Fourier Fringe Analysis Research Articles

Deep learning based coherence holography reconstruction of 3D objects.

We propose a reconstruction method for coherence holography using deep neural networks. cGAN and U-NET models were developed to reconstruct 3D complex objects from recorded interferograms. Our proposed methods, dubbed deep coherence holography (DCH), predict the non-diffracted fields or the sub-objects included in the 3D object from the captured interferograms, yielding better reconstructed objects than the traditional analytical imaging methods in terms of accuracy, resolution, and time. The DCH needs one image per sub-object as opposed to N images for the traditional sin-fit algorithm, and hence the total reconstruction time is reduced by N×. Furthermore, with noisy interferograms the DCH amplitude mean square reconstruction error (MSE) is 5×104× and 104× and phase MSE is 102× and 3×103× better than Fourier fringe and sin-fit algorithms, respectively. The amplitude peak signal to noise ratio (PSNR) is 3× and 2× and phase PSNR is 5× and 3× better than Fourier fringe and sin-fit algorithms, respectively. The reconstruction resolution is the same as sin-fit but 2× better than the Fourier fringe analysis technique.

Noise reduction method in both time and frequency domains for envelope peak position extraction of pulse-train interferometry measuring distance between interference fringes

Multi-pulse train interferometry is used to measure distance for meter-scale/nanometer-resolution geometric measurements. The core of multi-pulse train interferometry is object positioning accuracy, which is limited by the ability to position the interference fringe envelope peak. The Fourier fringe analysis method, optical Hilbert transform method, and other methods are used in the envelope demodulation of multi-pulse train interferometry. The matched filter, which provides good noise reduction capability in the time domain, is widely used in radar signal processing. In this study, a matched filter is combined with the Fourier fringe analysis method and used to demodulate the envelopes of a fringe in a multi-pulse train interferometry because the proposed combined method performs noise reduction in both the time and frequency domains for fringe envelope signal processing. Compared with two conventional methods, the proposed combined method was proven to be feasible for envelope demodulation of multi-pulse train interferometry.

Common-path off-axis single-pixel holographic imaging.

Common-path off-axis single-pixel holographic imaging (COSHI) is proposed to obtain complex amplitude information using an in-line interferometer and a single-pixel (point-like) detector. COSHI is more robust to disturbances such as vibration than the conventional single-pixel digital holography technique because of its common-path configuration. In addition, the number of measurements can be reduced due to COSHI's reconstruction process based on the Fourier fringe analysis. In COSHI, an off-axis digital hologram can be obtained using the structured patterns composed of Hadamard basis patterns and stationary tilted phase distribution. Interestingly, COSHI's space bandwidth is larger than of the conventional off-axis digital holography because COSHI does not reconstruct the self-correlation term of an object. The proposed method is theoretically confirmed and numerical and experimental results show its feasibility.

Uniaxial 3D Measurement with Auto-Synchronous Phase-Shifting and Defocusing Based on a Tilted Grating.

Conventional uniaxial techniques generally require shifting objects or projection grating with the assistance of a high-precision mechanical moving component. To overcome this limitation, we propose a novel uniaxial 3-D shape measurement system with auto-synchronous phase-shifting and defocusing by using a tilted and fixed projection grating. The tilted focused image plane (FIP), which is reflected by a mirror at about 90 degrees, could be shifted across the measured surface by slightly rotating the mirror within a small angle range. This procedure will simultaneously introduce the change in defocusing and phase-shifting of the fringe. The modulation curve of each point can be deciphered by Fourier fringe analysis after a sequence of fringe intensities is acquired. Since both the measured object and projection grating are fixed, the proposed method could make the measurement system more compact and flexible. Both computer simulation and experiments are carried out to demonstrate the validity of this proposed system.

