Spatial Carrier Frequency Research Articles

Snapshot imaging Mueller matrix polarimeter using polarization gratings

A snapshot imaging Mueller matrix polarimeter (SIMMP) is theoretically described and empirically demonstrated through simulation. Spatial polarization fringes are localized onto a sample by incorporating polarization gratings (PGs) into a polarization generator module. These fringes modulate the Mueller matrix (MM) components of the sample, which are subsequently isolated with PGs in an analyzer module. The MM components are amplitude modulated onto spatial carrier frequencies which, due to the PGs, maintain high visibility in spectrally broadband illumination. An interference model of the SIMMP is provided, followed by methods of reconstruction and calibration. Lastly, a numerical simulation is used to demonstrate the system's performance in the presence of noise.

Orientation gradient detection exhibits variable coupling between first- and second-stage filtering mechanisms

We investigated sensitivity to orientation modulation using visual stimuli with bandpass filtered noise carriers. We characterized the relationship between the spatial parameters of the modulator and the carrier using a 2-AFC detection task. The relationship between these two parameters is potentially informative of the underlying coupling between first- and second-stage filtering mechanisms, which, in turn, may bear on the interrelationship between striate and extrastriate cortical processing. Our previous experiments on analogous motion stimuli found an optimum sensitivity when the ratio of the carrier and modulator spatial frequency parameters (r) was approximately ten. The current results do not exhibit an optimum sensitivity at a given value of the ratio r. Previous experiments involving second-order modulation sensitivity show an inconsistent range of estimates of optimum sensitivity at values of r between 5 and 50. Our results, using a complementary approach, confirm these discrepancies, demonstrating that the coupling between carrier and modulator frequency parameters depends on a number of stimulus-specific factors, such as contrast sensitivity, stimulus eccentricity, and absolute values of the carrier and modulator spatial frequency parameters. We show that these observations are true for a stimulus limited in eccentricity and that this orientation-modulated stimulus does not exhibit scale invariance. Such processing can not be modeled by a generic filter-rectify-filter model.

Visual responses to contrast-defined contours with equally spatial-scaled carrier in cat area 18

Contrast-defined contours are one type of second-order contours, across which there are no differences in luminance. Although they can be always perceived, their responses have been only investigated when the spatial frequency of carrier, the background texture whose contrast is modulated to form contours, is much higher than that of contrast-defined contours, due to the interference of responses to luminance contours in other cases.In the present study, we examined visual responses in cat area 18 to the contrast-defined contours with carrier at same spatial frequency equal to neuron's preferred value for luminance contours, by establishing a control stimulus including all the luminance components but lack of the contrast contour information. Using single unit recording and intrinsic optical imaging, we demonstrated that contrast gratings with equally spatial-scaled carrier induced responses in a proportion of cat area 18 neurons with the preferred orientation similar to that for luminance contours, and the responses generated orientation maps similar to those for luminance contours.Our finding suggests that early visual cortex can process second-order contours regardless of the spatial frequency of carriers, in a way similar to the processing of luminance contours. This uniform manner of early visual processing might underlie the visual detection of both luminance contours and non-luminance second-order contours.

Modified Fourier-transform method for phase-shift calibration

Abstract A fast convergent algorithm to accurately measure phase-shift for phase shifter is proposed. In the presence of a spatial carrier frequency, an error function in the Fourier-domain is introduced and then the unknown phase-shift between two phase-shifted fringe patterns is determined by minimization of the error function with the help of a golden section search approach. Compared with the conventional Fourier-transform method, the modified method proposed in the paper is more immune to random noise and hence can give a more accurate result. The translation curve of a liquid-crystal spatial light modulator is also experimentally calibrated.

Single-shot parallel full range complex Fourier-domain optical coherence tomography

We present a method of parallel full range complex Fourier-domain optical coherence tomography (FDOCT) that is capable of acquiring an artifacts-free two-dimensional (2-D) cross-sectional image, i.e. a full range B-scan tomogram, by a single shot of 2-D CCD camera. This method is based on a spatial carrier technique, in which the spatial carrier-frequency is instantaneously introduced into the 2-D spectral interferogram registered in parallel FDOCT by using a grating-generated reference beam. The spatial-carrier-contained 2-D spectral interferogram is processed through Fourier transformation to obtain a complex 2-D spectral interferogram. From the 2-D complex spectral interferomgram, a full range B-scan tomogram is reconstructed. The principle of our method is confirmed by imaging an onion sample.

