FINAL REPORT:

EOS RADIOMETER CONCEPTS

FOR SOIL MOISTURE REMOTE SENSING

By Jim Carr, ORI, Inc,

10 February 1986

{NASA-CE- 177854) EOS PADICME1EF. CONCEPTS N86-23995

FOR SOIL MOISTUEE BEMCT E SENSIN G Final

Beport (Operations Research, IDC.) 175 p

HC A08/MF A 31 CSCL 08B Unclas

G3/43 09119

ORI, Inc. A Final Report

8201 Corporate Drive Under Contract

Suite 350 NAS5-28648

Landover, Maryland 20785
ORIGINAL PAGE IS

Of POOR QUAJJTY

FINAL REPORT:

EOS RADIOMETER CONCEPTS

FOR SOIL MOISTURE REMOTE SENSING

By Jim Carr, ORI, Inc.

10 February 1986

, : A Final ReDort

82)1 Co-Jorate Drive Under Contract

NAS5-28648

lover md 20785
MEMORANDUM 26 February 1986

TO: Distribution

FROM: J. Carr, ORI, Inc. _i .

RE: Erratum for Final Report Under Contract NAS5-28648

Please replace page 151 with the enclosed. We erred in stating that

the radiometric threshold defining "useful field-of-view" is 0.1 K. It is,

instead, 1.0 K.

Distribution:

Dr. A Chang, Code 624

Dr. D. LeVine, Code 675 (2)

Ms. P. Huey, Code 286

Graphic Arts Branch, Code 253

Patent Counsel, Code 204
I. OVERVIEW

This report is basically a compendium of memos submitted to Dr. A.

Chang and Dr. D. LeVine of NASA/GSFC during the course of this contract. Also

included are copies of the vugraphs presented by J. Carr of ORI to the NASA

Earth Observing System/High resolution Multifrequency Microwave Radiometer

(EOS/HMMR) panel. This presentation covers our preliminary work with aperture

synthesis concepts for EOS, and appeared in our preliminary report. New to

the final report is an exposition of the effects of nonvanishing bandwidths on

image reconstruction in apperture synthesis systems. It is found that

nonvanishing bandwidths introduce errors in off-axis pixels when naive Fourier

processing is used. The net effect is for bandwidth to limit sensor

field-of-view. Although known to radio astronomers, this effect has to our

knowledge never previously been quantified. To quantify this effect we wrote

a computer program (a copy of which is delivered with this report) which is

documented in this report. Example runs are included which illustrate the

resultant radiometric errors and effective fields-of-view for a plausible

simple sensor.

1
II. REAL APERTURE SYSTEMS

The study began by considering real aperture systems for EOS. These

concepts grew out of the considerations for a Shuttle-based instrument

examined under a previous contract with ORI.

It was decided that the instrument concepts should address the

measurement requirements of:

1) 10 km spatial resolution

2) 3 day temporal resolution

3) 1 K radiometric accuracy.

The requirements were derived from the "EOS Science and Mission Requirements

Working Group Report" (NASA-TM-86129) and the published experience of other

instruments (e.g., Skylab S-194).

The first memo attached considers an electronically scanned array

with a single beam. It was found that the constraints on integration time by

the need to form an image did not permit all of the measurement requirements

to be simultaneously satisfied. A factor of two improvement in the

sensitivity is required to meet .5 K radiometric sensitivity. The remainder

of the 1 K radiometric accuracy is budgeted for systematic errors. Several

ways to enhance performance were then studied. These are:

1) Increase the reception bandwidth beyond the 27 MHz reserved for

passive use only

2) Build a total power radiometer
3) Build a reference averaging radiometer

4) Build a multibeam (vnskbroom) radiometer.

The second attached memo examines the feasibility cf baniwidth

extension. It is rejected due to the large number and nigh powers of

interferers in neighboring bands. The third memo deals with total power

radiometry. It appears that total power radiometry may be a feasible option,

but that temperature and power supply stability are crucial. On the

performance spectrum between total power and Dicke radiometers is the

reference averaging radiometer. This is described in the fourth memo and does

appear attractive.

Finally, a wiskbroom system with four beams wil l certainly provide

the necessary sensitivity; however, this introduces antenna design

complications. Four beams are necessary since the number of beams increases

the integration time linearly and the sensitivity is inversely proportional to

the square-root of the integration time; hence the factor of four is required

to make-up the factor of two shortfall in sensitivity.

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January 25. 1985

TO: File

FROM: J. Carr and 6. Candey

RE: Bandwidth Extension

Analysis to establish a baseline real aperture L-band sensor for EOS

has found that Integration time constraints do not permit both the desired

spatial resolution and the desired radiometrlc resolution. It 1s also

anticipated that this Integration time constraint will place more severe

restrictions upon synthetic aperture systems. One possible solution Is to

Increase the bandwidth from the nominal 27 MHz (1400-1427 MHz). Initially

this seemed feasable since the 1370-1400 MHz band is designated for passive

use on a secondary basis. However, as the following analysis will indicate

bandwidth extension is infeasable due to the presence of numerous high powered

transmitters.

The frequency bands neighboring 1400 MHz have the following

allocations':

1) The 1300-1350 MHz band is allocated to radionavigation worldwide

except for fixed and mobile services in Indonesia and radiolocation

service in Ireland and the United Kingdom. Radionavigation use is

limited to ground-based radars and associated airborne transponders.

The U.S. government allocations also allow radiolocation but limited *

to the military services.

Manual of Regulations and Procedures for Federal Radio Frequency

Management, NTIA, May 1984. p. 4-53ff.

ft
2) The 1350-1400 MHz band 1s allocated to fixed, mobile, snd

radiolocation services 1n Region 1 (North and South Aue'-lca) and

radiolocation in Regions 2 and 3 (Europe, Africa and Asia) with some

existing radlonavlgatlon Installations In the Eastern Bloc, U.S., and

Canada. The 1370-1400 MHz band 1s also allocated to passive space

and earth research and observations on a secondary basis. In

addition, the frequency 1381 MHz 1s allocated 1n the US to Fixed and

Mobile Satellite Services (Space-to-Earth) for the relay of nuclear

burst data. In the U.S., over 100 high powered radars operate 1n the

1370-1400 MHz band and International listings also Indicate

extensive use.

3) The 1400-1427 MHz band 1s reserved solely for passive radio

astronomy, space research, and earth exploration-satellite

observations. Some second and third harmonics and various

Intermodular on products of television transmitters and extraband

radiation from radars may fall within the 1400-1427 MHz band.

4) The 1427-1525 MHz bands are allocated to fixed, mobile, and

space operation and are used heavily.

Ideally one wants a large bandwidth for enhanced sensitivity;

however, artificial sources are many orders of magnitude brighter than the

thermal emmissions of the earth and must be excluded from the instrument

bandpass. We determine the interference threshold as follows. The required

receiver sensitivity is &T = .5 K which corresponds to a power level of kGKT)"B

with fe. = 1.38 x 10 J/K and B the bandwidth. The maximum sensorInterferer range will occur just when the sensor rises above the Interferer's

horizon (see Figure 1). Coincidently this 1s where radiolocation services t

(e.g., FAA radars) would have their maximum gain directions and so this is the

anticipated worst case geometry dispite the large range. At a nominal

altitude of h = 700 Km, the sensor - interferer range is R « 3069 Km with the

Interferer at a 64° angle from the sensor's nadir. We assume a nominal 10m

x 10m sensor aperture which scans ± 33° to cover a 900 Km swath. This

places the interferer 31° off the maximum gain direction at the extreme

point of the scan. A uniformly weighted aperture would have a power pattern

which falls as

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Figure 1. Sensor - Interferer Geometry

15
where L 1s the aperture dimension (10m), X 1s the wavele'gth (21 cm), and

1s the angle off the maximum gain direction. For ^« 31° thli puts the peak

sldelobe level at 6 « -38 dB. However, 1t 1s better to taper the aperature

weighting 1n order to trade beam width for lower sldelobes (1r creased main

beam efficiency). Sldelobe levels at ^* 31° for a 90X main beam efficient

antenna would be more like G * -50 dB (see Figure 2). The power Into the

sensor's receiver from the Interferer Is then

where EIRP 1s the Interferer's Equivalent Isotropic Radiated Power. In which

case, the maximum tolerable EIRP to not exceed a* power threshold P is given by

We will conservatively set P =k(AT)B which 1s the receiver

sensitivity. For B = 27 MHz, P «= -157 dBW and for B = 100 MHz, P = -152 dBW.

Using R = 3069 Km, L « 10 m, G « -50 dB gives EIRP thresholds of + 14 dBW and

+19 dBW for the 27 MHz and 100 MHz bandwidths respectively.

