Dem generation february 2014 ieee transactions on geoscience and remote sensing 522. Phase unwrapping techniques address this problem by using multifrequency phase tof, where each frequency yields phasor measurement 22,3. Data of this form are found in many applications, but the advent in the early 1990s of synthetic aperture radar interferometry insar, in. Then in terms of the interferometric phase, it means we can write the first term represents the phase difference measured for the flat earth, i. The execution time for our algorithm is equivalent to the computation time required for performing. Interferometric synthetic aperture radar phase unwrapping. Interferometry has been successfully applied to both satellite and. Unwrap the phase angles by first comparing the elements columnwise. A phase unwrapping algorithm for interferometric fringes based. Discussion about the dctfft phaseunwrapping algorithm. This paper presents a new efficient algorithm of filtering and unwrapping phase images for interferometric synthetic aperture radar insar based on nonlinear phase model.
The phase overtime signal is extracted from ffts at the same fft bin for all the ffts. When performing the multilook process for data that will be used for phase unwrapping, the coherence band coh must be included along. Phase unwrapping the wrapped phase comes in the range of 0, 2x1 and the goal of phase unwrapping is to get a continuous phase out of it. Digital terrain elevation data level 2 specifications. Guidelines for sar interferometry processing and interpretation. We present an algorithm that solves the phase unwrapping problem, using a combination of fourier techniques. All these algorithms begin with the measured gradient of the phase field, which is subsequently integrated to recover the unwrapped phases. A fast, automated, ndimensional phase unwrapping algorithm. We will use matlab software to perform the required computer simulations. Eege 157 b, week 3 3 10 radar interferometry trigonometry continued now let represent the look angle to a point on a flat earth as shown in the figure.
The phase of the radar echoes may only be measured modulo 2 however, the whole phase at each point in the image is needed to obtain elevations. While interferometry concepts are old, by combining old interferometry concepts with modern electronics, computers, and software, interferometry has become an exciting modern topic. Go ahead and set it to the same value, then run step 6. This model allowed us to verify and test our phase interferometry df implementation before converting it to a c algorithm and performing tests with live data. The unwrapped phase can be evaluated by a simple pathindependent integration of the phase differences of adjacent wrapped phases, starting from a reference location and using the assumption that all phase differences are in the interval. Given a troublefree wrapped phase map, it is enoughforonetosearchrowbyrow orcolumnby column. Osa fast phase unwrapping algorithm for interferometric. And these phase unwrapping methods can be grouped into three main classes in aspects of operating domain. The issued phase is called the splitband phase figure 1.
Integrated laplacianbased phase unwrapping and background. Pdf threedimensional phase unwrapping for satellite radar. Osa spatiotemporal threedimensional phase unwrapping in. A wide range of interferometric techniques recover phase information that is mathematically wrapped on the interval. Mode 1 is manual operation of mouseselecting side peak the peak containing phase information of the interferogram in. The results presented for pumf were obtained with matlab coding max flow al. In all cases the problem is that the measuredphase signal can only take on values in a range, whilst the original phase signal can take on any value. The splitband interferometry approach to determine the. Then in terms of the interferometric phase, it means we can write the first term represents the. Phaseshifting interferometry avoids the need to track. Ieee transactions on geoscience and remote sensing, 52 2, 10591075. The inverse of the phase variance is used as a weighting factor to reduce the in. Matched spatialphaseshifting for the temporalphase.
Guidelines for sar interferometry processing and interpretation tm19, february 2007 editor. Several methods, 10 have been pro9 posed to solve the equation. Obtaining the true unwrapped phase is a longstanding problem. Fast unwrapping 2d phase image using the algorithm given in. The unwrapped phase values can be then calculated by the inverse fourier. Fast 2d phase unwrapping file exchange matlab central.
