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Design approach for a high-resolution microwave imaging radio camera
Design Approachfor a High-resolution Microwave Imaging Radio Camera bj’
BERNARD
D.
STEINBERG
Valley Forge Research Center, 7% Moore School of Electrical Engineering University of Pennsylvania, Philadelphia, Penqlvania ABSTFUCT: The angdar reaoltiti
of an imaging de??& is the order of the PX&WX& of
the number of wavelengtha amoee the aperture. To achieve the high reeolution typical of optical inatrummte at rntimvee, aperturea miik in eke mug be required.T?M requirernentefor such a device, eded
a radio camera, are confwmdity
&h
the terrain, a epartdy
jWed apertmre of randomly (w nearly 80)locded ekmmta,eelf-adaptive beam forming and a eource of wcimnmve i%midn. Baaed on thie de&n approach, a lOOO$ L-band radio camera ie under devebpmmt Thie paper
discwrsee
the
statw,
at the Valley Fwge Research Ceder
of cuwent devebpmmt
of the Moore School.
of the dex?ice.
I. Introduction
The term imu+g conventionally applies to devices which utilize infrared, optical or shorter wavelengths. Telescopes, cameras and microscopes are examples. A 241~ lens is IOaoptical wavelengths in size. Its available resolving power is 1O-5rad., which is 2 set of arc. Microwave wavelengths nominally r&nge from 1 in. (X-band) to 1 ft (L-band). The size of an aperture with corresponding resolution would be loh106 ft or 2-20 miles. At the Valley Forge Research Center of the Moore School, the technology leading to such a device, called a radio camera, is under development. This instrument should be capable of obtaining two-dimensional inmges of targets at radar ranges (tens to hundreds of miles) even in inclement weather. In this paper, we discuss the logical requirements for such a device, some basic problems, some design approaches and,the status of current development. II. Size of the Instrument
The parabolic dish, which is the microwave equivalent of the Newtonian telescope, is the most common microwave aperture (Fig. 1). Gravitational and thermal stresses limit its practical size to a few hundred feet. Achievement of significantly larger size requires that the aperture be broken into many smaller structures snd the distances from the parts to a source equalized by phase shifters, i.e. a phased array (Fig. 2). In most arrays the spacing between elements is constant. The phase progression required to form a beam steered to angle 0 is $4+1-#4 = 211 (dsin e/A) where d is the interelement spacing and h is the wavelength. Unlike the continuous aperture of Fig. 1, such an array samples the radiation field in discrete locations.
415
Bernard D. Steinberg Parabolic
mirrors
Eye Newtonian telescope
Microwave dish FIU.
piece
1. Microwave antenna and Newtonian telescope. Resolution N h/L. Phase shifters Elements
H
FIU.
2.
Phased array.
Unless the sampling distance d is sufficiently small, the sampling process crerttes spurious beams called grating lobes, avoidance of which requires that d does not exceed /\/2.* Such an ~~~rray is caBed a$&~! array. A fIlled aperture * Uniform sampling with interval d of an aperture excitation i(z) results in a set of samples i(z) 2 6(2 - 4). The radiation pattern f(u) = B’{+)} * .F{z:6(z - md)} = A(u) * I: & -4Wd)L wheref@(u), the radiation pattern of the unsampled aperture, is repeated at intervals of A/d. F{ } is the Fourier transform, u = sin 8.6 = angle from the normal. Only when d
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_ Design Approach for a High-Resolution Mimnmve Inmging Radio Camera of size L, therefore, requires the order of (L/h)* antenna elements. A fllled phased array with a resolving power of 10msrd. would require lolo elements, which is an impractically large number. High angular resolution requires a large aperture but does not require that the array be fllled. The beamwidth is a relatively insensitive function of the distribution of antenna elements. Table I gives the 3 dB beamwidth in units of I\/L for three d&rent apertures. The first is a uniformly illuminated aperture. The second has a semicircular taper. The third has a triangular taper. The number of elements may be reduced by orders of magnitude by thinning an aperture without sign&ant alteration to the beamwidth. TABLE I Aperture Uniform semicirmllFbr taper Triangular taper
3 dB Beamwidth CM8h/L 1.02 1.27
Provided that grating lobes may be avoided, such an array can be highly useful.* Grating lobes develop from the properties of the distribution of the sampling points, the Fourier transform of which is convolved with the beam pattern of the underlying or corresponding nonsampled aperture to produce the radiation pattern. Grating lobes require a coherent buildup of elemental signals at angles other than the steering angle 8. Spurious lobes are avoided by eliminating all periodicities in the element locations. Aperiodic element locations may be calculated by formula (l-9) or chosen at random (lfH8).It is shown later that a limiting factor iu the resolution of a microwave image is the level of the sidelobes in the side radiation pattern of the array. The method of distributing a fixed number of elements aperiodically over a large aperture should be dictated by this consideration. The ilrst decision to be made is whether to distribute the elements randomly or by some formula. Given some arbitrary distribution of randomly selected element locations, there is, with probability one, a better distribution and presumably some algorithm for finding it. Two factors mitigate against the algorithmic approach. First, for an array of suitably large size (see definition of large, below) it is often impossible to specify element locations with adequate accuracy to permit the use of algorithmic location procedures. Second, it has been found experimentally that the peak sidelobes of the algorithmically designed arrays referenced above are not lower than those of random arrays having similar design parameters (19). Thus, the most general design procedure should accommodate to the properties of the random, thin array. * The two element interferometer with its high density of grating lobes (the lobe spacing is sin-l A/L) is the epitome of en unfXed or thinned array. It is useful where high tmgular accuracy is required and where means are available for avoiding lobe ambiguity. It is not useful for the imaging of area-extensive objecta Imaging requirea that lobea be eliminated or at least suppressed around the mein lobe in the angular interval subtended by the object.
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Bemurd D. Steinberg 0onforrnu.I array. Another logical requirement for the design procedure relates to the array surface. An array measured in square miles cannot be required to be planar nor to assume any other particular surface. For generality of use, the design procedure should permit the implantation of array elements on any piece of ground or on buildings within the general array area. In short, the array surface should conform to the terrain within the array. Such an array is called a conform& array. Illumination. A camera requires a source of illumination. An optical camera uses the sun or a flash gun. Solar microwave radiation is inadequate; hence, the latter is a requirement. A pulsed radar transmitter is one way to satisfy this need.
,,,
--
/
Self-odaptiw signal processtng ckcuits to cohere the orray
Fm. 3. One thousand ft random array for Valley Forge camera.
Figure 3 illustrates a conformal array with low gain, nonscanning microwave horns randomly spaced by hundreds of wavelengths. Within the array is a radar transmitter and conventional antenna. The antenna beam is large compared to the resolvability of the array. Like a flash gun it provides general illumination in the direction of the object. The high angular resolution image is formed from operations upon the signals received by the distributed antenna elements. Large array. The conventional tolerance on the uncertainty of element * A large array is defined as one of such size that it is location is A/10. impossible in principle or impractical in practice to know the element locations to within this tolerance. Consider the 1O-6rad. resolution, L-band * The loss in gain due to random zero mean locetion errow is exp ( - ~3) where a* = 2nv& and us = rma location error (20). For CT,= h/IO the loss is 1.7 dB. 418
Journal of The FranklinInstitute
De&n Approach fw a High-Reaohticm i&mncuve Irrmging Radio Camera may mentioned earlier. Its diameter is 20 milea, which ia the kgth of the City of Philadelphia. Such an array, if located there, would satisfy the definition of large. An array on a nonrigid body such as an aircraft, notwithstanding the fact that its maximum usable dimension is only 100 fi, is another. An array in a fluctuating medium is a third. An example is an array of several square miles on an underwater mountain. The velocity of sound varies with depth in the ocean because of temperature and pressure variations. In addition to the spcttial variation in the refractive index, there are also temporal variations due to underwater ocean currents and other equivalents of weather. Adaptive away. For generality of use, the design procedures for the radio cameraa should include the large array as defined above. The presumption that the array may be large imposes a logical requirement for self-adaptivity. Illuminator
l-l
I
Amy output
‘I
Direct measurement I
Ret or meawrement criterion
I
FIG. 4. !ryJ+B of colltrol.
In that case, the army designer does not know the element locations with adequate accuracy for proper a e determination of the phase shifts. Hence the array system must somehow be made to accommodate for the inadequacy of the designer. Such an arra.y is called udaptive. Three distinct levels of adaptive control are illustr&ed in Fig. 4. The lowest order is celled Type I control ; it consists of dynamic, open-loop measurements of element locations by a subsystem within the array which feeds lo&ion information to the army processor. Type I control is limited in applicability to arrays of modest size (i.e. maximum dimension of hundreds or at most thousands of feet). Type II control operates upon measurement of the radiation field as sampled by the EIIT&~ elements. Phase comparisons are made between the signals received by each element and a reference signal. The phsse di%rences are assumed to be due entirely to the differential differences between array elements and the object and are eliminated by closed-loop feedback control to the phase shifters. Type II control is basio to the image formation process. Type III control utilizes information Corn
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Bernard D. &e&berg the array output, i.e., the image data, to vernier the image forming process 80 as to optimize image quality. III. Valley Forge Radio Camera
The Valley Forge system under development is shown in Fig. 6.* An L-band, AN/TPS-1D radar- transmitter is the illuminator. The signal from the target is received by the same antenna and passes through the radar receiver in conventional fashion. The °ree beam is broader than the
Satellite receiver
FIG
6. High resolution microwave
imaging.
angles subtended by most radar targets. Consequently target characteristics other than range and angle, which are displayed on a PPI, normally are lost. In addition to the conventional display, the IF echo of the target is used aa a reference waveform for adaptive phase shift oontrol at each array element (also called array module and satellite receiver). An echo also is received at each array modnle. A low-gain nonscanning antenna delivers the signal to a receiver in the module which compares the phase of the echo at IF with that of the reference IF pulse delivered from the main receiver. The phase difference is smoothed in a low-pass’ filter and delivered as a control voltage * Note
similarity to earlier design in (21).