Typical EIRPs for fixed stations operating near 1.4 GHz are 37 dBW to

y

55 dBW * which would definitely represent an interference threat.

Additional sidelobe rejection of -36 dB would be required to place the 55 dBW

transmitters at the received power threshold -152 dBW, and another -10 dB

should be added to place the Interferer below the redeved power threshold

with adequate margin. Then a sidelobe level of -96 dB is required at 31°

off the maximum gain direction. This would be extremely difficult to achieve.

^Recommendations and Reports of the CCIR, 1982; XVth Plenary Assembly in

Geneva, Volume II; Space Research and Radloastronomy, ITU, p. 386.

Ifc
ORIGINAL PAGE IS

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(Source: "L-band Radiometer Antenna Study", Hughes Aircraft

under contract NAS5-23418, May 1977)
Using a received power threshold of -165 dBW (compare with -157 dBW)

corresponding to an EIRP threshold of 12 dBW (compare with 19 dBW), the

International Radio Consultative Committee (CCIR) has performed an

Interference analysis for a 100 MHz bandwidth sensor3. The results are

shown 1n Figure 3 where total data loss occurs in the shaded regions. This

analysis Includes only the fixed services which populate the 1350-1400 MHz

band, so the actual Interference environment 1s 1n fact worse.

Transmitters in the 1250-1400 MHz band Include FAA aeronautical

radionavigation radars, DoD long range surveillance and search radars, DoD

communication radios, the GPS downlink for relay of nuclear burst data, the

TIPS Army transponder and classified military transmitters. A common FAA

radar, the ARSR-1, operates at frequencies of 1280-1350 MHz, has an antenna

gain of 34.2 dBi and 4 MW peak power over 2 microsecond pulses. DoD

communication radios, such as the AN/GRC-50 and AN/GRC-103, broadcast 1n the

1350-1849.5 MHz band with antenna gain of up to 20 dBi and peak power of 8-30

W. The TIPS transponder uses the 1350-1400 MHz band with a peak power of 120

In light of the above interference analyses, it appears that

bandwidth extension beyond the reserved 1400-1427 MHz band 1s infeasable.

This conclusion 1s corrobated by the opinion of David P. Struba, NASA

Headquarters Frequency Management Program Manager, that the secondary

allocation for passive use of the 1370-1400 MHz band 1s almost

meaningless. In addition there is also concern that extraband radiation

and TV transmitter harmonics could pollute the 1400-1427 MHz band. Although

there is no mention of interference problems in the literature reporting the

1973 Skylab L-band radiometer results, this issue should be studied further.

If It is determined that such emissions might pose an interference threat then

i

a Shuttle survey with a low cost low resolution antenna might be considered to

characterize the L-band environment.

3Ibid. pp. 379 - 399.

^Andrew Farrar, Spectrum Resource Assessment in the 1215-1400 MHz Band, NTIA

Report 81-83, Sept. 1981, pp. 36-8, 50.

^Private communications between David P. Struba and Bob Candey.
ORIGINAL PAGE is

OF POOR QUALITY

Figure 3. Regions of Total Data Loss

(Source Ibid., p. 387)
25 February 19E'5

TO: J. Carr

FROM: R. E. Prince

SUBJ: L - Band Amplifier Drifts with Respect to Total Power Radiometers

I have made a number of phone calls and managed to talk to about half

of the people I attempted to contact.

Two attempted contacts that never returned their calls were:

Chase Hearne, a specialist in GaAs amplifiers.

Hans Blume, a specialist in uncooled parameter amplifiers.

They are both NASA/Lang!ey (LaRC) people whose names were given me by

their boss at LaRC, Richard Harrington (804) 865-3631. Harrington said they

would call, but ... So be it. I mention this only because these two were

supposedly hot numbers (technically speaking). I got Harrington's name from

John Shien at 6SFC.

A man named Joe Rogers (GSFC, 344-8816) has tested a number of GaAs L

'- band amps. He particularly likes units manufactured by California Amplifier

and by Berkshire Technologies, Inc. (also in California). Rogers Indicates

that another GSFC person, David Buhl (344-8810) has a noise figure and gain

test setup for these devices based on an HP 8970 Instrument. Whether he can

measure the small variations we are looking for 1s another question. Buhl

also suggests that we talk to Robert Jones, RF Technology Branch In GSFC, Bldg

19. Apparently building 19 has a test setup based on an AIL Instruments.

Although nobody I talked to had test or analytical data for small

scale, short term GaAs L - band amplifier gain stability with temperature, all

my correspondents agreed that primarily temperature (and only slightly supply

voltage) controls amplifier gain. All agreed that with sufficient temperature

stabilization a gain stability of 10-3 (.30 db) was quite feasible.

Supply voltage requirements are typically +_ 15 volts £ 50 ma.

Regulation should be I 10% or better.

All of the amplifier people I spoke to quoted specifications for an

L - band unit similar to the following:

frequency range: 1.30 to 1.60 GHz

noise figure: .7 to 1.0 db at room temperature

ANF/^T approx. .05 db/10°c (down to a noise figure of

approx. .6 at -70°c)

gain: 35 to 40 db (power) at room temperature

^G/^T: -.02 db/°c to -.04 db/°c (gain increases with

dropping temperature)
This ^G/<J number corresponds to approximately .1° C temperature

stability to meet a -30 db ^G/G (or .010 C stability for a -40 db AG/G).

ASee attached calculation).

I have enclosed some test data I received from California Amplifier,

Inc.

I talked to Jim Bremer for a short while on the telephone concerning

his reference - averaging radiometer design. He Indicates that 1n

approximately 1977, Hughes Alrcarft did a computer simulation and then built a

labatory breadboard of the reference - averaging technique. Jim said that the

Hughes work verified the Bremer calculations but that simultaneous advances in

amplifier stability mode a total-power system feasible. The Hughes work was

at millimeter wave lengths.

Jim brought up something else to be remembered about total power

systems: a D.C. - Restore capability probably will be necessary. D.C. -

Restore 1s essentially 1s a calibration - 1t returns the analog output to the

A/D converter to a known D.C. level for a given Input every now and then.

Typically, it is done once per scan line (every few seconds) or whenever

practical. If the amplifier 1s stable enough that It's baseline plus dynamic

range never clamps or extends beyond the A/D converter useful range of inputs,

the D.C. - Restore function as a specific analog circuit could be omitted.

This function could then be subsumed under the calibration function and

accomplished digitally at the output of the A/D converter (or still as an

analog function, of course).

t\
People I have attempted to contact Include:

erson and Location Successful Unsuccessful

R. Harrington, LaRC x

(804) 865-3631

Chase Hearne, LaRC x

Hans Blume, LaRC x

01m Shleu, GSFC x

Roger Ratllff, GSFC x

Joe Rogers, GSFC x

David Buhl, GSFC x

Trontech Corp., Neptune, N.O. x

(201) 229-4348

Miteq, Hauppage, N.Y. x

(Jared S1ddiqu1) (516) 543-8873

Applied Microwave Corp., Lawrence, Kansas x

(Dr. David Brunfleld, formerly U.KS Remote

Sensing Center) (913) 749-3511

California Amplifier, Newbury Park, Cal. x

(John Ramsey) (805) 499-8535

Berkshire Technologies, Inc., Oakland, Cal. x

(415) 655-1986

Although I did not call them, several people suggested Amplica,

(805) 498-9671. They are a division of COMSAT.
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III. APERTURE SYNTHESIS SYSTEMS

As an alternative to real aperture systems we have considered

synthetic aperture systems. Aperture synthesis can offer high spatial

resolution with a sparse antenna array and so it can be economically

attractive. Initially the more general case of a synthesis/scanning hybrid

was considered (of which a pure synthesis instrument is a degenerate case).

Such a hybrid would step-scan its field-of-view across-track. Aperture

synthesis provides the imaging within each field-of-view. The first of the

following memos describes a one-dimensional scanning/synthesis hybrid. It

concludes that such instruments can perform the soil moisture mission. An

especially remarkable result is that the necessary radiometric resolution

could be achieved despite the diminished aperture area. This is because the

collection area loss is offset by both an increased integration time (set by

the real fleld-of-view) and the parallel channel structure of an aperture

synthesis instrument.

The second of the following memos details a two-dimensional

synthesis/scanning hybrid concept. It concludes that the sensitivity of such

an instrument is identical to the one-dimensional case for given aperture

area. Therefore, there is no advantage to this more complicated scheme and

only one-dimensional concepts were henceforth considered.

