Interferogram Phase Research Articles

Reducing ionospheric electron density errors in satellite radar interferometry applications

It has been demonstrated that ionospheric electron density disturbances can influence multi-pass satellite radar interferometry (SRI). This has been observed to occur near the magnetic poles, particularly during strong magnetic disturbances. Ionospheric disturbances most clearly appear in interferometric synthetic aperture radar (InSAR) as a kilometre-scale modulation in the azimuth pixel shift needed for optimal registration of the interferometric pair. This modulation (also known as "azimuth streaks") also affects the InSAR phase, and consequently such SRI applications as digital elevation model (DEM) generation and displacement measurement, and may appear as "streaks" in the coherence map. The effect is worse for L-band systems (e.g., Japanese Earth resources satellite 1 (JERS-1) and Phased array type L-band synthetic aperture radar (PALSAR)), but can be significant even at C band (e.g., European remote sensing satellites ERS-1/2 and RADARSAT I and II). The influence of ionospheric effects on interferogram phase can often be predicted, and the magnitude can be estimated, by an inspection of a map of the shift in azimuth position for optimal registration obtained using the "speckle tracking" technique. For DEM generation, the ionospheric phase contribution can be approximated, and removed from the interferogram phase, by the scaled and filtered integral of this azimuth shift map. For displacement-measurement applications, appropriate filtering of the distinct patterns of the azimuth streaks is the only resort.

On the evaluation of the true phase of interferograms

AbstractAn iterative technique that uses sine and cosine modulations along with low‐pass filtering to extract the true phase values of a carrier frequency interferogram is proposed in this paper. An illustrative example is given in which this technique is applied. Results generated from the application of this technique are compared with exact phase values, and excellent agreement between the exact and computed phase values is demonstrated. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 40–43, 2002.

Reduction of the edge effects induced by the boundary of a linear-carrier interferogram

There are a great variety of techniques used to obtain the wrapped phase of a carrier frequency interferogram. We are interested in interferograms whose data points lie in bounded region data. Analysis of this kind of interferogram with the Fourier or synchronous method contains an important source of error at its edge. In this paper we propose a new method that reduces this boundary error effect. This method consists of an iterative technique to obtain a very good estimate of the phase of a carrier frequency interferogram bounded by an arbitrary pupil's shape. We suggest a method in order to reduce the boundary effects at the edge by giving a first phase estimation obtained by the Fourier or synchronous method.

Iterative method to obtain the wrapped phase in an interferogram with a linear carrier

There is a great variety of techniques used to obtain the wrapped phase of a carrier frequency interferogram. We are interested in interferograms that have a bounded region data. Analyses of this kind of interferograms with the Fourier or synchronous method have an important source of error at the edge of the interferogram. In this paper we propose a new method that works out this boundary error effect. We describe an iterative synchronous method to obtain a very good phase estimation of a carrier frequency interferogram bounded by an arbitrary pupil's shape. We also show that the proposed iterative method has a continuous and stable convergence towards the true modulating phase of the interferogram.

Data-dependent systems profilometry of two-dimensional surfaces

Fourier-transform profilometry (FTP) and data-dependent systems profilometry (DDSP) are two methods that are available for recovering one-dimensional fine surface profiles from the phase of a single interferogram. FTP has already been extended to two-dimensional surfaces; a similar extension of DDSP is introduced here. Inasmuch as this extension involves autoregressive modeling of the rows or columns of an interferogram, the feasibility of using a common model order is explored. The common order reduces not only the amount of computation but also the errors caused by the heterodyned phase-removal procedure. As autoregression requires masking the first few data values, the length of the mask is determined by means of a Green's function. A comparison shows that DDSP outperforms FTP in roughness measurements in terms of rms and center-line average. The comparison also shows that DDSP is able to recover a detailed surface, whereas FTP outlines only the global features. An interferogram regeneration procedure provides a reference surface for the verification of results.

