Airborne Remote Sensing at Millimeter Wave Frequencies

Abstract

Advanced radar sensors are able to deliver highly resolved images of the earth surface with considerable information content, as polarimetric information, 3-D-features and robustness against changing environmental and operational conditions. This is possible also under adverse weather conditions, where electro-optical sensors are limited in their performance.

11.1 Introduction

Advanced radar sensors are able to deliver highly resolved images of the earth surface with considerable information content, as polarimetric information, 3-D-features and robustness against changing environmental and operational conditions. This is possible also under adverse weather conditions, where electro-optical sensors are limited in their performance.

Typical applications cover the control of agricultural activities, the survey of traffic during special events or even the regular monitoring of motorways. A special utilization for easily deployable imaging sensors are all kinds of natural or man-made environmental disasters, as the monitoring of volcanic activities, the survey of pipelines or of accidents like that at Chernobyl, where radiation hazard or other dangers are given for monitoring by humans.

All these utilizations require sensors, which have to cope with a high variability of atmospheric conditions while supplying complete information about the status of the earth surface. Millimeter wave SAR is able to serve these demands with best possible results and ease of operation as long as only short or medium ranges are required. Especially the latter condition can be fulfilled due to the unique properties of millimeter wave SAR, which are roughly described by short aperture length for given resolution, inherently low speckle, low blasting of strong scattering centers and simple processing.

11.2 Boundary Conditions for Millimeter Wave SAR

11.2.1 Environmental Preconditions

The electromagnetic wave, which is transmitted by the radar, scattered at the target of interest and the surrounding and than reflected back to the radar is influenced by the atmosphere. The propagation medium may be described by its refraction index and absorption by molecules in the atmosphere (clear air propagation) at one hand and influences of weather or other environmental conditions, as that is the presence of hydrometeors or dust.

11.2.1.1 Transmission Through the Clear Atmosphere

The millimeter wave region exhibits considerably different propagation properties if compared with classical radar bands (Skolnik 1980). This is due to resonance absorption at these frequencies, which is related to energy levels of vibration and rotation states of molecules in the atmosphere, like water vapor and oxygen.

For radar applications mainly the transmission windows around 35 GHz (Ka-Band) and 94 GHz (W-Band) are employed. It has however to be noted, that relatively high propagation losses are inhibitive for long range applications of millimeter wave radar ( > 10 km).

11.2.1.2 Attenuation Due to Rain

A severe influence on millimeter wave propagation is given by hydrometeors with a high density or, even worse, with a dropsize in the order of magnitude of the electromagnetic wavelength. The latter phenomenon is again due to resonance, where the drop is acting as an antenna, absorbing the energy of the resonant electromagnetic wave and is the determining factor for attenuation in the millimeter wave region (Marshall and Palmer 1948).

11.2.1.3 Propagation Through Snow, Fog, Haze and Clouds

For remote sensing applications the propagation through snow, fog, haze and clouds is determined by the same physical interactions as for the IR- and visible frequency region of the electromagnetic spectrum. While in the EO region the drop size within fog and clouds is in an order of magnitude, that interactions are most likely (Wei: ̧def: ̧defβ-Wrana et al. 1995), this does not apply in a comparable amount for millimeter waves. The effects are of much minor importance as long as the density of droplets is not too high. Snow has only marginal influence on millimeter wave propagation as long as the liquid water content is not excessively high (Kendra et al. 1995).

11.2.1.4 Propagation Through Sand, Dust and Smoke

The use of airborne sensors is essential for any mission of humanitarian or assisting nature in disaster areas. Besides darkness and adverse weather, dust and sand storms impose most critical conditions for remote sensing. Dust clouds in contrary to ordinary dust storms possess a wide spectrum of sand and dust particle sizes (Nüßler et al. 2007). The bigger particles may sometimes even have diameters in the order of magnitude of the wavelength related to the upper millimeter wave region. A further reason for propagation loss in the atmosphere is the smoke of the burning savannah or of volcanic eruptions. Only radar sensors in the microwave or millimeter wave region offer the capability of sufficient transmission to cope with the described environmental conditions (Skolnik 1980).

Concerning sand and dust, simulations have been conducted (Wikner 2008; Brooker et al. 2007) which start from the precondition that dust particles are almost spherical in shape and that their forward scattering can be described by Mie scattering. The results fit well with experiments and can be used for an estimation of propagation loss (Rangwala et al. 2007; Hägelen et al. 2008).