Design Approach for a High-Resolution
Microwave Imuging
Radio Camera
to the voltage controlled oscillator serving as the local oscillator of the satellite receiver. A phase-locked loop is therefore formed which forces the two IF target echoes into phase quadrature. The loop serves as a selfadaptive phase shifter for the array element. Two assumptions are implied. The first is that the IF echoes in the various receivers are identical in shape and vary only in time of arrival and that their additive noises are independent from receiver to receiver. The second is that the phase differences are due entirely to differential differences between the receivers and the reflecting object. Since the phase-locked loops eliminate these phase differences, the IF signals are cophased and may be added exactly as in the simpler phased arrays. Given N antenna elements the output of the summer of Fig. 5 is an echo voltage N-times larger than that of the individual echoes. The receiver noises being independent of each other, the noise contributions into the summer combine with random phases and, therefore, their powers rather than their voltages are additive. Hence the signal-to-noise power ratio (SNR) out of the summer is N-times larger than in each of the receivers. This calculation atices to produce a tlrst estimate of the minimum required number of elements. It is reasonable to require that the SNR of the high resolution array be no poorer than that of the main radar. Assuming common noise figures for all the receivers, the SNR in a satellite receiver is weaker than that of the main receiver by the gain ratio of the antenna of the main radar to that of the satellite receiver. The gain ratio is about equal to the area ratio, which in the Valley Forge equipment is 30 to 1. It is shown later that this is a very weak condition on the number of elements. Summing the phase-rotated IF echoes of the satellite receivers solves half the problem : it results in a narrow beam pointed somewhere within the beam of the main radar. The output signal strength is proportional to the back scattering cross-section of the particular part of the object intercepting the narrow beam. The beam must be scanned over the object so that the reflecting properties of the entire object can be measured. With such data, a high resolution image may be created. It is shown in the Appendix that even though there is considerable uncertainty in location of the elements, once the phase-locked loop has made the desired phase correction, scanning of the narrow beam may be accomplished by open-loop control. The angular extent over which open-loop scanning can take place is h/To, where u is the rms uncertainty in element location. Conversely, if a target subtends angle Br the tolerance on element location is h/78,. A severe situation would be an aircraft at the short range of 2 miles. Assuming the aircraft to be about 100 ft the tolerance is approximately 14 wavelengths, which is two orders of magnitude larger than the conventional array element tolerance. Thus, following phase synchronization of the array, open-loop control of the phase shifters driving the summer should permit scanning of the narrow beam across aircraft targets, resulting in a high angular resolution display, even with element location tolerances of 10 or 16 ft.
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Bernard D. Steinberg IV. Self-survey TypeI Control !I'ype I control provides as much a prkk information as practical so as to ease the strain in the adaptive circuits and/or to reduce the element location uncertainty to within tolerance. The latter appears relatively easy to achieve under most conditions. Two self-survey methods for locatiug the elements of the first lOOOft array at Valley Forge are sketched in Fig. 6.Each involves distance measurements from several points within the array to each array -D-
0
T
t
Microwave
FIG. 6. Type I-self-survey
techniques.
module. The distance information is fed to the array processor (see Fig. 4) from which calculations of element locations are made. The first method is a microwave technique in which an RF transmitter in the desired band is swept in frequency over a few tens of MHz. At each array module the reflection coefficient of the antenna is modulated by a 60-MEL5oscillator. The CW echo received by the transmitter mixes with the outgoing swept RF to yield a 60 MHz intermediate frequency, the envelope of which is a trignometric function of the distance. As shown in the figure the number of scallops per unit of frequency sweep is indicative of the distance. A second method being tested for a field of several hundred feet is an acoustic ring-a-round circuit. An acoustic source radiates an impulse to a microphone at an array module, where a pulse is generated and returned by cable to trigger the acoustic transmitter. The period between acoustic transmissions minus all accumulated elect&al delays is proportional to the distance. 422
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Design Approach for a High-Reeolukn V. Adaptiue Beam Forming-Type
Mkrmve
ImagGtg Radio Camera
ZZ Control
Figure 7 shows the phase-locked loop of Fig. 5 in somewhat greater detail. The IF waveform consists of signal echoes the order of 1~0 in duration, which is typical of conventional pulse radar, spaoed by the interpulse interval, typically the order of 1 msec. The SNR in the main receiver is larger than
FIG. 7. Type II--earn
pled data loop.
that in.the array module by the antenna gain ratio. Both signals are gated to avoid receiver noise and spurious signals between target echoes from entering the feedback loop. Gating is either at IF or within the loop. A range gate pulse in the main receiver gates the high SNR reference target echo onto the cable which delivers it to each satellite receiver. An envelope detector extracts it at the array module and a pulse shaper, such as a blocking oscillator, recreates the gating waveform to operate the gates and switches in the sampled data loop. An appropriate delay is inserted to account for amplifier and cable propagation delays. By virtue of the phase and frequency acquisition properties of the sampled data loop, it permits the radar transmitter to be nonphase coherent from pulse to pulse. Phase memory of the transmitted pulse is preserved in the target echo in the main receiver. Phase synchronization of the local oscillators is accomplished by the individual phase-locked loops. However, the same sampled data loop has two serious frailties, the East relating to SNl3 and the second to switching transients and memory tolerances. Loop closure requires a SNR within the loop at the input to the VCO in excess of 6 dB (22). Assuming that the SNR r,, of the main receiver is very much greater than unity, r, is about equal to rl which is weaker than r,, by the antenna gain
Vol. !296,180.6, December1978
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Bemurd D. &e&berg ratio. In a nonsampled loop, the improvement in SNR due to the low-pass filter in the loop is the ratio of the IF bandwidth to the loop video bandwidth. In the sampled data loop, it is smaller than this quantity by the duty cycle of the signal. In other words, the improvement in SNR from rl to rBis no larger than the number of pulses integrated during the memory time of the loop. This interval may not exceed the time interval over which an object of interest undergoes signi&ant change. For aircraft targets this may be as short as 0.01-0.1 sec. !I’hus as few aa 10-100 echoes may be integrated. Since r8 must be at least 6 dB, and preferably 10 dB for rapid signal acquisition, the input SNR rl at the low gain antenna of the satellite receiver should be between - 10 and 0 dB. The SNR r,, in the main receiver is larger by the antenna gain ratio. Although only 30: 1, or 15 dB, in the first Valley Forge equipment, a more likely gain ratio would be 30 dB. Thus the required SNR in the main receiver would be 20-30 dB, which is an undesirably high requirement. A second difficulty of the loop is the need to freeze its operation between pulses. Not only must the frequency of the VCO remain approximately fixed between pulses, but the phase drift from pulse-to-pulse must be held to a small fraction of a cycle, typically 2n/lO. In the interval T between pulses, the VCO may be presumed to drift from w0 to w,,+ alp. The accumulated phase error is Jr W?dt = orTa/2.Equating it to the pulse-to-pulse phase shift tolerance gives Af = cwT/27r= l/ST as the short-term frequency stability tolerance of the VCO, which is the order of 100 Hz. Although it is not intrinsically difficult to stabilize a microwave oscillator for 100 Hz short time stability, this oscillator needs to be both stable and modulatable simultaneously. The typical voltage sensitivity of such an oscillator is l-10 MHz/V, requiring that the driving voltage of the VCO be held constant to 10-100 U.V. between pulses. The peak voltage level in the feedback loop is the order of 1 V. Thus the decay in the memory storing the LPF output or the decay in the charge aoross the condenser of the LPF or the unbalance in the sample and hold switches need be held to one part in 10” or 105. If the requirement for noncoherent transmission is eliminated both design problems are eased considerably. Figure 8 shows one form of coherent array module which takes advantage of a phase coherent radar transmitter.* The low-level CW oscillator whioh drives the 6nal amplifier in the transmitter is permitted to radiate nearly continuously across the array. The phase coherent radiation received at each module is heterodyned via a stable local oscillator to IF where it drives the VCO of a phase-looked loop into phase and frequency synchronism with the broadcast reference. About one pulse duration before the arrival of the echo from the object, the broadcast reference is gated off so that all modules may receive the echo. The echo is coherently demodulated by the VCO in two quadrature deteotion ohanuels, thereby resolving the echo, which may be described by amplitude A and phase 8, into components x=Acos8andy= A sin 8. During the two or three pulse duration interval * Due to Earl N. Powers, member of the teohnical staff of VFRC.