Regularization methods for processing fringe-pattern images

A powerful technique for processing fringe-pattern images is based on Bayesian estimation theory with prior Markov random-field models. In this approach the solution of a processing problem is characterized as the minimizer of a cost function with terms that specify that the solution should be compatible with the available observations and terms that impose certain (prior) constraints on the solution. We show that, by the appropriate choice of these terms, one can use this approach in almost every processing step for accurate and robust interferogram demodulation and phase unwrapping.

Application of Gabor transformation to the two-dimensional projection extraction in interferometric tomography

In interferometric tomography, two-dimensional projection extraction, i.e., wave-front retrieval from interferograms, is a critical step for a successful three-dimensional reconstruction. We analyze the difficulty of locating the first-order frequency spectrum—a difficulty inherent in interferogram phase unwrapping by means of the traditional Fourier transform. The problem becomes more serious when we deal with interferograms obtained in real experiments, which usually lack exactly parallel and equally spaced references. To overcome this difficulty, we propose the method of localized matching filtration with Gabor filters and apply it, for the first time to our knowledge, to interferogram phase demodulation. A multi-channel Gabor spatial filter set is constructed to yield the optimally matched local spatial frequency. The optimization is aimed at maximizing the L2(R2) norm of the output of the filters. At the same time, noise and opaque objects are removed. The method, applied to both simulated and real interferograms, proves to be more effective and more flexible than the conventional Fourier transformation method, especially in cases in which references are not equally spaced and fringes are seriously deformed.

Validation of along-track interferometric SAR measurements of ocean surface waves

C-band HH-polarized along-track interferometric synthetic aperture radar (ATInSAR) images of ocean waves from the Canada Centre for Remote Sensing (CCRS) CV-580 SAR are used to study ATInSAR wave imaging fidelity. ATInSAR phase spectra are derived using cross spectra between the interferogram phase generated from individual look complex SAR images. The resulting observed phase spectra are quantitatively compared with forward-mapped in situ directional wave spectra collocated with the ATInSAR observations. The forward mapping models include two quasilinear forward transforms that include varying degrees of velocity bunching nonlinearity, both of which include an azimuth null in the modulation transfer function, and an implementation of the fully nonlinear forward transform. The null arises from the cancellation of upward and downward orbital velocity components within a resolution cell. The second of the two quasilinear transforms and the nonlinear forward transform are shown to have agreement with the observed velocity spectra, as measured by correlation coefficients between the observed spectra or forward-mapped spectra and the ATInSAR spectra. ATInSAR can allow a direct measurement of the orbital velocity spectrum. There is, however, an added layer of complexity caused by the cancellation of upward and downward orbital velocity components within a resolution cell. Furthermore, the SAR complication of velocity bunching nonlinearity is not avoided by using an ATInSAR.

Validation of alpine glacier velocity measurements using ERS Tandem-Mission SAR data

Five ascending and four descending ERS-1/2 tandem-mode synthetic aperture radar (SAR) interferometry (InSAR) data pairs with useful scene coherence are used to measure the surface flow field of an alpine glacier in the Canadian Rocky Mountains. The topographic component of the interferogram phase is calculated by using a digital elevation model (DEM) of the terrain and precise orbit data to reconstruct the ERS InSAR imaging geometry. The DEM is derived from the Canada Centre for Remote Sensing (CCRS) Convair-580 airborne SAR interferometer. As dual line-of-sight (LOS) measurements are not sufficient to completely resolve the three-dimensional (3D) surface flow field, several different assumptions for determining the missing variables are considered, and the 3D surface flow field is estimated by using single and dual LOS measurements. The InSAR results agree with historic and coincident displacement measurements made using traditional point surveying techniques.

