DEVELOPMENT OF

NEAR-FIELD TEST PROCEDURES FOR

COMMUNICATION SATELLITE ANTENNAS

PHASE 1, PART 2

Allen C. Newell

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

August 1988

#87-3081

1988

nulating America's Progress 1913-1988
NATIONAL INSTITUTE OF STANDARDS &

TECHNOLOGY

Research Information Center

Gaithersburg, MD 20399
NBSIR 87-3081

DEVELOPMENT OF

NEAR-FIELD TEST PROCEDURES FOR

COMMUNICATION SATELLITE ANTENNAS

PHASE 1, PART 2

Allen C. Newell

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303-3328

August 1988

U.S. DEPARTMENT OF COMMERCE, C. William Verity. Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

CONTENTS

Page

1. Introduction 1

2. Development of Scan Limits for Planar Near-Field Measurements

on Spacecraft Antennas in an "Antenna Farm" Environment

3. Development of Sampling Criteria for Planar Near-Field

Measurements on Spacecraft Antennas in an "Antenna Farm"

Environment 13

4. Development of Diagnostic and Design Assist Methods Which

Make Use of Untransformed Near-Field Data

4.1 Specification of a Standard Near-Field Pattern

4.2 Comparison of Measured and Standard Data

4.2.1 Beam Alignment 23

4.2.2 Feed Alignment

4.2.3 Reflector Surface Errors 24

4.3 Diagnostic Methods Involving Some Data Processing 24

5. Development of Beam Alignment Techniques 30

5.1 Introduction 30

5.2 Alignment Adjustments

5.2.1 Theodolite Autocollimator

5.2.2 Optical Micrometer

5.2.3 Laser Interferometer

5.2.4 Electronic Level

5.2.5 Optical Square

5.3 Definition of the Measurement Coordinate System, C m 5.4 Defining Antenna Coordinates 47

5.5 Aligning the Antenna Under Test (AUT) to the

Measurement Coordinates 47

5.5.1

Far-Field Angle Measurement

5.6 Measurement Errors Affecting Boresight Errors 51

6. Development of Near-Field Swept-Frequency Measurement

Techniques

6.1 Introduction V

6.2 Analysis

7. Specification of Hardware Requirements for Planar Near-Field

Testing of Satellite Antenna Systems 54

7.1 Introduction 54

7.2 Antenna System Measurement and Accuracy Requirements

7.3 Specification for Antenna Measurement System

8. Summary

9. References

DEVELOPMENT OF NEAR-FIELD TEST PROCEDURES

FOR COMMUNICATION SATELLITE ANTENNAS

PHASE I, PART 2

Allen C. Newell

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

The purpose of this program is to define and further develop the

capabilities of near-field antenna test techniques, specifically

for the requirements associated with the development and

verification testing of reconf i gurabl e, multibeam, frequency

reuse, commercial satellite antennas. This report, Phase I,

Part 2, focuses on the planar near-field measurement method and covers the determination of sampling criteria and scan limits,

development of diagnostic and design assist methods, development

of beam alignment techniques, development of swept-f requency

equivalent tests, and specification of hardware requirements for

the measurement system. Phase I, Part 1, a previous report, gave

a general survey, definition, and description of near-field and

compact range measurement methods as they apply to satellite

antenna systems testing. Each of these methods was evaluated to

determine how well they meet the measurement requirements.

Included for each technique was a summary of the measurement

method, discussions on probe correction and data processing,

measurement hardware considerati ons , a results available section,

and measurement accuracy and range certification considerations.

The basis for the choice of the best measurement technique was established with the planar near-field measurement method

receiving the best score for the directive antennas considered.

It is for this reason that the planar near-field method is the

focus of this report.