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ilGmmuve Imaging Rati% Camma
when the reference is not radiated, the VCO output is substituted for the reference wave into the phase-locked loop 80 that it continues to operate without significant disturbance. The composite vector echo represented by the in-phase and quadrature components may now be cophased axoss the array to form a narrow beam, which is then steered by the same open-loop control discussed earlier. Nearly CW RF ref I
I
STALO
FIO. 8. Type II-coherent
81~8~ module.
Both the sampled data module of Fig. 7, designed to work with the noncoherent transmitter, &d the continuous module of Fig. 8, designed for phase coherent illumination, are under development. The former is being built entirely from analog circuits ; in the latter the I and & channels are sampled and converted to digital pulse sequencea, following which all the processing is done digitally. . VI. Image Qwlity
FeedbackType
ZZZControl
Type III control is needed in principle to optimize image quality. Two distinct problems are involved. The first is the metric or criterion of image quality from which a control signal may be developed. The second is the search procedure by which control optimization is affected. It is believed that the contrast in the image will be a sensitive indicator of the extent to which the array is properly phased. In the absence of uncertainty aa to element location, the phase program generator labeled “hi res scan” in Fig. 5 would produce the optimum set of phase shift instructions for scanning. The result would be a, high-quality image. The fS&-order effect of emrs of estimation of element location is not in the width of the beam: provided that the errors are not so severe as to destroy the beem, the width of the beam is determined by the number of wavelengths NXWSSthe aperture. Instead the first-order effect is to decrease the energy in the main beam relative to the side lobe energy. The effect is a diminution in the ratio of
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Bernard
D. Steinberg
the strong echoes to the general background of the image. Hence a contrast measure between the largest target and the general background is expected to be useful in the development of an image quality criterion. Maximization of such a quantity will be the object of the search procedure. Unlike the phase-locked loops in which a direct one-to-one control is effected, Type III control is a 1 :N control process. As shown later N is not a small number; it will be between lo3 and 104.Aircraft dynamics require that the image forming process be effected in 10-a-10-1 sec.Rapid convergence is essential, therefore. Gradient search procedures are questionable in this regard. It is expected that more rapid search procedures will be necessary. One method to be explored is guided random search (23). In it an initial random phrasechange is made in each of the N elements in turn, and the successive changes in image quality observed. After the cycle S once completed, the effect produced by the first randomly chosen phase shift is examined. If the image improved from that choice a larger phase correction in the same direction ia made. If the first correction degraded the image the second selection for the first element is again made random. This procedure is applied to each element in turn.
VII. A FundumentaZ Problem
A conflict in principle exists between the properties of objects for which radio images are desired and Type II adaptive control. Each phase-locked loop serves as the phase shifter for its antenna element. By eliminating the phase difference between the signals received on its channel and in the main receiver, the phase-locked loop permits coherent or cophasal combining of its signal with all the rest. This is the ideal operation provided that the distant object is a point reradiator. In that case, the signals received by the elements would be identical in waveform, differing mainly in time of arrival (or phase) and somewhat in amplitude. However, the object is not a point scatterer; if it were it would deserve no interest. The array is assumed to be sufficiently large to permit resolving the object into several parts. Herein lies a fundamental conflict. Let the target of size S be at distance R. Let it be desired to resolve it in angle into k resolvable scattering centers. Hence, the angular resolution required by the array is about S/kR rad.To a first-order approximation the angular resolution may be identified with the beamwidth ;\/.L.Thus the length of the array must be L 2: kRA/X. This situation is pictured in Fig. 9(a). The target reradiates from its entire structure Fig. 9(b)]. Being of size S, the reradiation pattern is lobular with nominal angular lobe width h/S. (The far field reradiation pattern is the Fourier transform of the excitation of the object by the radar transmitter.) At the array the nominal cross-section of a lobe is Rh/X. The array length is k-times the lobe width. Thus the number of lobes which illuminates the array is the order of k, and array elements spaced by more than RX/S may be in different lobes. The relative phases of
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D&g% Approach for a High-Resolution blicrmve
Imaging Radio Camera
the sigmiis received by the elements 8re determined by the complex backsc8tter function 8cross the object. Small ch8nges in aspect angle alter the relative phases. Thus the relative phase between elemats sp8ced by more than M/S may be considered 8 random v8ri8ble, in which ~888 ph8sing the 8rr8y on such phase differences becomes 8 me8ningless tssk.
RX
-I-
L
s
I
x
L Array
Ib)
(a)
FICA9. Radiation from array and aircraft.
Figure 10(a) depicts this situation for an 8ircr8ft target. The 8ircr8ft is modeled 8s 8 random 8rr8y of smah scatterers of complex amplitudes a, 8t locations y$ where y is the distance along the 8ircr8ft. The equivalent current density of the 8ircraff 8s 8 rer8di8tor when ihuminated by 8 plane w8ve at 8ngle 0, from the norm81 to 8ircr8ft is i(y) = ~acbtS(y-y~)exp(-_j~sine,).
Sincethe a, h8ve rrtndom phases, the phase tilt of the illumin8ting wsve m8y be incorpor8ti into the backscstter coefficients without 8ltermg their st8tisticsl properties. The far field reradiation pattern f(u) = P{;(y)} = xaiexp
(j&u),
u = sintl,
where ai = a, exp ( - jky* sin e,) andf(u) is s random function with mndom amplitude arrdrandom phase (10). The correlation distance in u is the nominal lobe width h/S. The correlation distance in the reradi8tion field on the ground is M/S N L/k. The phase v8ri8tion 8cross the 8rr8y is 8 mndom vsri8ble with this correl8tion distance [Fig. 10(e)]. The lobe width, however, nomhmlly h/S, is itself s random v8riable. At times the reradiation pattern in the direction of the srr8y will be very much broader thsn h/S ss, for example, when 8 single strong reflector dominates the echo. Such s case might be a specularreturn from & corner reflector formed by wing and firselege. Figure 10(b) shows the Grcmft modeled 8s 8 random 8rr8y of sm8ll sc8tterers plus one large echoing center. The rer8diation pattern is the sum
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of two complex radiation patterns, the random functionf(u) described above plus the radiation pattern from the large, dominant source. The latter’s energy, arising from a small portion of the aircraft, radiates in broad lobes, each wide enough to contain all or most of the ground based array. Its pattern has a nominally constant phase slope across the array elements. Small random scatterers, none specular Scattering centers an aircraft
-Y
Plus single dominant scatter -r’Lr,r,Y
rizzr +fpjiffp _j=+TE& Phase of received
due to large scatterer (a)
(b)
FIQ. 10. Phase distributions amoss aimraft.
Provided that this single scatterer is large compared to the sum of all the rest, the phase of the sum pattern has a mean slope due to the strong reflector plus perturbations due to the weaker ones. The lower sketch in Fig. 10(b) portrays the situation. Whenever this situation prevails, the phase variation across the array elements is no longer meaningless. Instead it is biased with a mean phase front which disoloses the direction of the object, thereby permitting the phase-locked loops to adaptively form a coherent array. Phase synchronization will be accomplished during intervals when a common phase front dominates ; scanning and image formation will then follow. Experiments are underway to determine the statistics of the conditions illustrated in Fig. 10. VZZZ.ZmcrgsResoZutionandNumberofEZements
The number of elements has little influence upon the beamwidth of a radio camera. Nevertheless it is the dominant factor in the image resolution. Consider two scatterers of different sizes on an object to be imaged (Fig. 11). The array output traces the radiation pattern as the narrow beam scans by the larger scatterer. The sidelobes of the array pattern extend to the neighborhood of the smaller soatterer. To prevent the latter from being obscured, its main lobe response must rise above the sidelobes of the larger echoer. In more general terms, the smallest scatterer to be resolved must exceed the sidelobes of the larger. 428
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Design Approach for a High-Resolution Mkmwave Imaging Radio Camera Three questions need to be addressed. First, how is the sidelobe level related to the number of elements? Second, what clearance is required between the smallest scatterer and the sidelobe level of the largest saatterer ? Third, in order to obtain satisfactory image quality what is the maximum dynamic range of cross-sections which must be accommodated by this system ? The
------__ A, FIU.
11.
Large
Small
scatterer
scatterer
Importanceof low sidelobes.
fnst and second questions can be answered with known information. The third question requires conjecture until suitable experiments are performed. The ratio of the average power in the sidelobes to the main lobe is l/N for a random array (10). (Although specific element locations can produce lower sidelobes than the statistical average for a random array, the two reasons noted earlier preclude an assumption of greater sidelobe suppression.) The peak sidelobe is larger than the average by an amount which can only be specified statistically. One parameter involved in the estimation of the peak sidelobe relative to the average is the number of angular resolution elements across the object. The variation is minor, however, and it may be deduced that for objects 10-1000 beamwidths in size the peak sidelobe, with probability O-5, will not exceed the mean by more than 7-9 dB (18). Increasing the probability O-9raises the peak sidelobe to 9-10 dB over this range. Regarding the second problem, a recent study has disclosed that the smallest target must clear the peak sidelobe of the largest by 6 dB to establish, with probability 0.5, one gray level dip in intensity between the scatterer locations in the image (24). Increasing the clearance to 10 dB raises the probability of separate identification of the smaller target to O-9. By combining these figures it is evident that the smallest scatterer should be 13-20 dB above the average sidelobe level of the largest. Another factor reduces this requirement somewhat. The target dynamics, which adversely affect the performance of the phase-locked sampled data loop of Fig. 7, work to the system’s advantage in this problem. Each successive view of the object provides another opportunity to see each of the smaller scattering lo&ions. Designating by u the cross-se&on of a scatterer on the object, noncoherent smoothing of images should reduce the required excess toward 10 dB, resulting in N 2 lOt~,,,/u,~.
