satellite high resolution radar mapping techniques

SATELLITE HIGH RESOLUTION RADAR MAPPING TECHNIQUES

John J. Kovaly

Missile Systems Division, Raytheon Company Bedford, Mass.

INTRODUCTION

From a survey of planet characteristics and an estimate of the systems required to perform aerial mapping of planetary bodies, J. L. Sheehan,l shows that a radar system, for imagery and reflectivity measurements, will be one of the primary sensors. For the Jovian type of planets (gas giants), Jupiter, Saturn, Uranus, Neptune and probably Pluto, which are mostly encompassed in hydro- gen and helium, the resolution requirements of a radar system would be esti- mated from the expected size of waves in an Ocean of these gases. However, a resolution of better than one meter should be used to map the terrestrial type (Earth-like) Mercury, Venus, Mars, Earth and the Moon in order to map the topography and determine landing sites. In one case, that of Venus, a radar sensor may be the only way of seeing its surface because of its thick atmosphere.*

Extensive field measurements performed with a Side-Looking Airborne Radar ANIAPQ-972 have already demonstrated the many advantages derived from the use of radar for reconnaissance mapping of the Earth’s surface. J. H. Simons has demonstrated that this radar imagery provides good evidence of geological structure, geomorphologic features and cultural patterns of land uses.

A preliminary design of a radar system for mapping Venus from an orbiting spacecraft was shown to be feasible by R. F. Schmidt.3 This conceptual radar was designed to provide measurements of surface contour and surface area/ reflectivity. Within the constraints of beamwidth limits (1 degree and 2 degrees) and pulsewidth limits (1 psec and 10 psec), this radar could provide surface resolutions of 15-20 kilometers or better depending on orbit altitude.

In this tutorial paper, the primary purpose is to set forth the fundamental principles associated with coherent side-looking imaging radars which have produced radar maps with ‘photographic-like’ quality. High-resolution maps in two-dimensions can be produced by an airborne radar through the generation

*The Corps of Engineers is using a high-resolution side-looking airborne radar (SLAR), AN/APQ-97, to obtain topographical maps of large land areas in Panama and bordering Columbia which are perpetually concealed by continuous cloud cover; see Technology Week, May 22, 1967, p. 11, and Aviation Week and Space Technology, May 8, 1967, pp 57-64.

154

Kovaly : Radar Mapping Techniques 155

of a synthetic aperture4*6 in the along-track or azimuth direction, and pulse com- pression6 in the cross-track or range direction.* Excellent tutorial papers have been written on the separate topics of the general theory of side-looking synthetic aperture radar systems7 and linear FM pulse-compression radar systems.8 This paper shows that the high-resolution properties of these separate concepts are derived from identical fundamental principles. The radar system that employs these two techniques simultaneously, can produce a symmetrical, two-dimensional, high-resolution map by equating the time-bandwidth products in the two directions of azimuth and range.

SYNTHETIC APERTURE RADAR (SAR) WITH FM PULSE COMPRESSION

In general, the system geometry associated with a sidelooking radar is shown in FIGURE 1. An airborne vehicle, at Point A, is traveling in the positive x direction with velocity Vk Onboard the vehicle is a pulsedoppler radar system whose physical aperture, with beamwidth p, illuminates a ground-swath parallel to the flight path. The radar beam points in a direction that is orthogonal to the vehicle’s flight path.

I

FIGURE 1. Side-looking radar system geometry.

*A Synthetic Aperture Radar System (SAR) uses a relatively small physical aperture and in combination with the motion of the airborne vehicle and data processing electronics generates a synthetically long aperture. In contrast, some Side-Looking Airborne Radars (SLAR) utilize a physically-long antenna and by “brute force” obtain high azimuth resolution.

156 Annals New York Academy of Sciences

FIGURE 2 is a basic block diagram of a coherent radar system9 with a linear FM transmitter carried in the airborne vehicle. The synthetic aperture radar obtains range information by pulsing the transmitter. Fine range resolution and fine azimuth resolution is derived by storing the returned pulses over the time that a ground scatterer stays within the physical aperture beamwidth, and then processing the stored data through the correlator. Each pulse is linearly FMed within each pulse by the transmitter; and the sequence of pulses, gathered over a beam dwell time, are Doppler FMed due to the airborne vehicle’s motion across the ground scatterer.