Following this memo is a set of notes detailing the theory of

aperture synthesis. It covers the signal processing theory, resolution,

grating lobes, and nonlinear effects (fringe washing). The grating lobes and

fringe washing effects are particularly important as they restrict the fieldof-view.
Firully , details of how to construct a pure aperture synthesis

instrument we^e considered. In the last three memos an analog and two digital

architectures are [resented. All architectures have the same external data

rates, wherea: the digital architectures (they do correlations digitally as

opposed to using analog mixers) can have very significant internal rates.
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IV. EOS/HMMR PANEL PRESENTATION

What follows are the vugraphs from our presentation to the EOS/HMMR

panel. This presentation summarizes some of our results and was intended to

generate some confidence that aperture synthesis could be used to perform the

soil moisture mission. We took as science requirements:

1) 10 km spatial resolution

2) 3 day temporal resolution

3) 1 K radiometric resolution.

We took the 3 day temporal resolution requirement to mean that both

dayside and nightside overpasses count as revisits. At a presumed 700 Km

sun-synchronous circular orbit, a 450 km swath implies three day coverage (at

least in a statistical sense, i.e., mean revisit time). Since swath width is

the most difficult parameter to achieve due to grating lobes and fringe

washing, and since we wanted to present a "minimal" instrument, the swath

width goal was degraded to 400 km. This implies 3 day (statistical) coverage

in the temperate latitudes above 30° and 4 day (statistical) coverage at the

equator. Increasing the swath width to 450 km (or even 900 km which gives

precisely periodic 3 day coverage rather than statistical 3 day coverage) is

possible at the cost of more antennas.

The system presented consists of 11 13.2 m x .34 m antennas occupying

a 13.2 m x 16.2 m array. The array fill-factor is 23 percent. It provides 10

km resolution both along and across-track with a .6 K radiometric

sensitivity. With this one-dimensional concept, aperture synthesis provides

the across-track resolution; whereas, the width along-track of the antennas'

fields-of-view provides the along-track resolution.
A digital system architecture was presented. This arcmtecture joins

11 antenna/receiver units, arranged to form a minimum redundancy linear array,

with about 40 in-phase and 40 quadrature digital correlators. Each pair of

an ennas forming a unique baseline are joined with both in-phase and

quadrature correlators. In addition, several autocorrelation channels wojld

be required to measure the zero-baseline or DC component of the scene spatial

frequency distribution. Each channel need not physically correspond to a

unique piece of hardware, as different baselines could be time-phase

multiplexed on a common correlator. The instrument internal data rate would

be fairly high at 20 Mbps which is determined by the Nyquist sampling rate of

the signals being digitized by the antenna/receiver units. The external data

rates would, however, be quite modest at about 1 Kbps which is determined by

the dynamic range and noise levels in the measurements. Fourier processing to

construct an image could be easily done on the ground in real-time.
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V. BANDWIDTH AND RECONSTRUCTION

As noted earlier, a nonvanishing system bandwidth results in imaging

errors ("fringe washing") off-axis when naive Fourier processing is used for

image reconstruction. The net effect is for system bandwidth to limit

f ield-of-view. In this section we exhibit the theory behind this effect.

This is exploited in the computer simulation described in section VI.

The first attached memo derives the relationship between system

response and scene brightness distribution for a polychromatic extended

source. The problem of image reconstruction is cast as inverting an integral

equation:

ux

where

R(u) is the response at spatial frequency (or baseline) u

G(u)) is the filter power gain at radian frequency LJ

id is the center or fiducial radian frequency

K(x) is the integral kernal to be estimated at scene coordinate x

(sine of angle across track).
ORIGIN

OF POOR QUALIFY

The kernal K(x) is the product of the antenna power pattern, scene brigitne.s

distribution and Jacobian factor (i—X2) .*" This is almost a Fourier

relationship between R(u'i and K(x).

To see the connection between bandwidth and field-of-view, we perform

a change of variables ^ = (oa-cofl) and integrate over ^ . Then

-pa

where

-i

Here h(u,x) multiplies K(x) which contains the antenna power pattern. Then

h(u,x) can be thought of as an additional but spatial frequency dependent

pattern factor. For a single frequency bandpass h(u,x) in a constant, but as

the bandwidth increases, it becomes tapered away from x=0.

The second memo describes how this formalism is translated into the

discrete problem of inverting a finite sampling of spatial frequencies to

estimate scene brightness. There we have an almost discrete Fourier

relationship:

s)

R = I

n = i

where

R is R(u) sampled at u^fai-i) Ai^ and weighted by a phase factor

is K(x) sampled at x=(n

is a filter design dependent weighting

111
The samplings Av, Au- are such that A\ ^JIA - — where N -s the

number of baselines.

For a real sensor some baselines may occur with multiplicities other

than 1, in which case, we multiply VOft(Y> by the multiplicity factor /*w
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VI. COMPUTER SIMULATION

This section documents our aperture synthesis computer simulation

designed to quantify the nonvanishing bandwidth and reconstruction problem.

The source listing follows, it is written in Microsoft FORTRAN for the IBM

PC. The source and object codes for which are delivered on a floppy disk.

Two main programs appear - APSYNSIM and BASELINE. APSYNSIM calls subprograms

FOURT, SINC, and PLOT.

APSYNSIM is the main program for the aperture synthesis simulation.

It reads the run input data from file MASTER.DAT (listed after source

listings). The inputs are as in table VI-1. System parameters specified are

the number of baselines, null-to-null field-of-view, center frequency, and

bandwidth. The test scene is assumed to be of constant nominal brightness

temperature and limited to a specified scene width «180°) to avoid the

Jacobian factor in K(x) raising a division by zero error. APSYNSIM reads the

baseline multiplicities and processing weights from input specified files

(also listed). Input data sets can be concatenated for multiple runs.

The first step in the program is the creation of a scene weighted by

2

a (sine) antenna power pattern with the necessary null-to-null FOV, and the

Jacobian factor. This is stored in array SCENE corresponding to K in

section V. The unweighted scene has a constant nominal brightness

temperature. Receiver responses are then calculated according to section V

and stored in complex array R. The weightings W are based on an ideal

rectangular bandpass filter. A scene estimate SHAT is generated by Fourier

transforming R. FOURT is a Fourier transform subroutine from the ORI program

library. The difference between SHAT and SCENE and the fractional difference

are computed as measures of estimation error. The fractional difference
TABLE VI - 1

APSYNSIM Input Varlab'es

Name Meaning Format

RIDNAM

N

SWDTH

FOV

FO

BW

TEMP

MULTFI

WGTFIL

OUTFIL

Run ID name A20

Number of baselines 13

(power of 2)

Scene full width (degrees) F8.2

Null-to-null FOV (degrees) F8.2

Center frequency (GHz) F8.2

Bandwidth (MHz) F8.2

Constant scene temperature (K) F8.2

Multiplicity file name A20

Weighting file name A20

Output file name A20
(SCENE-SHAT)/SCENE is a measure of the rajiometric error induced since SCENE

and SHAT both are brightness district ion- weighted by the same antenra and

Jacobian factors. Since the scene nonina tempsrature is specified,

multiplying the fractional difference by t-.e noiinal temperature gives the

radiometric error.

Output at the various stages of the calculation are displayed on

printer plots generated by PLOT. In addition, an output file is created with

the input data as a header and four columns containing the abscissa (scene

coordinate x) and three ordinates-the test scene, scene and estimate

difference, and radiometric error. The output file is in a format suitable

for importation to LOTUS from which graphics can be readily generated.

Simulation results are discussed in the next section.

A second main program, named BASELINE, is included here. It reads

from a keyboard specified input file and writes to a keyboard specified output

file. The input file contains integer antenna locations in a one-dimensional

array. The output file lists the multiplicity for each baseline in the array.