Smoke consists of even smaller particles if compared with dust. Experimental data are available (Essen and Baars 1986) which show the low attenuation of any type of smoke for millimeter waves.

11.2.2 Advantages of Millimeter Wave Signal Processing

As at millimeter waves the wavelength is extremely short in comparison with classical radar bands, the related phase is changing very rapidly. One might suspect that this would be a disadvantage for any algorithm, which, like SAR, is based upon the evaluation of the phase of the backscattered signal. However, the contrary is true. This is partly due to the geometry for millimeter wave SAR, which is typical short range, and partly due to the specific scattering mechanism, which is dominated by a relatively rougher surface, scaled by a factor of 10 compared with X-band.

In addition imaging errors inherent to SAR processing are of minor importance. One of the major advantages is the short aperture length, which for equal cross-range resolution is also scaled by a factor of 10 in comparison to X-band and thus makes millimeter wave SAR more robust against uncontrolled movements of the carrier aircraft. In the following a short survey on general properties of the millimetre wave SAR is given. More details are presented during the description of a typical SAR system, the MEMPHIS radar (Boehmsdorff and Essen 1998).

11.2.2.1 Roughness Related Advantages

Roughness of surfaces gives reason for diffuse scattering, while smooth surfaces are resulting in specular reflection processes. Roughness, however, is not an absolute criterion, but related to the wavelength of the illuminating signal. At millimeter wave frequencies most surfaces appear rough, and the diffuse scattering dominates imaging with SAR. Diffuse scattering leads to an averaging, which has a similar effect as multilook processing. The consequence for the imaging process is, that the inherent speckle within scenes with equal surface structure is lower at millimeter wave frequencies than at X-band for an equal amount of multi look processing. Another effect is due to a higher requirement upon rectangularity of angles between perpendicular surfaces for a perfect corner reflector effect. The phase state of the electromagnetic wave incident on a flat plate has to be constant over the total surface area for a coherent superposition. If this is not the case, destructive interference between waves reflected at different loci of the surface will occur and thus a rapid decrease in the overall RCS. The consequence for SAR images is, that a strong overemphasis of corners and edges, which may give reason for processing lobes for point scattering at classical SAR bands are considerably reduced for millimeter wave SAR.

11.2.2.2 Imaging Errors for Millimeter Wave SAR

During SAR processing two main sources give reason to imaging errors: Range migration and depth of focus. A concise description of these problems is given in (Curlander and McDonough 1991). The azimuth resolution of a SAR process depends mainly on the bandwidth of the Doppler signal. The phase of the Doppler signal is given by $\Phi= 4\pi \mathrm{R(s)}/\lambda$. If a Doppler shift is present, the range to the target must change during the observation time and consequently the compressed target response is related to different ranges for consecutive samples. This is called the “range migration”. The locus of these effective range cells can be approximated by

$$\mathrm{R(s)} = \mathrm{{R}_{c}} + (\mathrm{dR/dt})(\mathrm{s} -\mathrm{{s}_{c}}) + ({\mathrm{d}}^{2}{\mathrm{R/dt}}^{2}){(\mathrm{s} -\mathrm{{s}_{ c}})}^{2}/2.$$

(11.1)

The linear part of this equation is the range walk, while the quadratic term is the range curvature. From this equation a precondition can be deduced, under which circumstances a compensation of the imaging errors has to be performed. Under the assumption that the maximum range migration ΔR should be less than about 1 ∕ 4 of the range resolution cell δR the criterion can be deduced to be

$${(\delta \mathrm{x}/\lambda )}^{2} > \mathrm{{R}_{ c}}/8\delta \mathrm{R}.$$

(11.2)

Due to the proportionality by 1 ∕ λ² the range for which a compensation is needed is bigger by a factor of 100 between W-band and X-band in favour for the W-band.

The second important imaging error is the depth of focus criterion. This is related to the fact, that the azimuth correlation parameters, which are denoted by f_DC and f_R, are dependent on range. Basically this is related to a mismatch between the azimuth chirp constant f_R if the range R_c used for the correlation differs from the range of the target. This mismatch causes a phase drift between correlator function and the signal. This gives the boundary condition (Curlander and McDonough 1991):

$$\mathrm{d{R}_{c}} < 2{(\delta \mathrm{x})}^{2}/\lambda.$$

(11.3)

Again the depth of focus at W-band is maintained for a ten times bigger range as at X-band.