Real-time 3D shape measurement with dual-frequency composite grating and motion-induced error reduction

Phase-shifting profilometry has been increasingly sought and applied in dynamic three-dimensional (3D) shape measurement. However, the object motion will lead to extra phase shift error and thus measurement error. In this paper, a real-time 3D shape measurement method based on dual-frequency composite phase-shifting grating and motion-induced error reduction is proposed for a complex scene containing dynamic and static objects. The proposed method detects the motion region of a complex scene through the phase relations of the dual-frequency composite grating and reduces the motion-induced error with the combination of the phase calculated by a phase-shifting algorithm and the phase extracted by Fourier fringe analysis. It can correctly reconstruct the 3D shape of a complex dynamic scene and ensure high measurement accuracy of its static object as well. With the aid of the phase-shifting image ordering approach, the dynamic 3D shape of complex scenes can be reconstructed and the motion-induced error can also be suppressed in real time. Experimental results well proved that the proposed method is effective and practical.

Investigation of temperature profile and temperature stability of micro diffusion flame under the influence of magnetic field by use of a holo-shear lens-based interferometer

Holo-shear lens-based interferometer is demonstrated to study the influence of gradient magnetic fields (i.e., upward decreasing and upward increasing) and uniform magnetic field on the temperature and temperature profile of a wick stabilized micro diffusion flame created from the candle. Sheared interferograms in the absence and presence of microflame are captured using CCD camera. Fourier fringe analysis method is used to extract the phase-gradient information of ambient air without flame and heated air of microflame separately. The phase difference map of microflame and ambient air is used for the extraction of refractive index difference and temperature distribution inside the microflame. The experimental investigations reveal that temperature and temperature stability of the microflame increase in the upward decreasing and uniform magnetic field, while the temperature and temperature stability inside the microflame decrease in upward increasing magnetic field in comparison to temperature inside the microflame in the absence of magnetic field. Increment in the temperature of the microflame in uniform magnetic field is contrary to macro diffusion flame, where there is a negligible influence on the temperature in uniform magnetic field. Holo-shear lens-based interferometer is simple, lightweight, easy to implement, less vibration-sensitive, and can cover microflame to macroflame under investigation.

Simultaneous fluorescence and quantitative phase imaging of MG63 osteosarcoma cells to monitor morphological changes with time using partially spatially coherent light source

Quantitative phase imaging (QPI) technique is used to determine various biophysical parameters, such as refractive index, cell thickness, morphology, etc. On the other hand, fluorescence microscopy is used to acquire information regarding molecular specificity of the biological cells and tissues. Conventionally, a fully coherent light source such as laser is used in QPI technique to obtain the interference fringes with ease; however, its high coherence is also responsible for the generation of speckle and spurious fringes, which results in degraded image quality and affects the phase measurement results too. In this paper, we report a multi-modal system that can be effectively utilized to acquire time varied diverse information about the biological specimen with high spatial phase sensitivity. Herein, a single unit comprising of a fluorescence microscope and the Linnik based interferometer specially equipped with a partially spatially coherent light source illumination was developed. The integrated system is capable to procure molecular specificity and phase information of biological specimen, in a single shot, utilizing a single-chip color CCD camera. Here, we performed experiments on MG63 osteosarcoma cells, and the composite interferometric-fluorescence images were obtained and then digitally decomposed into red and green colors; and, the phase maps were reconstructed using the Fourier fringe analysis method. Furthermore, the cultured cells were monitored over a time-span to observe and investigate the time dependent morphological changes along with the quantification of cellular adhesion and spreading. Hence, the proposed system can be utilized to quantify time dependent changes in the cell’s morphology and in cell adhesion which can be an indicator for the detection of various range of diseases such as arthritis, cancer, osteoporosis and atherosclerosis.

