Spatial Carrier Frequency Research Articles

Enhancing the Spin Hall Effect of Cylindrically Polarized Beams.

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate.

Adaptive phase-shifting interferometry based on a phase-shifting digital holography algorithm.

Phase-shifting interferometry (PSI) requires accurate phase shifts between interferograms for realizing high-accuracy phase retrieval. This paper presents an adaptive PSI through synchronously capturing phase shifts measurement interferograms and phase measurement interferograms, in which the former is a series of spatial carrier frequency phase-shifting interferograms generated by an additional assembly and the phase shifts are calculated with the single-spectrum phase shifts measurement algorithm (SS-PSMA), the latter is employed for phase retrieval with an adaptive phase-shifting digital holography algorithm (PSDHA) based on complex amplitude recovery. In addition to exhibiting excellent reliability, high-accuracy phase retrieval (0.02 rad), and short calculation time (<25 ms), the proposed adaptive PSDHA is suitable for various interferograms with different fringe shapes and numbers. Importantly, both simulation analysis and experimental result demonstrate that this adaptive PSI based on PSDHA can effectively eliminate phase-shifting errors caused by phase shifter and external disturbance, ensuring high-accuracy phase shifts measurement and phase retrieval, meanwhile significantly reducing phase-shifting interferograms acquisition time and phase retrieval calculation time.

Single-shot measurement of the Jones matrix for anisotropic media using four-channel digital polarization holography.

Dynamic measurement of the Jones matrix is crucial in investigating polarization light fields, which have wide applications in biophysics, chemistry, and mineralogy. However, acquiring the four elements of the Jones matrix instantly is difficult, hindering the characterization of random media and transient processes. In this study, we propose a single-shot measurement method of the Jones matrix for anisotropic media called "four-channel digital polarization holography" (FC-DPH). The FC-DPH system is created by a slightly off-axis superposition of reference light waves, which are modulated by a spatial light modulator (SLM), and signal light waves that pass through a Ronchi grating. The SLM enables flexible adjustment of the spatial carrier frequency, which can be adapted to different anisotropic media. The four elements of the Jones matrix can be obtained from the interferogram through the inverse Fourier transform. Optical experiments on anisotropic objects validate the feasibility and accuracy of the proposed method.

Real-Time Laser Interference Detection of Mechanical Targets Using a 4R Manipulator.

In this study, a laser interferometric sensing measurement (ISM) system based on a 4R manipulator system is developed to achieve detection of mechanical targets, which aims to realize the real-time, online detection of workpieces with high precision during processing. The 4R mobile manipulator (MM) system is flexible and can move in the workshop, aiming to preliminarily track the position of the workpiece to be measured and locate it at millimeter level. The reference plane of the ISM system is driven by piezoelectric ceramics with the spatial carrier frequency realized and the interferogram obtained by a charge coupled device (CCD) image sensor. The subsequent processing of the interferogram includes fast Fourier transform (FFT), spectrum filtering, phase demodulation, tilt elimination for wave-surface, etc., so as to further restore the surface shape of the measured surface and obtain the surface quality indexes. A novel cosine banded cylindrical (CBC) filter is used to improve the FFT processing accuracy, and a bidirectional extrapolation and interpolation (BEI) technique is proposed for the preprocessing operation of real-time interferograms before FFT processing. Compared with the results from a ZYGO interferometer, the real-time online detection results show the reliability and practicability of this design. The relative error of peak-valley value reflecting the processing accuracy can reach about 0.63%, with the root-mean-square value reaching about 1.36%. Some possible applications of this work include the surface of mechanical parts in the process of online machining, the end face of shaft-like structures, annular surfaces, etc.

An improved fourier transform method for measuring thermal boundary layer temperature field using fringe extrapolation

