Spatial Carrier Frequency Research Articles

Single-shot deflectometry for dynamic 3D surface profile measurement by modified spatial-carrier frequency phase-shifting method

We propose a new concept of single-shot deflectometry for real-time measurement of three-dimensional surface profile using a single composite pattern. To retrieve an accurate phase from one-frame composite pattern, we adapt the Fourier Transform (FT) method and the spatial carrier-frequency phase-shifting (SCPS) technique to our proposed deflectometry. Based on Lissajous figure and ellipse fitting method, we also correct the phase extraction error in SCPS technique by reducing the effect of background and modulation variations. The proposed technique is verified by comparing our measurement results with phase-shifting deflectometry, and the maximum difference between two measurement results is less than 30 nm rms. We also test the robustness to vibration and the measurement capability for dynamic object.

Modulation by task-difficulty in the default mode network varies with the complexity of perpetual information during decision making

Modulation by task-difficulty in the default mode network varies with the complexity of perpetual information during decision making

Double Imaging Mach–Zehnder Spatial Carrier Digital Shearography

ABSTRACTThis paper presents a Double Imaging Mach–Zehnder Spatial Carrier Digital Shearography (DIM-SCDS) system. Compared to traditional Spatial Carrier Mach–Zehnder shearography, DIM-SCDS has two advantages: one is that it can adjust shearing amount and spatial carrier frequency independently; the other one is that it can measure a larger area with a shorter working distance. Two pairs of imaging lenses and apertures are placed in the two arms of Mach–Zehnder interferometry, respectively. Shearing amount is adjusted by the mirrors in the two arms, and spatial carrier frequency is determined by the angle between the two apertures when they are mapped to the same optical axis. Shearograms of the object under test are recorded using a CCD. Shearogram phases are calculated as the measurement results. Finally, the performance of DIM-SCDS is proved by experiments.

Dynamic refractive index distribution measurement of dynamic process by combining dual-channel simultaneous phase-shifting interferometry and total internal reflection

We propose and demonstrate a novel method to measure dynamic refractive index distributions using a combination of total internal reflection (TIR) and dual-channel simultaneous phase-shifting interferometry (DCSPSI). First, a right-angle prism is introduced into the DCSPSI system, the reflection phase variation induced by TIR, which contains the refractive index information of tested sample, can be achieved by the spatial carrier-frequency phase-shifting algorithm from a pair of interferograms with the phase shifts of π/2 captured by DCSPSI system. Second, based on the relationship between the reflection phase variation and the refractive index, the 2D refractive index distribution can be calculated easily. Importantly, the proposed TIR-DCSPSI method will supply a useful tool for dynamic refractive index distribution measurement of dynamic process, such as the droplet evaporation, mutual solubilization and diffusion of different droplets, cell culture, colloid curing, etc.

Dynamic Phase Measurement Based on Two-Step Spatial Carrier-Frequency Phase-Shifting Interferometry

A dynamic phase measurement method based on a two-step spatial carrier-frequency phase-shifting (TS-SCFPS) technique is proposed. First, by the subtraction operation between a pair spatial carrier-frequency interferograms with a certain phase shifts, which are captured by dual-channel interferometry system, we can achieve one-frame background-removed carrier-frequency interferogram. Second, from two-frame phase-shifting subinterferograms splitting from the above background-removed carrier-frequency interferogram, we can rapidly achieve the accurate phase through using a two-step orthogonal and normalization algorithm. Compared with the existing SCFPS methods, the proposed TS-SCFPS method reveals good background deductions and antinoise performance. Moreover, by using a two-step phase-shifting algorithm, without any special requirement for the phase shifts, the proposed TS-SCFPS method can rapidly achieve high-accuracy phase retrieval relative to other SCFPS methods. Especially, the achieved experimental results demonstrate the outstanding performance of the proposed TS-SCFPS method in both static and dynamic phase measurements.

