2.6.1.2.3 Range-Doppler

2.6.1.2.3.1 Introduction

2.6.1.2.3.1.1 Overview

The range-Doppler algorithm is the most commonly used algorithm for processing continuously collected SAR data into an image (see Ref. [2.5 ] and Ref. [2.6 ] ). It is computationally efficient and, for typical spaceborne imaging geometries, the range-Doppler algorithm is an accurate approximation to the exact SAR transfer function. Thus, the algorithm is phase-preserving and Single Look Complex (SLC) images formed with the range-Doppler algorithm can be used for applications such as interferometry. The range-Doppler algorithm is designed for continuously collected data, in contrast to SPECAN 2.6.1.2.4. which is best suited to bursty data, and can process the full azimuth bandwidth.

The range-Doppler algorithm is used for the high-resolution Image Modes (IMS, IMP, IMG) and the high-resolution, single look complex Alternating Polarisation Mode (APS). ( See Table in the section entitled "Organisation of Products" in chapter 2 ). For the APS mode, the data between bursts is filled with zeros to maintain a continous-time input to the algorithm, and a modified range-Doppler algorithm is used to produce an SLC image from AP data 2.6.1.2.3.2. .

For the detected (magnitude) image products (IMP, IMG), a technique called multilooking is incorporated into the algorithm. In this method, separate images are formed from different azimuth spectral bands (looks), and the magnitude look images are averaged to reduce speckle.

SAR processing is a two-dimensional problem. In the raw SAR data, the signal energy from a point target is spread in range and azimuth, and the purpose of SAR focussing is to collect this dispersed energy into a single pixel in the output image. In range, the signal is spread by duration the linear FM transmitted pulse. In azimuth, the signal is spread by the duration it is illuminated by the antenna beam, or the synthetic aperture. As a point target passes through the azimuth antenna beam, the range to the target changes. On the scale of the wavelength, this range variation causes a phase variation in the received signal as a function of azimuth. This phase variation over the synthetic aperture corresponds to the Doppler bandwidth of the azimuth signal, and allows the signal to be compressed in the azimuth direction. The range variation to point target can result in a variation in the range delay to the target that is larger than the range sample spacing, resulting in what is called range migration. This range migration of the signal energy over several range bins must be corrected before azimuth compression can occur. The range-Doppler algorithm performs this correction very efficiently in the range-time, azimuth-frequency domain.

In order to process the correct part of the azimuth frequency spectrum, the range-Doppler algorithm requires as input the Doppler centroid. It is assumed here that Doppler centroid estimation has already been performed, as described in the Doppler Centroid Estimation 2.6.1.2.2. section. The range-Doppler algorithm also requires knowledge of the transmitted pulse for range compression, and of the imaging geometry such as the range and satellite velocity for construction of the azimuth matched filter.

The main steps in the version of the range-Doppler algorithm used in ASAR are shown in the block diagram below, and are described in the following sections.

Figure 2.22 Steps of range-Doppler algorithm used in ASAR processing

2.6.1.2.3.1.2 Range Compression

This matched filtering of the received echo is called range compression. Range compression is performed on each range line of SAR data, and can be done efficiently by the use of the Fast Fourier Transform (FFT). The frequency domain range matched filter needs to be generated only once, and it is applied to each range line. The range matched filter may be computed or generated from a replica of the transmitted pulse. In addition, the range matched filter frequency response typically includes an amplitude weighting to control sidelobes in the range impulse response.

The steps in range compression for each range line are:

• Range FFT: For most products, the range line is divided into two overlapping segments, and an FFT is taken of each segment. The amount of overlap corresponds to the length of the transmitted pulse.
• Range matched (MF) multiply: Each FFT'd segment is multiplied by the frequency response of the matched filter.
• Range Inverse FFT: An inverse FFT is applied to each segment to get the range compressed data. Part of each segment is thrown away since the compressed range data is shorter than the uncompressed range data by the length of the transmitted pulse. The range matched filter is designed so that the throw-away is at the end of the data after the inverse FFT. The results from each segment are then joined together to get the compressed data for the whole range line.
• Range dependent gain correction: The range compressed data is multiplied by a vector that corrects the effects due to elevation beam pattern and range spreading loss.
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2.6.1.2.3.1.3 Azimuth FFT

The range compressed data is stored in range line order. A group FFT algorithm is used which allows azimuth FFTs to be performed while still accessing the data in range line order. Thus the corner turn (transpose to azimuth line order) operation can be delayed until after RCMC.