Using Gerchberg fringe extrapolation as the interferogram preprocessing, we improve the spatial carrier Fourier transform method (FTM) for measuring temperature field of the thermal boundary layer. Since the fringes abruptly disappear on the solid boundary, large ripples may occur in the retrieved phase/temperature if the original interferogram is directly analyzed by the FTM. Using the extrapolated interferogram, the edge effect can be shifted to the region near the virtual extrapolated boundary, so the ripples are significantly reduced near the physical solid boundary. In our interference experiment, the spatial resolution of the interferogram is 5.47 μm. Through adjusting the fringe density, a large enough spatial carrier frequency can be obtained to void frequency aliasing for high temperature gradient measurement. We first validate the proposed FTM through the measurement of a stagnant air layer between a hot upper plate and a cold lower plate. In comparison with temperatures measured by the thermocouple, the maximum difference is less than 0.3 °C for temperature measurement and 2% for local temperature gradient measurement. We then study the free convection of a hot vertical plate. Through the temperature field measurement, we obtain the local heat transfer coefficient and the Nusselt number. Compared to the similarity solution, the deviation of the local Nusselt number is 2%–6%, except the upper and lower edge regions. The proposed method can also be used to capture the transient temperature field for further studying the convection formation and evolution.

Noise-resistant two-wavelength interferometry for single-shot measurement of high-gradient flows

This paper presents a new robust approach to measuring dynamic phenomena with high gradients using two-wavelength high-speed interferometry. A multiplexed interferogram with two different wavelengths and spatial-carrier frequencies is captured by a single high-speed camera shot. Quantitative processing of the interferogram is based on Fourier analysis, which is followed by a robust procedure to retrieve the unwrapped phase map with single-wavelength accuracy but with an extended range of unambiguity. This method is significantly more noise-resistant than the standard two-wavelength technique, which is sensitive to noise and synthetic phase distortion. The method was successfully applied to studying shock waves in a transonic compressor blade cascade in an industrial aerodynamic laboratory, where single-wavelength and standard two-wavelength approaches fail.

A novel scheme for ultrashort terahertz pulse generation over a gapless wide spectral range: Raman-resonance-enhanced four-wave mixing

Ultrashort energetic terahertz (THz) pulses have created an exciting new area of research on light interactions with matter. For material studies in small laboratories, widely tunable femtosecond THz pulses with peak field strength close to MV cm−1 are desired. Currently, they can be largely acquired by optical rectification and difference frequency generation in crystals without inversion symmetry. We describe in this paper a novel scheme of THz pulse generation with no frequency tuning gap based on Raman-resonance-enhanced four-wave mixing in centrosymmetric media, particularly diamond. We show that we could generate highly stable, few-cycle pulses with near-Gaussian spatial and temporal profiles and carrier frequency tunable from 5 to >20 THz. They had a stable and controllable carrier-envelop phase and carried ~15 nJ energy per pulse at 10 THz (with a peak field strength of ~1 MV cm−1 at focus) from a 0.5-mm-thick diamond. The measured THz pulse characteristics agreed well with theoretical predictions. Other merits of the scheme are discussed, including the possibility of improving the THz output energy to a much higher level.

Conjugate complex function coupling strategy of interferometric field: Synthetic-wavelength interferometric fringe extraction in simultaneous dual-wavelength interferometry

Simultaneous dual-wavelength interferometry (SDWI) supplies a better solution to extend the measurement range of traditional single-wavelength interferometry with higher efficiency. To decompose the needed longer beat-frequency synthetic-wavelength (λS) information from the generated moiré fringe pattern in SDWI, a conjugate complex function coupling strategy (CCFC) of interferometric field is proposed in this study. By the Fourier transform and the half-band filter in one side of the spectrum, the positive half spectrum is obtained. The inverse Fourier transform and conjugate operation are performed on the half spectrums to obtain the two conjugate complex functions of the interferometric field. Coupled by the multiplication for the conjugate complex functions, the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. And if the SDWI is implemented with the π/2 phase shift at λS, the obtained phase-shift interferogram for λS could be demodulated by the conventional phase-shift algorithm. Compared with other spatial-domain Fourier transform demodulation theory, the half-band filter used in CCFC method is appropriate for the different spectral width and carrier spatial frequency. The necessary introduced linear carrier is merely about 0.0947 times of the carrier in the former numerically. And it is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes. The feasibility and applicability of the CCFC method are verified using simulation and experimental results.

A Simultaneous Multi-Directional Defects Measurement Based on Polarization-Multiplexed Four-Directional Digital Shearography With Large Field of View

Since the sensitivity of digital shearography (DS) is related to its shearing direction and the anomaly of the relative deformation is sensitive to the defect direction in non-destructive testing (NDT), traditional single or two direction DS systems may miss defects in some directions. To avoid missing defects, a polarization-multiplexed four-directional digital shearography for simultaneous measurement of multi-directional defects is proposed in this paper. Four object beams whose relative shearing amount and spatial carrier frequency can be adjusted independently are constructed, with which four shearograms can be obtained simultaneously in one recorded interferogram. And by embedding a 4f system in front of the interferometers to transmit the captured image, the measurement field of view (FOV) is doubled. To verify the performance of the proposed four-directional DS system, an experimental setup was constructed, and two experiments of central force loading and non-destructive thermal loading were performed. Experimental results verify that the proposed system can effectively detect the defects in multiple directions simultaneously.