Instantaneous wavefront measurement of large aperture optical elements

In order to measure the instantaneous wavefront of large aperture optical elements, a method based on the structure of oblique incidence of reflective shearing point diffraction interferometer is proposed. A lateral displacement between the reference wavefront and the test wavefront is formed after passing this structure. The shear of two beams introduces linear spatial carrier frequency to the point diffraction interferogram. After receiving a good contrast interferogram, wavefront phase is retrieved by Fourier transform (FT) automatically to realize the dynamic measurement of instantaneous wavefront. The optical path is up to 20 m, so the air current is a significance factor to the result. Besides, because of the air current, the system itself can be seen as a instantaneous wavefront happening and measurement of large aperture optical elements. The results indicate that the root mean square value is in accord with that acquired by SID4 wavefront sensor (less than 1/50λ), so about the repeated accuracy. The method proposed can be applied in high resolution and accuracy measurement of instantaneous wavefront.

Dynamic measurement of first-order spatial derivatives of deformations by digital shearography

This paper presents a simple spatial phase shift shearography based on the Michelson interferometer. A novel digital shearography set-up with a large angle of view, which is based on a 4f system is demonstrated. In the system, the Michelson interferometer is used as a shearing device to generate a shearing distance by tilting a small angle in one of the two mirrors. In fact spherical wave fronts become plane after going through the first lens in 4f system. Tilting the mirror in the Michelson interferometer also generates spatial carrier frequency. Sinusoid fitting method is applied to evaluate the phase. This system can generate a phase map of shearography by using only a single image. The effects of shearing angle, the choice of algorithm and comparison result are discussed in detail. The theory and the application are presented.

A Rapid Spatial Carrier-Frequency Phase-Shifting Method Based on the Orthogonality of Diamond Diagonal Vectors

From a one-frame off-axis interferogram with unknown carrier-frequency, a rapid spatial carrier-frequency phase-shifting (SCFPS) method is proposed to achieve the phase measurement of the dynamic process. First, based on the SCFPS technique, four-frame phase-shifting subinterferograms are constructed from one-frame off-axis interferogram. Second, by using the orthogonality of diamond diagonal vectors, respectively, achieved through the subtraction and addition operations between two equal length vectors, which are generated from above four-frame phase-shifting subinterferograms, the accurate phase can be retrieved rapidly. Compared with current SCFPS methods, in addition to maintaining high accuracy of phase-shifting method, as well as no requirement for carrier-frequency calibration, the proposed method reveals an obvious advantage in processing speed of phase retrieval, and this will greatly facilitate its application prospect for dynamic phase measurement.

Non-phase unwrapping interferometric approach for a real-time in-plane rotation measurement.

This Letter proposes a novel interferometric approach for the in-plane rotation measurement. With a simple and compact measurement system, the rotation angle and its direction can be determined simultaneously in real time by applying the spatial carrier frequency. Besides, the phase unwrapping process is not required for the angular evaluation, which simplifies the data processing procedure. Theoretically, the relationship between the in-plane rotation and the phase change distribution has been deduced to demonstrate the possibility of this interferometric method. Practically, the preliminary experiments have been carried out to verify the feasibility of this approach and quantify the measurement accuracy.

Ultra-short pulsed off-axis digital holography for imaging dynamic targets in highly scattering conditions.

A single-shot digital holography system using an ultra-short pulsed laser is demonstrated to be very effective in suppressing the multiple-scattering noise associated with imaging dynamic targets in highly scattering environments, such as biological tissues and fuel injection systems. A planar off-axis reference wave configuration is used to generate a fixed carrier spatial frequency in the recorded holograms in order to separate coherent signal from incoherent noise in Fourier transformed holograms. The single-shot imaging system does not require averaging between multiple shots and can capture images of transient phenomena, such as the formation of diesel fuel injection sprays, and can overcome the problem of mechanical vibrations for recording holograms in industrial and laboratory environments.

Optical birefringence and molecular orientation of crazed fibres utilizing the phase shifting interferometric technique

In this article, the features of the phase shifting interferometric technique were utilized to investigate the effect of the presence of crazes in both outer and inner layers on optical birefringence and molecular orientation of polypropylene fibres. The Pluta polarizing interference microscope was used as a phase shifting technique. This method includes adding a stepper motor with a control unit to the micrometer screw of the Pluta microscope. This optical system was calibrated to be used as a phase shifting interferometric technique. The advantage of this technique is that it can detect the crazes in both inner and outer layers of the sample under test. Via this method, the relation between the presence of the crazes (in both inner and outer layers) and the optical molecular orientation of polypropylene (PP) fibres was demonstrated. To clarify the role of this method, the spatial carrier frequency technique was used to show the effect of the presence of the crazes only in the outer layers on the phase distribution values and hence the structural properties of PP fibres.