Key words: antenna alignment; antenna boresight measurements;

antenna diagnostics; antenna measurements; antennas; near-field

measurements; near-field testing; planar near-field scanning;

satellite antennas; swept-f requency measurements

1. Introduction

The purpose of this program is to define and further develop the capa' ' -

ities of near-field antenna test techniques, specifically for the req u i r . . associated with the development and verification testing of reconf i gurabl , multibeam, frequency reuse, commercial satellite antennas. The program includes two phases. Phase I was a study program that included the follows;

tasks as outlined in the statement of work:

1
Task I/A & I/I General survey, definition, and description of near-field and

compact range configurations including a description of their

comparative advantages. These tasks were discussed in two

parts:

1 . A clear and concise description of the antenna and satellite

systems to be measured, and the associated measurement problems.

2. A description of the three near-field measurement techniques being

studied along with the compact range approach. Each of these was evaluated to determine how well they met the requirements defined

in Part 1 above.

Task I/H Selection of the optimum measurement technique from the above

study.

The results of the above tasks were reported in Phase I, Part 1 of the

final report, March 1985 [1], Since the planar near-field method was chosen

as the optimum technique, the remainder of the study will focus on that

technique only. Items to be covered in the remainder of Phase I are:

Task I/B Determination of sampling criteria and scan limits.

Task I/C Development of diagnostic and design assist methods.

Task I/D Development of beam alignment techniques.

Task I/E Development of swept-f requency equivalent tests.

Task I/F Specification of hardware requirements for the measurement system.

Task I/G Outline available computer programs and make them available.

Task I/J Develop the test plan for Phase II.

Tasks I/B, I/C, I/D, I/E and I/F are considered in this report, thereby

completing the final report for Phase I (Tasks I/G and I/J have been reported

separately)

.

Phase II is a measurement program that will demonstrate the results of

Phase I.

2
2. Development of Scan Limits for Planar Near-Field Measurements on Spacecraft Antennas in an "Antenna Farm" Environment

The consideration of scan limits in planar near-field measurements is

related to the calculation of the angular spectrum of the measured near-field

data.

-i yd oo oo — i K • P D '(K) = 4"2 ~f'

'at f f B o(f) e dx dy (1)

— 00 —00

The notation employed here is 'the same as in Part I [1] [see appendix A,

eq ( A54 ) ] , where Bq (_P) represents the relative near-field data, and D'(_K) its

angular spectrum. The limits of integration in eq (1) are over an infinite

measurement plane. Whenever the plane is truncated to a realizable measurement system, there is a loss of information; therefore errors arise in the

calculation of D'(_K). A number of studies related to these errors involving

theoretical analysis, computer simulation, and measurements have been carried

out. The result is that the effect of scan area truncation is well understood

and a variety of techniques are available to reliably predict its effect. In the following section the results of the previous studies will be reviewed.

We will then consider to what extent they need to be modified for the

particular antenna types under consideration in this study.

The basic result of all the studies on truncation errors has been that

there are two distinct effects. First, the calculated spectrum, D'(K_) is

valid only within a limited angular region of the forward hemisphere; and

second, there are some errors even within this "angular region of validity."

The formulation of the first effect was derived originally from measurements

on a limited number of antennas [2] and was later derived analytically [3\

Subsequent to the early measurements, the result has been found to hold for a wide variety of antennas, some of which are noted in table 1. The basic

result is illustrated in figure 1 and shows that the region of validity can

•

determined from a very simple geometric relation.

3
Table 1. Sample of antennas measured on the NBS near-field facility.

Antenna type

Freq.

(GHz)

Major dimension

in wavelength Gain (dB)

Horn lens 48.0 90 47.0

Conical horn (JPL) 8.0 6 22.08

Cassegrain reflector 60.0 91 46.5

Lens array (constrained lens) 9.2 23 34.0

Phased array (volphase) 8.4 17 21.5

Phased array 7.5 15 30.5

Dipole array 1.4 5 20.3

Fan beam radar (linear and

circular polarization) 9.5 58 30.0

Ku-band reflector 14.5 60 42.0

Ku-band array (pencil and fan beam) 17.0 50 40.0

Shaped beam, C.P. (array

fed reflector) 4.0 20 27.5

Microstrip array 1.5 27 30.0

Parabolic reflector 1.5-1.

