Processing Interferograms Research Articles

Surface profile measurement using nonlinear optimization approach in diffraction phase microscopy

Nanoscale measurement of surface profile has important application in the field of non-destructive surface testing and evaluation. We propose a nonlinear optimization based phase retrieval approach in diffraction phase microscopy for nanoscale surface profile measurement. The proposed approach relies on minimizing an objective function derived from the interferogram signal and the application of total variation regularization. The performance of the method is demonstrated via numerical simulations for processing interferograms affected by sharp phase variations, noise and non-uniform amplitude fluctuations. In addition, the practical application of the method is validated for nanoscale surface topography by processing experimental interferograms obtained in diffraction phase microscopy.

Application of the non-uniform Fourier transform to non-uniformly sampled Fourier transform spectrometers

Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly overlooked. With the aid of experiments on a high-resolution interferometer with a variety of optical sources, these two methods are compared. It is found that the NUFFT is comparable to interpolation in spectral profile shape and spectral noise levels and is better in spectral amplitude and computer performance. A significant advantage is also found in the case of under-sampling and noise performance by NUFFT due to the unique non-periodic nature of non-uniform sampling. In addition, a novel implementation of NUFFT is presented and analysed.

FPGA-Based Hardware Implementation of Homodyne Demodulation for Optical Fiber Sensors

Homodyne demodulation is a convenient technique for signal detection in interferometric sensors. The demodulation process is typically developed using analog circuits. However, to improve the performance of the demodulator, a digital system must be employed. In this study, we developed an optical fiber sensor by combining: (a) a Michelson interferometer, (b) a micro-electro-mechanical system (MEMS) device, and (c) a field-programmable gate array (FPGA)-based interrogator. Signal processing was integrated into the FPGA-embedded system. The homodyne demodulation algorithm was implemented with hardware modules developed in the hardware description language (HDL) to provide a portable, low-cost, and scalable digital system. The present study successfully demonstrates the development and validation of an FPGA-based interrogator capable of processing interferograms through a homodyne demodulation scheme. The experimental results reveal proper displacement measurements of the proof-mass MEMS and the low amount of hardware resources used. The displacement measurements obtained from the system matched those obtained from a certified characterization system. As the system can be easily reconfigured to the required measured signal, a similar measurement methodology can be developed using other demodulation schemes and optical fiber sensors.

Deep neural network for fringe pattern filtering and normalization.

We propose a new framework for processing fringe patterns (FPs). Our novel, to the best of our knowledge, approach builds upon the hypothesis that the denoising and normalization of FPs can be learned by a deep neural network if enough pairs of corrupted and ideal FPs are provided. The main contributions of this paper are the following: (1) we propose the use of the U-net neural network architecture for FP normalization tasks; (2) we propose a modification for the distribution of weights in the U-net, called here the V-net model, which is more convenient for reconstruction tasks, and we conduct extensive experimental evidence in which the V-net produces high-quality results for FP filtering and normalization; (3) we also propose two modifications of the V-net scheme, namely, a residual version called ResV-net and a fast operating version of the V-net, to evaluate potential improvements when modifying our proposal. We evaluate the performance of our methods in various scenarios: FPs corrupted with different degrees of noise, and corrupted with different noise distributions. We compare our methodology versus other state-of-the-art methods. The experimental results (on both synthetic and real data) demonstrate the capabilities and potential of this new paradigm for processing interferograms.

Cascaded multi-baseline interferometry with bistatic TerraSAR-X/TanDEM-X observations for DEM generation

As the spaceborne mission dedicated to bistatic SAR interferometry (InSAR), the TerraSAR-X/TanDEM-X satellite constellation can acquire highly coherent data pairs with flexible baseline configurations and minimal atmospheric disturbances, which are well suited for high-accuracy DEM generation. However, hindered by the intrinsic contradiction between sensitivity of height measurement and reliability of phase unwrapping in terms of normal baseline length, as well as geometric distortions of layover and shadow, it is still difficult to generate high-quality DEM in mountainous areas using single-baseline InSAR data. Aiming at these two problems, we developed a cascaded multi-baseline InSAR processing framework for DEM generation from multiple bistatic InSAR observations with variable normal baselines and different imaging geometries. By starting from phase unwrapping and phase-to-height conversion for the interferogram with shortest normal baseline, this approach adopted a strategy of DEM updating assisted by a reference elevation dataset. The updated DEM is then used as the reference for processing interferograms with longer baselines successively. In this iterative way, the quality of the resultant InSAR DEM can be improved gradually. In addition, fusion between multiple geocoded InSAR DEMs derived from different orbits is carried out to further refine the results by filling data voids and reducing random height noise. To demonstrate the effectiveness of the proposed method, we apply it to four pairs of stripmap-mode TerraSAR-X/TanDEM-X bistatic data covering the Mount Song area in central China. The vertical accuracies of the generated DEMs are evaluated using an aerial photogrammetric DEM, ICESat/GLAS measurements, and the standard TanDEM-X global DEM product. The experimental results show that the absolute height error of the generated multi-baseline InSAR DEM at 5 m posting is less than 10 m in typical mountainous areas and can meet the American HRTI-3 standard, which means the generated DEM has similar height accuracy and higher spatial resolution in comparison with the 12 m TanDEM-X global DEM products.

