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• The parametric imaging model of the zoom micro vision system including ETL was established, in which the internal parameters were related to the input focal power of the ETL. • A unique image acquisition scheme that can greatly save the workload of image acquisition, and a corresponding feature extraction algorithm based on frequency domain were developed. • Details on how to calculate the initial value of the parameters in the imaging model and how to optimize these parameters globally were presented. For zoom micro-vision system containing electrically tunable lens (ETL), traditional calibration methods are usually ineffective or inefficient due to the limited field of view (FOV) and shallow depth of field (DOF). This article proposes a novel calibration method that can overcome these problems. Firstly, the geometric imaging model of the zoom micro-vision system considering the input focal power is established. Subsequently, a unique image acquisition scheme and the corresponding feature extraction algorithm developed in frequency domain are given, which can greatly reduce the calibration workload. In addition, how to calculate the initial value of the parameters in the imaging model and how to optimize these parameters globally are presented. Finally, calibration experiments including the comparisons with traditional multi-focus and fitting methods are designed and implemented. Experimental results show that the proposed method has good consistency and accuracy when calibrating at different focal intervals, and the average reprojection error is less than 0.25 pixels. Comparative experiments show that the traditional multi-focus and fitting methods not only need more calibration images and the auxiliary high-precision positioning stage, but also have poor applicability for zoom micro-vision systems in practical. [ABSTRACT FROM AUTHOR]

Highlights • We present a cryptosystem where the encryption key is a random reference beam. • The implemented cryptosystem allows improving the recovery image quality. • The whole input plane size is used for projecting the object to be encrypted. • A key rotation protocol for multi-user environment was implemented. • All the results presented are obtained with an optical experimental setup. Abstract The secure managing of sensible data is one of the main challenges nowadays. During the last years several advances have demonstrated the ability of optical encrypting systems to protect information. In spite of these developments, there are some evident issues to be solved. One of the main concerns is the limitation of the experimental cryptosystems in the size of the inputs that can be properly protected and recovered by the encrypting system. In the case of the experimental joint transform correlator (JTC) cryptosystem, the data to be encoded and the key are placed side by side in the input plane. Therefore, the size of the object to be encrypted is limited by the size of the encryption key and the separation between the input and the key. This limitation leads to degradation on the recovered data according the size and the spatial frequencies content of the object for a given recording media. In this work we experimentally implement an interferometric cryptosystem in which the encryption key is a ground glass diffuser (GGD) located in the reference arm. In the object arm, the information to be encoded is displayed in a spatial light modulator (SLM) and placed in contact with another GGD. This system allows the projection of the input object in the whole SLM area. The encryption process results from the interference between the reference beam and the Fourier transform of the input object plane. We experimentally analyze the quality of the decrypted object in relation with the size of the input original object. Then, we compare the performance of this system with the JTC cryptosystem. Finally, we implement a protocol for a multi-user environment under the rotation of the key. Experimental results show the viability, versatility and applicability of the proposal. [ABSTRACT FROM AUTHOR]

An advanced Fourier transform analysis ( AFTA ) method is proposed in this study for phase retrieval from a single-shot spatial carrier fringe pattern ( SCFP ). It firstly extracts four phase-shifted fringe patterns ( FP ) from the SCFP with one pixel malposition, and then performs Fourier transform to each of them for their Fourier spectrums. The innovation of AFTA is making a subtraction in frequency domain directly to calculate the spectrum difference, which can generally eliminate the direct current component, thus it could mitigate the spectrum leakage problem and the edge error of traditional Fourier transform analysis ( FTA ) method significantly. After that, by making an inverse Fourier transform to the spectrum difference and a simple average operation, the phase information could be reconstructed conveniently. The time cost is approximately twice of FTA , which is still highly efficient and time-saving for dynamic or real-time measurement. AFTA is adequately validated as a promising method in fringe analysis by various simulations and comparative experiments, with emphasis of this study on its performance in terms of accuracy, noise-tolerance, carrier frequency, time cost, etc. [ABSTRACT FROM AUTHOR]