Nov 22, 2016 in phase retrieval applications, such as interferometry, people are facing the problem of phase being wrapped i. Matlab function for extraction of phase from interferogram. Feb 23, 2009 two 2d phase unwrapping approaches are included. Whereas most books solely address the theory behind these 3d imaging techniques, this monograph concentrates on the exact code needed to perform complex mathematical and physical. The phaseovertime signal is extracted from ffts at the same fft bin for all the ffts.
An alternative, which will leave the data untouched, is phase wrapping. This 7 method represents the unwrapped phase function by a truncated taylor series and a residual function. Phase unwrapping in three dimensions with application to. The three main techniques used in passive direction nding df are time di erence of arrival tdoa, amplitude comparison, and phase interferometry. By demodulating the phase on a single reference point or multiple reference points using temporal phase unwrapping.
Phaseshifting interferometry is a powerful means of analyzing interferograms to recover the. A new method for temporal phase unwrapping of persistent. This is my built function for matlab used for extraction of phase from interferogram in interferometry. A twostage programming mb pu approach tspa proposed by h. Improvements are presented in order to use this method in areas with intensely fluctuated fringe lines. We investigate an iterative unwrapping technique recently published by ghiglia and romero j. Abstracttwodimensional 2d phase unwrapping is a key step in the analysis of interferometric synthetic aperture radar insar data.
A lissajous pattern is formed in phasor space by tracing out phasors at multiple frequencies. Then a modelbased method for phase unwrapping was introduced by liang. His main research interests are in the fields of phase unwrapping and synthetic aperture radar interferometry signal processing and applications. Current wholefield interferometric techniques yield a phase distribution in modulo 2 removal of the resulting cyclic discontinuities is a process known as unwrapping, which must be performed before the data can be interpreted. Because the phases are wrapped, so i need to do an unwrapping for the phases. Please refer to for detailed discussion of the algorithm. In order to understand this tutorial it is necessary for you to have. We propose a hybrid spatiotemporal threedimensional phase unwrapping algorithm for use in digital speckle pattern interferometry dspi.
A two stage programming mb pu approach tspa proposed by h. Whereas most books solely address the theory behind these 3d imaging techniques, this monograph concentrates on. Phase unwrapping is one of the key problems in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar insar or interferometric synthetic aperture. Dengfeng chai received his bs degree in surveying engineering from wuhan university, his ms degree in photogrammetry and remote sensing from wuhan university, and his phd in applied mathematics from.
Holography is the only truly threedimensional imaging method available, and matlab has become the programming language of choice for engineering and physics students. Satellite radar interferometry twodimensional phase unwrapping richard m. This paper discusses a phase unwrapping algorithm based on fringe line detection. Quantitative evaluation of interference fields for interferometric measurements consists of the. We present a robusttonoise phase unwrapping algorithm based on a global analysis of the interferogram. Two image pairs and no motion in one of them with two interferometric pairs four sar images and no terrain motion in one of them. Phasemeasuring, phaseshifting or phasestepping interferometry is a technique used in the analysis of interference patterns generated by multiple beam interferometry. Phase unwrapping once happy with the ps selection you can unwrap the phase using stamps step 6. Digital elevation models can be computed from ers interferometric products. For optimal unwrapping results, it is recommended to multilook i. Osa unwrapping of interferometric phasefringe maps by.
In phase retrieval applications, such as interferometry, people are facing the problem of phase being wrapped i. This thesis introduces a new energy minimization framework for phase unwrapping. Mode 1 is manual operation of mouseselecting side peak the peak containing phase information of the interferogram in the frequency space for the interferogram. This is a critical step in the insar processing chain, yet still one of its most challenging problems. Traditionally, interferograms were measured by locating the center of a fringe and then tracing along the fringe. Esa publications estec postbus 299 2200 ag noordwijk the netherlands tel. Matched spatialphaseshifting for the temporalphase unwrapping in electronic speckle pattern interferometry r. Shape measurements using temporal phase unwrapping diva. A method of filtering and unwrapping sar interferometric phase based on nonlinear phase model by h. Phase unwrapping is the inference of absolute phase from modulo2. This tutorial walks through the special considerations needed when working with s1 tops data for insar. Ulrych university of british columbia, vancouver, bc, canada computation of the complex cepstrum uses the logarithm, and in complex analysis the logarithm is multivalued. Psi has existed in its basic form for less than 3 decades, and may be regarded as temporal. Asynchronouscombinationspatialcarrierphase shifting and temporalphaseunwrapping.