2.6.1.2.3.1.4 Range Cell Migration Correction (RCMC)

RCMC is the step of correcting for the changing range delay to a point target as the target passes through the antenna beam (range migration). For a given target, this range depends on the closest approach range from the satellite to the target (zero-Doppler range), and on the angle from the satellite to the target, relative to the broadside (zero-Doppler) direction. As targets at the same closest approach range pass through the antenna beam, they all traverse the same interval of angles, and so have the same variation in range from the radar. That is, the signal trajectories from targets at the same closest approach range have the same shape, but are displaced in azimuth because of the different target positions. This is shown in the graph on the left in figure2.23 below. Because of the relationship between the satellite-to-target angle and Doppler frequency, the range migration of all targets at the same closest approach range can be expressed as a function of Doppler frequency. That is, all signal energy from targets at the same closest approach range is collected into the same trajectory in the range-Doppler domain. This allows RCMC to be performed very efficiently in the range-Doppler domain.

Figure 2.23 Illustration of trajectories in time domain and range-Doppler domain.

The shift in range that is needed to align the signal trajectory in a single range bin is determined for each azimuth frequency bin. This shift is then implemented by an interpolation in the range direction. The straightened trajectories are shown by the dotted lines in the figure.

Other steps in SAR processing that require interpolation in range are slant range to ground range conversion (SR/GR), which converts the distance from the radar (slant range) to distance along the ground, and the range resampling to a desired output pixel spacing. For maximum efficiency, all of these range interpolations are combined into one operation.

2.6.1.2.3.1.5 Azimuth Compression

The frequency response of the azimuth compression filter is precomputed using the orbital geometry. The azimuth filter also depends on range. Thus the data is divided into range invariance regions, and the same basic matched filter is used over a range interval called the FM rate invariance region. The size of this invariance region must not be large enough to cause severe broadening in the compressed image. Also included is an amplitude weighting to control sidelobes in the azimuth impulse response. Note that the position of the amplitude weighting in the azimuth frequency array depends on the Doppler centroid, which also depends on range.

The way the azimuth compression is implemented depends on the type of image product. For single look complex products (IMS and APS), a single portion of the azimuth bandwidth is multiplied by the azimuth matched filter frequency response, and an inverse FFT is taken of the entire frequency array. The output is complex valued and left at the natural pixel spacing.

For magnitude image products (IMP and IMG), a technique called multilooking is used to reduce speckle noise. In this case, the azimuth frequency spectrum is divided into several portions called looks. The part of the azimuth frequency array for each look is extracted, multiplied by the azimuth matched filter frequency response, and the inverse FFT is performed. The magnitude (detected) look images are then averaged to reduce speckle. This is described in more detail as follows.

The extraction of the looks from the frequency array is illustrated in the figure below. The looks are positioned symmetrically around the Doppler centroid frequency. As the Doppler centroid frequency varies with range, the look frequency positions are different for different range cells. In practice, they are kept constant within the look frequency position invariance region.

Figure 2.24 Look Position Parameters

The extracted frequency array for each look is multiplied by the matched filter frequency response and the inverse FFT is performed to form the complex look image. The matched filter frequency response is adjusted by a small linear phase ramp for each look. This is equivalent to shifting the compressed look in time, and is required to ensure that the images from different looks are aligned properly for look summation. The amount of azimuth shift is range-dependent. In addition, azimuth interpolation may also performed after look compression to achieve a desire azimuth pixel spacing, and it is done on each look separately.

After look compression, each of the look images is detected. That is, the power of each complex sample is calculated. The detected azimuth looks are then summed, and the square root of the result is calculated to convert to magnitude.

Finally, for the IMG product, the multilooked image is geocoded. This is a two dimensional resampling operation to convert the image to a desired map projection.