Phase correction in piezoelectric photoacoustic Fourier transform infrared spectroscopy of mica

Piezoelectric photoacoustic IR spectra of mica are obtained using a Fourier transform IR spectrometer and lead zirconate titanate (PZT) as a detector. The spectra exhibit negative intensities and transmission like bands, instead of more conventional absorption bands generally observed with a gas-microphone cell. Correct spectra of mica/PZT are calculated only when the interferogram phase is constrained to the first and fourth quadrants, similar to the case in differential spectroscopy where negative intensities occur. © 1997 Society of Photo-Optical Instrumentation Engineers.

Δk-radar equivalent of interferometric SAR's: a theoretical study for determination of vegetation height

Theoretical aspects of estimating vegetation parameters from SAR interferometry are presented. In conventional applications of interferometric SAR (INSAR), the phase of the interferogram is used to retrieve the location of the scattering phase center of the target. Although the location of scattering phase center for point targets can be determined very accurately, for a distributed target such as a forest canopy this is not the case. For distributed targets the phase of the interferogram is a random variable which in general is a function of the system and target attributes. To relate the statistics of the interferogram phase to the target attributes, first an equivalence relationship between the two-antenna interferometer system and an equivalent /spl Delta/k radar system is established. This equivalence relationship provides a general tool to related the frequency correlation function (FCF) of distributed targets, which can conveniently be obtained experimentally, analytically, or numerically, to the phase statistics of the interferogram. An analytical form for the p.d.f. of the interferogram phase is obtained in terms of two independent parameters: 1) /spl zeta/: mean phase and 2) /spl alpha/: degree of correlation. /spl zeta/ is proportional to the scattering phase center and n is inversely proportional to the uncertainty with which /spl zeta/ can be estimated. It is shown that /spl alpha/ is directly related to the FCF of the distributed target which in turn is a function of scattering mechanisms and system parameters. It is also shown that for a uniform closed canopy the extinction and the physical height of the canopy top can be estimated very accurately. Some analytical and numerical simulations are demonstrated.

Application of SAR data to monitoring of earthquake disaster

Surface changes and displacement caused by the Hyogoken-nanbu earthquake on 17 January 1995 are detected using JERS-1 SAR images with interferometric radar technology. The SAR signal data covering the damaged area were contaminated by serious bright line noise caused by interference with a ground radar system. With a spectral filtering technique, the signal data were processed into clear images. Collapsed non-wooden buildings and guarys were detected by comparing pixel brightness between a pair of images before and after the earthquake. A phase interferogram of the two images shows 0.6 m surface displacement along the radar line-of-sight direction around Kobe City, while it is 1.1 meter in Awaji Island where epicenter is located.

Harmonic analysis in a large ring laser with backscatter-induced pulling.

Analytical solutions for the beam intensity, interferogram, and instantaneous phase are found for a ring laser with backscatter. The harmonics of these signals form geometric progressions, whose ratios depend differently on pumping, pulling, and the net backscatter phase. The latter phase depends on the time-reversal symmetry of the scatterers and on their location. We also report confirmatory results in the Canterbury ring laser system, with a quality factor up to 7.5\ifmmode\times\else\texttimes\fi{}${10}^{10}$ and a present frequency resolution of 140 nHz, and where thermal changes in the net backscatter phase dominate other causes of drift.

Phase and Image Reconstruction from Pupil-Plane Observations in the Near Infrared: Integration of the Phasors

A new method to reconstruct the phase of bidimensional interferograms, obtained through pupil-plane interferometry is presented. We compute the average complex phasor components of the cross-spectrum on a data set to reconstruct the original unperturbed phase. We present preliminary results on simulated images which visibility phases are distorted using a model of atmospheric perturbed wavefronts.

Two-Dimensional Infrared Spectroscopy of Electric-Field-Induced Reorientation Dynamics of a Mixed Nematic Liquid Crystal

A two-dimensional infrared (2D IR) spectrometer has been modified by the following methods to solve several problems on the 2D IR spectroscopy of electric-field-induced reorientation dynamics of a mixed nematic liquid crystal: (1) The response of the liquid crystal (LC) to an electric field was stabilized by an amplitude-modulated ac electric field. (2) Formulation of an anti-reflection coating (ARC) has been proposed to suppress the interference caused by multiple reflections between IR liquid crystal cell windows. (3) The Fourier transform procedure has been modified to correct the phase of the dynamic difference interferograms without spectral anomalies. These modifications can provide a better signal-to-noise ratio and reproducible 2D IR spectrum of a mixed nematic liquid crystal.