/
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D2R = PI / 1SO.O

READ THE INPUT PARAMETERS

0='EN (21 , F I LE= ' MAST ER. DAT ' , STATUS-- Qi. D ;

10 READ (21 , 20,END=24'.)yRIDNAM,N,&WDTH,FOV,r-'.- , B''

IGUTFIL

20 FORMAT<A2O/,I3/,5(FS.2/>,2(A20/),A20;

C^EN(22,FILE=I-!ULTFI , STATUS--' OLD ' )

READ(22,70)MLTHED,f

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DQ 40 I = 1, f

READ(22,'(15) )MULT(I)

40 CONTINUE

Q-'EhU23,FILE=WbTFIL.STATUS='OLD )

F EAD'23,4?)WGT riED,L

45 FI.RMATCA20/ ,13)

D2 50 I --- 1 , L

READ (23, ' (2E12.5; ' > WEIGHT ', I )

51- CONTINUE

INITIALIZE THE SCENE

v>..> = PI / SIN (.5 * FOV )

XnIN = -SIN (.5 * SWDTH * DI'R)

LA - (-2 *• XNIN) / (N - 1)

DJ 70 I = 1, M

X (I) = (1-1) * E-X <- XMIN

P = S1NCCVO * X ', I) )

SCENE(I) = (P v P) / SORT',1 - (Xm i7O CONTINUE

D I,SPLAY SCENE

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CALL PLOT (N, X, SCENE)

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!=\ITE (* , 9O) N , FOV , SWL'TH

90 FORMAT (/ IX, 'TEST SCENE W1TH'/7X,'N = ' , \ 7/3 X . ' FOV -^',

6 ' DEGREES ' /3X , ' SWDTH = ' , F6 . 2 , 1 X . ' DEGREES ' )

COMPUTE RECEIVER RESPONSES '

FHIO = 2 *• PI / N

VO = (PI * BW) / (FO * 1000.0 *• N>

DO 110 I = 1, N

PHI = (I - 1) •)• FHIO

SUM = CMPLX(0,0)

DO 130 J = 1, N

U-(I-l)«i<(J - 0.5) - ('J.5 * N> i * VW - SINC(U)

SUM = SUM + SCENE CJ 5 + W

130 CONTINUE

R ( I ) = SUM / N * MULT '. I )

110 CC'NTlNUlr.

WEIBHT RESPONSES CALCULATED

E-J 115 I = 1, M

R-. I) == F <.!'> - wEIGHT (I)

t iM CONTINUE

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CGI-i-'UTE T :C £ :FNE ESTIMATE

CALL FQ'-'PT ( F< , -' , 1 , - i , 1 , WORI ' )

DO 150 1 - 1 , M

ShAT f I : = •£•:•_. ""- ' ! ) )

150 CONTINUE

DISPLAY THE SCENE ESTIMATE

WRITE**, ' (1H1 ' )

CALL PLOT(N,X,SH^T;

WRITEC*, 17O)FO,BW

17O FORMAT < /I X, 'SCENE ESTIMATE WITH'/3X,'FG = ' , F6. 2 , 1 X , 'GHz ' /3X , EW

7.F8.2, IX, 'MHz ' )

COMPUTE WEIGHTED SCENE ERROR

DO 200 I = 1 , N

SHAT ( I ) = SCENE ( I ) - SHAT ( I )

200 CONTINUE

DISPLAY WEIGHTED SCENE ERROR

CALL PLOT (IM,X, SHAT)

u Ljne« 1

57 C

56

59

60

1 61

62 C

63

64

65

66

67

68 C

69

1 70

1 71

72 C

73

74

75

76 210 FORMAT(/I X, 'SCENE ESTIMATE ERROR')

77 C COMPUTE SCENE ERROR

78 DO 220 I = 1, N

1 79 THAT(I) = (SHAT (I) / SCENE(I) ) *• TEMP

1 80 220 CONTINUE

81 C DISPLAY SCENE ERROR

82 WRITE(*,'(1H1)')

83 CALL PLOT(N,X,THAT)

84 WRITE**,230)

85 230 FORMAT(/IX,'SCENE ESTIMATE PERCENTAGE ERROR')

86 OFEN(241FILE=GUTFIL,STA7US='NEW')

87 WRITE(24,236)RIDNAM,N,SWD FH,FOV,Fu,BW,TEMP,MULT FI,WGTFIL,MLTHED,

83 2WGTHED

89 236 FORMAT <IH",A20,IH",/,I3,5F8.2,/,IH",A20,IH",IH",A2O,IH" , /,

90 3iH",A20,IH",IH",A20,IH")

91 DO 238 I = 1, N

I 92 WRITE(24,237)X(I) .SCENE (I) ,SHAT(I) ,THAT(I)

1 93 237 FORMAT(4E2O.5)

1 94 238 CONTINUE

95 GO TO 10

96 240 STOP

97 END

Name

PW

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I

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RE-L

INTEGER-4

INTEGER*-!

INTEGER-*-

9236

9464

9272

9268

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INTEGER*

CHAP- 20

INTEGER*

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CHAR~20

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REAL

REAL

REAL

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REAL

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REAL

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CHAR*20

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Type

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INTRINSIC

FUNCTION

INTRINSIC

ORIG8NAL PAGE §S

OF POOR QUALITY

Class

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PROGRAM

SUBROUTINE

FUNCTION

Pass One No

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2 I\JNCr:ON SINCvU)

IF (U . EO. 0) GO TO 1

4 E INC - STN(L); / U

5 FITUFr

6 1 SINC = 1

7 F E:TUF;.N

8 END

Nfime Type 0-ffset P Class

SIN INTRINSIC

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Name Type Si us Clays

SINC REAL FUNCTION

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"'•"iiC SUDROU1INE PLC G TO IDI--FC SCREENS

SUBROUTINE PLOT (N,<,Y)

PARAMETER (NX = 7o,iK = 20)

:.-! ivTi.-)5 I ON X ( i) , Y (1)

DIMENSION I XT(5> , IYT (5) , XLAB -5; , YLAi.' (G;

CHARACTER*1 SCREEN(.NX,NY)

XLO = X (1)

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IF (Xd) .

IF (Xd) .

IF (Yd) .

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SCREEllMd ,NY)

CONTINUE

DO 37 I = 1, NY

SCREEN (1,1) =

CONTINUE

XTIC = (XHI - XLO)

YTIC = (YHI - YLO)

DO 38 I = i , 5

XLABd) = XTIC

YLABd) = YTIC

h = (XLABd) -

I XT (I) = K

SCREEN (h,, NY) = ' + '

^ = (YHI - YLABd) )

lYTd) = H

SCREEN (!,»') = '+'

CONTINUE

DO 40 I = 1 , N IX = (Xd) - XLO

)

IY = (YHI - Yd)) *

SCREEN(IX,IY) =

CONTINUE

DO 50 J = 1 , NY

DO 51 I =1,5

IF (J .ED.

CONTINUE

WRITE(*,1OO)(SCREEN(I,J),

FORMAT'.! OX, 7OA1 )

GO TO 50

WRITE(*, 1O1) YLABO )

FORMA r d X,G9.2,7OA J )

CONTINUE

WRITE'.*, 102) XLAB

/ 4 . O / 4.O : * d * ( I

XLO)

- 1) + XLO

-!)•+• YLO

* XSCALE +

* YSCALE + 1

XSCALE

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IYTO ) ) GO TO 45

I = 1 NX

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INTEGER* 4

INTEGER* 4

INTEGER* 4

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i <: sur-r^TiNE FOUPT FOLLOWS

i ,,

4 S.-DROUTINE FOURT<DATA,NN,NL'in, I3IGN, IFORh,WUr-.l )

D T--1 rlE'-JS I ON DC~.'l H ( 1) , Ni-J < 1 > , I FACT « 32) . WORK ( J ;

TWOPI=6.2S71853O7

I~CNDIM-1)92O,1,1

NTOT=2

DO 2 IDIM=1,NDfM

IF (Nf-4 < IDIM) ) 92O , 920 , 2

NTOT==NTOT*-NN(IDIH)

MAIN LOOP FOR EACH DIMENSION

N-'l=-2

D'J 910 IDIM-l ,NDl!-i

IF(N-1)92O,9OO,5

FACTOR N

I- =N

1F=-1

IDIV=2

IOUOT=H/1DIV

IREM-M-IDIY* IOUOT

I- (1DUOT-IDIV)50, 11,11

IF(IREM^2O,12,2O

NTWO=NTWO+NTWO

M=IOUOT

GO TO 1O

IDIV=3

IOUOT=M/IDIV

IREM=M-IDIV*IOUQT

!F(IOUOT-IDIV)6O,31,31

IF(IREM)40,32,40

IFACT(IF)=IDIV

IF=IF+1

M=IOUOT

GO TO 30

GO TO 30

IF(IREN)60,51,60

NTWO-NTWO+NTWO

GO TO 70

IFACT(IF,'=M

SEPARATE FOUR CASES—

1. COMPLEX TRANSFORM OR REAL TRANSFORM FOR THE

DIMENSIONS.

2. REAL TRANSFORM FOR THE 2ND OR 3RD DIMENSION. METHOD—

TRANSFORM HALF THE DATA, SUPPLYING THE OTHER HALF- !?v CONJUGATE SYMMETRY.

3. REAL TRANSFORM FOR THE 1ST DIMENSION, N ODD. METi-"JD----

4TH,
D Linert 1 7 Mi -r nr.c-t FOF. TRAN77 V3.1SO Marcn 19c;i

1 57 C TRANSFORM HuLF THE DATA AT EACH ST f-iGE , SUPPLYING THE OTH£R

I 58 C HALF &/ CONJUGATE SYMMETRY.