11.3 The MEMPHIS Radar

The use of millimeter waves for SAR applications is a more recent trend (Boehmsdorff et al. 2001; Edrich 2004; Almorox-Gonzlez et al. 2007) and especially suited for small UAVs. The available technology and its potential for miniaturization with additional high scientific potential, as polarimetry and interferometry, are in favor for this frequency region. Additionally specific probing possibilities related to sensitivity on small-scale structures are typical for millimeter waves.

Most of the available data in the frequency bands of 35 GHz and 94 GHz were gathered with experimental radars onboard medium size aircrafts like C-160 “Transall” or similar. In Europe the RAMSES (Radar Aeroporte Multi-spectral d’Etude des Signatures) operated by ONERA (Dreuillet et al. 2006) with capabilities up to 94 GHz has been in operation for more than a decade, as well as the MEMPHIS (Millimeter Wave Experimental Multifrequency Polarimetric High Resolution Imaging System) of FGAN-FHR (Schimpf et al. 2002). In the US numerous data sets are available gathered by the Lincoln Lab millimeter wave SAR (Henry 1991).

11.3.1 The Radar System

The radar system (Schimpf et al. 2002) employs two front-ends, one at 35 GHz the other at 94 GHz, which can be operated simultaneously. Both are controlled by a common VME-bus computer and tied to the system reference, from which all frequencies and trigger impulses are derived. The IF-signals from both front-ends are fed to the data acquisition and recording electronics. The measured data are recorded by means of a high-speed digital recording system MONSSTR with a maximum recording speed of 128 MByte/s.

The architecture of both front ends is identical. The primary frequencies of 25 GHz and 85 GHz are generated by successive multiplication and filtering of the reference frequency of 100 MHz. For both subsystems the waveform and the IF-offset are modulated onto an auxiliary signal at about 10 GHz, which, together with the primary signal, is up-converted into the respective frequency band. Figure 11.1 shows the detailed diagram of the front-end.

Fig. 11.1

Block diagram of the MEMPHIS millimeterwave front-end

The radar waveform is a combination of stepped frequency waveform and a FM chirp (Schimpf et al. 2004). The pulse length can be adjusted in the range of 80 ns − 2 μs. For the high-resolution mode the frequency is stepped from pulse to pulse over a bandwidth of 800 MHz in steps of 100 MHz, while at each frequency step a chirp modulation over a bandwidth of 200 MHz is done with an overlap of + 50 MHz at both the lower and upper frequency limit of each successive chirp. This results in a range resolution of about 19 cm. The output power is generated by a TWT (Thales) at 35 GHz and an EAI (CPI) at 94 GHz. The transmit power is fed into a pin-switch assembly which allows to switch the transmit polarization from pulse to pulse between orthogonal components, linear horizontal or vertical or, manually switched, circular, left hand or right hand. The receiver has four channels with balanced mixers and a common local oscillator, which is coupled to the up-converter, which also supplies the transmitter stage via a SPDT-PIN switch. The down converted signals are quadrature demodulated to result in I- and Q-phase components and the logarithmically weighted amplitudes.

Depending on the application, the systems can be used with polarimetric monopulse feeds, sensing elevation and transverse deviations or an interferometric pair of antennas with orthomode transducers to sense both polarimetric components. The elevation/azimuth-asymmetry of the beam, which is generally necessary for SAR applications, is achieved by aspheric lenses in front of the feed horns. The performance data of the front-ends are summarized in Table 11.1. In addition to the radar data, inertial data from the aircraft as well as time code and GPS data are recorded.

Table 11.1 Performance data of the MEMPHIS millimeterwave front-end

For interferometric SAR measurements the MEMPHIS radar is equipped with a multi-baseline antenna consisting of an array of six horns followed by a cylindrical lens. The complete antenna has a 3 dB beam width of 3^∘ in azimuth and 12^∘ in elevation. Figure 11.2 shows a photo of the 35 GHz front-end, equipped with the horn antenna array.

Fig. 11.2

The MEMPHIS millimeterwave front-end

Due to the geometry of the horn ensemble, five independent interferograms can be generated. The possible combinations with the respective baselines are given in Table 11.2. These different interferograms are used to resolve the height ambiguity. The advantages of this multiple baseline approach for the phase unwrapping procedure is discussed in detail later on.

Table 11.2 Interferometric baselines of the MEMPHIS millimeterwave front-end

11.3.2 SAR-System Configuration and Geometry

For SAR applications the radar is mounted into a “Transall” aircraft looking out of a side door, as shown in Fig. 11.3. If the complete information of a specific area is required, courses with different headings are flown, covering at least the four cardinal directions.