One example of image digital processing of experimental data obtained by the method of photoelasticity

The article is devoted to the digital processing interferograms (isochromatic fringe patterns) obtained by the photoelasticity method. The application to interpretate the isochromatic fringe patterns allows us to automate image processing, gets to avoid the routine and time-consuming work. The features of the developed software package are described in detail by means the problem of stretching plate with two symmetrical edge notches. The application’s algorithm includes following main steps: image pre-processing, localization interference fringe, fringe tracing. The application creates a text file containing all the necessary data to further determine the stress-strain state (isochromatic fringe’s number and locus of fringes).

DIGITAL PROCESSING OF INTERFEROGRAMS OBTAINED BY THE PHOTOELASTICITY METHOD

The article is devoted to the digital processing interferograms (isochromatic fringe patterns) obtained by the photoelasticity method. An application to interpretate the isochromatic fringe patterns is developed. It allows us to automate this procedure, gets to avoid the routine and time-consuming work. The features of the developed software package are described in detail by means of the classic problem of a diametrically compressed disk. The applications algorithm includes following main steps: image pre-processing, localization interference fringe, fringe tracing. The application creates a text file containing all the necessary data to further determine the stress-strain state (isochromatic fringes number and locus of fringes).

Effective Method for Determining Chromatic Dispersion From a Spectral Interferogram

We present a novel method for determining chromatic dispersion profile from a broadband spectral interferogram obtained by using a white-light interferometry technique. The proposed method is based on direct calculations of a second derivative of the registered spectral intensity at extremal points, which in result gives a spectral phase difference derivative further used for dispersion determining. Although the method is best suited for processing interferograms with modulation around a zero level (zero-mean value interferograms) and slowly changing envelope, the conducted numerical tests show that it is highly tolerable to different types of perturbations of the input interference signal. The proposed method can be applied both to spectral interferograms with monotonically changing phase difference as well as containing stationary phase difference points. We demonstrate the effectiveness and accuracy of the proposed method in measurements of chromatic dispersion of commercially available samples like the BK7 glass plate and the Corning SMF-28 optical fiber.

Spectrum reconstruction in Fourier transform imaging spectroscopy based on high-performance parallel computing.

In this paper, parallel-processing algorithms for spectrum reconstruction in Fourier transform imaging spectroscopy are proposed using high-performance parallel computing. Because of the huge amount of interference data, traditional algorithms are inefficient and time-consuming. It is necessary to process interference data as soon as possible to form spectral data for research and economy. We take advantage of parallel computing based on the graphics processing unit (GPU) to enable higher efficiency and reduced operation time. Furthermore, traditional algorithms for processing interferograms on the central processing unit are introduced for comparison. The experimental results show that the runtime is reduced from 1.144 to 0.332ms using our parallel algorithms, and for the huge amount of data, the designed parallel-processing mechanism on the GPU has advantages over the traditional pipeline.

Features of interferometry of small-sized plasma channels obtained during nanosecond discharge

The applicability of the method of smooth perturbations for processing interferograms of small (5–100 μm) objects by taking into account the diffraction is investigated. The test problems showed the consistency of the method to the range of parameters that are interesting for us. The requirements for preliminary processing of experimental data are determined, adhering to which it is possible to improve the accuracy of the final results. The analysis of experimental interferograms by assuming the cylindrical symmetry of the plasma object is carried out: the two-dimensional map of the electron density for the plasma object formed at the initial stage of nanosecond discharge was obtained from the phase map.