General spatial phase-shifting interferometry by optimizing the signal retrieving function.

A general spatial phase-shifting (GSPS) interferometry method is proposed to achieve phase retrieval from one-frame spatial carrier frequency interferogram. By optimizing the internal signal retrieving function of the spatial phase-shifting (SPS) method, the accuracy, anti-noise ability and speed of phase retrieval can be significantly improved, meanwhile the corresponding local calculation property is reserved. Especially, in the case that the ratio of the spatial carrier to the phase variation rate are small, the proposed method reveals obvious advantage in the accuracy improvement relative to the conventional SPS methods, so the more details of measured sample can be effectively reserved through introducing smaller spatial carrier frequency, and this will facilitate its application in interference microscopy. The principle analysis, numerical simulation and experimental result are employed to verify the performance of the proposed GSPS method.

Single Shot White Light Interference Microscopy for 3D Surface Profilometry Using Single Chip Color Camera

We present a single shot low coherence white light Hilbert phase microscopy (WL-HPM) for quantitative phase imaging of Si opto-electronic devices, i.e., Si integrated circuits (Si-ICs) and Si solar cells. White light interferograms were recorded by a color CCD camera and the interferogram is decomposed into the three colors red, green and blue. Spatial carrier frequency of the WL interferogram was increased sufficiently by means of introducing a tilt in the interferometer. Hilbert transform fringe analysis was used to reconstruct the phase map for red, green and blue colors from the single interferogram. 3D step height map of Si-ICs and Si solar cells was reconstructed at multiple wavelengths from a single interferogram. Experimental results were compared with Atomic Force Microscopy and they were found to be close to each other. The present technique is non-contact, full-field and fast for the determination of surface roughness variation and morphological features of the objects at multiple wavelengths.

Characterization of axially tilted fibres utilizing a single-shot interference pattern

We proposed a method to solve the problem of extracting meaningful phase information for a single-shot interference pattern taken for an axially tilted fibre sample. Conventionally such interference patterns can be not evaluated with appropriate accuracy. Here, such an interference pattern is considered to be a special hologram since it contains information about light propagated through a laterally fixed sample located at different axial planes. Thus, part of the test object in such a hologram is in focus and the other parts are out of focus. The proposed method can be considered as two complementary steps. In the first step the complex amplitude across the hologram plane is recovered using an adaptive spatial carrier frequency method. This is followed by the second step where the complex amplitude is numerically propagated within a given volume. Thus, planes where the test object is in focus are defined. Consequently, the phase distributions corresponding to all of these planes are together stitched. Thus a complete focus phase map for the fiber sample under test is obtained. From the obtained phase map the two dimensions refractive and the two dimensions birefringence of isotactic polypropylene fibre were calculated.

Nonlinear Y-Like Receptive Fields in the Early Visual Cortex: An Intermediate Stage for Building Cue-Invariant Receptive Fields from Subcortical Y Cells.

A significant fraction of neurons in early visual cortex have specialized receptive fields that allow them to selectively respond to the orientation of boundaries that are invariant to the cue (luminance, contrast, texture, motion) that defines them. However, the neural mechanism to construct such versatile receptive fields remains unclear. Using multielectrode recording, we found a large fraction of neurons in early visual cortex with receptive fields not selective for orientation that have spatial nonlinearities like those of subcortical Y cells. These are strong candidates for building cue-invariant orientation-selective neurons; we present a neural circuit model that pools such neurons in an imbalanced "push-pull" manner, to generate orientation-selective cue-invariant receptive fields.

In-vivo retinal imaging with off-axis full-field time-domain optical coherence tomography.

With a simple setup, mainly composed of a low coherence light source and a camera, full-field optical coherence tomography (FF-OCT) allows volumetric tissue imaging. However, fringe washout constrains its use in retinal imaging. Here, we present a novel motion-insensitive approach to FF-OCT, which introduces path-length differences between the reference and the sample light in neighboring pixels using an off-axis reference beam. The temporal carrier frequency in scanned time-domain OCT is replaced by a spatial carrier frequency. Volumetric in-vivo FF-OCT measurements of the human retina were acquired in only 1.3 s, comparable to the acquisition times of current clinically used OCT devices.