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The third problem less readily succumbs to numerical calculation. At optical wavelengths even relatively smooth surfaces scatter light diffusely and, hence, are “seen” as surfaces. At miorowaves, however, scattering is rarely from the surface ; it is mostly from coiners and edges and more often from specular or near specular reflectors on the target. Hence, a manufaotured surface is at best outlined by its edges and often only spotted by highlights arising from seemingly random locations on the targets. Images of the same target formed from separate and independent data, however, will exhibit different highlights. A composite formed by noncoherent combining of images has more sample points relating to the object and, therefore, eases somewhat the dynamic range requirements. Experiments are planned to determine the answer to the third question; until then it is assumed that no less than 20 dB is useful and that 30 dB may au&e. The required number of elements, therefore, is between lOa and 104. IX.
Status of Valley Forge Radio Camera and Plans
A 50-element L-band array is under construction on a lOOO-ftmeadow at the Valley Forge Research Center of the Moore School. It is designed to be steerable over the hemisphere. Coherent array modules similar to the design of Fig. 8 are being used. Array processing will be digital. Some Type I assist in element location will be used. Experiments will be conducted with Type III optimization along the lines discussed in the paper. Image immobilization and noncoherent image smoothing will be accomplished digitally. An output visual display will be provided on a cathode ray tube. Following the current plan, the system will grow by one to two orders of magnitude in numbers of elements, one order of magnitude in size (extending to a 1600-ft field about 9000 ft away from the flrstj and one order of magnitude in resolution by changing frequency from L-band to X-band. With these modifications, high-quality, 10d6rad., angular resolution imagery is expected. Beyond this work, extension into the optioal region is planned. An optical adaptive phased array in which the transducers are small, high-quality, diifraction-limited telescopes, can in principle have their images combined by extension of the concept described above into a diffraction-limited optical image with resolution far exceeding the normal limits set by atmospheric seeing conditions. X. Summary
The logical requirements for a microwave radio camera are large size, conformality with the terrain, a sparsely fllled aperture, random or quasirandom element locations, self-adaptive beamforming and a source of microwave radiation. Based on this design approach; a lOOOft L-band imaging array, designed to be steerable over the hemisphere, is under construction at the Valley Forge Research Center of the Moore School. A radar transmitter is the source of microwave illumination. 430
Journal of The Franklin
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De&m Approach for a High-Resolution Microwave Imaging Rudio Camera
(1) D. D. Ring, R. F. Packard and R. K. Thomas, “Unequally spaoed, broad-band antenna arrays”, IRE Travw Antennua Propagdion, Vol. A-P-8, pp. 380-335, July 1960. (2) 5. 5. Sandier, “Some equivalence between equally and unequally spaced arrays”, IRE Tmna. Antennaa Pmpap.tion, Vol. AP-3, pp. 493-600, Sept. 1960. (3) A. L. M&&t, “Array factors with nonuniform spacing parameters”, IRE Tmm. AntenmurPropagation, Vol. AP-10, pp. 131-136, Mamh 1962. (4) R. E. W&y, “Spaoe tapering of linear and planar arrays”, IRE Tmvw. Antennua Propagahn, Vol. Al?-10, pp. 136Q-1377, July 1962. (5) A. Ishimaru, “Theory of unequally-spaoed arrays”, IRE Tmna. Antenlaas Pmpagahn, Vol. AP-10, pp. 691-702, Nov. 1962. (6) M. I. Skolnik, G. Nemhauser and J. W. Shermsn, III, “Dynamic programming applied to unequally spaced arrays”, IEEE Tmru. Antennas Propagation, Vol. AP-12, pp. 35-43, Jan. 1964. (7) M. I. Skolnik and J. N. Sherman, “Planar arrays with unequally spaced elements”, Radio and ElectronicEngineer, Vol. 23, No. 3, Sept. 1964. (8) A. Ishimaru and Y. S. Chen, “Thinning and broadbanding autem arrays by unequal spacing”, IEEE Tmm. Antennae Pmpga.tion, Vol. AP-13, pp. 34-42, Jan. 1966. (9) M. I. Skolnik, “Nommiform arrays”, Chap. 6 of “Antenna Theory”, Part I (Ed. by Collin and Zucker), McGraw-Hill, New York, 1969. (10) John L. Allen, “Some extensions of the theory of random error effects on array patterns”, Chap. III, Pt. 3 of “Phased Array Rsdar Studies”, Lincoln Lab. Rpt. 236, Nov. 1961. (11) T. M. Maher and D..R. Cheng, “Random removal of radiators from large linear arrays”, IEEE Trnrw An&nPropagation, Vol. AP-11, pp. 106-112, March 1963. (12)Y. T. Lo, “A mathematical theory of antenna arrays with randomly speced elements”, IRE Trans. AntenPmpagaGn, Vol. AP-12, pp. 267-268, May 1964. (13) Y. T. Lo, “A probabilistio approach to the problem of large antenna arrays”, Radio Science,Vol. 68D, pp. 1011-1019, Sept. 1964. (14) Y. T. Lo and S. W. Lee, “Sidelobe level of nonuniformly a@ entenna arrays”, IEEE Tram. Antennas Propagahn, Vol. AP-13, pp. 317-318, Sept. 1966. (15) Y. T. Lo and S. W. Lee, “A study of spaoe-tapered arrays”, IEEE Tmne. AratennaaPropagakn, Vol. AP-14, pp. 22-30, Jan. 1966. (16)Y. T. Lo and R. J. Simcoe, “An experiment on antenna arrays with randomly spaced elements”, IEEE Tmna. AntennauPmpagatbn, Vol. AP-16, pp. 231-235, March 1967. (17) A. R. Pan&Ii and Y. T. Lo, “A probabilistio approaoh to large cimular and sphericalarrays”, IEEE Tmm. Antenna Propagatkm,Vol. AP-17, pp. 514-622, July 1969. (13) B. D. Steinberg, “The peak sidelobe of the phased array having raudomly located elements”, IEEE Tmna. Antennae Prapagahn, Vol. AP-20, pp. 129-135, Mamh 1972. (19) B. D. Steinberg, “Comparison between the peak sidelobe of the random array and algorithmically designed aperiodic arrays”, IEEE Tmm. Antenw Propagzth, B&y 1973. (20) J. Ruze, “The effect of aperture errors on the antenna radiation pattern”, Nwrvo Cimanto,Suppl. 3, 9, pp. 364-380, 1962. (21) B. D. Steinberg, “Self-cohering nonrigid array”, Proc. IEEE Ecet Coast Conf. on Aerospace and NavigcstionalElectmnk, Baltimore, Md., Oct. 1966. (22) F. M. Gardner, “Phase Lock Techniques”, Wiley, New York, 1966.
Vol.298.No.6, December1978
431
Bernard
D. Be&&erg
(28) R. L. Bsrron, “Adaptive flight control systems”, in “Principles and Prsotice of Bionics” (Ed. by H. E. Von Gierke, W. D. Keidel snd H. L. Oestreicher), TeohnivisionServioes, Slough, England, 1970. (24) B. D. Steinberg, “Angu&r resolution in large mys”, Velley Forge Research Center, Quart. Prog. Rep. Nos. 4 and 6, Feb. end May 1973.
Figure 12 shows sn element et position (2, y) in 8 coordinste system defined by the dire&ion of phase synchronization of the army and a referencelocetion in the army. The element ooordinstes stored in the srrtly processor are (o = 82, y +&). During phase synchronization the adaptive loop adds phase shift & = -ky. The processor Sync angle
x Assumed x Actual
8mox =!-
x IO us
Fra. 12. Tolerance on element location uncertainty. assumes thet the phase shift is &, = - k(y +&). To steer the beam 8 from the synchroniration angle the new phase shift should be +I = - k(y cos 6 + z sin 8) ; the correct mod&&ion for saenning, therefore, is A# = #i -+0 = k[y( I- COFJ 6) -z sin 81. The processor, however, cslouletea the new phase shift to be 4; = -k[(y+&/)cosO+(z+&z)sin8] and epplies the correction A& = &-4; = k[(y+8y)(l-~os8)-(z+Sz)sinC)1. The error 8$ = A&-A4 = k[&y(l -cos8)-6~sin8]mustbeheldtoabout2w/lO. Except in unusual situ&ions 6~ snd Sy are sero mesn, random variables with equal rms deviations u,, end o,.. 84 1 -use the m&mum seen gurgleis the order of the angle subtended by the object rtt the srray. Therefore w II -k&x and Us = 2&r& is the standard deviation of the phsse error. Equating a&to the phase tolerenoefor the maximum angle of soen tl,, 2x@,, U& = 2w/lO or t?,, = h/lOa,. If the object subtendeen engle 8, the &olerenoe on element location is u, = h/10&. The y-tolerance is the s&me.Hence the allowed rms uncertainty in element location is h/78,.
432
Journal of !Che kanklin
Institute
BERNARD
D.