Fig. 11.3

MEMPHIS radar in C-160 “Transall” aircraft

The radiometric calibration is based on pre- and post flight measurements against trihedral and dihedral precision corner reflectors on a pole. Sufficient height of the pole is necessary to avoid a strong influence of multipath propagation.

11.4 Millimeter Wave SAR Processing for MEMPHIS Data

11.4.1 Radial Focussing

Data are recorded with the MONSSTR system to be calibrated and evaluated by an off-line process. Images are generated by the regular SAR-process employed with the MEMPHIS data if only a linear chirp waveform with a total bandwidth of 200 MHz is used. As mentioned above, high range resolution is obtained using an LFM chirp with either 100 or 200 MHz bandwidth. Chirp length ranging between 400 and 1,200 ns can be handled by the chirp generator, which is in accordance with the required PRFs and the available duty cycles. As the required range ( > 1, 000 m) is much more than the chirp length, the usual “deramp-on-receive” is not a viable technique to be implemented. Instead, the receive signal is only down-converted to the basic frequency and then the complex values sampled at a rate of 1/B (B = bandwidth of the individual chirp).

In order to increase the range resolution beyond the value of c/2B given by the chirp bandwidth, a stepped-frequency mode is implemented, using eight steps with a spacing of 100 MHz thus limiting the instantaneous bandwidth and required sample rate.

Using a synthesized chirp combining N pulses with an instantaneous bandwidth of B, post-processing is necessary to combine the individual chirps. Several methods for this processing are known, as “stepped-frequency chirp” (Levanon 2002), “frequency-jumped burst” (Maron 1990) or “synthetic bandwidth” (Berens 1999; Zhou et al. 2006). Concatenation of the individual chirps to one long chirp can be done either in the time domain (Keel et al. 1998; Koch and Tranter 1990) or in the frequency domain (Brenner and Ender 2002; William 1970; Kulpa and Misiurewicz 2006), or in a deramp-mode. The latter is used for high-resolution MEMPHIS SAR processing. Detailed results have been published in (Essen et al. 2003).

11.4.2 Lateral Focussing

For the test of the lateral focusing algorithm data were taken for urban areas with strong point scatterers and additionally an only weakly structured terrain with low dynamic range.

For the lateral focusing the Doppler resolution of the system is the determining parameter, which is given by:

$$\mathrm{{F}_{d}} = {2}^{{_\ast}}{\mathrm{f}}^{{_\ast}}\ {\mathrm{v/c}}^{{_\ast}}\alpha$$

(11.4)

f = Frequency, v = Speed of Aircraft, c = Speed of Light, α = Squint Angle.

If the Doppler frequency within the relevant angular interval is not exceeding the PRF an unambiguous determination is possible. The unambiguous interval is given by:

$$\mathrm{ED} ={ \mathrm{PRF}}^{{_\ast}}{\mathrm{R}}^{{_\ast}}\mathrm{c}/({2}^{{_\ast}}{\mathrm{f}}^{{_\ast}}\mathrm{v})$$

(11.5)

In the case under consideration the following parameters were relevant:

The length of the appropriate FFT is given by $\mathrm{N} = \mathrm{ED/R}$, resulting in N = 1024 for a range of R = 2 km and N = 512 for a range of R = 700 m.

The algorithm is demonstrated for an arrangement of corner reflectors of different RCS and different distances. Figure 11.4 demonstrates the arrangement and gives pseudo color representations of the respective SAR image of the reflector array.

Fig. 11.4

Three Scatterers separated by 0.45 and 100 m with 0.2 and 0.8 m resolution

The test arrangement was flown with different radar parameters. It turned out, that for lowest processing sidelobes the longer pulse width of 1,200 ns was the best choice.

11.4.3 Imaging Errors

During numerous SAR flights it was observed, that generally imaging errors have a much lower importance at millimeter wave frequencies than at microwave bands, however there is also an indication, that at Ka-band the “Range-Walk” has already a slight effect. Three effects give reason for the movement of a point scatterer from one range gate to the next during one period of the Doppler FFT. These are the:

• 1. Drift: The aircraft axis is not exactly aligned to the flight direction.

• 2. Beam-Width Effect: The radar look direction covers a certain angle, given by the 3-dB-beamwidth of the antenna.

• 3. The aspect angle to the target changes during the aperture length.