空间载频干涉法全场测量长度技术

Based on the study of basic principle of interferometry using 2-D FFT arithmetic,a method to measure the length is proposed.The gauge block,as a measured sample,is placed into the light path in a Twyman-Green interferometer,and the interference fringes are generated between the reference beam and the reflected beam of the tested block upper surface and the assistant plane respectively.The interferogram is collected by a image acquisition system.The algorithm processing software is used to achieve block edge identification,region extension,filtering,phase unwrapping etc.The length distribution with block information can be obtained in the whole field and the length of the gauge block can be obtained automatically.The results indicate that the proposed method has advantages of high precision,whole field and non-contact in the measuring.

CCD非线性效应对剪切干涉法波前检测的影响

When radial shear interferometer is used in high-power laser wavefront detection, due to the influence of the nonlinearity of CCD, there exist not only the first order frequency with wave-front information but also the second and the third order frequency. They may lead to overlapping spectrum, which makes it difficult to extract useful information and reduces the detection accuracy of wavefront. A theoretical analysis on mechanisms of high-order spectral component and spectrum aliasing caused by the nonlinearity of CCD is established, and the condition to avoid spectrum aliasing is pointed out. Finally, a method by increasing the spatial carrier frequency to reduce or eliminate the spectrum aliasing is proposed. Computer simulation and experimental results have verified the feasibility of

Laser Differential Interferometer for Diagnostics of Gas-Puff $Z$-Pinch

Laser shearing interferometers (LSIs) are suitable for measuring the plasma-density profile on the condition that the spatial-frequency shift of the interference fringes induced by the plasma is less than the spatial-carrier frequency of the fringes. When it is applied to the diagnostics of plasmas with very large density gradient and Laplacian, such as a plasma shell produced by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinch, the fringe pattern obtained in the experiment seldom meets the requirement. A new type of laser differential interferometer has been developed on the basis of a cyclic LSI. By placing a ring interferometer between the two lenses of a 4-f imaging system, the interferometer has the ability to change the ratio of frequency shift to carrier frequency arbitrarily, and thus, it is applicable to the diagnostics of plasma with large density gradient and Laplacian. The principle of the 4-f differential interferometer was illustrated. Gas-puff experiments were conducted on a Yang accelerator. The high-definition interferograms of the imploding plasma shell were obtained. The electron-density profiles and the plasma-shell shape were calculated from the interferograms.

Interpolated local model fitting method for accurate and fast single-shot surface profiling

The local model fitting (LMF) method is a useful single-shot surface profiling algorithm based on spatial carrier frequency fringe patterns. The measurement principle of the LMF method relies on the assumption that the target surface is locally flat. In this paper, we first analyze the measurement error of the LMF method caused by violation of the locally flat assumption. More specifically, we theoretically prove that the measurement error is zero at fringe intensity extrema in an interference pattern even when the locally flat assumption is violated. Based on this theoretical finding, we propose a new surface profiling method called the interpolated LMF (iLMF) algorithm, which is more accurate and computationally efficient than the original LMF method. The practical usefulness of the iLMF method is shown through experiments.

Temporal integration of the chromatic channels in peripheral vision

We measured the temporal summation properties of paired flashes to investigate the temporal responses of the chromatic channel in peripheral vision in comparison with those of the luminance channel. The size of the stimulus was scaled according to the cortical magnification factor. The temporal response was biphasic to complementary-chromatic pulse pairs, and was accelerated in peripheral vision in the same way as luminance pulse pairs. On the other hand, the temporal response was monophasic to same-chromatic pulse pairs, and was decelerated in the periphery. We proposed a model of the chromatic channel in which biphasic and monophasic internal channels were arranged in parallel. The sensitivity of the biphasic channel at high temporal frequency in the periphery was comparable to that in the fovea, whereas the sensitivity of the monophasic channel at low temporal frequency in the periphery matched that in the fovea. Similar results were obtained with pairs of flashed chromatic Gabor patches with their spatial frequencies scaled according to the cortical magnification factor. The inhibition phase of the biphasic channel was degraded with the spatial carrier frequency of the Gabor patch. The properties of the biphasic channel were consistent with the double duty hypothesis, while those of the monophasic channel were consistent with the two-channel hypothesis. The biphasic channel may correspond to the parvocellular pathway and the monophasic channel may reflect the properties of the koniocellular pathway.