• Automatically detection of the correct sign of non-monotonous displacements in TSPI without using a temporal carrier. • Sign ambiguity resolved due to a function that determines the correct sign of the displacement between two consecutive speckle interferograms. • The performance of the method is determined through a numerical analysis. • Results are also compared with those obtained using three different phase recovery techniques. • Results obtained from the processing of experimental data are finally presented. In this paper, we present a generalized function to automatically detect the correct sign of non-monotonous displacements in temporal speckle pattern interferometry without the introduction of a temporal carrier in the optical setup. This approach can be used with any phase retrieval technique. Here, when the phase change is evaluated, the sign ambiguity is resolved due to a function that determines the correct sign of the displacement between two consecutive speckle interferograms. The errors introduced by the proposed function are determined using computer-simulated speckle interferograms, and its performance is analyzed using three phase recovery techniques and different phase distributions and average speckle sizes. A relation between the sliding window used to compute the correct sign and the speckle sizes is also presented. Finally, the presentation is illustrated with an experimental application of the proposed method to detect the correct sign of the out-of-plane displacement field of a metal plate. [ABSTRACT FROM AUTHOR]

In recent years, InfraRed Thermography (IRT) has become a widely accepted non-destructive testing technique to evaluate the structural integrity of composite sandwich structures due to its full-field, remote, fast and in-service inspection capabilities. This paper presents a novel infrared thermographic approach named as Golay complementary coded thermal wave imaging is presented to detect disbonds in a sandwich structure having face sheets from Glass/Carbon Fibre Reinforced (GFR/CFR) laminates and core of the wooden block. [ABSTRACT FROM AUTHOR]

The orthogonal fringe projection technique has as wide as long practical application nowadays. In this paper, we propose a 3D shape retrieval method for orthogonal composite fringe projection based on a combination of variational image decomposition (VID) and variational mode decomposition (VMD). We propose a new image decomposition model to extract the orthogonal fringe. Then we introduce the VMD method to separate the horizontal and vertical fringe from the orthogonal fringe. Lastly, the 3D shape information is obtained by the differential 3D shape retrieval method (D3D). We test the proposed method on a simulated pattern and two actual objects with edges or abrupt changes in height, and compare with the recent, related and advanced differential 3D shape retrieval method (D3D) in terms of both quantitative evaluation and visual quality. The experimental results have demonstrated the validity of the proposed method. [ABSTRACT FROM AUTHOR]

A new method based on the shearlet transform is presented for phase extraction in fringe projection profilometry (FPP) from a single fringe pattern. We apply the advanced shearlet transform to the fringe pattern to obtain the transform coefficients, and extract the fundamental frequency component of the fringe pattern in the 2-D frequency domain. We test the introduced method on a simulated pattern and two actual objects with edges or abrupt changes in height. The results show that the proposed method is more effective and accurate than the Fourier transform method and wavelet transform method. [ABSTRACT FROM AUTHOR]

Abstract: Phase retrieval from single frame projection fringe pattern is of fundamental importance, and is also a challenging problem in fringe projection measurement. In this paper, we present a new method for phase retrieval from a single frame projection fringe pattern based on variational image decomposition (VID) methods. We propose a new image decomposition model TV-G-Shearlet in order to effectively split a projection fringe pattern into background part, fringe part and noise part. The performance of the proposed approach is verified by simulated and real projection fringes as well as the comparison with the widely used and well-known Fourier transform method and wavelet transform method. [Copyright &y& Elsevier]

Abstract: The measurement of the diameter change of a piezoelectric transducer (PZT) cylinder with the white-light interferometry is proposed and experimentally demonstrated. One arm of a Mach–Zehnder interferometer (MZI) is wrapped on the PZT cylinder, and the phase change of the interferogram of the MZI is used to determine the diameter change when a DC voltage is applied on the PZT cylinder. The Fourier transform white-light interferometry is used for recovering the phase change of the interferometer. The experimental results show that the diameter change resolution of 0.8nm for the PZT cylinder with diameter of 40mm is achieved. [Copyright &y& Elsevier]