Under which angle the Range-Walk is of importance demonstrate the following considerations:

The time related to an FFT of length N (Aperture Time) to give a resolution Δl is given by:

$$\mathrm{{t}_{a}} = \mathrm{N/PRF}$$

(11.6)

which is: $\mathrm{{t}_{a}} ={ \mathrm{R}}^{{_\ast}}\ \mathrm{c}/({2}^{{_\ast}}\ {\mathrm{f}}^{{_\ast}}\ {\mathrm{v}}^{{_\ast}}\ \Delta \mathrm{l})\quad \vert \mathrm{{t}_{a}} = 0.58\,\mathrm{s}$

The aperture length is given by:

$$\mathrm{{S}_{A}} ={ \mathrm{v}}^{{_\ast}}\mathrm{{t}_{ a}}$$

(11.7)

Which is: $\mathrm{{S}_{A}} ={ \mathrm{R}}^{{_\ast}}\ \mathrm{c}/({2}^{{_\ast}}\ {\mathrm{f}}^{{_\ast}}\ \Delta \mathrm{l})\quad \vert \mathrm{{S}_{A}} = 45.7\,\mathrm{m}$

During this period the lateral displacement (Range-walk) has to be lower than the range resolution, which results in an angle of:

$$\begin{array}{rcl} & & \beta = \Delta \mathrm{l/{S}_{A}} \\ & & \mathrm{Which\ is\! :}\ \beta = \Delta {\mathrm{l}}^{2{_\ast}}\ {2}^{{_\ast}}\ \mathrm{f}/({\mathrm{R}}^{{_\ast}}\ \mathrm{c})\vert \beta = 0.2{3}^{\circ }\end{array}$$

(11.8)

It is obvious, that the maximal angle increases linear with frequency and quadratic with the resolution. Table 11.3 gives some characteristic numbers.

Table 11.3 Range-walk effect at different radar frequencies, ranges and resolutions

The drift results in a range gradient linearly dependent on time. This can be compensated by shifting the start frequency of the chirp modulation, which can be done continuously, as appropriate.

The beam-width effect is not relevant at 94 GHz for a 3-dB-beamwidth of about 1. At 35 GHz, where the beam width is about 3^∘, this has to be taken into account. A simple solution is offered by using only part of the Doppler-FFT result, which is related to an evaluation of only a fraction of the full beamwidth. It has however to be considered, that for an adequate overlap of images (multilook) the data must not be shifted by a bigger portion, which leads to an increase of processing time.

The third effect caused by the aspect angle different from 90^∘ produces non-linear (quadratic) Range-Walk due to the non-linear range gradient during the aperture time. If a circular course around a target would be flown, the range would be constant. As however, the flight course is linear, a range gradient is generated which is equal to the arch rise. For small angles the arch rise is given by:

$$\begin{array}{rcl} & & \mathrm{h} ={ \mathrm{s}}^{2}/8\mathrm{r}\ (\mathrm{s} = \mathrm{bow\ string},\ \mathrm{r} = \mathrm{radius},\ \mathrm{h} = \mathrm{arch\ rise})\end{array}$$

(11.9)

$\mathrm{here\! :}\ \mathrm{h} = \Delta {\mathrm{l}}^{2}/({8}^{{_\ast}}\ \mathrm{R})\quad \vert \mathrm{h} = 0.13\,\mathrm{m}$

$\mathrm{or\! :}\ \mathrm{h} ={ \mathrm{R}}^{{_\ast}}\ {\mathrm{c}}^{2}/(3{2}^{{_\ast}}\ {\mathrm{f}}^{2{_\ast}}\ \Delta {\mathrm{l}}^{2})$

This range gradient is smaller than the resolution and thus may be neglected. Fig. 11.5a demonstrates the effect of Range Walk. The images show series of the single-look range profiles. Structures are moving through the representations from below to above. It is remarkable, that all structures appear as diagonal stripes from above left to below right. This is caused by the range-walk. The drift angle, which results in this effect, is related to the tilt angle of the single look stripes. The series of range profiles shown below has undergone a correction process. The single scatterers show now a horizontally aligned pattern, as obvious from Fig. 11.5b.