Interocular differences in temporal integration drive anomalous Pulfrich percepts

Temporal differences in visual processing between the eyes can cause dramatic misperceptions of motion and depth. Processing delays between the eyes cause the Pulfrich effect: oscillating targets in the frontal plane are misperceived as moving along near-elliptical motion trajectories in depth. Here, we explain a previously reported but poorly understood variant of the effect. In the anomalous Pulfrich effect, the illusory motion trajectory appears oriented left- or right-side back in depth, rather than aligned with the true direction of motion. Our data strongly suggests that this apparent misalignment is due to interocular differences in neural temporal integration periods. Differences in temporal integration dampen the amplitude of effective motion in one eye relative to the other. In a dynamic analog of the ‘geometric’ effect in stereo-surface-orientation perception (Ogle, 1950), the differential motion amplitudes cause the perceived misorientation. First, four observers tracked, with a cursor, Gabor targets with different spatial frequencies. Longer temporal integration periods—hence, increased motion damping—were associated with higher spatial frequencies. Next, the observers viewed dichoptic Gabor stimuli oscillating in the frontal plane, with different carrier spatial frequencies in each eye. Observers reported perceiving more ‘left-side back’ orientations in depth when the left eye was presented the lower spatial frequency, and vice versa. Then, we measured psychometric functions with onscreen damping as the independent variable. The point of subjective equality (PSE) indicates the onscreen damping that is equal in magnitude but opposite in sign to the neural damping. All experiments indicate that neural damping is greater for higher spatial frequencies. The current findings expand the body of knowledge regarding the dependence of temporal processing on stimulus properties, while highlighting the striking perceptual consequences of interocular imbalances in temporal processing. Future work will aim to determine the computations that minimize the impact of temporal processing differences under natural conditions.

Modified achromatic Savart polariscope for broadband spatially modulated snapshot imaging polarimeter

This paper presents the modified achromatic Savart Polariscope for constructing broadband spatially modulated snapshot imaging polarimeter. The modified achromatic Savart Polariscope can be made from two different birefringent crystals. The achievements and performances of the modified achromatic Savart Polariscope are demonstrated with numerical simulations. The chromatic variations in spatial carrier frequencies can be reduced by an order of magnitude. The spatially modulated snapshot imaging polarimeter constructed by the modified achromatic Savart Polariscopes can achieve the root mean square errors with a magnitude of 10−4 across the spectral range 0.48–0.96 μm as it does in monochromatic light conditions.

Behavioral signatures of Y-like neuronal responses in human vision

Retinal ganglion cells initiating the magnocellular/Y-cell visual pathways respond nonlinearly to high spatial frequencies (SFs) and temporal frequencies (TFs). This nonlinearity is implicated in the processing of contrast modulation (CM) stimuli in cats and monkeys, but its contribution to human visual perception is not well understood. Here, we evaluate human psychophysical performance for CM stimuli, consisting of a high SF grating carrier whose contrast is modulated by a low SF sinewave envelope. Subjects reported the direction of motion of CM envelopes or luminance modulation (LM) gratings at different eccentricities. The performance on SF (for LMs) or carrier SF (for CMs) was measured for different TFs (LMs) or carrier TFs (CMs). The best performance for LMs was at lower TFs and SFs, decreasing systematically with eccentricity. However, performance with CMs was bandpass with carrier SF, largely independent of carrier TF, and at the highest carrier TF (20 Hz) decreased minimally with eccentricity. Since the nonlinear subunits of Y-cells respond better at higher TFs compared to the linear response components and respond best at higher SFs that are relatively independent of eccentricity, these results suggest that behavioral tasks employing CM stimuli might reveal nonlinear contributions of retinal Y-like cells to human perception.