8

15-183 26-47

Compact range reflector 18 & 55 285 & 870 -60.0

Slotted waveguide array 3.0 60 30.0

Lx

4
The predicted region of validity has been confirmed for antennas very

similar to the INTELSAT VI types. From near-field measurements on the engineering model of the INTELSAT IV A antenna, computer tests were performed to

gradually reduce the size of the scan area and note the change in the resulting far-field pattern. As predicted by the equation in figure 1, the pattern

results within the angle 0 S were virtually identical to results for larger

scan areas, but as the scan area decreased, the pattern at the outer limits

would systematically change.

The impact of this first effect on the satellite antenna testing was discussed in some detail in Part 1 [1] of the final report (see section 3.1.4).

If the complete antenna farm of the Intelsat VI satellite is included, scan areas of up to 10.4 x 6.6 m may be required. While this is technically

feasible, it may be more practical to limit the testing to each reflector and

its feed. This requires a much smaller scanner and will still give very good

results for each separate antenna. There are also alternate approaches that

allow use of moderate size scanners for measurements over quite large scan

areas. One technique that has been used successfully in a number of applications is represented schematically in figure 2. The antenna is mounted on a set of rails that run parallel to the scan plane and moved to a series of

positions in front of the scanner. In each of these positions the antenna is

precisely aligned and the scanner obtains a set of near-field data for each

position. The data sets are then combined as illustrated in figure 3 to provide an effective scan area a number of times larger than the scanner. This

technique could be used to study scattering effects over large areas, and then

single sets over one scan area could be used in final testing of each antenna

system.

This technique has been used to measure large arrays [4], and in another

measurement facility [5] the antenna is always moved in one axis while the

probe is moved in the orthogonal direction. The technique has therefore bee-'

tested and shown effective and reliable.

The second effect of scan area truncation is that it produces some errors

in the pattern even within the region of validity. Equations to estimate tn,> magnitude of these errors were first derived by Yaghjian [3]. He snow-’ • r this error can be estimated from a knowledge of the measured data on th>* boundary of the scan area even though the error results from neglecting ,<.’1

5
PROBE

SCAN

(M)

3.84

0

« SEGMENT 1 SEGMENT 2 > 4 SEGMENT 3 J

f ^ L - f

S 3C AN OVERLAP REQION

I

_J< ULSA

STOP

0

START PROBE STEP DISTANCE (M)

10.44

Figure 2. Schematic for probing of large antennas by segmented scanning.

. KJ

- 5.50 - 4.40 - 3 . SO - 2.20 - I . 10 -.00 1.10 2.20 3.30 «.40 5.50 PROBE X-POSITION IN METERS

Figure 3. Composite data from three segments.

6
the data on the infinite plane outside the scan area. If we denote the plane

polar coordinates of the boundary as (p',<t> ), the data within and on the boundary, respectively, as B(_P_) and B(p* ,<t> ), and the spherical coordinates of the

far-field directions by (9,<j>), then the fractional error in that direction is

UD(e,*)

>{9,irr <

f 2*

X

I

- 0 B(p ' ,<|> ) e -ikp'sine cos(<j>-tj> ) P

' deb

2tt6 6 x y

-iK*P

T B(P) e COSy

max

( 2 )

In eq (2), y max

is the maximum acute angle between the plane of the scan area

and any line connecting the edges of the antenna aperture and the scan area,

and

K = k sine cos<j> e

x + k sine sm<j> e . -y

(3)

Equation (2) can be easily evaluated after complete measurements have been

completed and B(P‘,<j>

p

) is known. If preliminary estimates of the truncation

error are desired, another relation is available [3] requiring less information, but generally predicting much larger upper bound errors. This is

|aD(K)

|

~iwr * aXL B ( p

1 ,rj> ) max max

VK ’ 'p' ,

2 A cos y

^ —

max

(4

where A = area of antenna aperture

Lmax = maximum width of scan area

a = a taper factor (see discussion by Yaghjian in reference)

a * 1 - 5

g(_K) =

| D(K_o )/D(_K)

| = ratio of peak pattern amplitude at K 0 to the

ampl i tude at K_.