• Crossed fringes provide an optional solution which requires only one pattern in each position for camera calibration • The addition of some markers in crossed fringes pattern can establish a unique world coordinate system. • we use global coding, and we can arbitrarily select the feature points of different regions (non-overlapping region, overlapping region or the region contained by both) for calibration to obtain calibration parameters. Stereo cameras have been widely used for three-dimensional (3D) imaging, and their performances are highly depended on the calibration accuracy. This paper presents a marked-crossed fringe pattern for the calibration of stereo cameras. Some coded markers are also encoded into the crossed fringe pattern, and the feature points are encoded into the carried phase. Two wrapped phase maps are recovered by using the Fourier transform, and the markers are extracted and decoded for absolute phase unwrapping. Referring to the absolute phase values, the one-to-one mapping between the world points and the image points can be established to calibrate the stereo cameras. Compared with the traditional method, the proposed method adopts global coding, which can flexibly select any part of the feature points for calibration and obtain high-precision camera parameters. Simulations and experiments show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract: Phase demodulation techniques from one fringe pattern have been widely studied because it can measure dynamic objects by capturing single image. These techniques mainly include Fourier transform (FT), windowed Fourier transform (WFT), and wavelet transform (WT). FT has been widely used to demodulate phase information from single deformed fringe pattern on smooth objects. However, for objects having discontinuities and/or large slopes, FT cannot obtain correct phase at the edges because of its global processing. WFT and WT have been applied to nonstationary fringe pattern analysis. Since local fringe information used to extract phase information, WFT and WT are better than FT for phase calculation at discontinuities and/or slopes. In this paper, we discuss the pro and con of the three methods on phase calculation at discontinuities and/or slopes. Simulated and experimental data are tested at edges in order to confirm which method is appropriate to measure objects having discontinuities by using one-frame fringe pattern acquisition method. [Copyright &y& Elsevier]

Abstract: The four phases stitching algorithm is proposed to demodulate the circular carrier interferogram, which can eliminate the sign ambiguity and avoid serious local errors in the Fourier transform method. A pair of orthogonal low-pass filters is used to obtain four demodulated phases with local errors concentrated in different areas, then their reliable parts are chosen and combined to get the phase without sign ambiguity by a stitching strategy, which makes a significant error suppression. Furthermore, due to the stitching strategy the sign flip location just needs to be detected approximately, therefore the detection can be done using an automatic procedure. The algorithm is validated by the numerical simulations, where the calculation precisions are better than λ/50 with suitable carrier. Besides, an actual interferogram is analyzed and the result is in good accordance with the Zygo phase-shifting interferometer. [Copyright &y& Elsevier]

Abstract: For checking the collimation of an optical beam Fourier fringe analysis has been incorporated into the wedge plate interferometric setup. Typical interferograms corresponding to ‘in-focus’, ‘at-focus’ and ‘out-of-focus’ positions of an optical beam have been recorded. As per the testing procedure, FFT of the recorded interferometer is computed digitally, and necessary processing for direct determination of phase is undertaken. Finally, the phase data is unwrapped and plotted as a function of pixel position along the direction perpendicular to the shear. The slope of the phase provides the information regarding collimation position of the collimator. As the collimation position is detected by the direct measurement of the phase over the whole area of the interferogram, high accuracy, reliability and precision are achieved. [Copyright &y& Elsevier]

Abstract: Fringe projection profilometry is widely used for three-dimensional (3-D) surface shape measurement using phase-shifting (PS) methods with multiple images or transform methods with single projected fringe pattern. In this paper, phase extraction methods from a single fringe pattern using different transform methods are compared using both simulations and experiments. The principles of Fourier transform (FT), windowed Fourier transform (WFT) and wavelet transform (WT) methods for fringe pattern processing are introduced. Implementation of 1-D and 2-D algorithms and phase compensation are discussed. Noisy and non-sinusoidal waveforms are involved into this comparison. The merits and limitations of each of these processing methods are indicated. [Copyright &y& Elsevier]

Abstract: A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms. [Copyright &y& Elsevier]

Abstract: The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders). [Copyright &y& Elsevier]