Monocular blur alters the tuning characteristics of stereopsis for spatial frequency and size.

Our sense of depth perception is mediated by spatial filters at different scales in the visual brain; low spatial frequency channels provide the basis for coarse stereopsis, whereas high spatial frequency channels provide for fine stereopsis. It is well established that monocular blurring of vision results in decreased stereoacuity. However, previous studies have used tests that are broadband in their spatial frequency content. It is not yet entirely clear how the processing of stereopsis in different spatial frequency channels is altered in response to binocular input imbalance. Here, we applied a new stereoacuity test based on narrow-band Gabor stimuli. By manipulating the carrier spatial frequency, we were able to reveal the spatial frequency tuning of stereopsis, spanning from coarse to fine, under blurred conditions. Our findings show that increasing monocular blur elevates stereoacuity thresholds ‘selectively’ at high spatial frequencies, gradually shifting the optimum frequency to lower spatial frequencies. Surprisingly, stereopsis for low frequency targets was only mildly affected even with an acuity difference of eight lines on a standard letter chart. Furthermore, we examined the effect of monocular blur on the size tuning function of stereopsis. The clinical implications of these findings are discussed.

Simultaneous displacement and slope measurement in electronic speckle pattern interferometry using adjustable aperture multiplexing.

This paper suggests the use of adjustable aperture multiplexing (AAM), a method which is able to introduce multiple tunable carrier frequencies into a three-beam electronic speckle pattern interferometer to measure the out-of-plane displacement and its first-order derivative simultaneously. In the optical arrangement, two single apertures are located in the object and reference light paths, respectively. In cooperation with two adjustable mirrors, virtual images of the single apertures construct three pairs of virtual double apertures with variable aperture opening sizes and aperture distances. By setting the aperture parameter properly, three tunable spatial carrier frequencies are produced within the speckle pattern and completely separate the information of three interferograms in the frequency domain. By applying the inverse Fourier transform to a selected spectrum, its corresponding phase difference distribution can thus be evaluated. Therefore, we can obtain the phase map due to the deformation as well as its slope of the test surface from two speckle patterns which are recorded at different loading events. By this means, simultaneous and dynamic measurements are realized. AAM has greatly simplified the measurement system, which contributes to improving the system stability and increasing the system flexibility and adaptability to various measurement requirements. This paper presents the AAM working principle, the phase retrieval using spatial carrier frequency, and preliminary experimental results.

Dynamic phase measurement based on spatial carrier-frequency phase-shifting method.

Combining spatial carrier-frequency phase-shifting (SCPS) technique and Fourier transform method, from one-frame spatial carrier-frequency interferogram (SCFI), a novel phase retrieval method is proposed and applied to dynamic phase measurement. First, using the SCPS technique, four-frame phase-shifting sub-interferograms can be constructed from one-frame SCFI. Second, using Fourier transform method, the accurate phase-shifts of four sub-interferograms can be extracted rapidly, so there is no requirement of calibration for the carrier-frequency in advance compared to most existing SCPS methods. Third, the wrapped phase can be retrieved with the least-squares algorithm through using the above phase-shifts. Finally, the phase variations of a water droplet evaporation and a Jurkat cell apoptosis induced by a drug are presented with the proposed method. Both the simulation and experimental results demonstrate that in addition to maintaining high accuracy of the SCPS method, the proposed method reveals more rapid processing speed of phase retrieval, and this will greatly facilitate its application in dynamic phase measurement.

Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres

We present an extension of the adaptive spatial carrier frequency method which is proposed for fast measuring optical properties of fibrous materials. The method can be considered as a two complementary steps. In the first step, the support of the adaptive filter shall be defined. In the second step, the angle between the sample under test and the interference fringe system generated by the utilized interferometer has to be determined. Thus, the support of the optical filter associated with the implementation of the adaptive spatial carrier frequency method is accordingly rotated. This method is experimentally verified by measuring optical properties of polypropylene (PP) fibre with the help of a Mach–Zehnder interferometer. The results show that errors resulting from rotating the fibre with respect to the interference fringes of the interferometer are reduced compared with the traditional band pass filter method. This conclusion was driven by comparing results of the mean refractive index of drown PP fibre at parallel polarization direction obtained from the new and adaptive spatial carrier frequency method.