2.6.1.2.3.1.6 Summary

• Precision products: All steps (up to and including multilooking) except geocoding are performed.
• Single look complex products: Only the steps up to and including the azimuth IFFT, for only one look, are performed.
• Geocoded products: All steps are performed with the addition of geocoding (The normal square root step is bypassed but is later performed as part of geocoding).
• APS products: A slightly modified version of the range-Doppler algorithm 2.6.1.2.3.2. is used for the APS product .
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2.6.1.2.3.1.7 References

Ref 2.6

J. C. Curlander, R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing, John Wiley and Sons, 1991.

2.6.1.2.3.2 Processing Algorithms For AP SLC

2.6.1.2.3.2.1 Introduction

This section provides an overview of the processing approach for generating an ASAR APS product that is suitable for InSAR applications. The algorithm is the range-Doppler 2.6.1.2.3. algorithm, modified to process bursty data.

2.6.1.2.3.2.2 Background

The algorithm used to form the APS product must be capable of preserving the phase information required for SAR Interferometry. Thus, a form of the range-Doppler algorithm is required since in general SPECAN is not phase-preserving. The image quality requirements for the ASAR APS product are derived from the typical requirements for an Image Mode SLC product, which includes phase preservation and adequate focussing. Adequate focussing is typically determined by measurements of the impulse response shape. However, because of the bursty nature of AP data, there are some important considerations in the processing and use of APS data.

Interferometry requires that the two images be well correlated, in order for the phase difference to be an accurate measurement of terrain height. Because of this, the Doppler spectral components must be common to both images. Doppler components that are not common to both images are a source of decorrelation between the images, which introduces phase noise and degrades the accuracy of the terrain height measurement. If two Image Mode images are combined, the full Doppler spectrum is available in both images, and if the antenna pointing is controlled properly then there is sufficient overlap of the Doppler spectra of the two images. In burst mode data, such as AP data or ScanSAR data, the bursts contain only part of the signal from a point target, and thus contain only part of the Doppler spectrum. If an APS image is combined with an IM image, the IM image contains the full Doppler spectrum so again there is sufficient overlap with the Doppler spectrum of APS image.

If the two images are acquired in burst mode, such as two APS images, the amount of Doppler overlap depends on the relative positions of the bursts in the two data sets. If the bursts occurred at the same locations in the two data sets, then the Doppler components overlap. If the bursts do not overlap at all, then there are no common Doppler components, the images are decorrelated, and interferometry cannot be performed. Since the two products are processed without knowledge of the other, it is desired to preserve as much Doppler information as possible. This is referred to as systematic processing. If systematically generated SLC products are to be used for interferometry, without reverting back to the level 0 data, then azimuth bandpass filtering must be performed on the SLC images to extract the common portions of the Doppler spectrum.

Finally, it should be noted that the APS product will not be suitable for phase measurements between the interleaved polarisation because the Doppler spectrums of the two focussed images will be disjoint (non-overlapping), which implies that the phases will be completely uncorrelated. The magnitude of the APS product could be used for polarimetry in a similar manner to the APP product. For this reason the two output SLC images are co-registered.

This section reviews burst mode interferometry, and presents the considerations in range-Doppler processing of APS data.

2.6.1.2.3.2.3 Burst Mode Interferometry

An illustration of data acquired in discrete bursts as shown in figure.2.25 The figure shows the timing of the bursts, and the exposure times of 16 targets, labelled by to . The lines for each target represent the exposure time (synthetic aperture time), which is the duration of time during which the target is within the beam footprint. In the case of the AP mode, the azimuth aperture covers a little more than 5 bursts' duration. Any one target is captured from two to three bursts in the same polarisation., thus allowing 2-look processing in forming a multi-look image (such as APP).

Let us just examine the spectrum of the targets in the burst marked by X. The duration of the Doppler spectrum for each target is shown in figure2.26 (ignoring the azimuth beam pattern effects). It is clear that the Doppler components contained in this burst, for a given ground target, depend upon the location of the target relative to the burst timeline. The Doppler centroid frequency in this context is the center frequency of the spectrum for a given target.

