Spatial Carrier Frequency Research Articles

Recording a Hologram Transmitted over a Communication Channel on One Sideband

The paper presents experimental results on the recording and restoration of 3D holographic frames suitable for transmitting 3D holographic images with the frame rate required for TV images and a resolution of the Full HD standard and higher. The Patent RF No. 2707582 proposed a method for compressing holographic information and transmitting it using a procedure similar to SSB over conventional communication channels. In this work, the holographic information of a 3D portrait of a person, transmitted and received via the Wi-Fi communication channel, was restored in the form of a rainbow hologram, as one of a variety of holograms, by the computer addition of the carrier spatial frequency, and then hologram was actually produced on a photoresist. This technology can be used to create a holographic phototelegraph or, if there is a dynamic holographic display, to create a holographic television and 3D augmented reality.

INVESTIGATION OF THE METHOD OF DIRECT LASER WRITING OF OPTICAL ELEMENTS WITH BINARY HIGH-CONTRAST AMPLITUDE-PHASE TRANSMISSION

A method is proposed for formation on one substrate of two superimposed optical structures - a binary phase structure and an analog high-contrast amplitude structure made on a thick chromium film in the form of a regular two-dimensional zero-order diffraction grating with a variable fill-factor of cells. A numerical and experimental study of this method is carried out as applied to an optical transparency for generating the structure of a gamma-coupled laser beam. The quality of a high-contrast structure, suitable for practical application, was experimentally achieved, with an optical density of a chromium film of about 4.3, when measured at a wavelength of 532 nm, and with a minimum size of transparent and opaque windows of the order of 1x1 μm. This method can be used to synthesize amplitude-phase transparencies with a large alternating range of change in the amplitude optical transmittance, with a relatively slow (smooth) change in the transmittance (with the carrier spatial frequency of the amplitude modulation determined by the period of the above two-dimensional zero-order diffraction grating).

Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique* *Project supported by the National Natural Science Foundation of China (Grant No. 61705254) and the Key Research and Development Program of Shaanxi Province of China (Grant No. 2020GY-114).

The transient radial shearing interferometry technique based on fast Fourier transform (FFT) provides a means for the measurement of the wavefront phase of transient light field. However, which factors affect the spatial bandwidth of the wavefront phase measurement of this technology and how to achieve high-precision measurement of the broad-band transient wavefront phase are problems that need to be studied further. To this end, a theoretical model of phase-retrieved bandwidth of radial shearing interferometry is established in this paper. The influence of the spatial carrier frequency and the calculation window on phase-retrieved bandwidth is analyzed, and the optimal carrier frequency and calculation window are obtained. On this basis, a broad-band transient radial shearing interference phase-retrieval method based on chirp Z transform (CZT) is proposed, and the corresponding algorithm is given. Through theoretical simulation, a known phase is used to generate the interferogram and it is retrieved by the traditional method and the proposed method respectively. The residual wavefront RMS of the traditional method is 0.146λ, and it is 0.037λ for the proposed method, which manifests an improvement of accuracy by an order of magnitude. At the same time, different levels of signal-to-noise ratios (SNRs) from 50 dB to 10 dB of the interferogram are simulated, and the RMS of the residual wavefront is from 0.040λ to 0.066λ. In terms of experiments, an experimental verification device based on a phase-only spatial light modulator is built, and the known phase on the modulator is retrieved from the actual interferogram. The RMS of the residual wavefront retrieved through FFT is 0.112λ, and it decreases to 0.035λ through CZT. The experimental results verify the effectiveness of the method proposed in this paper. Furthermore, the method can be used in other types of spatial carrier frequency interference, such as lateral shearing interference, rotational shearing interference, flipping shearing interference, and four-wave shearing interference.