)l 59 C 4. REAL TRANH-ORM FOR THE 1ST DIMENSTON. N EVEN. METHOD—

1 60 C TRANSFORM A COMPLEX ARRAY OF LE»JG'H N/2 WHOSE REAL PARTS

1 61 C ARE THE EVEN NUMEERED REAL VAL'JFS AND WHOSE IMAGINARY PART.

1 62 C ARE THE ODD NUMBERED REAL VALUES. SEPARATE AND SUPPLY

1 63 C THE SECOND HALF BY CONJUGATE SYMMETRY.

1 64 C

1 65 70 NON2=NP1-MNP2/NTWO>

1 66 ICASE==1

1 67 IF(IDIM-4)71,9O,9O

1 68 71 IF(IFQRM)72,72,90

1 69 72 ICASE=2

1 70 IF(IDIM-1)73,73,90

1 71 73 ICASE=3

1 72 IF(NTWO-NPl)90,90,74

1 73 74 ICA5E=4

1 74 NTWO=NTWO/2

i 75 N=N/2

1 76 NP2=NP2/2

1 77 NTOT=NTOT/2

1 78 1=3

1 79 DO 60 J=2,NTOT

2 80 DATA(J)=DATA(1>

2. 81 8O 1 = 1+2

1 82 9O I1RNG=NP1

1 83 IF(ICASE-2)1OO,95,100

1 84 95 IlRNG-NP'.)*(l4NPREV/2)

^^ 1 85 C

^P 1 86 C SHUFFLE ON THE FACTORS OF TWO IN N. AS THE SHUFFLING

| 1 87 C CAN BE DONE BY SIMPLE INTERCHANGE, NO WORKING ARRAY IS NEEDED

I I 8 8 C

11 89 100 IF(NTWO-NP1)60O,60O,110

1 90 110 NP2HF=NP2/2

1 91 J=l

1 92 DO 150 12=1,NP2,NON2

2 93 IFCJ-I2)120,130,130

2 94 120 IlMAX=I2+NQN2-2

2 95 DO 125 11=12,I1MAX,2

3 96 DO 125 13-11,NTOT,NP2

4 97 J3=J+I3-I2

4 98 TEMPR=DATA<I3)

4 99 TEMPI=DATA(I3+1)

4 100 DATA(I3)=DATA(J3)

4 101 DATA(I3+1)=DATA(J3+1)

4 102 DATA(J3)=TEMPR

4 103 125 DATA(J3+1)=-TEMPI

2 1O4 13O M=NP2HF

2 105 140 IF (J-M) 150,ISO,145

2 106 145 J=J-M

2 1O7 M="1/2

2 108 IF(M-NON2)15O.140,14O

2 109 ISO J=J+M

I HOC

f I 131 C MAIN LOOP FOR FACTORS OF TWO. PERFORM FOURIER TRANSFORMS OF

I 112 C LENGTH FOUR, W1VH ONE OF U-.NGTH TWO IF NEEDED. THE TWIDDLE FACTOR
-

OF PfVtr.

 rA«t IS

TOOR

 QUAL/TY

1 c.: 7 1': 7

lj Linprt 1 "/ Micr-.sn-'T: r- -_i;; T r-,.' j v / V7.70 i^c?"'h. 19L-:

117 L W=E/P(IS!GN>2*PI+-SDRT(-l)+-M/(4*'-1M^'.) ) . CHELr FOR W= ISIGN-SORT (- i .

11^ c AMD REPEAT FOR W= I SIGN* SORT (-1)-*CCM JUGATE • W) .

115 C

116 NO\'2T=NON2+NON2

1 117 IFAR=N7WO/WP1

1 118 310 IF (IPAR-2) 350,330, 320 ORfGHV/»

1 119 320 IPAR=IPAR/4

1 120 GO TO 31O

1 121 330 DO 34O I 1 = 1,IlftNG, 2

2 122 DO 340 J3=I1,NON2,NP1

3 123 DO 34O K1-J3,NTOV,NON2T

4 124 h2=l 1+NON2

4 125 TEMPR=DATA(K2)

4 126 TEMPI=DATA<h2+l>

4 127 DATAU'2)=DATA<h 1)-TEMPR

4 128 DATAa 2+l)=DATAU 1 + 1)-TEMPI

4 129 DATA(t 1) =DATA U 1)+TEMPR

1 131 35O MMAX=NON2

1 132 760 IF(MMAX-MP2HF)370,600,600

1 133 37O LMAX=MAXO(NQN2T,MMAX/2)

1 134 IF(MMAX-NOH2)4O5,405,7BO

I 135 38O THET A=-TWOP I AFLOAT < N0hl2 )/FLCJAT (4-1

1 136 IF(ISIGN)4OO,390,390

1 137 390 THETA=-THETA

1 138 4OO WR=COS(THETA)

1 139 WI=SIN(THEFA)

140 WSTPR=-2.*WI*WI

141 W5TPI=2.*WR*WI

142 405 DO 57O L=NON2,LMAX,NON2T

2 143 M=L

2. 144 IF (MMAX-NON2) 420,420,410

2 145 410 W2R=WR*WR-WI*WI

2 146 W2I=2.*WR*WI

2 147 W3R=W2R*WR-W2I*WI

2 148 W3I=W2R*WI+W2I*WR

2 149 420 DO 530 I1^1,I1RNG,2

3 150 DO 530 J3=I1,NON2,NP1

4 151 HMIN=J3+IPAR*M

4 152 IF\MMAX-NON2)43O,430,440

4 153 430 J'MIN=J3

4 154 440 \ DIF=IPAR*MMAX

4 155 450 KSTEP=4*KDIF

4 156 DO 520 Kl=kMIN,NTOT,fSTE^

5 157 K2=K1 «-^ DIF

5 158 K3=^ 2-^J DIF

5 159 K4=r3+K'DIF

5 16O IF(MMAX-NON2)460,46O,4BO

5 161 460 U1R=DATA<K1)*DATA(I'2)

5 167. U2R=DATA<K3> +DAFA(K4 )

5 164 U2I=DATA(f,3+l)+DATA(J 4+1)

5 165 U7R=DATA(^ 1)-DATA(L2)

LJ7I=DATAO 1 + 1 )-DATA (f,2+1 >

i

ir(ISIGN)470,475,475

470 L-iR^DATA vL3+l) -DATA '.K4+1)
Mi crov.o f t FOF-.'I RAf J71

1C::

3'.' Marc:'-i 1 — - —.

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2

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169

170

171

172

173

174

175

176

177

178

179

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182

183

184

185

186

187

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189

190

191

192

193

194

195

196

197

198

199

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203

204

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206

207

208

209

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211

212

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214

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216

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213

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223

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475

480

490

500

510

520

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540

550

560

565

570

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U4I=DATAU 4) -DAT A (I ~)

GO TO 510

U4R=DATAO 4+ i) -DATA O 3+1)

U4 I -DA V A (1-3) -DAI AU "'•

GO TO 51O

T2R- W2R*DA FA ( \ 2 ) -W2 1 *OA V A (K2+ 1 )

T2I=W2R*-DATA<r2+l)-H'J2I*DATA(f 2)

T3R=WR*DATA ( \' 3 ) -W I * DATA ( K3+ 1 )

T3I=WR*-DATA(K3+1)+WI^DATA(( 3)

T4R=W3R*DATA<K4) -W3I*-DATA(f 4<-l)

T4I=W3R•>1•DATA(^ 4+1 ) +W3I*DATA (t 4)

U1R=DATA(K1)+T2R

U 1 1 =DATA ( K 1 + 1 ) +T2 1

ORIGINAL PAGE IS

OF POOR QUALTTY

U2I=T3I+T4I

U3R=DATA'.f 1>-T2R

U3I=DATA(L1-H)-T2I

I F ( I S I GN ) 490 , 500 , 50O

U4R=T3I-T4I

U4I=T4R-T3R

BO TO 510

U4R=T4T-T3l

U4I=T3R-T4R

DATA a 1)=U1R-HJ2R

DATA (Kl + 1 ) =U1 H-U2I

DATA(K2)=U3R+U4R

DATA ( K2+ 1 > =U3 1 +U4 1

DATA(H'3)=U1R-U2R

DATACf 3+l)=UlI-U2I

DATA(K4)=U3R-U4R

DATA ( K4+ 1 ) =U3 I -U4 I

KMIN=4* (KMIN-J3) +J3

^ DIF=t STEP

I F ( ^ D I F-NP2 ) 450 , 53O , 53O

CONTINUE

M=MMAX-M

I F ( I S I GN ) 540 , 550 , 55O

TEMPR=WR

WR=-W I

WI=-TEMPR

GO TO 56O

TEMPR=WR.