Figure 2.25 Target Exposure Extents Relative to the Burst Timeline

Figure 2.26 Location of Spectra Energy for Targets in Burst X

A problem directly related to the varying Doppler centroid lies in the synchronisation between the two passes. figure2.27 shows the burst coverage of two typical passes where the bursts are slightly misaligned. If the burst timing of the level 0 data is known, the lines of level 0 data corresponding to non-overlapping areas can be zeroed prior to SAR processing. In this way, only burst data with common Doppler components are retained, so the zeroing out of data is also equivalent to applying a time varying band pass filter to the data in each pass.

Figure 2.27 Synchronisation of Bursts in Two Slightly Misaligned Passes if Reprocessing from Level 0 Data (the beams are the same)

Figure 2.28 Spectra of Targets in a Burst for Two Slightly Misaligned Passes

Figure2.29 shows the azimuth spectrum for all bursts for a single pass when zeros are inserted in the alternate polarisation. Note that the data from a single target is bursty in nature in both the azimuth time domain and the Doppler frequency domain due to the coupling between time and frequency inherent in linear FM signals. Here it has been assumed that the burst cycle time is an integral multiple of the Pulse Repetition Interval (PRI) which is important for the zero padding to work. This assumption is true for the AP mode but is generally not true for ScanSAR modes.

Figure 2.29 Spectra of Targets After Zero Fill Showing IFFT Positions

Since the zero-padded data is stored in the same representation as continuous moded data, it can be processed with the range-Doppler algorithm. Including all the available bursts for a given output point simultaneously ensures that all the Doppler spectrum is maintained for a given target and it can be done independently for both passes. This is discussed in the section below.

During InSAR processing azimuth varying bandpass filters can be used to select out common continuous spectral regions from each image of each pass. This operation has approximately the same result as zero padding the level 0 data prior to SAR processing. This technique has been used successfully to obtain high quality InSAR results (Guarnieri et al 2.6.1.2.3.2.6. ).

One side-effect of processing the entire Doppler spectrum is that the resulting APS product will have an impulse response that is modulated due to the non-continuous spectrum used for compression. This impulse response shape will not meet the current PF-ASAR requirements for this product but can fully meet the requirements of the InSAR application. In addition, there will be azimuth banding, due to different number of bursts being used to generate the output points. This approach is described further in the algorithm described below and is the recommended version for the PF-ASAR, due to its ability to satisfy the InSAR application requirements, for use with another APS or an IMS, without complicating the ASAR product structure and interpretation.

2.6.1.2.3.2.4 Modifications To Range Doppler Algorithm

Let us assume a case in which the beamwidth covers exactly five bursts' duration (closely resembling that in the AP Mode). Now let us focus our discussion on only one polarisation. Each polarisation will be processed separately. The first step is to zero pad the gaps when data of the other polarisation is acquired. Assume 16 equally spaced targets as shown in figure2.25 , and denote them by to, and assume that they all have the same slant range of closest approach so that they are confined in one range gate after Range Cell Migration Correction (RCMC). Because of the missing data, the spectra of the targets after azimuth Fast Fourier Transform (FFT) and RCMC are bursty, as shown in figure2.29 .

The energy received from a target depends on its position in the antenna azimuth beam during the burst, which corresponds to the position of its Doppler components in the azimuth-frequency domain. To avoid scalloping, the target energy can be corrected by applying the inverse of the azimuth beam pattern to the Doppler spectrum. This is similar to Descalloping 2.6.1.2.4.2. in SPECAN.

The general steps of the modified RD algorithm are the following:

1. Range compression.
2. Zero pad the missing data to simulate continuous data.
3. Perform an azimuth FFT to transform the data into the Range-Doppler domain.
4. Perform RCMC.
5. Apply inverse of azimuth beam pattern to spectrum.
6. Perform azimuth matched filtering without any windowing applied.
7. Perform the azimuth IFFT.
8. Repeat algorithm for alternate polarisation and include phase ramp term in azimuth matched filter to achieve co-registration.

