryption may involve the capture of full field information, i.e. phase and intensity. Applications of Digital Holography go beyond applications to optical encryption. They include Holographic Interferometry (metrology) and Holographic displays. In this paper we discuss the design and analysis of systems used in the capture, encryption/decryption and display of 2-D (image) data and present our recent experimental and theoretical results.

Measurement of out-of-plane deformation by combination of speckle photography and speckle shearing interferometry

Image watermarking using polar harmonic transform with parameters in [formula omitted

The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.

3D strain evolution in concrete using in situ X-ray computed tomography testing and digital volumetric speckle photography

The efficiency of different fuels in combustion processes has been an ongoing quest. Temperature measurements and color spectrum of premixed combustion flames are the accepted parameters to study. This work’s aim is to do so simultaneously, with a very simple setup and saving computational resources. This method does not ask to synchronize two sets of measurements, avoid the need for complicated setup alignments, and use a single digital camera. Instead, the temperature and color spectrum are measured simultaneously using digital laser speckle photography and an image processing approach. The recorded data for both measurements are acquired using only a color digital camera, where the red (r) color channel is used to record data for temperature measurements, and the blue (b) and green (g) color channels are utilized to record the flames’ color spectrum. To calculate the flames’ temperature field, the Abel inversion technique was carried out, while the image processing required crosstalk image correction, image segmentation, and image filtering. The crosstalk image correction is the main feature that establishes an unequivocal relationship between image color and color spectrum of flames. The technique was tested on flames produced with a liquefied petroleum gas fed torch using different equivalence ratios. The temperature values obtained with this method are in good agreement with those obtained with a thermocouple.

Interior strain analysis of a woven composite beam using X-ray computed tomography and digital volumetric speckle photography

Abstract: We explore the validity of moiré gap equation in terms of the digital speckle photography technique and show that the equation can be adapted to measure the shape or surface strain of curved objects. Examples of the utility of this approach are demonstrated using a spherical rubber ball.

Stress and strain homogeneity, in tested samples, is a crucial assumption during a dynamic test. Whenever this assumption is true, the conventional recovery of the mean strain and stress is valid. However, when the stress and strain fields in the sample are not homogeneous, more sophisticated treatment must be considered. Inverse problem techniques are then proposed. Nevertheless, they may yield a non-physical result. In this paper, a non-parametric solution to the problem of non-homogeneity in dynamic tests is presented. The stress field is deduced from the displacement field measured via a Digital Speckle Photography (DSP) technique and a force boundary condition.

Functional analysis of genes and proteins involved in wood formation and fiber properties often involves phenotyping saplings of transgenic trees. The objective of the present study was to develop a tensile test method for small green samples from saplings, and to compare mechanical properties of juvenile European aspen (Populus tremula) and hybrid aspen (Populus tremula × tremuloides). Small microtomed sections were manufactured and successfully tested in tension parallel to fiber orientation. Strain was determined by digital speckle photography. Results showed significantly lower values for juvenile hybrid aspen in both Young’s modulus and tensile strength parallel to the grain. Average Young’s moduli spanned the ranges of 5.9–6.6 and 4.8–6.0 GPa for European aspen and hybrid aspen, respectively. Tensile strength was in the range of 45–49 MPa for European aspen and 32–45 MPa for hybrid aspen. The average density (oven-dry) was 284 kg/m3 for European aspen and 221 kg/m3 for hybrid aspen. Differences in mechanical properties correlated with differences in density.

How to reveal subsurface defects in Kevlar® composite materials after an impact loading using infrared vision and optical NDT techniques?