Fig. 11.5

SAR series of range profiles at 35 GHz without and with drift correction

If the SAR sensor is accelerated in a direction perpendicular to the flight path, the point scatterer response is blurred in cross range. While a linear movement gives reason to a constant Doppler shift, resulting in a range walk, a non-linear movement (acceleration) results in a blurring. In the following an estimation is given, for which acceleration a correction is not necessary without notable blurring:

It is quite reasonable, that the excursion due to the acceleration should be less than half of the wavelength, which can be formulated as:

Accelerated path (35 GHz): $\mathrm{s} = \mathrm{a}/{2}^{{_\ast}}{\mathrm{t}}^{2} < \lambda /2\quad \lambda= \mathrm{c/f},\vert \lambda= 8.6\,\mathrm{mm}$

$$\mathrm{Max.\ acceleration\!\! :}\ \mathrm{a} < \mathrm{c}/({\mathrm{f}}^{{_\ast}}{\mathrm{t}}^{2})$$

(11.10)

• t is the aperture time t_a

• which gives: $\mathrm{a} < \mathrm{c}/({\mathrm{f}}^{{_\ast}}\ {(({\mathrm{R}}^{{_\ast}}\ \mathrm{c})/({2}^{{_\ast}}\ {\mathrm{f}}^{{_\ast}}\ {\mathrm{v}}^{{_\ast}}\Delta \mathrm{l}))}^{2})$

• or shorter: $\mathrm{a} < {4}^{{_\ast}}\ {\mathrm{f/c}}^{{_\ast}}\ {\mathrm{v}}^{2}{_\ast}\ {(\Delta \mathrm{l/R})}^{2}\quad \vert \mathrm{a} < 0.026\,{\mathrm{m/s}}^{2}$

The maximum acceleration error increases linearly with the radar frequency but quadratically with the relation resolution/range.

The acceleration for all three axes are given by the Mil-Bus data of the TRANSALL carrier aircraft, which allows the calculation of the acceleration in flight direction. Correction of the data for this acceleration results in a well-focused image.

Tests of the focusing implemented in the MEMPHIS SAR algorithm were conducted to maintain good focusing also over longer ranges. A scene over the Nymphenburg Palace in Munich was chosen. It turned out that the algorithm, as applied initially, is not sufficient for high-resolution processing over the range, relevant for that scene, and a higher sophistication is necessary. The main problem is, that for high-resolution processing a model, which is based upon a constant acceleration is not sufficient. The determination of the effective acceleration by auto-focusing methods only allow to generate optimized single look images, but do not lead to a general improvement of the SAR image. The only way to generate focussed high resolution images is based upon a combination of autofocus (for the determination of the constant offset during one FFT period) and acceleration information of sensors directly incorporated into the radar front-end. The latter deliver the information of the acceleration gradient within a single FFT period. This combined method gives the best focussing and in addition a constant acceleration error of about 0. 15 m∕s², which is related to a depression angle error of about 1^∘ (at 30^∘ depression angle). An image processed with a respective optimized algorithm shows Fig. 11.6 together with the results of three processing steps for a section of that image related to a fence at a parking lot close to the palace.

Fig. 11.6

SAR image of Nymphenburg palace at 94 GHz, (a) + (c) resolution 75 cm, (b) with optimized algorithm and resolution 19 cm, (d) detail with optimum range processing, (e) detail with full range/Doppler correction

For the conditions discussed here with the MEMPHIS radar the following statements are true:

• 1. For slant ranges between sensor and scene below 1 km a SAR processing without the application of correction algorithm delivers images of good quality only under very calm flight conditions.

• 2. Simple correction algorithms which solely take into account a constant acceleration deliver images of good quality up to a slant range of 1 km.

• 3. For slant ranges above 2 km this model is only sufficient for calm flight conditions.

• 4. For greater height or range a motion compensation process has to be applied which corrects data within one FFT-length.

This is only possible with fast acceleration sensors at the locus of the radar. For these the influence of gravitation has to be taken into account.

A typical MEMPHIS SAR image, with all necessary corrections applied, is shown in Fig. 11.7. It shows an image of the Technical University of Munich.

Fig. 11.7

High-resolution SAR image of TU Munich at 94 GHz

11.4.4 Millimeter Wave Polarimetry

The MEMPHIS radar is equipped with four receive channels. Two of them are generally dedicated to retain polarimetric information on the measured scene. Whenever polarimetric information is required, a thorough calibration has to be performed. For the data under consideration a technique was employed which uses the data stream itself for calibration and elimination of cross-talk and channel imbalance. This is done in two steps. The first step generates a symmetric data matrix from the not symmetric matrix of measured data. The second step removes the channel imbalance.