Experimental validation and characterization of a real-time metrology system for photopolymerization-based stereolithographic additive manufacturing process

Exposure Controlled Projection Lithography (ECPL) is a stereolithography-based additive manufacturing process, curing photopolymer parts on a stationary substrate. To improve the process accuracy with a closed-loop control, an in situ interferometric curing monitoring and measurement (ICM&M) system was developed to infer the output of cured height. The authors have previously reported an ICM&M method which consists of a sensor model for the ICM&M system and online parameter estimation algorithms based on instantaneous frequency. In this paper, to validate the ICM&M method, an application program was created in MATLAB to integrate the ECPL and ICM&M systems and to acquire and analyze interferograms online. Given the limited computing power, the ECPL process interferograms were acquired real time and analyzed off-line. A series of experiments was performed curing square samples by varying exposure time and intensity. Results show that the ICM&M can provide a cost-effective measurement for cured heights with excellent accuracy and reliability, and possess decent capability of estimating lateral dimensions. The off-line ICM&M is a convincing demonstration and benchmark for the real-time ICM&M metrology, providing a comprehensive evaluation of the ICM&M system’s measurement characteristics as well as its utilities in modeling and control of the additive manufacturing process dynamics.

Demodulation of two-shot fringe patterns with random phase shifts by use of orthogonal polynomials and global optimization.

We propose a simple and robust phase demodulation algorithm for two-shot fringe patterns with random phase shifts. Based on a smoothness assumption, the phase to be recovered is decomposed into a linear combination of finite terms of orthogonal polynomials, and the expansion coefficients and the phase shift are exhaustively searched through global optimization. The technique is insensitive to noise or defects, and is capable of retrieving phase from low fringe-number (less than one) or low-frequency interferograms. It can also cope with interferograms with very small phase shifts. The retrieved phase is continuous and no further phase unwrapping process is required. The method is expected to be promising to process interferograms with regular fringes, which are common in optical shop testing. Computer simulation and experimental results are presented to demonstrate the performance of the algorithm.

Generalized phase-shifting interferometry by parameter estimation with the least squares method

A simple non-iterative algorithm for generalized phase-shifting interferometry is proposed. This algorithm recovers the wrapped phase from two or more interferograms with unknown phase steps between 0 and π rad. The proposal is based on the least squares method to calculate four parameters: background and modulation light, phase steps and wrapped phase distribution. This algorithm, by a new interferogram normalization procedure, can handle interferograms with variable spatiotemporal visibility overcoming the restriction and drawbacks from usual variable spatial visibility approaches. The algorithm works very well for processing interferograms which include many fringes. This behaviour will be explicated and discussed. The effectiveness and robustness of this algorithm are supported by numerical simulation and by the evaluation of experimental interferograms. The phase-shift estimation quality is verified by two different techniques. By the properties of this algorithm, such as the low computing time and free of user intervention, we believe it could be used in automatic real-time applications.

A technological program for processing interferograms by Fourier transformation

This paper describes the production of topographical maps of the surfaces of optical items by Fourier transformation. Software is presented that is used in fabricating high-accuracy aspheric optics. A comparative analysis is carried out of this method with the amplitude method used earlier in the process of shaping and monitoring the surfaces of optical items. It is concluded that this method is suitable for monitoring the surfaces of optical items.

Technique for obtaining and processing spectral information with static fourier spectrometer

We propose a technique and algorithm for processing interferograms obtained with a static Fourier spectrometer. Spectra of secondary radiation from certain compounds are obtained in the visible and near-UV spectral ranges upon excitation by different radiation sources. We present and discuss results of experimental data processing.

Reconstructing wave-front topography from an interferogram by means of digital holography

This paper discusses the question of reconstructing wave-front topography from an interferogram, using the method of digital holography. An implementation of the method that makes it possible to process interferograms in the automatic regime is discussed.

Two-step phase-shifting algorithm

A novel two-step phase-shifting algorithm for use in detecting wavefront phase is presented. This algorithm is very insensitive to detuning. The short time needed to acquire and process interferograms helps to minimize phase errors caused by vibration, temperature effects, and nonlinear errors of the piezoelectric transducer. The rms error due to detuning does not change as in classical phase-shifting algorithms with respect to the selected ideal phase shift. The resulting wrapped phase is modulo 2π. Finally the phase error is analyzed.

Correlation-Based Data Processing for an Inductively Coupled Plasma/Fourier Transform Spectrometer System

A simple cross-correlation technique is presented for processing interferograms generated by an ultraviolet-visible Fourier transform spectrometer coupled to an inductively coupled plasma. Interferograms resulting from the emission of samples in the ICP can be automatically interrogated for the presence or absence of up to 70 elements, and automatic qualitative analysis is possible, complete with an assessment of spectral overlaps. In concept, the cross-correlation method amounts to “software slew-scanning” as it provides one with an a posteriori method to study and select the spectral information about the sample as measured with the FTS-ICP system. This represents a unique spectrochemical measurement capability compared with current dispersive-based, direct-reading, and slew-scanning spectrometers as applied to ICP emission spectrometry.