The character of the truncation error can be seen clearly from tne

results of a computer simulation using the actual near-field data.

’

f

‘ *

program, the FFT is not used to evaluate the integral in eq (1); ratner a direct summation is used so that the path of integration can be chosen • - .i special way. First a single direction in the far-field corresponding

to K = K

0 is chosen. For instance, if the on-axis direction along

is desired, K = 0 is used. Next, the integral of eq >1) is evaluated f r

7
value of _K, and the path of integration starts at the center of the measurement area and spirals out along the boundaries of the gradually increasing

rectangular areas shown in figure 4. The result of this evaluation for a sample antenna and for K_ =

0_ correspondi ng to the peak of the main beam is

shown in figure 5. When the integration area is less than the projected area

of the antenna, the results may vary over a wide range. As the size of the

integration rectangle approaches the value where e $

of figure 1 is equal to

the direction to the sidelobe under consideration, the integral begins to con- verge to a relatively constant value. There are, however, some oscillations in

the computed value of D(_K) as the area is increased, and these oscillations

represent the effect of the truncation error. For comparison, the error

bounds as predicted by eqs (2) and (4) are also shown on figure 5, showing

that they do indeed give realistic upper bound estimates of the effect of

truncati on.

Another way of estimating the effect of truncation involves the use of

eq (2) and the actual measured data to calculate an effective error spectrum

resulting from the finite scan area. This error spectrum is obtained by calculating the Fourier transform of the measured data with all measured amplitudes not on the boundary set to zero. This spectrum is basically the numerator of eq (2) and represents an upper bound estimate of the error spectrum

produced by truncation.

An example of this test is shown in figures 6 through 8. Figure 6 is a perspective plot of the measured near-field amplitude for a sample antenna,

and figure 7 the far-field spectrum resulting from the combined amplitude and

phase. Figure 8 is then the spectrum for the s‘ame far-field directions when

only the boundary points are used, indicating that for the scan area utilized

truncation errors are negligible. Similar results can be obtained for any

portion of the far-field.

One other approach is also useful for estimating the effect of truncation, and is often used in the initial phases of a measurement to determine

the required size of the scan plane. This is the use of one-dimensional,

centerline measurements data. Typically, these measurements are near or along

the lines x = 0 and y

= 0, or along regions of highest amplitude. Computer

programs have been developed to compute the Fourier transforms of the one- dimensional data for the complete data sets and for partial data sets with

8
OPERATIONAL SCHEMATIC OF AREA TRUNCATION PROGRAM

Figure 4. Rectangular spiral path of integration used in truncation s'

9
Gain

(dB)

Figure 5. Results of truncation simulation study for Intelsat IV A antenna.

10
Relative

Power

in

dB

0.0

- 60.0

Figure 6. Near-field amplitude on complete measurement ,'i .

11
RELATIVE

POWER

IN

DB

RELATIVE

POWER

IN

DB

NW PORT, 4,195 GHZ AZ CUT

AZIMUTHAL angle in degrees

Figure 7. Far-field spectrum in principal plane.

-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0 7

SPECTRAL RELATIVE WAVENUMBER Kx/k

Figure 8. Error spectrum due to area truncation.

12
varying amounts of edge data deleted. These one-dimensional transforms are an approximation to the actual far field, and the change resulting from edge

deletion is generally indicative of the change that will result from truncation in two dimensional scans. It is an approximate technique, but one that

is useful in the initial set up of a measurement.

In summary, then, there are a number of techniques available to predict

or estimate the error due to scan area truncation. In a sense they are similar to the techniques for estimating the effect of other sources of error.

That is, as the information about the error increases, the error bound of the

effect on the far-field becomes smaller. Listed in order of increasing information, and generally decreasing error bounds, they are:

A. Given the geometry of the measurement plane and antenna, the region of

validity is determined.