Angle-dependent encoding of multiple asymmetric symbols in a binary phase hologram with a spatial segmentation

A method of encoding multiple asymmetric symbols into a single thin binary Fourier hologram is presented. It assumes a combination of a spatial segmentation and carrier frequencies in order to achieve multiple reconstructed images selectable by the angle of the incident laser beam. The proper segmentation function with an optimized period allows us to encode a number of different objects with little loss of reconstruction quality. A special sequence of phase encoding steps and a binarization enable recording of asymmetric symbols into a binary hologram. The description of the design procedure is given, followed by the experimental results confirming the conclusions conceived from numerical simulations. The method can be used practically for the design of simple translucent holographic head-up displays.

Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement

We report a sinusoidal fringe projection system based on superluminiscent diode (SLD) as a broad-band light source in conjunction with an acousto-optic tunable filter (AOTF) as frequency tuning device for three-dimensional shape measurement. The present system is based on a compact low-coherence Michelson interferometer system. The conventional interferometric system was modified in which one side of the beam splitter was coated with aluminum oxide which is used as reference mirror. With this modified version, interference fringes can easily be obtained by simply placing the external mirror in contact on the other side of beam splitter. Sinusoidal fringes with multiple spatial-carrier frequency can be generated in real-time using the present system by means of changing the radio-frequency signal to AOTF electronically without mechanically moving any component in the system. The present system was tested by projecting the sinusoidal fringes on a step-like object and 3D shape of the object was reconstructed using Fourier transform fringe analysis technique. The main advantages of the proposed system are completely non-mechanical scanning, easy to align, high stability because of its nearly common-path geometry and compactness.

Algorithm for multiple-beam Fizeau interferograms with arbitrary phase shifts

The objective of this paper is to describe a novel method for phase extraction from multiple-beam Fizeau interferograms with arbitrary phase shifts. The approach begins with applying FFT method to estimate the phase shifts and then utilizes least-squares iterative algorithm to extract phase and phase shifts simultaneously. If the spatial carrier frequency of the fringes is high enough to separate the phase of the first-order maximum in the Fourier domain, the proposed method requires only two iterative cycles to accurately extract phase information from seven multiple-beam Fizeau interferograms with arbitrary phase shifts. Numerical simulations and experiments demonstrate the effectiveness of the proposed algorithm. A comprehensive analysis of the influences of systematic errors (spatial carrier frequency, reflectivity coefficient, and random noise) on the evaluation of phase shifts and phase is presented. The method has applications in high precision interferometry.

One-shot parallel complex Fourier-domain optical coherence tomography using a spatial carrier frequency

We propose a novel method of one-shot parallel complex Fourier-domain optical coherence tomography using a spatial carrier frequency for full range imaging. The spatial carrier frequency is introduced into the 2-D spectral interferogram in the lateral direction by using a tilted reference wavefront. This spatial-carrier- contained 2-D spectral interferogram is recorded with one shot of a 2-D CCD camera, and is Fourier-transformed in the lateral direction to obtain a 2-D complex spectral interferogram by a spatial-carrier technique. A full-range tomogram is reconstructed from the 2-D complex spectral interferogram. The principle of this method is confirmed by cross-sectional imaging of a glass slip object. (c) 2008 Society of Photo-Optical Instrumentation Engineers.

Digital speckle pattern interferometry using spatial phase shifting: influence of intensity and phase gradients

Spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS) provides the phase information due to the object displacement from two images, one stored before and other after loading. The technique needs a carrier fringe system. The double aperture mask in front of the imaging system is one of the methods for introducing the spatial carrier frequency for phase evaluation. The size of the apertures and their separation are important criteria to obtain appropriate phase shift/column within the desired size of the speckle for phase retrieval. The assumptions of constant intensity and phase on adjacent pixels of the camera while calculating phase in spatial phase shifting (SPS) are not met as the speckled object wave contains intensity and phase gradients, resulting in distortions in the calculated phase profiles. In this paper we discuss a strategy to overcome these problems. The contrast of the correlation fringe obtained using this approach is much improved. It also eliminates the distortion in the unwrapped phase map like wave ripples. The experimental results on an edge clamped circular plate loaded at the center are presented.