WR=WI

WI=TEMPR

I F (M-LMAX > 565 , 565 , 4 1 0

TEMPR=WR

WR= WR* WSTPR- W I * WSTP I +WR

w i - w T *WSTPR+'TEMPR-*WSTP i +w i

IPAR=3-IPAR

MMAX=MMAX*-MMAX

GO TO 360

MAIN LOOP FOR FACTORS NOT EQUAL TO TWO. APPLY THE TWIDDLE FACTOR

W-EXP<ISIGN*2*PI~SC!RT<-1)*(J2-1 >~<J 1 -J2) / (IMP2*IFP1) ) , THEN

PERFORM A FOURIER TRANSFORM OF LENGTH IFACT(IF), MAKING USE OF

CON J UGATE SYMMETR I E 3 .

135
r-=>ae: 5

"'.•-(••7-S"

\ -.:'

D Lint--- 1 7 r.icroiu-' v. t-'URVF-:HN7~ V...30 net en 1VB:

1 223 C

226 60'.'' IF (NTWO-NP2) 605 , 7OO , 70O

227 6O5 IFP1=NON2

1 223 IF=1

1 229 NPlHF-=NPl/2

1 23O 61O IFP2=IFP1/JFACT(IF)

1 231 J1RN6=NP2

1 232 IF(ICASE-3)612,611,612

1 233 611 J1RNG=(NP2+IFP1)/2

1 234 J2STP=NP2/IFACT<IF)

1 235 J1RG2=(J2STP<-IFP2) /2

1 236 612 J2MIN=1-UFP2

1 237 IF(IFP1-NP2)615,640,640

1 238 615 DO 635 J2=a2MIN,IFP1,IFP2

2 239 THETA=-TWQPI AFLOAT (J2-1)/FLOAT(NP2)

2 240 IF(ISIGN>625,620,620

2 241 620 THETA=-THETA

2 242 625 SI!MTH=SIN <THETA/2. )

2 243 WSTPR=-2.-*SIWTH*SINTH

2 244 W3TPI=SIN(THETA)

2 245 WR=WSTPR-H.

2 246 WI=WSTPI

2 247 J1MIN=J2+IFP1

2 240 DO 635 J1=J1MIN,J1RNG,IFP1

3 249 IlMAX=Jl+IlRNG-2

3 250 DO 63O I1=J1,I1MAX,2

4 251 DO 63O 13=11,NTOT,NP2

5 252 J3MAX=I3+IFP2-NP1

5 253 DO 63O J3=I3,J3MAX,NP1

254 TEMPR=DATA(J3)

6 255 DATA(J3)=DATA<J3)*WR-DATA<J3+1)*WI " -

6 256 63O DATA(J3+l)=TEMPR*WI+DATA(J3-i-n*WR

3 257 TEMPR=WR

3 258 WR=WR*WSTPR-WI*WSTPI+WR

3 259 635 WI=TEMPR*WSTPI+WI-vWSTPR+W I

1 260640 THETA=-TWOPI/FLOAT(IFACT(IF))

1 261 IF(ISIGN)650,645,645

1 262 645 THETA=-THETA

1 263 650 SINTH-SIN(THETA/2.)

1 264 WSTrR=-2.*SINTH*-SINTH

1 265 WSTPI=SIN(THETA)

1 266 KSTEP=2*N/IFACT(IF)

1 267 KRANG--^ STEP* (IFACT < IF) /2)+l

1 268 DO 69Q I1=1,I1RNG,2

2 269 DO 698 13=11 , NTOT, 1MP2

3 27O DO 690 KMIN=1,fRANG,\ STEP

4 271 J1MAX=I3+J1RNG-IFP1

4 272 DO 680 J1=13,J1MAX,IFP1

5 273 J3MAX=J1-HFP2-NP1

5 274 DO 68O J3=J1,J3MAX,NP1

6 275 J2MAX^J3t-lFPl-IFP2

6 27o K=KMIN+<J3-Jl+(Jl-I3>/IFACT'I'r) i/NP1HF

6 277 IF(hMIN-l)655,655,665

,-D 270 655 SUMR=0.

tt 279 SUM1=0.

28O DO 660 J2=J3, J2I-1AX, IFP2
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t-.C""! a ) = SUt R

I _ "J- O '-!)=£ MM I

L-- TO :SO

I CUNJ=« +2* IN-KMIN+1 )

J2=J2NAX

£L'MR=DATA(J2)

SUMI=DATA<J2+1>

D-..DSR-0.

OLDS 1=0.

J2=J2-IFP2

TEr1PR=SUMR

TEMPI=S(JMI

£UMR=TWOWR*-SUMR-OLDSR+DATA(J2>

£UMI^TWOWR*SUMI-QLDSI^DATA(J2+1)

OLDSR=TEMPR

OLDSI=TEMPI

J2=--J2-IFP2

IF(J2-J3)675,675,670

TEMPR=WR*SUMR-OLDSR+DATA(J2)

TEMPI=WI*SUMI

WDRl (\ )=TEMPR-7O1PI

U.'QRMhCQNJ)=.TEMPR+TEMFI

TEMPR=WR*SUMI-OLDSI+DATA(J2+1)

TEMPI=WI*EUMR

WOR^ <K+1)=TEMPR+TEMPI

WORf (KCONJ+1)=TEMPR-TEMPI

CONTINUE

IF (KM IN- 1)685, 685,686

WR=WSTPR+1. " -

WI=WSTPI

GO TO 690

TEMPR-=WR

WR=WR*WSTPR-WI*WSTPI+WR

WI=TEMPR*WSTPI+WI*WSTPR+WI

TWOWR=WR+WR

IF(ICASE-3)692,691,692

IF(IFP1-NP2)695,692,692

^,= l •

I2MAX=I3+NP2-NP1

DO 693 12=13 , I2MAX ,NP1

DATA(I2)=WORf (K)

DATA(I2+l)=WORr (\ +1)

k=K+2

GO TO 698

COMPLETE A REAL TRANSFORM IN THE 1ST DIMENSION, N ODD

JJOATE SYMMETRIES AT EACH STAGE.

J7MAX=I3-HFP2-NP1

DO 697 J-;=I3,J3MAX,NP1

J2MAX=J3-HNP2-J2STP

DO 697 J2=J3 , J2MAX , J2STP

jlMAX=J2+JiRG2-IFP2

: i CNJ= J3+J2MAX +-J2ST P-J2

BY CON-
It.:

P D

5

^^Hr6

1

 6

1 ^

1

 6

1 ^

1 6

1 3

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337

339

339

34O

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

1

696

697

698

C

C

C

C

700

70 1

702

703

710

720

725

730

731

735

740

r-Iicroso-ft FOKTRAN77 V1. 3O March 5 rGz

CO c=--'7 J1=JJ. J1NAX, IFP2

1

 = H- : i --1 3

L'-TA Jl )=UORi O >

ORIGINAL PAGE IS

OF POOR QUALITY

IF ^Ji-J2)697,o97,696

DATA(JlCNJ)=WORf <D

DATA'.JlCNJ+l)=-WORf CJ+1 )

J1CNJ-=J1CNJ-IFP2

COtJTINUE

IF=IF+1

IFP1=IFP2

IF (IF P1-NP1)700,7OO,610

COMPLETE A REAL TRANSFORM IN THE 1ST DIMENSION, N EVEN, BY CONJUGATE SYMMETRIES.

EO TO ( 9OO , ec-0 , 9OO , 70 1 )

NHALF=N

N=N+N

THETA=-TWQPI/FLOAT (N)

IF ( IS I GN> 703, 702, 702

THETA--THE7A

SINTH=SIN(THETA/2. )

WSTPR=-2.*-SINTH*SINTH

WSTPI=SIN(THETA)

WR=WSTPR*1.

WI=W5TPI

I CASE

JMIN=2*NHALF-1

GO TO 725

J=JM.IN

DO 720 I = IMIIM,NTOT,NP 2

S'JMR= (DATA (I )-*-DATA<J) ) /2.

SUMI=(DATA(H-1)+DATA(J*1) ) /2.

DIFR=(DATA(I)-DATA(J) ) /2.

DI FI= (DATA U-t-1) -DATA <J-»-l) > /2.