STEINBERG
Valley Forge Research Center, 7% Moore School of Electrical Engineering University of Pennsylvania, Philadelphia, Penqlvania ABSTFUCT: The angdar reaoltiti
of an imaging de??& is the order of the PX&WX& of
the number of wavelengtha amoee the aperture. To achieve the high reeolution typical of optical inatrummte at rntimvee, aperturea miik in eke mug be required.T?M requirernentefor such a device, eded
a radio camera, are confwmdity
&h
the terrain, a epartdy
jWed apertmre of randomly (w nearly 80)locded ekmmta,eelf-adaptive beam forming and a eource of wcimnmve i%midn. Baaed on thie de&n approach, a lOOO$ L-band radio camera ie under devebpmmt Thie paper
discwrsee
the
statw,
at the Valley Fwge Research Ceder
of cuwent devebpmmt
of the Moore School.
of the dex?ice.
I. Introduction
The term imu+g conventionally applies to devices which utilize infrared, optical or shorter wavelengths. Telescopes, cameras and microscopes are examples. A 241~ lens is IOaoptical wavelengths in size. Its available resolving power is 1O-5rad., which is 2 set of arc. Microwave wavelengths nominally r&nge from 1 in. (X-band) to 1 ft (L-band). The size of an aperture with corresponding resolution would be loh106 ft or 2-20 miles. At the Valley Forge Research Center of the Moore School, the technology leading to such a device, called a radio camera, is under development. This instrument should be capable of obtaining two-dimensional inmges of targets at radar ranges (tens to hundreds of miles) even in inclement weather. In this paper, we discuss the logical requirements for such a device, some basic problems, some design approaches and,the status of current development. II. Size of the Instrument
The parabolic dish, which is the microwave equivalent of the Newtonian telescope, is the most common microwave aperture (Fig. 1). Gravitational and thermal stresses limit its practical size to a few hundred feet. Achievement of significantly larger size requires that the aperture be broken into many smaller structures snd the distances from the parts to a source equalized by phase shifters, i.e. a phased array (Fig. 2). In most arrays the spacing between elements is constant. The phase progression required to form a beam steered to angle 0 is $4+1-#4 = 211 (dsin e/A) where d is the interelement spacing and h is the wavelength. Unlike the continuous aperture of Fig. 1, such an array samples the radiation field in discrete locations.
415
Bernard D. Steinberg Parabolic
mirrors
Eye Newtonian telescope
Microwave dish FIU.
piece
1. Microwave antenna and Newtonian telescope. Resolution N h/L. Phase shifters Elements
H
FIU.
2.
Phased array.
Unless the sampling distance d is sufficiently small, the sampling process crerttes spurious beams called grating lobes, avoidance of which requires that d does not exceed /\/2.* Such an ~~~rray is caBed a$&~! array. A fIlled aperture * Uniform sampling with interval d of an aperture excitation i(z) results in a set of samples i(z) 2 6(2 - 4). The radiation pattern f(u) = B’{+)} * .F{z:6(z - md)} = A(u) * I: & -4Wd)L wheref@(u), the radiation pattern of the unsampled aperture, is repeated at intervals of A/d. F{ } is the Fourier transform, u = sin 8.6 = angle from the normal. Only when d
416
Journal
of The Franklin
Institute
_ Design Approach for a High-Resolution Mimnmve Inmging Radio Camera of size L, therefore, requires the order of (L/h)* antenna elements. A fllled phased array with a resolving power of 10msrd. would require lolo elements, which is an impractically large number. High angular resolution requires a large aperture but does not require that the array be fllled. The beamwidth is a relatively insensitive function of the distribution of antenna elements. Table I gives the 3 dB beamwidth in units of I\/L for three d&rent apertures. The first is a uniformly illuminated aperture. The second has a semicircular taper. The third has a triangular taper. The number of elements may be reduced by orders of magnitude by thinning an aperture without sign&ant alteration to the beamwidth. TABLE I Aperture Uniform semicirmllFbr taper Triangular taper
3 dB Beamwidth CM8h/L 1.02 1.27
Provided that grating lobes may be avoided, such an array can be highly useful.* Grating lobes develop from the properties of the distribution of the sampling points, the Fourier transform of which is convolved with the beam pattern of the underlying or corresponding nonsampled aperture to produce the radiation pattern. Grating lobes require a coherent buildup of elemental signals at angles other than the steering angle 8. Spurious lobes are avoided by eliminating all periodicities in the element locations. Aperiodic element locations may be calculated by formula (l-9) or chosen at random (lfH8).It is shown later that a limiting factor iu the resolution of a microwave image is the level of the sidelobes in the side radiation pattern of the array. The method of distributing a fixed number of elements aperiodically over a large aperture should be dictated by this consideration. The ilrst decision to be made is whether to distribute the elements randomly or by some formula. Given some arbitrary distribution of randomly selected element locations, there is, with probability one, a better distribution and presumably some algorithm for finding it. Two factors mitigate against the algorithmic approach. First, for an array of suitably large size (see definition of large, below) it is often impossible to specify element locations with adequate accuracy to permit the use of algorithmic location procedures. Second, it has been found experimentally that the peak sidelobes of the algorithmically designed arrays referenced above are not lower than those of random arrays having similar design parameters (19). Thus, the most general design procedure should accommodate to the properties of the random, thin array. * The two element interferometer with its high density of grating lobes (the lobe spacing is sin-l A/L) is the epitome of en unfXed or thinned array. It is useful where high tmgular accuracy is required and where means are available for avoiding lobe ambiguity. It is not useful for the imaging of area-extensive objecta Imaging requirea that lobea be eliminated or at least suppressed around the mein lobe in the angular interval subtended by the object.
Vol. 296, No. 6, December 1878
417
Bemurd D. Steinberg 0onforrnu.I array. Another logical requirement for the design procedure relates to the array surface. An array measured in square miles cannot be required to be planar nor to assume any other particular surface. For generality of use, the design procedure should permit the implantation of array elements on any piece of ground or on buildings within the general array area. In short, the array surface should conform to the terrain within the array. Such an array is called a conform& array. Illumination. A camera requires a source of illumination. An optical camera uses the sun or a flash gun. Solar microwave radiation is inadequate; hence, the latter is a requirement. A pulsed radar transmitter is one way to satisfy this need.
,,,
--
/
Self-odaptiw signal processtng ckcuits to cohere the orray
Fm. 3. One thousand ft random array for Valley Forge camera.
Figure 3 illustrates a conformal array with low gain, nonscanning microwave horns randomly spaced by hundreds of wavelengths. Within the array is a radar transmitter and conventional antenna. The antenna beam is large compared to the resolvability of the array. Like a flash gun it provides general illumination in the direction of the object. The high angular resolution image is formed from operations upon the signals received by the distributed antenna elements. Large array. The conventional tolerance on the uncertainty of element * A large array is defined as one of such size that it is location is A/10. impossible in principle or impractical in practice to know the element locations to within this tolerance. Consider the 1O-6rad. resolution, L-band * The loss in gain due to random zero mean locetion errow is exp ( - ~3) where a* = 2nv& and us = rma location error (20). For CT,= h/IO the loss is 1.7 dB. 418
Journal of The FranklinInstitute
De&n Approach fw a High-Reaohticm i&mncuve Irrmging Radio Camera may mentioned earlier. Its diameter is 20 milea, which ia the kgth of the City of Philadelphia. Such an array, if located there, would satisfy the definition of large. An array on a nonrigid body such as an aircraft, notwithstanding the fact that its maximum usable dimension is only 100 fi, is another. An array in a fluctuating medium is a third. An example is an array of several square miles on an underwater mountain. The velocity of sound varies with depth in the ocean because of temperature and pressure variations. In addition to the spcttial variation in the refractive index, there are also temporal variations due to underwater ocean currents and other equivalents of weather. Adaptive away. For generality of use, the design procedures for the radio cameraa should include the large array as defined above. The presumption that the array may be large imposes a logical requirement for self-adaptivity. Illuminator
l-l
I
Amy output
‘I
Direct measurement I
Ret or meawrement criterion
I
FIG. 4. !ryJ+B of colltrol.
In that case, the army designer does not know the element locations with adequate accuracy for proper a e determination of the phase shifts. Hence the array system must somehow be made to accommodate for the inadequacy of the designer. Such an arra.y is called udaptive. Three distinct levels of adaptive control are illustr&ed in Fig. 4. The lowest order is celled Type I control ; it consists of dynamic, open-loop measurements of element locations by a subsystem within the array which feeds lo&ion information to the army processor. Type I control is limited in applicability to arrays of modest size (i.e. maximum dimension of hundreds or at most thousands of feet). Type II control operates upon measurement of the radiation field as sampled by the EIIT&~ elements. Phase comparisons are made between the signals received by each element and a reference signal. The phsse di%rences are assumed to be due entirely to the differential differences between array elements and the object and are eliminated by closed-loop feedback control to the phase shifters. Type II control is basio to the image formation process. Type III control utilizes information Corn
Vol. 296, No. 6, December 1978
419
Bernard D. &e&berg the array output, i.e., the image data, to vernier the image forming process 80 as to optimize image quality. III. Valley Forge Radio Camera
The Valley Forge system under development is shown in Fig. 6.* An L-band, AN/TPS-1D radar- transmitter is the illuminator. The signal from the target is received by the same antenna and passes through the radar receiver in conventional fashion. The °ree beam is broader than the
Satellite receiver
FIG
6. High resolution microwave
imaging.
angles subtended by most radar targets. Consequently target characteristics other than range and angle, which are displayed on a PPI, normally are lost. In addition to the conventional display, the IF echo of the target is used aa a reference waveform for adaptive phase shift oontrol at each array element (also called array module and satellite receiver). An echo also is received at each array modnle. A low-gain nonscanning antenna delivers the signal to a receiver in the module which compares the phase of the echo at IF with that of the reference IF pulse delivered from the main receiver. The phase difference is smoothed in a low-pass’ filter and delivered as a control voltage * Note
similarity to earlier design in (21).