Improved accuracy and defect detection in contour line determination of multiple-beam Fizeau fringes using Fourier fringe analysis technique

Improved accuracy and defect detection in contour line determination of multiple-beam Fizeau fringes using Fourier fringe analysis technique

3D Surface Measurement of Human Abdomen by Fourier Fringe Analysis and Chinese Remainder Theorem

3D Surface Measurement of Human Abdomen by Fourier Fringe Analysis and Chinese Remainder Theorem

Circular fringe projection technique for out-of-plane deformation measurements

Fringe projection is a widely used technique for measurement of out-of-plane deformation of diffusely reflecting objects. Among the various fringe patterns employed for projection, usage of linear fringes is most common. However, the phase function of linear fringes has 2π periodicity, thereby leading to ambiguity in determining whole-field out-of-plane deformation of dynamic objects. This paper presents a new method of measurement of whole-field out-of-plane deformation of targets by projecting a circular fringe pattern. New technique of fringe analysis is introduced to estimate the underlying phase distribution of the fringe pattern from a single image. In this technique, the fringe pattern is coordinate transformed into polar coordinates, and then Fourier fringe analysis technique is employed to obtain its phase. Subsequent to unwrapping, the phase map is re-transformed to Cartesian coordinates. The phase map obtained after coordinate transformation is converted to out-of-plane deformation map using camera calibration parameters. Simulations are carried out to establish the analysis method. Experimental validation is performed with the development of circular grating based fringe projection system.

Improved accuracy in slope measurement and defect detection using Fourier fringe analysis

This communication reports investigation undertaken towards measurement of slope and defect detection of bent plates (rectangular and circular) using moiré deflectometry in conjunction with Fourier transform technique. For slope mapping, specimen is illuminated by collimated light from a laser. The back reflected light from the front surface of the specimen is incident on a set of two gratings placed in tandem, resulting in the formation of laterally sheared interferograms. The interferograms are recorded using a CCD (charge coupled device) camera. Direct phase measurement using Fourier transform method has been used for measurement of slope and detection of defects. The experimental setup is simple and the slope measurement and detection of defects are undertaken successfully in each case. Experimental results conclusively establish the viability of the technique. Good accuracy and precision in measurement have been achieved.

Collimation testing using deflectometry in conjunction with windowed Fourier transform analysis.

In this paper, we demonstrate a simple automated procedure for the detection of collimation of an optical beam by incorporating the windowed Fourier fringe analysis technique into a deflectometric setup. The experimental arrangement consists of a deflectometry-based system in which light from a laser is expanded and passed through a collimating lens. The transmitted light illuminates a coarse sinusoidal grating. The grating image is directly captured through a charge-coupled device. Typical image patterns corresponding to "in-focus," "at-focus," and "out-of-focus" positions of an optical beam are recorded. Depending on the position of the collimating lens, the grating line spacing and the resulting phase of the emerging wavefront varies. Direct phase measurement using the windowed Fourier transform method has been used to obtain the slope map of the wavefront. The slope of the phase map depicts the diverging, collimated, or converging nature of the optical beam. The positioning error of light beam collimation was approximately 1 μm. The experimental arrangement is simple, low cost, and compact. The technique is fully automatic and provides high resolution, high precision, and good sensitivity.

Improved quantitative visualization of hypervelocity flow through wavefront estimation based on shadow casting of sinusoidal gratings.

A simple noninterferometric optical probe is developed to estimate wavefront distortion suffered by a plane wave in its passage through density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a continuous-tone sinusoidal grating. Through a geometrical optics, eikonal approximation to the distorted wavefront, a bilinear approximation to it is related to the location-dependent shift (distortion) suffered by the grating, which can be read out space-continuously from the projected grating image. The processing of the grating shadow is done through an efficient Fourier fringe analysis scheme, either with a windowed or global Fourier transform (WFT and FT). For comparison, wavefront slopes are also estimated from shadows of random-dot patterns, processed through cross correlation. The measured slopes are suitably unwrapped by using a discrete cosine transform (DCT)-based phase unwrapping procedure, and also through iterative procedures. The unwrapped phase information is used in an iterative scheme, for a full quantitative recovery of density distribution in the shock around the model, through refraction tomographic inversion. Hypersonic flow field parameters around a missile-shaped body at a free-stream Mach number of ∼8 measured using this technique are compared with the numerically estimated values. It is shown that, while processing a wavefront with small space-bandwidth product (SBP) the FT inversion gave accurate results with computational efficiency; computation-intensive WFT was needed for similar results when dealing with larger SBP wavefronts.