The finely resolved images are displayed on a two-dimensional display to form a radar map of the ground. On this display, the range coordinate is in the “cross-track” direction, and azimuth is in the “along-track” direction.

In the analyses that follow, attention is focused on the frequency histories of the returned signals at the output of the coherent detector, and on how these histories are matched to the center frequency, time duration, and bandwidth of the correlator.

DOPPLER FREQUENCY HISTORY OF STATIONARY GROUND OBJECTS

Consider a stationary point reflector P on the ground at time t when it first enters the radar beam of the physical aperture (see FIGURE 1 ) . The slant range R to this point is given by the approximation:

and since (x - xo) = VA(t - to), then

Now, the Doppler shift in frequency for this point is:

2 R (t) fD(t) = - - A

where A is the wavelength of the transmitted RF signal. After taking the time derivative of Equation 1, substitution in 2 gives:

The received frequencies at the input to the coherent detector (see FIGURE 2) becomes:

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where f, is the primary transmitted frequency. The reference frequency to the coherent detector is:

(5)

where f, is the recording offset frequency which is used to keep the Doppler information band away from DC, and thus, avoid frequency foldover. Basically, the coherent detector performs the function of subtracting the reference frequency (Equation 5) from the input-received frequency (Equation 4) so that the coherently-detected frequency is:

fREF = fC - fo

2v,2 ARO

fDET(f) = fRGVB - fItEF = (f, -k fD) - (fC - fo) = fo - - (t - to).

( 6 ) This time function of the detected frequency is commonly referred to as the

“Doppler-frequency history” of a point scatterer. FIGURE 3 is a plot of this history, with the center of the diagram taken to be at time to, when the ground scatterer is in the center of the physical aperture and when the frequency is the offset frequency, f,. With the scatterer at broadside, its Doppler frequency falls to zero. The slope of the frequency history, or the FM rate, is -2vA2/AR, Here, the quantity -2VA2/R, is recognized as the two-way radial acceleration of the point scatterer along the boresight of the physical aperture towards the aircraft.

Now, the -3db lineal azimuth width of the physical aperture is R,P, so that the time extent over which the scatterer stays within the beam is essentially:

The bandwidth BW of the Doppler history is the product of its slope and its time duration, so that:

and, thus, the time-bandwidth product is :

Linear FM Transmitted Pulse

Recall that the pulse Doppler radar obtains its range information by transmitting pulses to the ground scatterer. Furthermore, in order to obtain more efficient use of the average transmitted power, and to increase range resolution, the pulse is transmitted with a linear FM sweep of its carrier frequency under

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The transmitted waveform for the linear FM pulse can be written:

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carrier frequency rate of frequency sweep (AfR/7-) swept spectrum bandwidth uncompressed pulsewidth.

The frequency content of each transmitted pulse is obtained from the argument of the cosine function so that:

In the absence of any Doppler shifts in frequency of the returned pulses from a ground scatterer, the frequency content of each coherently-detected pulse, after mixing with the reference signal, as in Equation 6 above, gives:

f,,, = f, - u t . PULSE

Comparing Equations 6 and 12 provides an insight into the similarity of the FMing functions in the two directions of azimuth and range. It is to be noted that the intentional frequency slope a for each transmitted pulse in the range direction is similar (but not equal) to the frequency slope 2V,2/XRO for the Doppler frequencies of a point scatterer. The range FMing a is introduced to each pulse by a function generator in the radar transmitter, whereas the azimuth FMing is produced by the change in aspect angle of the ground scatterer as the airborne vehicle moves along the ground track. Both of these quantities are frequency rates, and only their magnitudes may be different. The frequency slope a (in the range direction) sweeps over the pulse interval, 7, whereas the frequency slope, 2VA2/XR,, sweeps over the time interval T for which the ground scatterer remains within the azimuth beamwidth.