Abstract: For full-field phase measurement methods, many algorithms have been developed to extract a phase map from fringe image(s). Both phase wrapping and unwrapping algorithms have been extensively investigated by many researchers, but few papers can be found on how to calculate the coordinates of surface points from a phase map. This paper focuses on algorithms that show how a phase map can be used to calculate coordinates. Details are given for single image methods such as Fourier transform, spatial carrier methods, and multiple image methods like traditional phase-shifting methods. Algorithms that can be used to convert a phase map to coordinates and some issues related to these conversion algorithms are discussed. An artifact is measured using these phase measurement methods. The results show that using the correct algorithm to convert a phase map to coordinates is a key to obtaining accurate measurement results. [Copyright &y& Elsevier]

A simplified approach is presented, to obtain two-channel computer-generated holograms of detour type. The method allows effectively to handle up to two flat objects (two digitized images), in x and y directions. The experimental results demonstrate the effectiveness of the suggested procedure. [Copyright &y& Elsevier]

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented. [Copyright &y& Elsevier]

The Fourier transform method, widely applied in photomechanics for the automated analysis of interferometric fringe patterns, has been recently extended to the photoelastic isochromatic fringe patterns analysis. Unfortunately, its use in photoelasticity involves some limitations that have not been completely highlighted in literature. This work deals with the influence of the quarter-wave plate tolerance on the evaluation of the retardation. Both theoretical and experimental analyses have shown that the quarter-wave plate error does not affect the retardation only if the principal stress directions in the model and in the carrier are aligned. In general, instead, the tolerance of the quarter-wave plates leads to an amplification of the retardation error due to the influence of the isoclinics with a subsequent restriction of the field in which the method can be applied. For instance, using common quarter-wave plates and tolerating a maximum retardation error of about 0.03 fringe order, than the Fourier transform method cannot be applied as a full-field technique but only in the model zones in which the misalignment between the principal stresses in the model and in the carrier is less than 15°. [Copyright &y& Elsevier]

• Thes security of a nonlinear cryptosystem based on DRPE is analyzed • Shortcomings of the method are discussed and new constrains are highlighted • Modified chosen-plaintext attack and known-plaintext attack is proposed to crack the nonlinear cryptosystem • The numerical simulation results have been discussed for the proposed attack algorithms In this paper, security of a nonlinear optical cryptosystem based on double random phase encoding (DRPE) is analyzed. In the cryptosystem, a time-varying nonlinear term is combined with the classical DRPE technique to enhance security. The advantages of the nonlinear term are its easy distribution and no effect on the decrypted image. Also, it is confirmed that the method is resistant to conventional plaintext attacks such as known-plaintext attack, chosen-plaintext attack, and ciphertext only attack. However, our security analysis shows that the method is vulnerable to the modified chosen-plaintext, and known-plaintext attacks. The original image can be recovered successfully using the proposed attack algorithms. Numerical simulation results are presented to validate the proposed attack methods and test effectiveness of our analysis. [ABSTRACT FROM AUTHOR]

• Compact, low-cost system capable of Digital Holographic Interference Microscopic (DHM) imaging of immobilized micro-particles including cells. • System developed from off the shelf optical and imaging components. • A simple glass plate provides quantitative phase images of trapped particles. • A low-cost QPD developed for corner frequency measurement of trapped particles. • Low cost alternative to observe and quantification, characterization, discrimination and sorting of cells in their natural environment A compact and low-cost system capable of Digital Holographic Microscopic (DHM) imaging of immobilized micro-particles is presented. The proposed design, integration, and manufacturing can lead to wider use and increased accessibility of this device for research, education, and biomedical applications. The optical tweezer system for particle immobilization is built using the optical pickup unit taken from a DVD burner. DHM is integrated into the system through the addition of a glass plate which enables one arm of the system to operate as a lateral shearing digital holographic interferometer. The operation of the system is confirmed by trapping, quantitative phase imaging and analysis of polystyrene micro-spheres for which the corner frequency measurements, carried using an in-house developed low-cost Quadrant Photodiode, compare favorably with simulated results. Furthermore, the system is illustrated for trapping and simultaneous quantitative phase imaging of micro-particles, including biological specimen such as red blood cells. The use of a low-cost easily implementable DHM integrated optical tweezer system provides vast information content, which enable in-depth analysis of immobilized micro-particles. [ABSTRACT FROM AUTHOR]