Design Approach for a High-Resolution
Microwave Imuging
Radio Camera
to the voltage controlled oscillator serving as the local oscillator of the satellite receiver. A phase-locked loop is therefore formed which forces the two IF target echoes into phase quadrature. The loop serves as a selfadaptive phase shifter for the array element. Two assumptions are implied. The first is that the IF echoes in the various receivers are identical in shape and vary only in time of arrival and that their additive noises are independent from receiver to receiver. The second is that the phase differences are due entirely to differential differences between the receivers and the reflecting object. Since the phase-locked loops eliminate these phase differences, the IF signals are cophased and may be added exactly as in the simpler phased arrays. Given N antenna elements the output of the summer of Fig. 5 is an echo voltage N-times larger than that of the individual echoes. The receiver noises being independent of each other, the noise contributions into the summer combine with random phases and, therefore, their powers rather than their voltages are additive. Hence the signal-to-noise power ratio (SNR) out of the summer is N-times larger than in each of the receivers. This calculation atices to produce a tlrst estimate of the minimum required number of elements. It is reasonable to require that the SNR of the high resolution array be no poorer than that of the main radar. Assuming common noise figures for all the receivers, the SNR in a satellite receiver is weaker than that of the main receiver by the gain ratio of the antenna of the main radar to that of the satellite receiver. The gain ratio is about equal to the area ratio, which in the Valley Forge equipment is 30 to 1. It is shown later that this is a very weak condition on the number of elements. Summing the phase-rotated IF echoes of the satellite receivers solves half the problem : it results in a narrow beam pointed somewhere within the beam of the main radar. The output signal strength is proportional to the back scattering cross-section of the particular part of the object intercepting the narrow beam. The beam must be scanned over the object so that the reflecting properties of the entire object can be measured. With such data, a high resolution image may be created. It is shown in the Appendix that even though there is considerable uncertainty in location of the elements, once the phase-locked loop has made the desired phase correction, scanning of the narrow beam may be accomplished by open-loop control. The angular extent over which open-loop scanning can take place is h/To, where u is the rms uncertainty in element location. Conversely, if a target subtends angle Br the tolerance on element location is h/78,. A severe situation would be an aircraft at the short range of 2 miles. Assuming the aircraft to be about 100 ft the tolerance is approximately 14 wavelengths, which is two orders of magnitude larger than the conventional array element tolerance. Thus, following phase synchronization of the array, open-loop control of the phase shifters driving the summer should permit scanning of the narrow beam across aircraft targets, resulting in a high angular resolution display, even with element location tolerances of 10 or 16 ft.
Vol. 296, No. 6, December 1973
421
Bernard D. Steinberg IV. Self-survey TypeI Control !I'ype I control provides as much a prkk information as practical so as to ease the strain in the adaptive circuits and/or to reduce the element location uncertainty to within tolerance. The latter appears relatively easy to achieve under most conditions. Two self-survey methods for locatiug the elements of the first lOOOft array at Valley Forge are sketched in Fig. 6.Each involves distance measurements from several points within the array to each array -D-
0
T
t
Microwave
FIG. 6. Type I-self-survey
techniques.
module. The distance information is fed to the array processor (see Fig. 4) from which calculations of element locations are made. The first method is a microwave technique in which an RF transmitter in the desired band is swept in frequency over a few tens of MHz. At each array module the reflection coefficient of the antenna is modulated by a 60-MEL5oscillator. The CW echo received by the transmitter mixes with the outgoing swept RF to yield a 60 MHz intermediate frequency, the envelope of which is a trignometric function of the distance. As shown in the figure the number of scallops per unit of frequency sweep is indicative of the distance. A second method being tested for a field of several hundred feet is an acoustic ring-a-round circuit. An acoustic source radiates an impulse to a microphone at an array module, where a pulse is generated and returned by cable to trigger the acoustic transmitter. The period between acoustic transmissions minus all accumulated elect&al delays is proportional to the distance. 422
Journal of TheFrtmklhInstitute
Design Approach for a High-Reeolukn V. Adaptiue Beam Forming-Type
Mkrmve
ImagGtg Radio Camera
ZZ Control
Figure 7 shows the phase-locked loop of Fig. 5 in somewhat greater detail. The IF waveform consists of signal echoes the order of 1~0 in duration, which is typical of conventional pulse radar, spaoed by the interpulse interval, typically the order of 1 msec. The SNR in the main receiver is larger than
FIG. 7. Type II--earn
pled data loop.
that in.the array module by the antenna gain ratio. Both signals are gated to avoid receiver noise and spurious signals between target echoes from entering the feedback loop. Gating is either at IF or within the loop. A range gate pulse in the main receiver gates the high SNR reference target echo onto the cable which delivers it to each satellite receiver. An envelope detector extracts it at the array module and a pulse shaper, such as a blocking oscillator, recreates the gating waveform to operate the gates and switches in the sampled data loop. An appropriate delay is inserted to account for amplifier and cable propagation delays. By virtue of the phase and frequency acquisition properties of the sampled data loop, it permits the radar transmitter to be nonphase coherent from pulse to pulse. Phase memory of the transmitted pulse is preserved in the target echo in the main receiver. Phase synchronization of the local oscillators is accomplished by the individual phase-locked loops. However, the same sampled data loop has two serious frailties, the East relating to SNl3 and the second to switching transients and memory tolerances. Loop closure requires a SNR within the loop at the input to the VCO in excess of 6 dB (22). Assuming that the SNR r,, of the main receiver is very much greater than unity, r, is about equal to rl which is weaker than r,, by the antenna gain
Vol. !296,180.6, December1978
423
Bemurd D. &e&berg ratio. In a nonsampled loop, the improvement in SNR due to the low-pass filter in the loop is the ratio of the IF bandwidth to the loop video bandwidth. In the sampled data loop, it is smaller than this quantity by the duty cycle of the signal. In other words, the improvement in SNR from rl to rBis no larger than the number of pulses integrated during the memory time of the loop. This interval may not exceed the time interval over which an object of interest undergoes signi&ant change. For aircraft targets this may be as short as 0.01-0.1 sec. !I’hus as few aa 10-100 echoes may be integrated. Since r8 must be at least 6 dB, and preferably 10 dB for rapid signal acquisition, the input SNR rl at the low gain antenna of the satellite receiver should be between - 10 and 0 dB. The SNR r,, in the main receiver is larger by the antenna gain ratio. Although only 30: 1, or 15 dB, in the first Valley Forge equipment, a more likely gain ratio would be 30 dB. Thus the required SNR in the main receiver would be 20-30 dB, which is an undesirably high requirement. A second difficulty of the loop is the need to freeze its operation between pulses. Not only must the frequency of the VCO remain approximately fixed between pulses, but the phase drift from pulse-to-pulse must be held to a small fraction of a cycle, typically 2n/lO. In the interval T between pulses, the VCO may be presumed to drift from w0 to w,,+ alp. The accumulated phase error is Jr W?dt = orTa/2.Equating it to the pulse-to-pulse phase shift tolerance gives Af = cwT/27r= l/ST as the short-term frequency stability tolerance of the VCO, which is the order of 100 Hz. Although it is not intrinsically difficult to stabilize a microwave oscillator for 100 Hz short time stability, this oscillator needs to be both stable and modulatable simultaneously. The typical voltage sensitivity of such an oscillator is l-10 MHz/V, requiring that the driving voltage of the VCO be held constant to 10-100 U.V. between pulses. The peak voltage level in the feedback loop is the order of 1 V. Thus the decay in the memory storing the LPF output or the decay in the charge aoross the condenser of the LPF or the unbalance in the sample and hold switches need be held to one part in 10” or 105. If the requirement for noncoherent transmission is eliminated both design problems are eased considerably. Figure 8 shows one form of coherent array module which takes advantage of a phase coherent radar transmitter.* The low-level CW oscillator whioh drives the 6nal amplifier in the transmitter is permitted to radiate nearly continuously across the array. The phase coherent radiation received at each module is heterodyned via a stable local oscillator to IF where it drives the VCO of a phase-looked loop into phase and frequency synchronism with the broadcast reference. About one pulse duration before the arrival of the echo from the object, the broadcast reference is gated off so that all modules may receive the echo. The echo is coherently demodulated by the VCO in two quadrature deteotion ohanuels, thereby resolving the echo, which may be described by amplitude A and phase 8, into components x=Acos8andy= A sin 8. During the two or three pulse duration interval * Due to Earl N. Powers, member of the teohnical staff of VFRC.