The radar pulses are transmitted at a pulse repetition frequency (PRF) consistent with: (a) at least two samples per cycle at the highest Doppler- received frequency; (b) avoidance of second-time range ambiguities; and, (c) sufficient energy to get a good S/N. As such, the Doppler frequency history along the azimuth direction is a sampled function rather than the continuous

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function shown in FIGURE 3. For the purposes of the paper, this intermediate sampling process may be neglected, since reconstructed Doppler histories are readily derived from the samples. However, the PRF must be high enough to adequately sample the Doppler bandwidth in the azimuth angle illuminated by the radar.

Two-Dimensional Resolution

As shown previously, it takes time to sample the Doppler bandwidth associated with a point scatterer during the interval it remains within the beamwidth of the physical aperture. The information within this bandwidth is required in order to derive the full resolution capability of the synthetic aperture. Therefore, the sampled data is stored on some medium, e.g., film, tape, or storage tube, over this interval before processing in the two-dimensional correlator.

Now, the focusing or collapsing of this information, which lasts for T seconds in the azimuth dimension and T seconds in the range direction (and whose frequency is changing with a rate of 2VA2/XR0 cycles/second/second in the azimuth dimension and a cycles/second/second in the range dimension) into a finely-resolved or narrow image is accomplished in the correlator.1°

There are any number of equivalent methods11 for describing the focusing function of the correlator, e.g., vector summation, matched filter, or cross- correlation. All of these methods can be summarized, pictorially, as in FIGURE 5. The input pulse of constant amplitude* A and width T with linear FM rate, a, is passed through the correlator which “matches” these characteristics. The output compressed pulseI2 has a sin x/x envelope with a pulse width l /aT when measured 4 db down from the peak amplitude. The spacing between the first zeros of this envelope is 2/ar, and the peak amplitude is A d s . This compressed pulse is referred to, in our case, as the image of the ground scatterer.

The above general correlator output characteristics for a linear FM pulse input are directly applicable to the two orthogonal directions of range and azimuth. FIGURE 6 shows the format of the input data to the two-dimensional correIator. Note the similarities of the two-dimensional packet of input data. In the range direction, there is a time interval, 7, microsecond long with intra- pulse bandwidth (Af), = a7 megacycles, whereas in the azimuth direction there is T seconds of samples with poly-pulse bandwidth (Af),. = 2V2,/AR,,T cycles. In both directions, bandwidths are generated by linear FM over time intervals given. A two-dimensional correlator, e.g., an optical correlator13 can

*The amplitude A is an involved radar quantity which depends on radiated power level, phase shift, fourth-power range law, and average-target reflectivity.

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focus the input packet in each dimension without any coupling between them. Then, as shown in FIGURE 6, the focused image in each direction is a sin x/x function. Thus, the image of the ground scatterer at the correlator output is a bivariate sin x/x function. The resolution of this output function is the width of the image at the -4 db level down from the maximum. It is at this point in the system, and at the time, when this image is formed, that the

TABLE 1

(SR) AND AZIMUTH RESOLUTION (SAz)

Range Direction Azimuth Direction

COMPARISON OF DERIVATIONS FOR RANGE RESOLUTION

1. Time width T~ of image at -4 db level 1. Time with T,, of image at -4 db level (Refer to Figure 5 ) : (Refer to Figure 5 ) :

2.

T~ = l/(Af)R TAz = l / (Af)Az

where ( Af) is transmitting FM band- where ( Af ) is Doppler bandwith. width.

Multiply both sides of above equation by C/2 where C is velocity of light

2. Multiply both sides of above equation by airborne vehicle velocity V,:

(factor of 2 required for two-way range) : = v A / tAf) A s

3 = C/2(Af), 2

CTR 2

3. Here V,T& is defined as the azimuth resolution SAz: 3. Here - is defined as the range

resolution SR:

SR = C/2(Af),

SAz = VA/(Af),,

4. Multiplying the numerator and 4. Multiplying the numerator and denominator by dwell time T, during which ground scatterer stays in

denominator by pulse width T gives range resolution in terms of range time-bandwidth product 7(Af)R: physical aperture, gives azimuth

resolution in terms of azimuth tirne- (13) product T(Af)Az: S, = C 7 / 2 ~ ( A f ) ~

S,, = V,T/T(Af),, (14)

combination of airborne vehicle, coherent radar with linear FM transmitter, and correlator have generated the “synthetic aperture.”