TEMPR=WR*SUM I +W I *D I FR

TEMP I =W I *SUM I -WR*D I FR

DATA ( I ) =SUMR+TEMPR

DATA ( 1+ 1 ) =D I F I +TEMP I

DATA ( J ) =SUMR-TEMPR

DATA ( J+l ) =-DIFI+TEMPI

J=J+NP2

IMIN=IMINH-2

JMIN=JMIN-2

TEMPR-WR

WR= WR » WSTPR- W I * WST P 1 4 WR

W I =TEMPR » WST P I *W I - l-JSTF P-f-W I

I F ( I M I N- JM I N ) 7 1 O , 730 . 74 0

IF(1SIGN>731 ,74O, 7-10

DO 735 I=IMIN,NTOT,NP2

DATA < 1 + 1 ) =-DH r A < I «- 1 )

NP2=NP2+NP2

NTOT=NTOT-"NTQT

J=NTOT+1

IMAX=-NrOT/2*l
Faqt?

0 L

1

1

^

1

1

1

1

1

1

1

1

1

1

1

1

1

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1

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1

1

1

1

1

1

1

1

1

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2

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3

3

3

3

4

4

4

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4

4

4

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3

c/3

3^4

3^5

3

c-6

~.= '7

398

399

40O

40 1

402

^03

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

42O

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

-147

1

745

730

755

76O

765

770

775

780

C

C

C

C

8-1)0

SOS

81O

820

830

84 O

850

860

C

C

C

9OO

91 0

92' '

~ I'!1, c T?SCD- t FGMRHNV

 ; '.-". .3'.- lv

I f'l N= I I1AX-2*NHALF

I -IMIN

GG TO 755

D^TA(J)=DATA( I)

E/-TA ( JH- 1 ) =-DATA ( I + i )

1=1+2

J=J-2

I F ( I - 1 MA X ) 750 , 76O , 76O

DATA (J ) =DATA ( IMIN) -DATA ( IMIN+1 )

DATA(J+1)=O.

IF ( I- J) 770, 780, 780

DATA(J)=DATA<I)

DATA(J+1)=DATA(I+1)

1=1-2

J = J-2

IF (I -IMIN) 775, 775, 765

DATA ( J ) =DATA (IMIN) +DAT A ( I M I N+ 1 )

DATA<J+1)=0.

I

f-1AX = IMIN

GO TO 745

DATA ( 1 ) =DATA ( 1 ) +DATA (2 )

D^TA (2) -0.

GC TO 90O

COMPLETE A REAL TRANSFORM FOR THE 2ND OR 3RD DIMENSION BY

CONJUGATE SYMMETRIES.

I F ( I 1 RNG-NP 1 ) 805 , 900 , 900

CO S6O I3=1,NTOT,NP2

1 2MAX= 1 3+NP2-NP 1

DO 860 12=13, I2MAX,NP1

IMIN=I2-H1RNG

IMAX=I2+NPl-2

JMAX=2*I3+NP1-IMIN

IF(I2-I3)820,B20,810

JMAX=JMAX+NP2

IF ( ID I M-2) 850 ,850 ,830

J=JMAX+NPO

DO 84O I-IMIN,IMAX,2

DATA(I)=DATA(J)

DATA ( I + 1 ) =-DATA ( J + 1 )

J=J-2

J=JMAX

DO 86O I=IMIN, IMAX,NPO

DATA(1)=DATA(J)

DATA(I+1)=-DATA(J+1>

J=J-NPO

END OF LOOP ON EACH DIMENSION

N-'O=NP1

NC-1-NP2

N~REV=N

RETURN

E-JD

19cL
t Line*- 1

Type

Microsoft FOKTPi,N77

Offset P Class

c =

DATA

D:FI

DIFR

FLOAT

I

11

UMAX

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12

I2MAX

13

I CASE

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K

Kl

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I- CONJ

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i_

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INTEGER*-4

INTEGER>4

INTEGER*4

INTEGER*-4

INTEGER*4

INTEGER*-4

INTEGERS

.-INTEGER- 4

INTEGER* 4

INTEGER*- 4

INTEGER*4

INTEGER* 4

INTEGER--^

INTEGER+-4

INTEGER-4

INTEGER*4

1NTEGER-4

!NTEBER*-4

INTEGER* 4

INTEGER*4

INTEGER*4

INTEGER+-4

INTEGER*-4

INTEGER*4

INrEGER-»4

INTEGERf-4

INTEGER*4

INTEGER-^4

INTEGER*4

INTEGER*4

INTEGER*4

INTEGER*4

INTEGER-^-4

INTEGER*4

INTEGER* 4

INTEGER*4

INTEGER* 4

INTEGEP-4

INTEGER* 4

INTEGER* 4

INTEGER* 4

INTEGER- 4

INTEGER* 4

INTEGER* 4

INTEGER- 4

INTEGER- 4

INTEGEP-4

0

704

7 GO

208

252

248

220

236

640

260

204

152

188

18-a

16

16

472

480

716

684

288

192

196

12

212

520

66Q

580

516

492

484

500

60O

496

488

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544

736

688

6O4

304

316

408

412

624

392

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396

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INTRINSIC

INTRINSIC

j/O-D
Paue 1 _>

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1-1

MAXO

IJHA/.

"

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NN

NON2

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SI NTH

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W3I

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WORK

WR

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3 7

INTEGER-M

INTEGER* 4

INTEGER- 4

INTEGERS

INTEGER*4

INTEGERS

INTEGERS

INTEGER*4

INTEGER*4

INTEGERS

INTEGER*4

INTEGERS

INTEGER* 4

INTEGER*4

INTEGER*4

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REAL

REAL

REALREAL

REAL

REAL

REAL

REAL

REAL

REAL

REAL

REAL

REAL

REAL

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REAL

REAL

REAL

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176

320

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660

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200

284

224

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456

468

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280

276

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360

372

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340

cf a-?•''- ^'.".nli .Ui? / V~.r O March

1NTRIM5 IC

ORIGINAL PAGE §§

OF POOR QUALfTY

INTRINSIC

Naine Type Sine C\ as5

|4\
Mi zroijof -_ f:ORl"i"'HhiV7 Vj.:;O March

FOUR!

Pu-s One.' Ho Errors Detected

447 Source Line1-
r

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],>(.---•

j •:•: 5 ' •

H-I i 7 MJ _f-o^-<. '. ' •!". t-'-iiJ/"' V..3" (ierch 1-t~';

a C L'f l'Gr."h READS '.O^F.N) DATA BY \ tLYBOAFD DEF IN i'' ION

1 DIMENSION I AN V(32) ,MULT (496/

C-:->.RACTER*64 INF IL , OUTFIL , F NAME

J WRITE(-,' (3X,AN." ')'INPUT FtLE W i-E I A:>!T •. N / . DAI ^ '

5 nEAD-'* , ' (A) ' ) INFIL

6 OPEN (12 , FI LE= INFIL , S TATUS== ' OLD ' )

7 READ(12,10)FNAME,NANT

B 1-4 FORMAT (A 10 / , 15)

9 DO 15 I = 1, NANT

10 READ(12,12)1ANT(I)

ORIGSNAL PAGE 0s

13 NBASE = NANT+ (NANT - 1) / 2 @C POOR QUAJLfTY

14 DO 2O 1=1 , NBASE

1 15 M'JLT(l) = 0

1 li: 2O CONTINUE

17 I MAX = NANT - 1

13 DO 3O 1 = 1, I MAX

1 19 J1-1 IN = I + 1 —

1 2O DO 25 J == JMIN, NANT

2 21 IDASE = ABS(IANTU) -- ]Arir<.J> '

2 22 N-JLT(IPASE) = MULT (I BASE) <- 1

2 2".' 25 CONTINUE

1 24 30 CONTINUE

25 IMAX = NBASE

26 DO 32 I = IMAX, 1, -1

1 27 IF(MULT(I) .GT. 0) THEN

1 28 GO TO 33

1 2^ END IF

1 30 IF(MULT(I> .ED. 0) THEN

1 31 NBASE = NBASE - 1

1 32 END IF

1 33 32 CONTINUE

34 33 WRITE (*-,' <3X,A\> ') OUTPUT FILE NAME MULT (N). DAT ^'

35 READ(*,'(A)')OUTFIL

36 OPENd4,FILE=OUTFIL,5TATUS='NEW' )

37 WRLTE(14,35)FNAME,NBASE

38 35 FORMAT (IX, 'DATA TAt EN FROM ' , A10, ' POGS1FLE DASFILINE COMBOS IS '15;

39 WRIT Ed 4, 36)

40 36 FORMAT (IX , 'BASELINE' ,5X, 'MULTIPLICITY')

41 WRITE(14,37)O,NANT

42 37 FORMAT(4X,13,10X,15)

43 DO 40 I •= 1 , NBASE

1 44 WRITE(14,38)I,MULTd>

1 45 38 FORMAT(4X,13,1 OX,15)

1 46 4O CONTINUE

4 7 STOP

48 END

Name Type 0-f-fset P Class

ABS INTRINSIC

F NAME

I

I ANT

IB^SE"

CHAR*64

INTEGER* 4

INTrGil"- «4

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23-2

2260

2286

23 IB

49

Name Type

MAIN

Size Class

PROGRAM

Pc.se One No Errors Detected

A~ Source Lines

r
TYPE MASTER.DAT

m-ATION F.L-4

MULT.DAT

WGT.DAT

OUTPUT1.PRN

DEMONSTRATION RUN 2

32

90.