424
Joumd of The FranklinImtitute
De&gn Appwach for a High-Resolution
ilGmmuve Imaging Rati% Camma
when the reference is not radiated, the VCO output is substituted for the reference wave into the phase-locked loop 80 that it continues to operate without significant disturbance. The composite vector echo represented by the in-phase and quadrature components may now be cophased axoss the array to form a narrow beam, which is then steered by the same open-loop control discussed earlier. Nearly CW RF ref I
I
STALO
FIO. 8. Type II-coherent
81~8~ module.
Both the sampled data module of Fig. 7, designed to work with the noncoherent transmitter, &d the continuous module of Fig. 8, designed for phase coherent illumination, are under development. The former is being built entirely from analog circuits ; in the latter the I and & channels are sampled and converted to digital pulse sequencea, following which all the processing is done digitally. . VI. Image Qwlity
FeedbackType
ZZZControl
Type III control is needed in principle to optimize image quality. Two distinct problems are involved. The first is the metric or criterion of image quality from which a control signal may be developed. The second is the search procedure by which control optimization is affected. It is believed that the contrast in the image will be a sensitive indicator of the extent to which the array is properly phased. In the absence of uncertainty aa to element location, the phase program generator labeled “hi res scan” in Fig. 5 would produce the optimum set of phase shift instructions for scanning. The result would be a, high-quality image. The fS&-order effect of emrs of estimation of element location is not in the width of the beam: provided that the errors are not so severe as to destroy the beem, the width of the beam is determined by the number of wavelengths NXWSSthe aperture. Instead the first-order effect is to decrease the energy in the main beam relative to the side lobe energy. The effect is a diminution in the ratio of
Vol. 286. No. 6, December 1978
426
Bernard
D. Steinberg
the strong echoes to the general background of the image. Hence a contrast measure between the largest target and the general background is expected to be useful in the development of an image quality criterion. Maximization of such a quantity will be the object of the search procedure. Unlike the phase-locked loops in which a direct one-to-one control is effected, Type III control is a 1 :N control process. As shown later N is not a small number; it will be between lo3 and 104.Aircraft dynamics require that the image forming process be effected in 10-a-10-1 sec.Rapid convergence is essential, therefore. Gradient search procedures are questionable in this regard. It is expected that more rapid search procedures will be necessary. One method to be explored is guided random search (23). In it an initial random phrasechange is made in each of the N elements in turn, and the successive changes in image quality observed. After the cycle S once completed, the effect produced by the first randomly chosen phase shift is examined. If the image improved from that choice a larger phase correction in the same direction ia made. If the first correction degraded the image the second selection for the first element is again made random. This procedure is applied to each element in turn.
VII. A FundumentaZ Problem
A conflict in principle exists between the properties of objects for which radio images are desired and Type II adaptive control. Each phase-locked loop serves as the phase shifter for its antenna element. By eliminating the phase difference between the signals received on its channel and in the main receiver, the phase-locked loop permits coherent or cophasal combining of its signal with all the rest. This is the ideal operation provided that the distant object is a point reradiator. In that case, the signals received by the elements would be identical in waveform, differing mainly in time of arrival (or phase) and somewhat in amplitude. However, the object is not a point scatterer; if it were it would deserve no interest. The array is assumed to be sufficiently large to permit resolving the object into several parts. Herein lies a fundamental conflict. Let the target of size S be at distance R. Let it be desired to resolve it in angle into k resolvable scattering centers. Hence, the angular resolution required by the array is about S/kR rad.To a first-order approximation the angular resolution may be identified with the beamwidth ;\/.L.Thus the length of the array must be L 2: kRA/X. This situation is pictured in Fig. 9(a). The target reradiates from its entire structure Fig. 9(b)]. Being of size S, the reradiation pattern is lobular with nominal angular lobe width h/S. (The far field reradiation pattern is the Fourier transform of the excitation of the object by the radar transmitter.) At the array the nominal cross-section of a lobe is Rh/X. The array length is k-times the lobe width. Thus the number of lobes which illuminates the array is the order of k, and array elements spaced by more than RX/S may be in different lobes. The relative phases of
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the sigmiis received by the elements 8re determined by the complex backsc8tter function 8cross the object. Small ch8nges in aspect angle alter the relative phases. Thus the relative phase between elemats sp8ced by more than M/S may be considered 8 random v8ri8ble, in which ~888 ph8sing the 8rr8y on such phase differences becomes 8 me8ningless tssk.
RX
-I-
L
s
I
x
L Array
Ib)
(a)
FICA9. Radiation from array and aircraft.
Figure 10(a) depicts this situation for an 8ircr8ft target. The 8ircr8ft is modeled 8s 8 random 8rr8y of smah scatterers of complex amplitudes a, 8t locations y$ where y is the distance along the 8ircr8ft. The equivalent current density of the 8ircraff 8s 8 rer8di8tor when ihuminated by 8 plane w8ve at 8ngle 0, from the norm81 to 8ircr8ft is i(y) = ~acbtS(y-y~)exp(-_j~sine,).
Sincethe a, h8ve rrtndom phases, the phase tilt of the illumin8ting wsve m8y be incorpor8ti into the backscstter coefficients without 8ltermg their st8tisticsl properties. The far field reradiation pattern f(u) = P{;(y)} = xaiexp
(j&u),
u = sintl,
where ai = a, exp ( - jky* sin e,) andf(u) is s random function with mndom amplitude arrdrandom phase (10). The correlation distance in u is the nominal lobe width h/S. The correlation distance in the reradi8tion field on the ground is M/S N L/k. The phase v8ri8tion 8cross the 8rr8y is 8 mndom vsri8ble with this correl8tion distance [Fig. 10(e)]. The lobe width, however, nomhmlly h/S, is itself s random v8riable. At times the reradiation pattern in the direction of the srr8y will be very much broader thsn h/S ss, for example, when 8 single strong reflector dominates the echo. Such s case might be a specularreturn from & corner reflector formed by wing and firselege. Figure 10(b) shows the Grcmft modeled 8s 8 random 8rr8y of sm8ll sc8tterers plus one large echoing center. The rer8diation pattern is the sum
Vol. 298. No. 6. December 1978
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of two complex radiation patterns, the random functionf(u) described above plus the radiation pattern from the large, dominant source. The latter’s energy, arising from a small portion of the aircraft, radiates in broad lobes, each wide enough to contain all or most of the ground based array. Its pattern has a nominally constant phase slope across the array elements. Small random scatterers, none specular Scattering centers an aircraft
-Y
Plus single dominant scatter -r’Lr,r,Y
rizzr +fpjiffp _j=+TE& Phase of received
due to large scatterer (a)
(b)
FIQ. 10. Phase distributions amoss aimraft.
Provided that this single scatterer is large compared to the sum of all the rest, the phase of the sum pattern has a mean slope due to the strong reflector plus perturbations due to the weaker ones. The lower sketch in Fig. 10(b) portrays the situation. Whenever this situation prevails, the phase variation across the array elements is no longer meaningless. Instead it is biased with a mean phase front which disoloses the direction of the object, thereby permitting the phase-locked loops to adaptively form a coherent array. Phase synchronization will be accomplished during intervals when a common phase front dominates ; scanning and image formation will then follow. Experiments are underway to determine the statistics of the conditions illustrated in Fig. 10. VZZZ.ZmcrgsResoZutionandNumberofEZements
The number of elements has little influence upon the beamwidth of a radio camera. Nevertheless it is the dominant factor in the image resolution. Consider two scatterers of different sizes on an object to be imaged (Fig. 11). The array output traces the radiation pattern as the narrow beam scans by the larger scatterer. The sidelobes of the array pattern extend to the neighborhood of the smaller soatterer. To prevent the latter from being obscured, its main lobe response must rise above the sidelobes of the larger echoer. In more general terms, the smallest scatterer to be resolved must exceed the sidelobes of the larger. 428
Journal of The
Franklin Institute
Design Approach for a High-Resolution Mkmwave Imaging Radio Camera Three questions need to be addressed. First, how is the sidelobe level related to the number of elements? Second, what clearance is required between the smallest scatterer and the sidelobe level of the largest saatterer ? Third, in order to obtain satisfactory image quality what is the maximum dynamic range of cross-sections which must be accommodated by this system ? The
------__ A, FIU.
11.
Large
Small
scatterer
scatterer
Importanceof low sidelobes.
fnst and second questions can be answered with known information. The third question requires conjecture until suitable experiments are performed. The ratio of the average power in the sidelobes to the main lobe is l/N for a random array (10). (Although specific element locations can produce lower sidelobes than the statistical average for a random array, the two reasons noted earlier preclude an assumption of greater sidelobe suppression.) The peak sidelobe is larger than the average by an amount which can only be specified statistically. One parameter involved in the estimation of the peak sidelobe relative to the average is the number of angular resolution elements across the object. The variation is minor, however, and it may be deduced that for objects 10-1000 beamwidths in size the peak sidelobe, with probability O-5, will not exceed the mean by more than 7-9 dB (18). Increasing the probability O-9raises the peak sidelobe to 9-10 dB over this range. Regarding the second problem, a recent study has disclosed that the smallest target must clear the peak sidelobe of the largest by 6 dB to establish, with probability 0.5, one gray level dip in intensity between the scatterer locations in the image (24). Increasing the clearance to 10 dB raises the probability of separate identification of the smaller target to O-9. By combining these figures it is evident that the smallest scatterer should be 13-20 dB above the average sidelobe level of the largest. Another factor reduces this requirement somewhat. The target dynamics, which adversely affect the performance of the phase-locked sampled data loop of Fig. 7, work to the system’s advantage in this problem. Each successive view of the object provides another opportunity to see each of the smaller scattering lo&ions. Designating by u the cross-se&on of a scatterer on the object, noncoherent smoothing of images should reduce the required excess toward 10 dB, resulting in N 2 lOt~,,,/u,~.