The derivation of the range resolution (6R), and azimuth resolutions (6Az) are given in TABLE 1, for easy comparison. Note the direct similarity of the


resolution Equations 13 and 14. The resolutions in either direction are funda- mentally related to the total information content" 2 T(Af)R and 2 T(Af)Az, the velocities C and VA; then the time intervals 7 and T. These resolution forms show that, as the total information content is increased, the resolution becomes smaller or greatly improved. Furthermore, the condition for making the image symmetrical in both directions is to let 6R = 6Az and r(Af), = T(df)A, so that CT = VAT.

Some other familiar forms for the resolution in the azimuth direction are easily obtained. Since:

substitution into Equation 14 gives the azimuth resolution in terms of the time on target T as:

Here, the product VAT is usually considered as the length L of the generated synthetic aperture, so that:

Furthermore, since L = R,@, where p is the beamwidth of the physical aperture on board the airborne vehicle, and since p = X/D, where D is the actual length of the physical aperture, then:

(17) D 2 6 A z = - .

Here, Equation 17 shows that, if all the data from a point scatterer is processed optimally, then the theoretical azimuth resolution of a synthetic aperture is independent of transmitted frequency or wavelength and is dependent only on the length D of the physical aperture. In practical systems, the theoretical resolution may not be obtainable, due to the many sources of phase errors15J6 that may be introduced throughout the system. TABLE 2 summarizes the salient characteristics for imaging a stationary point scatterer by a focused synthetic aperture radar system? in the azimuth or along-track direction.

tA comparison of the azimuth resolution obtainable from a physical aperture, an unfocused SAR, and a focused SAR has been treated by L. J. Cutrona and G. 0. Hall in Refereme 17.

Kovaly : Radar Mapping Techniques

TABLE 2

SYNTHETIC APERTURE RADAR SYSTEM a. Useful Relationships

SUMMARY OF RELATIONSHIPS FOR A FOCUSED

167

Theoretical Forms

2V,' f" + - (t-t,)

A R O Doppler History

Time on Target

2 v 2 Doppler Bandwidth (BW) A T AR"

2v,2

A R O

Time Bandwidth Product (TBW) - TZ

b. Equivalent Forms for Azimuth Resolution Theoretical Forms

Time on Target (T) Formulation hR, 2V,T

A R O Synthetic Aperture Length (L) -

Physical Aperture Length (D) - Formulation 2L

D Formulation 2

Time-Bandwidth Product (TBW) pc Formulation 2 T(Af)aE

Where : fo = recording offset frequency

A = carrier wavelength

t = time to = time when scatter is

in beam center /3 = beamwidth of physical

aperture

V, = airborne vehicle velocity

SYNTHETIC APERTURE RADAR IMAGERY

The first experimental demonstration of the synthetic aperture radar concept was performed by a group at the University of Illinois. In a report dated 8 July, 1953, Kovaly, Newell, Prothe and Sherwin produced a strip map (see FIGURE 7a) of a section of Key West, Florida. With this early system, the 4.13-degree physical aperture beamwidth was used to make an effective synthetic beamwidth of 0.4 degree. Even in this first synthetic aperture radar (SAR)


FIGURE 7a. Strip maps produced early in 1953 of a section of Key West, Fla. These radar maps were made entirely by means of frequency analysis, entirely inside the natural geometrical beamwidth of the nonscanning radar beam. On the left is shown an optical photograph of the same region, demonstrating the close correspondence between the two methods of observation. (Published in 1EEE Transactions on Military Electronics, April 1962, Figure 2, pg. 113; Reproduced by permission of editors.)

imagery, the land-water boundaries, with correct geometrical forms, were clearly visible, and individual buildings were resolved.

Since the first SAR map was made back in 1953, many and significant advances have been made in the design of SAR systems. The group at the Radar and Optics Laboratory, University of Michigan, have been the forerunners in advancing the state-of-the-art in the design of this elegant electronic system. An example of the high-resolution SAR imagery produced by this group is shown in FIGURE 7b. This map is a radar image of the Detroit, Mich. area. The water areas of Lake St. Clair and the Detroit River, with the Ambassador and MacArthur bridges, are easily identified. Of significant geological interest are the broken ice floes on Lake St. Clair. Man-made structures like buildings and roads, as well as natural terrain, are easily recognized.