Study on 3D shape and deformation measurement of a radiator fan based on high-speed binary defocused fringe projection

The binary defocused fringe can overcome the nonlinear effect of an ordinary commercial digital projector and generate a good sinusoidal light field. In this paper, the binary fringe encoding method was chosen to complete the high-speed fringe projection using a DLP Lightcrafter 4500 model in dynamic Fourier transform profilometry, and then a camera was synchronously triggered to record the deformation fringes on the surface of a high-speed rotating radiator fan, whose time-changing 3D surface shape was reconstructed with Fourier fringe analysis. Further deformation analysis of the measured radiator fan blade and rotating shaft is helpful to improve the performance of the radiator. The experimental results on a tested radiator fan with the rotation speed of 4800rpm identified the validity of the presented setup, and this method can effectively expand the application of dynamic 3D shape measurement.

Visualization of acoustic wave using coherent gradient sensing and Fourier fringe analysis

In this communication, we present the results of investigation undertaken towards real time mapping of acoustic wave using coherent gradient sensing and Fourier fringe analysis method. The acoustic wave to be visualized is introduced in the sensing arm of double grating interferometer. Local strain variation, induced because of acoustic wavefront, results in local refractive index modulation. This results in light intensity modulation which allows visualization of strain field. Phase gradient information in the direction perpendicular to grating lines has been determined using Fourier fringe analysis technique. The experiment showed good visibility of the acoustic wave under observation.

Measurement of temperature and temperature profile of candle flame using holo-shear lens and Fourier fringe analysis technique

Holo-shear lens made on dichromated gelatin (DCG) is used as a lateral shear interferometer for measurement of temperature and temperature profile of an axi-symmetric gaseous flame. By using a Fourier fringe analysis technique, high-frequency speckle noise can be filtered out and disturbances of a nonspectral component may also be compensated for. The method is simple and easy to implement.

Vortex array embedded in a partially coherent beam.

Method of generating a vortex array embedded in a partially coherent beam is proposed and experimentally demonstrated. The vortex array exists in the complex coherence function of a random field arising due to interference of three independent coherence functions with appropriate phase profiles. Existence of the vortex array is confirmed by presenting amplitude and phase distributions of the complex coherence function. The phase structure of the complex coherence function, embedded with a vortex array, is obtained by interfering it with an independent fourth coherence function known as a reference and applying the Fourier fringe analysis technique to the cross-covariance of the intensity of the resultant random field.

Improved measurement characteristics in collimation testing using Lau interferometry and Fourier fringe analysis technique

We demonstrate an automated procedure for the detection of collimation position of an incoherent beam in Lau interferometry using Fourier fringe analysis technique. The experimental arrangement consists of a Lau based interferometer in which light from a source grating illuminates a set of two coarse gratings separated by self imaging distance. Direct phase measurement using Fourier Transform Method (FTM) has been used to obtain the slope map of the wavefront and hence the detection of collimation position is undertaken advantageously. The experimental arrangement is simple and interferometric noise is lower. Detailed uncertainty analysis has also been reported. The technique is fully automatic and provides good accuracy and high precision.

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis

A procedure for the measurement of focal length and radius of curvature of a lens using coherent gradient sensing system and Fourier transform fringe analysis technique has been demonstrated. Light from the laser illuminates the specimen and the wavefront emerging from the specimen is tested using coherent gradient sensing interferometer. The fringe pattern corresponding to the test wavefront is stored, and analyzed using Fourier fringe analysis technique. The slope of the wavefront in the direction of shear has been evaluated. It provides the information regarding exact location of points corresponding to the focus/center of curvature of the lens. High accuracy and precision has been achieved.