Fringe analysis for automotive applications

The capabilities of Ford USA's Computer Aided Holometry (CAH) system for stepped phase interferometry are presented. Holographic test equipment and facilities are briefly reviewed. Fringe analysis algorithms and procedures for practical semi-automated processing of stepped phase interferograms of complex real life structures for quantitative measurement of deformation and shape are discussed. Several automative applications illustrating the fringe analysis technique are presented, including: (1) the use of CAH combined with Finite Element Analysis (FEA) methods to study frictional effects of the thermal insertion of a wrist pin into a connecting rod; (2) a study of engine deformation due to hydraulic loading of the cylinders; and (3) the computation of sound pressure from CAH measured vibration amplitude/phase and shape using the Rayleigh integral and SYSNOISE TM methods. In the past, holometry methods have been used primarily for problem solving in structures that were already in production, often where limited opportunities existed to make expensive modifications to existing tooling. Infrequently holometry was used by knowledgeable engineers to develop optimized components in the prototype stage even without the current CAE methods. The opportunity and challenge of our day is to closely couple CAE (FEM, EFA) methods and experimental methods (CAH, modal, etc.) to optimize structural performance in the upstream product development process where necessary tooling modifications can and will be made.

Simulation studies of ultrasonic backscattering and B-mode images of liver using acoustic microscopy data

Data obtained from a scanning laser acoustic microscope (SLAM) were used to examine several aspects of ultrasonic backscattering from the liver. Phase interferograms from normal and abnormal human-liver specimens were digitized, and a series of algorithms was used to compute images of propagation velocity within the specimens. The propagation velocity images were then employed to simulate A- and B-mode results. These initial simulations were used to investigate how ultrasonic echo signals are related to tissue microstructure. Among the topics examined were B-mode speckling, frequency and beamwidth effects, and angulation dependencies.

Phase Correction of Vibrational Circular Dichroic Features

Several sources of phase-correction-induced spectral anomalies in FT-IR vibrational circular dichroism (VCD) spectra have been investigated. Misidentification of the zero-phase retardation position in dichroic interferograms that exhibit no optical or electronic bias can produce spectral errors. Production of such errors is from the introduction of linear phase error into the phase curve. When the zero-phase retardation position is correctly identified, other spectral anomalies, such as “reflected peaks,” can appear in VCD spectra. These peaks are readily observed in quarterwave plate reference spectra. The anomalies are directly correlated to the arctangent function used to define the phase curve and result only from the nature of the VCD signal. VCD spectra can exhibit negative, as well as positive, peaks; consequently the phase correction must be designed to accommodate negative features. Both Mertz and Forman phase-correction algorithms have been modified to correct the phase of VCD interferograms without error. Such corrections are not necessary, or even desirable, for normal absorption spectrometry.

Modified phase correction algorithms in VCD/FT-IR spectrometry

Phase correction induced spectral anomalies in FT-IR vibrational circular dichroism (VCD) spectra have been investigated. Spectral anomalies can appear in VCD spectra such as “reflected peaks”. These peaks are readily observed in quarterwave plate reference spectra. The anomalies are directly correlated to the arctangent function used to define the phase curve and result only from the unique nature of the VCD signal. Both Mertz and Forman phase correction algorithms have been modified to correct the phase of VCD interferograms without error.

Interferometry holographic investigation of a laser spark

The image of laser spark in three phases of its development is produced with two beam holographic method. For the same phases of breakdown holographic interferograms are produced by use of two exposures method. Both type of holograms allow one to define electron density in the range 2×10 19 - 0.7×10 19 within 40–120 nsec after beginning of breakdown.