CONCLUSION

With the capability of performing in day or night, good weather or bad, and gaseous media, radar should play a significant role as one of the primary


sensors for planetary aerial mapping. In addition, and far more importantly, radar systems can provide the high-resolution radar imagery that results in “photo-like” quality to the maps. This paper has shown that fine azimuth or along-track resolution can be achieved through the generation of a synthetic aperture. A physical aperture, whose dimensions are commensurate with the size of a spacecraft, in combination with a coherent radar and data processor, can synthesize a very-long antenna, which is required to achieve a narrow beam in the azimuth dimension. In addition, fine-range resolution can be obtained by linear FM modulation of the transmitted radar pulse. Here, appropriate transmitter modulation makes for efficient use of peak-power limited tubes to achieve the necessary average power. The combination of a synthetic aperture radar, with linear FM transmitter modulation, can result in a symmetrical, two-dimensional, high-resolution response function by

FIGURE 7b. Recent synthetic aperture radar imagery of Detroit area. (Courtesy of Radar and Optics Laboratory, The University of Michigan.)


designing equal time-bandwidth products in both the azimuth and range direction. Through this tutorial paper, the two sophisticated electronic concepts, synthetic aperture radar and linear FM transmission, can be treated together with the same fundamental concepts.

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SIMONS, J. H. 1964. Some applications of side-looking airborne radar. Proceed- ings of the Third Symposium on Remote Sensing of Environment, Oct. 14-16, 1964. : 563-571. Infrared Physics Laboratory, University of Michigan. Ann Arbor, Mich.

SCHMIDT, R. F. 1964. Radar mapping of Venus from an orbiting spacecraft. Pro- ceedings of the Third Symposium on Remote Sensing of Environment. Oct. 14-16, 1964. : 51-61. Infrared Physics Laboratory, University of Michigan. Ann Arbor, Mich.

CUTRONA, L. J., W. E. VIVIAN, E. N. LEITH, a G. 0. HALL. 1961. A high-resolution radar combat-surveillance system. IEEE Transaction on Military Electron- ics MIL-5: 127-131.

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COOK, C. E. 1960. Pulse compression-key to more efficient radar transmission. Proceedings of the IEEE 48 (3): 310-316.

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BERNFELD, M., C. E. COOK, J. PAOLILLO, a C. A. PALMIERI, 1964-5. Matched filtering, pulse compression and waveform design. The Microwave Journal (Part I) October, 1964: 57-64; (Part 11) November, 1964: 81-90; (Part 111) December, 1964: 70-76; (Part IV) January, 1965: 73-81.

SKOLNIK, M. I. 1962. Introduction to Radar Systems. : 143-163. McGraw-Hill Book Company, Inc. New York, N. Y.

CUTRONA, L. J., E. N. LEITH, L. J. PORCELLO, a W. E. VIVIAN. 1966. On the application of coherent optical processing techniques to synthetic-aperture radar. Proceedings of IEEE 54: 10261032.

MCCORD, H. L. 1962. The equivalence among three approaches to deriving synthetic array patterns and analyzing processing techniques. IEEE Transac- tions on Military Electronics MIL-6 (2) : 116-1 19.

KLAUDER, J. R., A. C. PRICE, S. DARLINGTON, a W. I. ALBERSHEIM. 1960. The theory and design of chirp radars. Bell System Technical Journal 39: 745-808.

CUTRONA, L. J., E. N. LEITH, C. J. PALERMO, & L. J. PORCELLO. 1960. Optical data processing and filtering systems. IEEE Transactions on Information Theory IT-6: 386-400.

WOODWARD, P. M. 1955. Probability and Information Theory with Application to Radar. McGraw-Hill Book Company. New York, N. Y.

GREENE, C. A., a R. T. MOLLER. 1962. The effect of normally distributed ran- dom phase errors on synthetic array gain patterns. IEEE Transactions on Military Electronics MIL-6 (2): 130-139.

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