Changing the trajectory of Airy beam sets with spatial carriers

In this paper, we study a change in the propagation trajectory of a set of autofocusing laser beams using a fractional Fourier transform. Clusters of displaced bounded Airy-Gaussian beams supplemented by a phase function that deflects the beam similarly to a prism are considered. The shift and phase deviation (according to the carrier spatial frequencies) make it possible to change the propagation trajectory of a set of autofocusing beams. The influence of the parameters under consideration on the properties of autofocusing of a cluster of Airy-Gaussian beams is investigated by means of numerical simulation.

Single-shot off-axis digital holographic system with extended field-of-view by using multiplexing method

We propose a new configuration of single-shot off-axis digital holographic system to realize double the camera field-of-view (FOV) of the existing off-axis Mech-Zehnder type holographic setup. The double FOV is obtained by double spatial frequency multiplexing of two different areas of an object beam by inserting a Fresnel bi-prism in it, which divides the object beam into two, both carrying different object information. The image sensor is placed at the plane where these two different FOVs overlap so as to record simultaneously two parts of the wavefront of the object in a single-shot. The multiplexed hologram is carrying two interferometric images corresponding to two different FOVs of the object which are modulated with two different spatial carrier frequencies. The feasibility of the proposed digital holographic system is experimentally demonstrated by imaging two different areas of a resolution test target. The limitation of the proposed system and a method to overcome it, are also discussed. The proposed system is useful in a wide range of applications including microscopy and optical metrology.

Real-time 3D measurement of freeform surfaces by dynamic deflectometry based on diagonal spatial carrier-frequency pattern projection

Deflectometry is a three-dimensional optical technique based on structured light projection for measuring and inspecting specular freeform surfaces. Conventional deflectometry method needs complicated calibration and time-consuming phase-extraction algorithm, which are not suitable for industrial metrology requiring dynamic and high-speed measurement. In this paper, a novel dynamic deflectometry method with a simple system setup and calibration is proposed for the three-dimensional measurement of specular freeform surfaces with high speed and high accuracy. We developed a very simple calibration method using a reference flat mirror which helps to save calibration time and computer resources. We also proposed a one-shot method by using a spatial carrier-frequency diagonal fringe pattern for screen projection along with an algorithm to separate a diagonal phase into vertical and horizontal phases. We extensively evaluated the feasibility of proposed calibration and one-shot method by different simulations and measuring several specular surfaces experimentally. Our novel deflectometry gives similar measurement accuracy compared to traditional contact measurement technique while offering much higher measurement speed. Dynamic surface shape measurement of silicon wafer due to temperature’s variation proved the real-time measurement ability of our proposed method.

Interocular Phase Disparity Tuning of Binocular Contrast Summation Depends on Carrier Spatial Frequency and Orientation.

Binocular summation is a sensitive metric of binocular integration. As such, characterization of the mechanisms underlying binocular summation is a key step in translating and applying this knowledge to abnormal binocular systems afflicted with strabismus and amblyopia. Computational models of binocular summation have advocated the operation of mechanisms sensitive to the interocular phase disparity of first-order carrier gratings. This study investigated if such generalization depended on carrier spatial frequency and orientation. Monocular and binocular contrast detection thresholds were measured in nine observers with normal binocular vision. Stimuli comprised Gabor targets presented with one of three spatial frequencies (1, 3, and 9 cycles per degree [cpd]), two orientations (horizontal and vertical), and five interocular phase disparities (0, ± π /2, ± π radians). Horizontal and vertical fixation disparities were measured for each binocular threshold condition. Binocular summation ratios were computed by dividing the mean monocular detection threshold by the respective binocular detection threshold. Binocular summation ratio varied significantly with interocular phase disparity for the 1- and 3-cpd horizontal and vertical gratings. Phase dependency was reduced with the 9-cpd horizontal grating and absent for the 9-cpd vertical grating, even though binocular summation ratio exceeded predictions of probability summation. Computational modeling that incorporated the variability of fixation disparity into a vector summation model predicted a reduction in peak binocular summation ratio with increasing carrier spatial frequency but did not account for the reduction of phase sensitivity noted with the 9-cpd stimulus. Binocular summation magnitude is less dependent on interocular phase disparities for carrier spatial frequencies that exceed 3 cpd, especially with vertical gratings. Although vergence variability due to fixation disparities contributes to the overall reduction in binocular summation magnitude with increasing carrier spatial frequency, it does not provide a complete account for the lack of interocular phase disparity tuning noted with high grating spatial frequencies.