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The third problem less readily succumbs to numerical calculation. At optical wavelengths even relatively smooth surfaces scatter light diffusely and, hence, are “seen” as surfaces. At miorowaves, however, scattering is rarely from the surface ; it is mostly from coiners and edges and more often from specular or near specular reflectors on the target. Hence, a manufaotured surface is at best outlined by its edges and often only spotted by highlights arising from seemingly random locations on the targets. Images of the same target formed from separate and independent data, however, will exhibit different highlights. A composite formed by noncoherent combining of images has more sample points relating to the object and, therefore, eases somewhat the dynamic range requirements. Experiments are planned to determine the answer to the third question; until then it is assumed that no less than 20 dB is useful and that 30 dB may au&e. The required number of elements, therefore, is between lOa and 104. IX.
Status of Valley Forge Radio Camera and Plans
A 50-element L-band array is under construction on a lOOO-ftmeadow at the Valley Forge Research Center of the Moore School. It is designed to be steerable over the hemisphere. Coherent array modules similar to the design of Fig. 8 are being used. Array processing will be digital. Some Type I assist in element location will be used. Experiments will be conducted with Type III optimization along the lines discussed in the paper. Image immobilization and noncoherent image smoothing will be accomplished digitally. An output visual display will be provided on a cathode ray tube. Following the current plan, the system will grow by one to two orders of magnitude in numbers of elements, one order of magnitude in size (extending to a 1600-ft field about 9000 ft away from the flrstj and one order of magnitude in resolution by changing frequency from L-band to X-band. With these modifications, high-quality, 10d6rad., angular resolution imagery is expected. Beyond this work, extension into the optioal region is planned. An optical adaptive phased array in which the transducers are small, high-quality, diifraction-limited telescopes, can in principle have their images combined by extension of the concept described above into a diffraction-limited optical image with resolution far exceeding the normal limits set by atmospheric seeing conditions. X. Summary
The logical requirements for a microwave radio camera are large size, conformality with the terrain, a sparsely fllled aperture, random or quasirandom element locations, self-adaptive beamforming and a source of microwave radiation. Based on this design approach; a lOOOft L-band imaging array, designed to be steerable over the hemisphere, is under construction at the Valley Forge Research Center of the Moore School. A radar transmitter is the source of microwave illumination. 430
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De&m Approach for a High-Resolution Microwave Imaging Rudio Camera
(1) D. D. Ring, R. F. Packard and R. K. Thomas, “Unequally spaoed, broad-band antenna arrays”, IRE Travw Antennua Propagdion, Vol. A-P-8, pp. 380-335, July 1960. (2) 5. 5. Sandier, “Some equivalence between equally and unequally spaced arrays”, IRE Tmna. Antennaa Pmpap.tion, Vol. AP-3, pp. 493-600, Sept. 1960. (3) A. L. M&&t, “Array factors with nonuniform spacing parameters”, IRE Tmm. AntenmurPropagation, Vol. AP-10, pp. 131-136, Mamh 1962. (4) R. E. W&y, “Spaoe tapering of linear and planar arrays”, IRE Tmvw. Antennua Propagahn, Vol. Al?-10, pp. 136Q-1377, July 1962. (5) A. Ishimaru, “Theory of unequally-spaoed arrays”, IRE Tmna. Antenlaas Pmpagahn, Vol. AP-10, pp. 691-702, Nov. 1962. (6) M. I. Skolnik, G. Nemhauser and J. W. Shermsn, III, “Dynamic programming applied to unequally spaced arrays”, IEEE Tmru. Antennas Propagation, Vol. AP-12, pp. 35-43, Jan. 1964. (7) M. I. Skolnik and J. N. Sherman, “Planar arrays with unequally spaced elements”, Radio and ElectronicEngineer, Vol. 23, No. 3, Sept. 1964. (8) A. Ishimaru and Y. S. Chen, “Thinning and broadbanding autem arrays by unequal spacing”, IEEE Tmm. Antennae Pmpga.tion, Vol. AP-13, pp. 34-42, Jan. 1966. (9) M. I. Skolnik, “Nommiform arrays”, Chap. 6 of “Antenna Theory”, Part I (Ed. by Collin and Zucker), McGraw-Hill, New York, 1969. (10) John L. Allen, “Some extensions of the theory of random error effects on array patterns”, Chap. III, Pt. 3 of “Phased Array Rsdar Studies”, Lincoln Lab. Rpt. 236, Nov. 1961. (11) T. M. Maher and D..R. Cheng, “Random removal of radiators from large linear arrays”, IEEE Trnrw An&nPropagation, Vol. AP-11, pp. 106-112, March 1963. (12)Y. T. Lo, “A mathematical theory of antenna arrays with randomly speced elements”, IRE Trans. AntenPmpagaGn, Vol. AP-12, pp. 267-268, May 1964. (13) Y. T. Lo, “A probabilistio approach to the problem of large antenna arrays”, Radio Science,Vol. 68D, pp. 1011-1019, Sept. 1964. (14) Y. T. Lo and S. W. Lee, “Sidelobe level of nonuniformly a@ entenna arrays”, IEEE Tram. Antennas Propagahn, Vol. AP-13, pp. 317-318, Sept. 1966. (15) Y. T. Lo and S. W. Lee, “A study of spaoe-tapered arrays”, IEEE Tmne. AratennaaPropagakn, Vol. AP-14, pp. 22-30, Jan. 1966. (16)Y. T. Lo and R. J. Simcoe, “An experiment on antenna arrays with randomly spaced elements”, IEEE Tmna. AntennauPmpagatbn, Vol. AP-16, pp. 231-235, March 1967. (17) A. R. Pan&Ii and Y. T. Lo, “A probabilistio approaoh to large cimular and sphericalarrays”, IEEE Tmm. Antenna Propagatkm,Vol. AP-17, pp. 514-622, July 1969. (13) B. D. Steinberg, “The peak sidelobe of the phased array having raudomly located elements”, IEEE Tmna. Antennae Prapagahn, Vol. AP-20, pp. 129-135, Mamh 1972. (19) B. D. Steinberg, “Comparison between the peak sidelobe of the random array and algorithmically designed aperiodic arrays”, IEEE Tmm. Antenw Propagzth, B&y 1973. (20) J. Ruze, “The effect of aperture errors on the antenna radiation pattern”, Nwrvo Cimanto,Suppl. 3, 9, pp. 364-380, 1962. (21) B. D. Steinberg, “Self-cohering nonrigid array”, Proc. IEEE Ecet Coast Conf. on Aerospace and NavigcstionalElectmnk, Baltimore, Md., Oct. 1966. (22) F. M. Gardner, “Phase Lock Techniques”, Wiley, New York, 1966.
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D. Be&&erg
(28) R. L. Bsrron, “Adaptive flight control systems”, in “Principles and Prsotice of Bionics” (Ed. by H. E. Von Gierke, W. D. Keidel snd H. L. Oestreicher), TeohnivisionServioes, Slough, England, 1970. (24) B. D. Steinberg, “Angu&r resolution in large mys”, Velley Forge Research Center, Quart. Prog. Rep. Nos. 4 and 6, Feb. end May 1973.
Figure 12 shows sn element et position (2, y) in 8 coordinste system defined by the dire&ion of phase synchronization of the army and a referencelocetion in the army. The element ooordinstes stored in the srrtly processor are (o = 82, y +&). During phase synchronization the adaptive loop adds phase shift & = -ky. The processor Sync angle
x Assumed x Actual
8mox =!-
x IO us
Fra. 12. Tolerance on element location uncertainty. assumes thet the phase shift is &, = - k(y +&). To steer the beam 8 from the synchroniration angle the new phase shift should be +I = - k(y cos 6 + z sin 8) ; the correct mod&&ion for saenning, therefore, is A# = #i -+0 = k[y( I- COFJ 6) -z sin 81. The processor, however, cslouletea the new phase shift to be 4; = -k[(y+&/)cosO+(z+&z)sin8] and epplies the correction A& = &-4; = k[(y+8y)(l-~os8)-(z+Sz)sinC)1. The error 8$ = A&-A4 = k[&y(l -cos8)-6~sin8]mustbeheldtoabout2w/lO. Except in unusual situ&ions 6~ snd Sy are sero mesn, random variables with equal rms deviations u,, end o,.. 84 1 -use the m&mum seen gurgleis the order of the angle subtended by the object rtt the srray. Therefore w II -k&x and Us = 2&r& is the standard deviation of the phsse error. Equating a&to the phase tolerenoefor the maximum angle of soen tl,, 2x@,, U& = 2w/lO or t?,, = h/lOa,. If the object subtendeen engle 8, the &olerenoe on element location is u, = h/10&. The y-tolerance is the s&me.Hence the allowed rms uncertainty in element location is h/78,.
432
Journal of !Che kanklin
Institute