Polarimetry plays an important role for the segmentation of different classes of vegetation within a SAR image (Ulaby and Elachi 1990).

A simple way to visualize the capabilities of polarimetry, is to apply a color code to each of the orthogonal polarization components, that is for H–H and H–V channel, and the difference between those components (HV–HH). An example is shown in Fig. 11.8, which some rural terrain.

Fig. 11.8

Pseudo colour representation of polarimetrically weighted SAR image of rural Terrain

A further case is shown in Fig. 11.9, which gives the characteristics of some rocky terrain in a different polarization state. Specifically it can be seen, that rocks show a higher reflectivity for the polarization left-hand circular/left-hand circular (L/L), but the gravel road has a more dominant signature at left-hand circular/right-hand circular (L/R). The polarimetric differences can be attributed to different micro geometries: For circular polarization, odd returns are sensed by the cross-polarized channel, while the co-polarized channel is sensitive for even numbers of reflections.

Fig. 11.9

Polarimetric SAR images at 94 GHz for T-R-Polarization L-L (left), polarimetric weighting and Polarization L-R

For a thorough study of polarization features SAR scenes have to be subdivided into mainly homogenous sub areas. Determination of statistical parameters for these sub-areas and of their specific polarimetric characteristics allow the extraction of knowledge upon the vegetation and even its state.

11.4.5 Multiple Baseline Interferometry with MEMPHIS

Interferometry at millimeter wave frequencies has an important advantage and at the same time exhibits a general shortcoming: The first is a considerably better height estimation accuracy at a fixed interferometric base length, the latter is a lower unambiguity.

For a fixed baseline the height estimation accuracy is linearly dependent on the radar frequency. That means, that at W-band the accuracy for a given interferometric base is by a factor of ten higher than at X-Band. This would be a considerable advantage, as on small aerial vehicles, which can accommodate only small interferometric antenna assemblies the operation at millimeterwaves would be the solution. Unfortunately this advantage is coupled with a disadvantage, namely the unambiguity is also lower by the same factor, which means, that the phase unwrapping is much more time consuming. Figure 11.10 shows the relation between interferometric base and unambiguous range for 10, 35 and 94 GHz.

Fig. 11.10

Unambiguous range versus interferometric base (lowest curve 94 GHz, then 35 GHz, then 10 GHz)

A solution to this discrepancy between height estimation accuracy and unambiguous range can be found by extending the** hardware to a multiple baseline antenna as described under Section 4.1. With this approach the advantages of big height estimation accuracy with a wider base length and of a bigger unambiguous range with a smaller base length can be combined. The approach is roughly the following: From the data for the smaller base length a first estimation with lower accuracy but within a wide unambiguous range is given and this is successively improved by using data for wider base lengths. It is obvious, that with increasing interferometric baselength the number of phase periods is increasing.

The phase unwrapping algorithm using multiple baseline data, sorts the interferograms related to different base lengths according to these bases. The interferogram for the smallest base length is suspected to be unambiguous. If this is not the case, it has to be unwrapped with a standard method, like the dipole method. An absolute phase calibration is not necessary, as only phase differences are evaluated. In the next step a scale factor is determined, which is given by the relation between the base length belonging to the reference interferogram and the next, which has to be unwrapped. The reference interferogram is multiplied by this factor and subtracted from the latter, modulo 2π. This procedure leads to the interval chart, which contains the information, how many 2π intervals have to be added to the unwrapped interferogram. A special algorithm takes care upon the amount of phase noise and, if necessary, generates a correction term. If the correction does not deliver a valid value, the original number is taken. For the algorithm it is only tolerable, that single pixels of this kind exist. After all pixels are generated, this interferogram is used as a starting point for the iteration, using the next bigger baselength. This process is consecutively done for all available interferograms.

11.4.6 Test Scenarios

The first test area is a former mine with a conical pit-head stock.

Figure 11.11a–f show the interferograms for the sample area, which are related to the five different interferometric base lengths and additionally a SAR image of that terrain.

Fig. 11.11

Interferograms for the baselengths 0.055 m (a), 0.110 cm (b), 0.165 cm (c), 0.22 cm (d) and 0.275 cm (e) and the related SAR Image (f)

It has to be noted, that pixels with a reflectivity below − 25 dB are cancelled and assigned “black”.

