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A Note on the Continuous Tomography functionality

 

This technique allows resolution enhancement along SAR elevation direction exploiting a series of interferometric images. The name continuous indicates that the method is suited for retrieval of the backscattering coefficient in case of volume scattering. This implies that a series of SAR acquisitions at longer wavelength (e.g. L- and/or P-band), capable of penetration within the scattering medium, should be used in order to provide meaningful results.

 

On the other side, it is important to understand that the continuous tomographic technique is not suited for urban scenario and shorter wavelength (e.g. X-band) where the predominant backscattering happens at the surface of objects. The word discrete indicates in the case of discrete tomography methods that the backscattering coefficient is retrieved only at a discrete, previously selected according to a priori knowledge, number of locations along the elevation direction.

 

The continuous tomographic method relies on coherence of the phase history of the interferometric series. As such, atmospheric effects must be removed during a preprocessing stage and it is assumed that displacement does not occur between any two acquisitions forming the interferometric series. The atmospheric layers estimation is performed leveraging the information provided by a set of coherent points which are identified using the PS approach.

 

The strategy used to focus the signal along elevation is the so-called beamforming one which achieves improved resolution correlating the observed interferometric signal with a reference kernel predicted by the InSAR geometry model.

 

The output products are stored in step-specific folders, which the program creates during the processing execution. These folders are automatically created inside the root output directory named using, as prefix, the "Output Root Name" and "_Tomographic_processing" as suffix, which is entered in the first processing step.

All intermediate files generated from each step are stored inside the _Tomographic_processing/work sub folder. In order to avoid processing failures it is recommended not to move any file from its original repository folder.

 

The "Auxiliary file" (marked by the name auxiliary.sml) is saved in the root output directory and it is updated during the execution of the different processing step. From the Interferometric Process step onwards, throughout the whole processing chain; it is important to note that the first input to enter, in any processing panel, is the "Auxiliary file". This file contains information to understand which steps have been executed, and what are the products generated.

The "work_parameters.sml" is saved in the work sub folder and contains information about the processing parameters setting.

 

It is possible to copy the whole [rootname]_Tomographic_processing folder together with the input and DEM files to another location/another drive (e.g. if the disk is full). The process can be resumed from the break point simply by re-launching the Connection Graph (inserting the inputs in the new location). Once the new Auxiliary file has been created it is necessary to edit it by inserting the DEM path in the new location and setting to "OK" or "NotOK" according to the steps performed in the previous location.

 

Note: Please do not create your results in a folder containing spaces in the path.

 

The processing sequence is shown in the following block diagram:

 

1) Connection Graph

The Reference selection is performed according to an optimization of the temporal and spatial baselines distribution. The distribution of the spatial baselines and the range of spanned values defines the properties of the tomographic impulse response in terms of resolution and aliasing/ambiguity.

 

This kind of information is contained in the tomography_info file under the main processing directory. This is a simple ASCII text file which provides:

The nominal impulse response width that determines height resolution. The larger the baseline span the finer (i.e. smaller value) the resolution.

 

The height ambiguity interval. This is the interval at which replicas of the impulse response are positioned. Replicas are unavoidable because of the discrete sampling of the spatial baseline. A denser sampling of the baseline interval provides a larger ambiguity interval thus enabling tomographic discrimination for objects separated by a larger height interval.  

 

Both these figures are purely theorical as they are computed assuming that the spatial baselines samples are regularly distributed (i.e. constant baseline spacing). If this is not the case, the actual impulse response will be degraded in terms of resolution loss and distortion and the both the concepts of height resolution and ambiguity are much more difficult to interpret leading to a difficulty in providing meaningful figures.

 

To this aim, at the end of the connection graph procedure plots of the actual impulse response and its replicas are generated for convenience.  The user can analyse these plots to understand qualitatively what kind of performance can be expected in terms of tomographic reconstruction with the data set at hand.  

 

2) Interferometric Workflow

The flattened interferograms (and related SAR intensity images), together with the intensity images are generated.

 

3) Tomography First Inversion

The first height (correction values ) related products are generated without removing any phase component due to the atmosphere;

 

4) Tomography Second Inversion

The atmospheric corrections, related to spatial and temporal variations, are performed in this step; then this component is estimated and finally subtracted from the interferogram files in order to generate the final tomogram.

 

5) Geocoding

Each tomogram layer is projected assuming its constant ellipsoidal height and using the cartographic system of the input "DEM file".

 

 

 

References

 

Reigber, Andreas, and Alberto Moreira. "First demonstration of airborne SAR tomography using multibaseline L-band data." IEEE Transactions on Geoscience and Remote Sensing 38.5 (2000): 2142-2152.

 

Pasquali, P., et al. "A 3-d sar experiment with emsl data." 1995 International Geoscience and Remote Sensing Symposium, IGARSS'95. Quantitative Remote Sensing for Science and Applications. Vol. 1. IEEE, 1995.

 

Giardino, Andrey, et al. "Experimental SAR Processors for Bistatic Concepts Considering Companion Satellites." IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2019.