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.

Spatial phase-shifting technique in large image-shearing electronic speckle pattern interferometry

A technique for deformation measurement by carrier is pre- sented, which is based on large image-shearing shearography. A refer- ence object is fixed on the side of a test object. They are all illuminated by one expanded laser beam. When a large image-shearing Wollaston crystal is used in front of a charge-coupled device CCD camera, one image of the object is superposed by one image of the reference surface. The carrier can be introduced by tilting the reference surface at a small angle. When Fourier transform is used to demodulate the modulated fringe pattern, the phase of deformation can be calculated and the de- formation can be measured accurately. The principle of spatial carrier frequency modulation in large-shearing electronic speckle pattern inter- ferometry ESPI is discussed. A typical experiment using a centrally loaded clamped circular plate is completed. Some experimental results are presented. The experimental results prove that the method can modulate a speckle pattern very well and the displacement fields can be measured effectively. © 2007 Society of Photo-Optical Instrumentation

Neural mechanisms mediating responses to abutting gratings: Luminance edgesvs.illusory contours

The discontinuities of phase-shifted abutting line gratings give rise to perception of an "illusory contour" (IC) along the line terminations. Neuronal responses to such ICs have been interpreted as evidence for a specialized visual mechanism, since such responses cannot be predicted from conventional linear receptive fields. However, when the spatial scale of the component gratings (carriers) is large compared to the neuron's luminance passband, these IC responses might be evoked simply by the luminance edges at the line terminations. Thus by presenting abutting gratings at a series of carrier spatial scales to cat A18 neurons, we were able to distinguish genuine nonlinear responses from those due to luminance edges. Around half of the neurons (both simple and complex types) showed a bimodal response pattern to abutting gratings: one peak at a low carrier spatial frequency range that overlapped with the luminance passband, and a second distinct peak at much higher frequencies beyond the neuron's grating resolution. For those bimodally responding neurons, the low-frequency responses were sensitive to carrier phase, but the high-frequency responses were phase-invariant. Thus the responses at low carrier spatial frequencies could be understood via a linear model, while the higher frequency responses represented genuine nonlinear IC processing. IC responsive neurons also demonstrated somewhat lower spatial preference to the periodic contours (envelopes) compared to gratings, but the optimal orientation and motion direction for both were quite similar. The nonlinear responses to ICs could be explained by the same energy mechanism underlying responses to second-order stimuli such as contrast-modulated gratings. Similar neuronal preferences for ICs and for gratings may contribute to the form-cue invariant perception of moving contours.

Active, LCoS based laser interferometer for microelements studies

The modification of classical Twyman-Green interferometer by implementation of Liquid Crystal on Silicon (LCoS) spatial light modulator as the reference mirror allows introducing arbitrary phase in the reference wavefront. This special capability is applied to facilitate the measurements of shape and deformation of active microelements and extend the range of such measurement. This can be realized by introducing linear or circular spatial carrier frequency into interferogram or by compensating object wavefront deformation. Moreover LCoS display can be used as an accurate phase shifter if the proper calibration is introduced. The analysis of sources of measurement errors introduced by LCoS display is presented and the ways of their elimination are discussed. The possible application of LCoS based laser interferometer for initial microelement shape determination and transient deformation monitoring as well as active reference phase modification are shown and experimentally confirmed during silicon micromembranes studies.

Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry

We propose a simple multifrequency spatial-carrier and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry (LSI). In this system a wedge-shaped plate lateral shearing interferometer is used and, owing to the presence of tilt, a finite number of fringes parallel to the direction of the shear appears; hence a significant spatial-carrier frequency is generated at the focus position. We further enhance the spatial-carrier frequency either by changing the wavelength of the laser light or by slight defocusing. A synthetic interferogram with low spatial-carrier frequency is obtained by use of laser light of two wavelengths simultaneously in the lateral shear interferometer. We obtain the phase-shifted fringe patterns from the same setup by simply moving the wedge plate in an in-plane parallel direction, using a linear translator. The fringe projection system was tested for measurement of the three-dimensional shape of a discontinuous object. The present system has many advantages; e.g., it is a common-path interferometry and hence is insensitive to external vibrations, is compact in size, and is relatively inexpensive.