Generalized phase unwrapping for multiwavelength interferometry. Phase unwrapping is a problem that occurs in several. The results presented for pumf were obtained with matlab coding maxflow al. Phase wrapping is an artifact occuring in phase tof where depth can only be recovered to a modulo factor.
Discussion about the dctfft phaseunwrapping algorithm for. Threedimensional phase unwrapping for satellite radar. Image parts zero for 0 or in absence of noise real and imaginary parts never crosses. Temporal phase unwrapping algorithms for fringe projection. Twodimensional phase unwrapping theory, algorithms and. The splitband interferometry approach to determine the phase. Thus the brightness distribution of a source with the coordinates.
Phase unwrapping refers to the process of recovering the absolute phase. In for example a detector with 8bit depth the intensity. During unwrapping, the data are temporarily resampled to a grid. Phase unwrapping, interferometric synthetic aperture radar. Threedimensional phase unwrapping for satellite radar interferometry, i. Efficient phase unwrapping architecture for digital. The feature of the proposed algorithm is the integration of onedimensional temporal and twodimensional spatial phase unwrapping algorithms. In order to clear the contribution of the previous work on the incremental breadthfirst search ibfs method applied to the puma algorithm, we add one more reference to the existing reference list, as in this erratum. While phase unwrapping algorithms have proliferated over the past 10 years, two main approaches are currently in use. Data of this form are found in many applications, but the advent in the early 1990s of synthetic aperture radar interferometry insar, in particular, spurred interest in developing reli. Denoising phase unwrapping algorithm for precise phase. Zebker and yanping lu department of geophysics, stanford university, stanford, california 943052215 received may 5, 1997. This means that the development of a robust phase unwrapping algorithm is an.
E unified theory of phase unwrapping approaches in multiwavelength interferometry. Phase unwrapping, least square optimisation, digital elevation model introduction. Matlab and octave have a function called unwrap which implements a numerical algorithm for phase unwrapping. The tutorial covers creating subsets, coregistration, spectral filtering, interferogram formation, coherence estimation, topographic phase removal, phase filtering, phase unwrapping. An interferogram contains an enormous amount of information. Phase unwrapping algorithms for radar interferometry. In this paper, we propose an algorithm that modifies the boykovkolmogorov bk algorithm. Background phase removal using harperella including phase unwrapping, vsharp and pdf excluding phase unwrapping needs 108, 101 and 836 sec, respectively. Nov 30, 2018 fast unwrapping 2d phase image using the algorithm given in. This is a revision of the reference list reported in the original article. This information is the phase variance and the probability density function pdf of the parameters describing the temporal model. Interferometric synthetic aperture radar insar is a powerful tool to. A simulated terrain generated by the matlabs membrane function was.
A comparison of phase unwrapping techniques in synthetic. Comparison of phaseunwrapping algorithms by using gradient of first fai lure. This scripts implements the algorithm from ghiglia and romero 1994 that uses leastsquare methods to solve the problem. From the received signal, i want to see the phase of the object over time. To make the results more useful, one needs to unwrap the phase.
New methods of phase unwrapping in sar interferometry. Each is most useful only for certain restricted applications. While challenging even in the best of circumstances, this problem poses unique difficulties when the dimensions of the interferometric input data exceed the limits of ones computational capabilities. The measured interferometric intensity distribution ix,y can be. Phase unwrapping is the process of recovering unambiguous phase values from phase data that are measured modulo 2.
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