Метод формирования единственного сфокусированного порядка дифракции при помощи бинарных амплитудных дифракционных элементов без пространственной несущей

The method of synthesis of self-focusing amplitude DOE without the carrier spatial frequency working in divergent beams and forming single focused diffraction order which can occupy whole DOE reconstruction field because there is no necessity for spatial separation of diffraction orders, which is the case with holograms, is presented. Synthesis was carried out in two stages. The first one was carried out by the iteration algorithm similar to Gerchberg-Saxton algorithm, with those differences that synthesizable DOE is an amplitude one and incident wave front is divergent. Then the method of direct search with random trajectory was applied. As a result for binary amplitude DOE synthesis error of 6% and diffraction efficiency of 6% was achieved. Results of experimental DOE implementation using DMD are presented.

Amplitude-Modulated Leaky-Wave Antennas

Borrowing the idea of amplitude modulation from classical communications theory, this article proposes and demonstrates a new concept of amplitude-modulated (AM) leaky-wave antennas. In the proposed concept, the traveling wave in a wave-guiding structure serves as the carrier wave whose amplitude is spatially modulated by a predefined modulating waveform to generate the desired modulated waves. Two analysis methods are subsequently developed to analyze the amplitude modulation effects. It is demonstrated that spatial amplitude modulation corresponds to shifting the spatial spectrum of the modulating wave up to the carrier spatial frequency. Therefore, one can judiciously design the modulating waveform to control the spatial frequency spectrum of the modulated waves. The spatial frequencies fallen within the radiation region are fast waves, which can radiate into free space. In this manner, the AM structure works as a leaky-wave antenna. To justify the proposed concept, two AM leaky-wave antennas based on corrugated transmission line are designed. The first one is a sinusoidally modulated AM leaky-wave antenna for high-gain application. The second is a beam-forming AM leaky-wave antenna, whose modulating waveform is synthesized to generate flat-top radiation pattern. Both simulated and measured results are given to demonstrate the concept, theory, and design of the AM leaky-wave antennas.

Enhanced Fourier-transform method for high-density fringe analysis by iterative spectrum narrowing.

We propose a model-based fringe analysis technique that enables the Fourier transform method to analyze dense fringe patterns with large phase variations. The conventional Fourier-transform method has a limited dynamic range of measurable phase because the Fourier spectra broadened by large phase variations cannot be separated by the spatial carrier frequency. Our model-based iterative technique effectively narrows the broad spectrum and reduces phase errors. Results of simulations and experiments are presented that demonstrate the validity of the proposed spectrum-narrowing technique for high-density fringe patterns.

A computational phase-shifting interferometric method using a single-shot microinterferogram and its application

In this article, a fast computational phase-shifting interferometry (PSI) method for extracting the phase object from a single-shot two-beam microinterferogram has been proposed. This technique bases on utilizing the features of the two-beam microinterferometry to yield three daughter microinterferograms with accurately known phase shift between them from a recorded mother microinterferogram. The main idea of the proposed method relies on analyzing the recorded mother microinterferogram to compute the width of its bright and dark fringes which resulted equal in this study. Furthermore, we utilize the fact that the complete change from bright fringe to dark fringe or vice versa, in the two-beam microinterferogram, is identical to shift in phase by π radians. The proposed method is characterized by high ability to perform in-situ investigation for the objects on the contrary with the traditional PSI technique. The phase-shifting Pluta interference microscope is used for verifying this computational method for the polypropylene (PP) fiber. The calculated phase distribution values via this method show a good agreement with the obtained results by the phase-shifting Pluta interference microscope for the same fiber sample. Also, the proposed method is utilized to perform accurate in-situ investigation for the structural properties of the polypropylene fiber at different draw ratios. In addition, the proposed method is valid to investigate the fractures modes of fibers in short time comparing to the spatial carrier frequency algorithm and the spatial carrier-frequency phase-shifting (SCFPS) algorithm.

Shear-unlimited common-path speckle interferometer.