60.

1.4

10.

250.

MULT.DAT

WGT.DAT

OUTPUT2.PRN

DEMONSTRATION RUN 3

32

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WGT.DAT

OUTPUT3.PRN

DEMONSTRATION RUN 4

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WGT.DAT

OUTPUT4.PRN

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OUTPUTS.PRN

DEMONSTRATION RUN 6

32

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WGT.DAT

OUTPUT6.PRN
T i F E MUL T . DI-. T

VE'l-T

— —%

1

1

1

1

1

1

1

* ORI65N&L PAGE G§

| ©F. POOR QUALITY

i

i

i

i

i

i

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i

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i

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i

i

i

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144,

/
1 V

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1.

1.

1. 1. 1.i. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. t. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. i.

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ORIGINAL PAQt 15

OF POOR QUALITY
UU'l OUT f-LIT. r-

,"_~r. i.'H.r

•r.j

"WfjT.L -

"TEST

ORIGINAL PAGE £

Of POOR QUAUtY

-.98481E+OO

-.92127E+00

-.85774E+00

-.7942CE+OO

-.73O66E+00

-.66713E+OO

-.60359E-+00

-.54OO6E+00

-.47652E+OO

-.41298E+00

-.34945E+00

-.2B591E+OO

-.22238E+00

-.158B4E+00

-.95304E-01

-.31768E-01

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.28591E+00

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. 41298EH-00

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11993E+02

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17222E+01

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15966E+00

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18109E+02

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61980E+03
VII. SIMULATION RESULTS

In this section we present our simulation results using a simple but

realistic sensor as an example. The sensor parameters are listed in table

VII-1. A scene width of 90 and a nominal temperature of 250K are used.

The sensor resolution is approximately the scene sampling interval

, At an altitude of 300 km this corresponds tc

with an antenna array dimension given approximately by

(90°/32). At an altitude of 300 km this corresponds to 15 Km resolution

. . > ,

Jj — — -\ L

The value .21 m is the wavelength. There are no grating lobes as the value

Figure VII-1 shows the constant test scene weighted by the antenna

power and Oacobian factors as a function of scene coordinate (sineof across

track angle). Figures VII-2 to 7 show the weighted errors in the scene

estimates. By this we mean the error before the antenna and Jacobian factor

are removed. Figure 2 is for zero bandwidth, in this case the Fourier

processing is perfect and only random round-off error is present. Figures VII

- 3 to 7 have bandwidths of 10, 20, 30, 40, and 50 MHz respectively. As the

bandwidth increases the error amplitude envelope increases.

/
TABLE VII - 1

Sensor Parameters

Name Parameter Value

N Number of baselines 32

FOV Field-of-view 60°

FO Center frequency 1.4 GHz

BW Bandwidth 0, 10, 20, 30,

40, 50 MHz

Uniform multiplicities

Uniform processing weights

150
The most Important information is contained in figures VII - 8 to 12

which show the radiometric (or unweighted) errors. These errors are small but

nonzero near nadir (scene coordinate 0). Off-nadir they become large,

especially near the pattern nulls. In general, a region around nadir exists

where radiometric errors are uniformly tolerable. Defining this region to

have radiometric errors less than say l.OK specifies the useful field-of-view

of this sensor. In figure VII - 13 we have plotted useful field-of-view

versus bandwidth by interpolating the scene coordinate for which the

radiometric error exceeds l.OK. At zero bandwidth the entire 60°

field-of-view is usable, but this diminishes as the bandwidth increases.

Finally, at 50 MHz there is no usable field-of-view since nadir radiometric

errors exceed l.OK. The bandwidth of 30 MHz (just greater than that

allocated for passive use) has a useful field-of-view of about 30° by this

definition. Obviously there is a tradeoff here between radiometric errors

induced by this effect and the receiver radiometric sensitivity, since the

former increases with bandwidth and the latter decreases.
TEST SCENE

N =- 32, «"O''' = 5O, SV»C'TH=9O

*-!.

2

*WJ i*

2

s

UJ

I

C

U.'

^

.c. o •_* —

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220 -

200 -

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14O -

120 -

•

/ /

////

/

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Figure VII-1- Test Scene
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SCENE ESTIMATE ERRO R

FO = 1.4 GHz. BW = O

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Figure VII-2. Scene Estimate Error, BW = 0.
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8

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SCEXE ES7:NLA E ERRO R

FC=1.-i THz, =A = 10

ORIGINAL PAGf IS

OF POOR QUALITY

-O.2 O O.2

SIN (THETA)

O.6 O.B

Figure VII-3. Scene Estimate Error, BW = 10 MHz.

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SCENE ESTIMATE ERRO R

,- 1 ^ OKI ?..=:..•

en

UJ

Ul

c

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-O.B -0.6 -O..A -O.2 0-2 O.4 0.6 O.B

Figure VII-4. Scene Estimate Error, BW = 20 MHz.
SCENE ESTIMATE ERROR

Vf

z

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fe'

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-O.B O.B

Figure VI1-5. Scene Estimate Error, BW = 30 MHz.
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k.

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C

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SCENE ESTIMATE ERROR

ORIGINAL PAGE IS

OF POOR QUAl/Tt

-O.B -O.B -O.4- O.4 O.B O.8

SIN (THETA)

Figure VII-6. Scene Estimate Error, BW = 40 MHz.
z

UJ

ICi

SCENE ESTIMATE ERROR

4 GHz. BW=5O

-O.6 -O.B -0.4- -O.2 0 0.2

SIN (THETA)

0.4 O.B 0.8

Figure VII-7. Scene Estimate Error, BW = 50 MHz.
en

z

Ul

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UJ

o

A -

3 -

2 -

1 -

O

1 -

2 -

3 -

-5

SCENE ESTIMATE

I

I I §

-O.B -O.B -0.4 -O.2 O O.2

SIN (TMETA)

O.4 O.B O.B

Figure VII-8. Radiometric Error, BW = 10 MHz.

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5 -TORIGINAL PAGE

OF POOR f*"*

. EN't icr.

VI

z

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1 -

O

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-2 -

-3 -

-A -

-S

-O.B -O.B -O.4- -O.2 O

SIN

O.2 O.B O.B

Figure VII-9. Radiometric Error, BW = 20 MHz.

IP
SCENE ESTIMAT E

PERCENT/CE ERRC.R

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/\

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1 O.2 0

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1

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SIN (THETA)

Figure VII-10. Radiometric Error, BW = 30 MHz.
in

z

8in

o

UJ

o

LU

SCENE ESTIMATir

PERCENTAGE ERROR

-o.e -O.2 O O.2

SIN (THET/0

POOR

PAGC IS

0.4 0.6 O.B

Figure VII-11. Radiometric Error, BW = 40 MHz.
VI

z

V)

Ul

O

SCElsE ESTIMATE

PERCENTAGE ERROR

-O.B -O.B -O.4. -O.2 O O.2

SIN (THETA)

0.4 O.B O.B

Figure VII-12. Radiometric Error, BW = 50 MHz.
'ul Fielci-c-I'-Viev;

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L PAGE IS

OF POOR QUALTTY

tu

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50 -j

20 -

10 -}

20

BANDWIDTH C

Figure VI1-13. Useful Fleld-of-View.
V. CONCLUSIONS AND AREAS FOR FURTHER STUDY

Aperture synthesis may be an attractive approach to perform the soil

moisture measurement mission. It can have both a resolution and a sensitivity

advantage over real aperture systems. Further study is needed especially in

the areas of:

1) Technologies

a) antenna design

b) signal distribution

c) digital correlator design

2) Calibration

3) Antenna and array structural tolerances

4) Trade-offs between pure and hybrid aperture synthesis techniques

5) Trade-offs between real and synthetic aperture systems (i.e.,

when does the cost of electronics exceed the savings from

antenna area).

6) Failure modes and reconfigurability

7) Adapting of the spacecraft concepts to aircraft prototypes.