• A new technology combines the characteristics of time-domain ghost imaging and a Fourier transform to directly obtain the spectral information of the signal. • The time-varying light intensity with a definite sinusoidal and cosine distribution is employed. • Very simple, inexpensive and robust design of experimental setup. In a traditional time-domain ghost imaging system, it is necessary to employ a Fourier transformation to obtain the spectral information of a signal when the time-domain signal is recovered. In this paper, a new technology combines the characteristics of time-domain ghost imaging and a Fourier transform and uses the time-varying light intensity, which has a definite sinusoidal and cosine distribution, to directly obtain the spectral information of the signal according to the detection intensity information. The experimental results demonstrate the effectiveness of the proposed method. Fourier-temporal ghost imaging combines the advantages of time domain ghost imaging and Fourier spectrum analysis has important applications and scientific value in the fields of weak and instantaneous signal acquisition and analysis. [ABSTRACT FROM AUTHOR]

• Optical coherence tomography (OCT) allows for 3D imaging of living tissue. • OCT can be modified to provide spectroscopic information (sOCT - spectroscopic OCT). • Spectral and time domain optical coherence spectroscopy is a new sOCT technique. • STdOCS can be regarded as a bridge between OCT and Fourier transform spectroscopy. We propose a novel method for spectroscopic optical coherence tomography (OCT). This method uses the dependence of the Doppler frequency spectrum on the wavenumber. Controlled modulation of the light in the spectral OCT interferometer allows for an instantaneous depth-resolved reconstruction of the backscattered light spectrum from all depths. The feasibility of the spectroscopic analysis using the proposed scheme was confirmed experimentally. [ABSTRACT FROM AUTHOR]

• Fourier transform based feature detection method robust against to defocusing. • Both of the centers and corners can be extracted as feature points. • Two-stage calibration framework can obtain more precise calibration results. • Potential usage in camera calibration for long-distance photogrammetry. Clear and focused pattern images are essential prerequisites for accurate feature detection in traditional camera calibration methods, which introduce numerous limitations in various areas, such as long-distance photogrammetry. A feature detection method robust against defocusing is proposed for extracting the centers or corners of a planar square periodic target. A Fourier transform is employed to calculate two wrapped phase maps from the periodic target images, which are then used to accurately extract the feature points. The calibration procedure is divided into two stages to obtain more accurate results. A rough calibration is performed to calculate the rotation angles between the target and the camera. If the tilt angle is larger than 12°, the corresponding images are removed. Subsequently, the remaining images are used for precise calibration. The simulations and the experiments demonstrate that the proposed method can accurately calibrate a camera with a planar square periodic pattern, even in the case of severe defocusing. [ABSTRACT FROM AUTHOR]

• The pattern-illuminated Fourier ptychography and biometric features are introduced to implement the optical image encryption. • The chaotic parameters can replace the random phase masks to serve as secret keys, which facilitates the management and transmission of the secret keys. • The fingerprint and illumination pattern can further enhance the security of the encryption scheme. An optical image encryption scheme based on chaotic fingerprint phase masks (CFPMs) and pattern-illuminated Fourier ptychography (FP) is proposed. During the encryption process, the primary image that is under the non-uniform intensity patterns' illumination can be encrypted into multiple low-resolution intensity images with the CFPMs placed respectively at the input plane and the Fourier plane. And during the decryption process, the primary image can be recovered from these encrypted images with a Fourier ptychographic recovery algorithm and CFPMs. In this proposed image encryption scheme, the fingerprint image and the chaotic parameters are served as secret keys directly, and the CFPMs are just used as interim variables and functions. If the fingerprint image is shared by the sender and the authorized receiver, the security of the proposed image encryption scheme will be enhanced greatly, and the management and transmission of the secret keys will also become convenient to some extent. Additionally, the illumination pattern can also act as an additional secret key. Numerical simulations have been performed to verify the feasibility, security and robustness of the proposed image encryption scheme. [ABSTRACT FROM AUTHOR]