A single-aperture common-path speckle interferometer with an unlimited shear amount is developed. This unlimited shear amount is introduced when a Wollaston prism is placed near the Fourier plane of a common-path interferometer, which is built by using a quasi-${4f}$4f imaging system. The fundamentals of the shear amount and the spatial carrier frequency generation are analyzed mathematically, and the theoretical predictions are validated by a static experiment. Mode-I fracture experiments through the three-point bending are conducted to prove the feasibility and the capability of this method in full-field strain measurement with various shear amounts. A remarkable feature of this setup is that no tilt is required between the optical components to produce the unlimited shear amount in off-axis holography.

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

ABSTRACTShearography 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.

Automatic wavefront reconstruction on single interferogram with spatial carrier frequency using Fourier transform

Optical interferometry can be applied to obtain the wavefront phase and reconstruct the three-dimensional wavefront by analyzing interference fringes. Single interferogram analysis based on two-dimensional Fourier transform is proposed. This method just needs to acquire and analyze single interferogram to solve the wavefront phase. Compared with phase-shift method, Single interferogram analysis can reduce experiment cost and the limitation of measuring environment like vibration, airflow and noise, and meet the requirement of real-time and dynamic interferometry. Because the wavefront phase information is included in the carrier frequency components of single interferogram, an image edge detection method is used to automatically extract the center and boundary of the first-order carrier component of the spatial spectrum of the interferogram in the frequency domain.

Dual-channel interferometer for vibration-resistant optical measurement

A dual-channel interferometer (DCI) is proposed for vibration-resistant optical measurement. The DCI employs a dual-channel interference optical path design, wherein an assistant channel is used to generate dense fringe patterns by introducing a spatial carrier frequency, and the coefficients of the vibration tilt phase plane are then extracted. The sparse fringe patterns of the main channel are combined with the coefficients of the tilt phase plane to calculate the measured phase distribution. This study reports the optical path and principles of the interference system. Simulations are performed using the proposed DCI phase extraction algorithm. To verify the DCI performance, phase measurements are carried out in a vibrating environment, and the results obtained using the proposed method are compared with those obtained using spatial phase-shifting interferometry (SPSI). The experimental results demonstrate that the DCI can effectively overcome the effect of vibration. Unlike spatial carrier frequency interferometry, although the spatial carrier frequency is also introduced in the assistant channel in the proposed DCI method, the dual-channel information extraction algorithm helps eliminate the calibration process of the retrace error before measurement, making this a calibration-free measurement. Moreover, the DCI utilizes environmental vibration to generate a ‘phase shift’, thus not only eliminating the need for a vibration isolation platform but also the need for a precise phase shifting device, with advantages such as structural simplicity, ease of operation, and low cost.

Phase Extraction Algorithm Based on the Spatial Carrier-Frequency Phase-Shifting Gradient

For improving the accuracy and processing speed of phase extraction, a new phase extraction algorithm based on the spatial carrier-frequency phase-shifting gradient (SCFPS-G) is proposed. First, three-frame sub-interferograms along the direction of spatial carrier-frequency phase-shifting gradient (SCFPS-G), which can be constructed by the differential method from only one-frame spatial carrier-frequency interferogram (SCFI). And then, the measured phase will be extracted by unknown phase-shifting algorithms. Compared with the existing spatial carrier-frequency phase-shifting (SCFPS) algorithms, the proposed SCFPS-G algorithm not only can improve the efficiency of constructing sub-interferograms, but also decrease one-frame sub-interferogram requirement for phase extraction, so the data redundancy of interferogram and the influence of noise will be reduced. Specially, it is found even if the carrier frequency becomes very small, corresponding to the large spatial bandwidth utilization of image sensor, the proposed SCFPS-G algorithm still can work well. And the obvious advantages of the SCFPS-G algorithm in accuracy, processing time and feasibility of phase extraction can be demonstrated by the numerical simulations and the experimental results.