Holograms of a 3D object synthesized at the receiving end of the communication channel in Dot Matrix technology

The manuscript 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 the resolution of the Full HD standard and higher. The method is based on the previously proposed technology for recording and transmitting a depth map and surface texture of the holographic object over the communication channel and digital synthesis of the hologram at the receiving end of the communication channel. The obtained result reduces the frequency band required for the transmission of 3D holographic information, similar to SSB technology, since the carrier spatial frequency of the hologram in this method is not transmitted through the communication channel, but is synthesized in the hologram already at its receiving end. Experimental results of hologram synthesis at the receiving end of the communication channel in DotMatrix technology are presented. The method considered in this manuscript is convenient for multiplexing 3D images, transferring them from one part of the electromagnetic spectrum to another, as well as for creating hyperspectral images. The work implements the technology of a holographic phototelegraph, which, when using high-speed dynamic holographic monitors, can solve the problems of creating 3D TV and augmented reality.

Compressing 3D holographic information similar to data transmission via a single sideband

Subject of study. The possibility of real-time transmission of holographic information using standard radio channels by its compression through the removal of the carrier frequency and the use of a single sideband is investigated. Main results. We demonstrate that, according to Russian patent 2,707,582, information about a three-dimensional (3D) object can be stored in the form of two two-dimensional frames, one of which is the texture of the object surface, whereas the other is the depth map of its surface. After considering two principal methods for the formation of such a depth map, namely, the time-of-flight method and the method of structured light, we selected the latter owing to several advantages. This method was used to simulate the real-time recording process of a 3D portrait of a live person. Practical significance. We report the results of a numerical experiment demonstrating the possibility of transmission of 3D holographic images using standard communication channels intended for application in television and augmented reality without specialized glasses and other devices worn by the observer. This result is based on the proposed method for the separation of the carrier spatial frequency and frequencies containing the information about the holography object.

Holographic sight with a one-dimensional telescopic optical system

A scheme of a holographic collimator sight with a one-dimensional telescopic optical system is proposed. The scheme is based on an optical system of a sight comprising a one-dimensional telescopic optical system composed of an achromatizing diffraction grating and hologram forming the image of the aiming mark. We establish that a plane diffraction grating and hologram positioned nonparallelly can function as a one-dimensional telescopic system. This system allows compensation of the different divergences of radiation in the principal cross sections of the laser diode comprising the sight and reducing the aperture of the parallel ray beam formed in the sight and used for hologram reconstruction in one of its principal cross sections. However, such a mutual alignment of the grating and hologram results in limitation of the spectral range in which the compensation of the thermal drift of the aiming line position is ensured. Equations that allow determination of the ratios of the spatial frequency of the grating and carrier spatial frequency of the hologram, which result in minimization of the thermal drift of the aiming line, are presented. Geometric parameters of the sight scheme that ensure the residual thermal drift of the aiming line that does not exceed the angular resolution of the eye while maintaining its minimum dimensions are reported. Technological aspects of the fabrication of the diffractive optical elements of the sight are considered. The scheme of the holographic collimator sight proposed in this study combines the main advantage of the light-guide-type sight scheme, i.e., the small distance from the sight base to the aiming line of 0.8 times the hologram aperture height, with relatively simple assembly and alignment of the elements of the sight optical scheme characteristic of a sight composed of a concave diffraction grating.

Characterization of Supersonic Compressible Fluid Flow Using High-Speed Interferometry.

This paper presents a very effective interference technique for the sensing and researching of compressible fluid flow in a wind tunnel facility. The developed technique is very sensitive and accurate, yet easy to use under conditions typical for aerodynamic labs, and will be used for the nonintrusive investigation of flutter in blade cascades. The interferometer employs a high-speed camera, fiber optics, and available “of-the-shelf” optics and optomechanics. The construction of the interferometer together with the fiber optics ensures the high compactness and portability of the system. Moreover, single-shot quantitative data processing based on introducing a spatial carrier frequency and Fourier analysis allows for almost real-time quantitative processing. As a validation case, the interferometric system was successfully applied in the research of supersonic compressible fluid discharge from a narrow channel in a wind tunnel. Density distributions were quantitatively analyzed with the spatial resolution of about . The results of the measurement revealed important features of the flow pattern. Moreover, the measurement results were compared with Computational Fluid Dynamics (CFD) simulations with a good agreement.