In this approach, a single azimuth IFFT is applied to the Doppler spectrum after application of the matched filter. This approach satisfies the requirements for InSAR processing, but the impulse responses of the APS products suffers from modulation as shown in figure2.30 below. The modulation arises from the fact that the spectrum of each target is segmented in the IFFT . Ref. [2.8 ]

Figure 2.30 Impulse Response from Multiple Burst Processing for Target 1 (dotted curve is envelope of one continuous burst)

If range-Doppler algorithm is used without further modification, the APS product will not meet the radiometric requirements. This is due to the fact that targets have different number of bursts or partial bursts and therefore will have different energies. The energies are modulated along azimuth based upon the target location relative to the burst timeline. This will appear as azimuth banding in the resulting image. This poses a problem if the APS product is to be used for radiometric purposes by forming the magnitude image from the complex samples. It is desirable to attempt to remove this banding if possible.

The azimuth radiometric banding that results in the single IFFT method can be removed by modifying the processed azimuth bandwidth. If the processed bandwidth is exactly four times the burst bandwidth then there will always be the energy from two bursts captured. Therefore, when the inverse beam pattern is applied and there is no weighting applied to the matched filter (i.e. just rectangular window) the total energy processed for each target will be the same. The truncation of the spectrum by the rectangular window will either capture two complete bursts or will capture one complete burst and two partial bursts. In the latter case the two partial bursts add up to a full burst in terms of energy. Since the burst bandwidth is range dependent, the processed bandwidth must be adjusted across range.

There are implications to changing the processed Doppler bandwidth to remove the azimuth radiometric banding:

• Less of the total available Doppler bandwidth is retained for InSAR.
• The azimuth resolution is range dependent (but recall that the impulse response is modulated anyway).

In order to support InSAR filtering it is necessary to supply the following parameters in the product annotation: burst return time, time of the start of a burst for a specified polarisation., Doppler centroid coefficients, azimuth FM rate coefficients, and zero Doppler time of first output line. Using these parameters and knowing that the processed bandwidth is centred at the Doppler centroid with an extent of a specified bandwidth, the location of the available burst spectra can be computed for any pixel in the output image.

2.6.1.2.3.2.5 Conclusions

In this approach a small amount of Doppler information is lost, with only moderate implications for InSAR, in order remove the radiometric banding in the amplitude image.

During InSAR processing the APS images are azimuth-varying bandpass filtered to achieve common Doppler spectra.

2.6.1.2.3.2.6 References

Ref 2.8

R. Balmer and M. Eineder," ScanSAR Processing Using Standard High Precision SAR Algorithms", IEEE Transactions on Geoscience and Remote Sensing, Vol. 34, No. 1, January 1996.

2.6.1.2.4 SPECAN

2.6.1.2.4.1 Introduction

2.6.1.2.4.1.1 Overview

Compared to the range-Doppler 2.6.1.2.3. algorithm, the SPECAN algorithm is not as accurate in matching the exact SAR transfer function, and so is not appropriate for phase-preserving applications. Essentially, the SPECAN algorithm trades resolution, or number of looks, for computational efficiency.

Typically, several bursts occur within a synthetic aperture time. Thus, successive burst images contain overlapping views of the same ground area. These burst images, or looks, are averaged to reduce speckle.

A consequence of SPECAN or burst imaging is an effect called scalloping. During the relatively short burst, targets within the synthetic aperture are viewed through different parts of the azimuth antenna beam. The azimuth beam pattern then results in an azimuth-varying weighting of the target intensity in the image. Given the antenna pattern and the antenna beam centre location (Doppler centroid 2.6.1.2.2. ), this effect can be corrected. (See Descalloping 2.6.1.2.4.2. ).

The main steps in the version of the SPECAN algorithm used in ASAR are shown in the block diagram below, and described in the following sections.

Figure 2.31 Main steps in the version of the SPECAN algorithm used in ASAR

2.6.1.2.4.1.2 Range Compression

2.6.1.2.4.1.3 Linear Range Cell Migration Correction (RCMC)

In SPECAN processing, the range migration trajectory is approximated by a straight line of a certain slope in the two-dimensional data array. Thus, RCMC is done by simply skewing the data - that is, applying a range shift that varies linearly with azimuth time - in order to align the trajectory from a target in a single range bin. The range shift is done by an interpolation of the range line.