A spatial-phase-shift-based defect detection shearography system with independent adjustment of shear amount and spatial carrier frequency

Digital shearography has a wide application in defect detection. Phase-shift-technique-based shearography has a higher phase measurement sensitivity than the real-time shearography. This phase shift technique can be divided into temporal phase shift shearography and spatial phase shift shearography. The latter has the advantage of fast detection and can be used in dynamic detection. In a traditional spatial carrier frequency shearography system, shear amount adjustments and spatial carrier frequency are not completely independent. In some shearography systems, shear amount and spatial carrier frequency are adjusted by rotating mirrors. The amounts of rotation required to obtain the appropriate shear amount and spatial carrier frequency are different, thereby reducing the accuracy of detection results. In other shearography systems, although the two adjustments are divided into two parts, using a rotating mirror to obtain the appropriate shear amount will also introduce additional spatial carrier frequency which will also have some influence on the result. This paper introduces a detection method with independently adjusting shear amount and spatial carrier frequency. Shear amount adjustment is achieved by changing the written image of a spatial light modulator (SLM). No additional spatial carrier frequency is introduced. Spatial carrier frequency is only controlled by the relative position between the dual apertures. Experimental results of undamaged and damaged specimens indicate that this system is suitable for detecting the phase distribution of the deformation and internal defects.

Dual-sensitive spatial phase-shifting shearography based on a common-path configuration

A common-path spatial phase shifting digital speckle pattern shearing interferometry setup is introduced for simultaneous measurement of in-plane and out-plane strain components under dynamic loading using two laser beams with different wavelengths that symmetrically illuminate the test object and a single detector. The simplicity, stability, and efficiency of the arrangement are provided by using a glass plate as a shearing device, which is capable of tuning the sensitivity continuously. The phase is recovered from a single frame by the Fourier method. In this setup, the spatial carrier frequencies can be adjusted independent of the amount of the lateral shear. Ultimately, the desired field of view can easily be achieved by simple imaging optics. To validate the feasibility and the flexibility of our technique, the proposed setup is used to evaluate the in-plane and out-plane strain maps of an aluminum plate, which is deformed under dynamic stress in its plane. The temporal phase stability of the proposed system is also investigated.

Binary multi-order diffraction optical elements with variable fill factor for the formation and detection of optical vortices of arbitrary order.

In this paper we consider the calculation of binary diffraction optical elements (DOEs) for the formation and detection of optical vortices of arbitrary order. The synthesis of binary DOEs is based on a combination of the method of carrier spatial frequencies and binary coding with a variable fill factor. Unlike various methods of multiplication, the method of carrier spatial frequencies is characterized by great flexibility and versatility. It allows us to not only form the given field distributions in arbitrary diffraction orders, but also to give them arbitrary weight ratio (energy distribution in orders). As a rule, such universality leads to the need to form a complex amplitude-phase distribution in the input plane. To avoid this, in this paper it is proposed to use binary coding with a variable level. The effect of such coding is studied in detail both theoretically and numerically. It is shown that the level variation makes it possible to change the set of the observed diffraction orders. The positions and orders of the optical vortices formed are uniquely determined by the values of the carrying spatial frequencies and the topological charges of the vortices in the basic order. The results can be useful in optical communications.

Common-path spatial phase-shift speckle shearography using a glass plate

In this paper, a spatial phase shifting digital speckle pattern shearography setup based on a common path interferometer and modest components is proposed for direct measurement of dynamical deformation gradient of objects. The simplicity, stability, and efficiency of the setup are provided by employing a plane parallel glass plate as a shearing device. The desired field of view can easily be achieved by employing two lenses. Moreover, adjustable spatial carrier frequencies within the speckle pattern which is needed to evaluate the phase difference before and after deformation by Fourier transformation can easily be produced. Ultimately, the slope of the deformations on the test surface can be obtained with tunable sensitivity. To demonstrate our technique, the proposed setup is used to evaluate the phase change in a center-loaded aluminum plate. Experimental results for out of plane deformation gradient are presented and discussed.