To deliver a height, calibrated in meters, an appropriate calculation has to be performed. As additional inputs the flight height, the depression angle and the slant range have to be known. Equation (11.11) has to be solved numerically:

$$\begin{array}{rcl} \frac{\lambda } {\mathrm{2}}& & \equiv\Delta \left (\Delta \mathrm{R}\right ) = \left ({\mathrm{r}}_{\mathrm{22}} -{\mathrm{r}}_{\mathrm{21}}\right ) -\left ({\mathrm{r}}_{\mathrm{12}} -{\mathrm{r}}_{\mathrm{11}}\right ) = \\ & & = \left [\sqrt{{\left (\mathrm{y} - \mathrm{Bsin } \left (\alpha \right ) \right ) }^{\mathrm{2} } +{ \left (\mathrm{H} + \mathrm{Bcos } \left (\alpha \right ) - \mathrm{z} \right ) }^{\mathrm{2}}} -\sqrt{{\mathrm{y} }^{\mathrm{2} } +{ \left (\mathrm{H} - \mathrm{z} \right ) }^{\mathrm{2}}}\right ] \\ & & \quad -\left [\sqrt{{\left (\mathrm{y} - \mathrm{Bsin } \left (\alpha \right ) \right ) }^{\mathrm{2} } +{ \left (\mathrm{H} + \mathrm{Bcos } \left (\alpha \right ) \right ) }^{\mathrm{2}}} -\sqrt{{\mathrm{y} }^{\mathrm{2} } +{ \mathrm{H} }^{\mathrm{2}}}\right ] \end{array}$$

(11.11)

As the range difference λ ∕ 2 is equivalent to a differential phase of π each differential phase value of ψ_i,j can be related to a height h_i,j and a digital elevation model of the imaged terrain is deduced (DEM). Figure 11.12 shows a respective example for the test area shown in Fig. 11.11.

Fig. 11.12

DEM for the test scene of Fig. 11.11

An interesting application is the interferometry in urban terrain. MEMPHIS was operated over an urban area in Switzerland. The data evaluation was done in cooperation with RSL University Zurich (Magnard et al. 2007). Figure 11.13 shows the respective SAR image at 94 GHz. Figure 11.14 shows the related interferogram, Fig. 11.15 shows details of that scene for a built up area.

Fig. 11.13

94-GHz SAR image of an area at Hinwil, Switzerland

Fig. 11.14

Related interferogram

Fig. 11.15

SAR image, DEM and photo of section of Hinwil scene

The example shows very good the height structure of the terrain, calibrated in meters and the geometry of the flat roofed houses in the scene. The shadow regions, which are always critical for urban terrain, are handled quite well. Such data can serve as basis for further investigations on the structure of inhabited areas.

11.4.7 Comparison of InSAR with LIDAR

The standard method to determine digital elevation maps of terrain is the employment of a Laser scanner (LIDAR), as that of TOPOSYS (TopoSys Topographische Systemdaten GmbH). To validate InSAR results some typical areas were investigated using both, InSAR and the TOPOSYS system (Morsdorf et al. 2006). A test area was chosen, which contains urban and rural terrain, forests, rivers, high power lines and other man made structures. Figure 11.16 shows the related SAR image.

Fig. 11.16

SAR image and map for the test scene “Lichtenau”

For the comparison it has to be noted, that the radar and lidar data have not been taken simultaneously and that a different geometry was used. This leads to some possible referencing errors between the two images.

Due to the depression angle, different from 90^∘ the InSAR images show shadowing effects, which in the interferogram appear as “black”, as there are no valid phase values available, as obvious from Fig. 11.17. This is not the case for the TOPOSYS data, which are sampled in a vertical scanning mode (Fig. 11.18). Both images exhibit ground cells 1. 5 ×1. 5 m in size with a height estimation accuracy of about 0.15 m.

Fig. 11.17

DEM measured with TOPOSYS (above) and with InSAR (below)

Fig. 11.18

Error map for the data pair TOPOSYS/InSAR

Qualitatively both elevation maps show a good correspondence. Obvious are the shadow regions, which do not contain height information in the InSAR image. For a quantitative comparison an error map is generated, which is shown in Fig. 11.18. For a numerical evaluation some sample areas were chosen, as a wooded and urban terrain and an open field.

Table 11.4 summarizes the deviations of average height estimations for TOPOSYS and InSAR data for the three different terrain types. It is quite obvious, that both methods to derive a digital elevation map are comparable. The InSAR has the big advantage, that data can be gathered also under bad-weather conditions and, as the ground resolution for radar is independent on range, under considerably longer range.

Table 11.4 Height estimation differences for three types of background