Note that this linear RCMC is done in the range-time, azimuth-time domain, rather than the range-Doppler domain. While the trajectories of all targets are aligned in single range bins, an effect of linear RCMC in the time domain is that the target range positions are shifted as a function of azimuth-time, resulting in a skewed image. In practice, rather than increasing the size of the data array to hold the skewed data, the skewed data is wrapped around in range in the data array, forming a "barber pole" effect that is undone in the output image. This is illustrated in figure2.32 below.

Figure 2.32 Trajectories before and after linear RCMC.

2.6.1.2.4.1.4 Azimuth Processing

A convenient representation of the signal, for purposes of deramping, is the frequency-time diagram. This is a plot of the instantaneous frequency of the signal versus time. For a linear FM signal, it is a sloping straight line, where the slope is the frequency rate. For a sinusoid of constant frequency, the frequency-time diagram is a horizontal line. figure2.33 below shows the frequency-time diagram of azimuth SAR signals, assumed to be linear FM. Each line represents the signal from a target at a different azimuth position. The portions of the signal that are contained in the burst are shown. After deramping of the burst, as shown in the bottom part of the figure, the signals have been converted to sinusoids, with frequencies related to the target positions.

Figure 2.33 Illustration of SPECAN with frequency-time diagrams.

The basic steps of SPECAN, then, are the reference function multiply of the burst in the azimuth direction (deramp), followed by an azimuth FFT. The FFT length must be as least twice as long as the azimuth block size to achieve the oversampling that is necessary prior to detection. The output of the FFT is the compressed image formed from the burst, and from this image the good points are selected. Good points correspond to targets that were illuminated by the antenna beam during the entire burst. Finally, a radiometric correction of the burst image is performed with a vector multiply in the azimuth direction. This corrects for a variation in target intensity due to the azimuth antenna beam pattern, as described in the section on descalloping. 2.6.1.2.4.2.

The location of a target position depends on the slope of the frequency-time diagram, or the frequency rate of the linear FM signal. In the SAR azimuth signal, the azimuth frequency rate depends on range. This geometric distortion needs to be corrected by an azimuth interpolation of the burst image, as described later under resampling.

2.6.1.2.4.1.5 Look Summation and Resampling

First, the burst image is shifted in range to correct for the skew that was applied during linear RCMC. This step is called deskew. Only the integer portion is corrected in this step. The fractional portion is handled during the SR/GR resampling step.

Next, an optional range multi-looking is applied. This consists of applying a set of range bandpass filters to the image to extract range-look images corresponding to different range frequency bands.

The squared magnitude of the complex burst image for each range look is then computed. This is called detection. The squared magnitude, rather than the magnitude, is taken to avoid aliasing during the following interpolation steps.

The squared magnitude looks are then summed in range. Also, different burst images of the same area of the ground form different azimuth looks, and these are summed. The summation of looks is done to reduce speckle.

The look-summed image is then resampled in range. This is a shift and interpolation to correct for the fractional sample part of the deskew. At the same time the data is resampled in range in order to convert to ground range and to achieve the required output sample spacing.

Then, azimuth resampling to the desired output pixel spacing. This compensates for the range-depend pixel spacing at the output of deramp and FFT. This may also include averaging to extract additional azimuth looks.

Finally, the square root of the image is taken to obtain the magnitude image.

2.6.1.2.4.1.6 Product Processing

• Block Averaging: The image is averaged and subsampled to form a browse product (IMB, APB, WSB, GMB). ( See Table 2.47 in the section entitled "Browse Products" ).
• Geocoding: For the geocoded product (APG), the image is resampled in two dimensions convert the image to a desired map projection.
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2.6.1.2.4.1.7 Summary

• Alternating Polarisation Precision product, and all medium-resolution products: All steps except geocoding and block averaging are performed.
• Geocoded products: All steps except azimuth resampling (resampling is done during geocoding) and block averaging are performed.
• Browse Product: All steps except geocoding are performed.
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2.6.1.2.4.1.8 References