Measurement of In-Plane Displacement in Two Orthogonal Directions by Digital Speckle Pattern Interferometry

The measurement of in-plane displacement in two orthogonal directions is of considerable significance for modern industries. This paper reports on a spatial carrier phase-shift digital speckle pattern interferometry (DSPI) for the simultaneous measurement of in-plane displacement in two orthogonal directions. The object is illuminated from a single direction and observed from four symmetrical directions simultaneously. One pair of the four observation directions is sensitive to in-plane displacement in one direction, and the other pair is sensitive to in-plane displacement in the perpendicular direction, resulting in the displacement in two directions being measured independently. The polarization property of light is used to avoid cross-interference between the two pairs of beams. Spatial carrier frequencies are generated by aperture misalignment, and the displacement in two directions is modulated onto the same interferogram. With a spatial carrier phase-shift technique, the displacement can be separated in the frequency domain and the phase can be evaluated from a single interferogram in real time. The capability of DSPI is described by theoretical discussions and experiments.

Fast and high precision spatial carrier frequency phase shifting algorithm based on the second order difference

A spatial carrier phase shifting algorithm based on the second-order difference (SCFPS-SD) is proposed. By numerically calculating the first and second order difference of one spatial carrier frequency interferogram (SCFI) and then using a normalization algorithm, the high accuracy of phase extraction will be obtained rapidly. Based on the original differential extraction phase (SCFPS based on derivative method, SCFPS-DM) method, the proposed SCFPS-SD algorithm does not need to calculate the carrier frequency in advance and the achieved result is not affected by the accuracy of the extraction carrier frequency algorithm. Compared with current SCFPS algorithm, the proposed algorithm reveals obvious advantage in calculation speed and precision even if the sample height, carrier frequency and noise level are greatly changed. Both advantages and effectiveness of the proposed SCFPS-SD algorithm can be demonstrated by simulation and experiment.

Spatial phase-shift digital shearography for simultaneous measurements in three shearing directions based on adjustable aperture multiplexing

Because the sensitivity of shearography is determined by its shearing direction, aeolotropic defects could be difficult to detect in nondestructive testing (NDT) using a digital shearography system with a single shearing direction. We report an adjustable aperture multiplexing spatial phase-shift digital shearography system for simultaneous measurement of displacement derivatives in three directions. By setting the aperture parameters properly, three spatial carrier frequencies are produced within the speckle pattern, and the information of three interferograms can be separated in the frequency domain. Phase maps of the three shearograms can be obtained by applying a windowed inverse Fourier transform, which enables simultaneous measurement of the displacement derivative. The system is suitable for NDT with a dynamic load. The capability of the triple-directional spatial phase-shift digital shearography system is described by theoretical discussions as well as experiments.

Classical Polarimetry with a Twist: A Compact, Geometric Approach

We present an approach to classical polarimetry that requires no moving parts; is compact and robust; and that encodes the complete polarization information on a single data frame, accomplished by replacing the rotation of components such as wave plates with position along a spatial axis. We demonstrate the concept with a polarimeter having a quarter-wave plate whose fast-axis direction changes with location along one axis of a 2D data frame in conjunction with a fixed-direction polarization analyzer, analogous to a classical rotating quarter-wave plate polarimeter. The full set of Stokes parameters is obtained, with maximal sensitivity to circular polarization Stokes V if a quarter-wave retarder is used. Linear and circular polarization terms are encoded with spatial carrier frequencies that differ by a factor two, which minimizes cross-talk. Other rotating component polarimeters lend themselves to the approach. As the polarization modulation spatial frequencies do not change greatly, if at all, with wavelength such devices are close to achromatic, simplifying instrument design. Because the polarimetric information is acquired in a single observation, rapidly varying, transient and moving targets are accessible, loss of precision due to sequential data acquisition is avoided, and moving parts are not required.