B. With the maximum amplitude at the edge of the scan area and eq (4) a conservative upper bound error on far-field results is determined.

C. Using centerline data and computer simulation more realistic estimates

of error are possible.

D. When the complete two-dimensional data are obtained, eq ( 2 ) can be

used for more realistic estimates of upper bound errors.

E. By using the complete data and the previously described computer program where integration is performed from the center to the outside,

the actual level of truncation error can be determined for any direction in the far field.

3. Development of Sampling Criteria for Planar Near-Field Measurements

Spacecraft Antennas in an "Antenna Farm" Environment

In the actual near-field measurements, it is not practical to obtain : - - tinuous data as a function of the position vector _P_; instead, data are obtained at equally spaced points of a rectangular lattice

P-r,sr 5 e + s x-x

5 e . y-y

13
The integral in eq (1) is also evaluated by a summation, and this combination

of incremental data and summation has the potential for introducing an error,

termed an aliasing error, in D'(_K). The magnitude and character of the error depends on the data point spacings 6 X

, 6 y, and the spectral bandwidth of the

measured data. In principle, if the spacings are made small enough the aliasing error can be reduced to the noise level; but if they are too small, both

the measurements and calculations become inefficient. We desire techniques to

predict the optimum data point spacings for a given application to achieve a given level of accuracy and methods to estimate the aliasing error. The

details of these techniques will now be described.

We denote the actual measured data as B

e

(_P) and the true spectrum of

these measurements as F(K_). The term "true spectrum" as used here means that

F(_K) is the Fourier transform of Be

(_P_) and there are no aliasing errors in

F(_K). The measured data include some errors due to such effects as scattering, nonlinearity, and noise, and these errors will have an influence on

F(_K). We are therefore not excluding measurement errors and their effect on

F(K_) at this point, only aliasing errors in the determination of the Fourier

transform. In principle, this is accomplished by taking data at very close

spacings, and conceptually F(_K) may be considered to have been calculated from

data with 6 Y and 6 V much less than x/2, where X is the operating wavelength.

a y

If data are obtained at more realistic spacings, and the digital Fourier

transform (DFT) used to evaluate the integral of eq (1), the result is

co F (K) = y F(k

x + 2mk x

, k + 2nk 2 ), (6)

m,n= -°° y

where k

1 = y

5-, k 2 =

x y

The aliasing error is due to the contribution of the terms for m ± 0,

n t 0 within the region IkJ < ki, Ik I < k 2 . This is illustrated in figure 9

I x I

\ y

i for a one-dimensional spectrum and shows how the sidelobes of the true spectrum overlap and cause errors in the calculated result. If the true spectrum

is band limited, that is, if

F(K) = 0

14
miAtivr

PowrR

paturn

in

nm

Figure 9. Aliasing error due to overlapping of offset spectra.

0 -r yr ; 11 III - ,0 i

I I -20 H

z -3D -

z f fl | t

r t

—40 -

<

CL

JY5o

Cl

-50 -

—60 —

k

it, f,

* -

Hi "

i »

k

1 fl "

\

k

•j

ILlII >

< -70 -

t

li *

o: -80 J *

f f J t /

,! 1 V < if -90 - « 1

| 1 1 — 1 GO - LL LI

Figure 10. 3and-limited spectrum with no alias'n; err

15
for all values of |k x | > ki, |ky| > k 2 , as illustrated in figure 10, and the

data point spacings are

5 < t—9 x ki ’ ( 7 )

then there is no aliasing error. This is because there are no contributions

for the terms in eq (6) involving m * 0, n * 0 within the band-limited region.

The problem of minimizing and estimating aliasing errors then reduces to

determining the degree to which band limits ki and k 2 exist for a given

antenna/probe combination. If a band limit does not exist, or if measurements

are made at larger spacings than required by eq (7), we then need to estimate

the magnitude and character of the resulting error spectrum produced by aliasing. This can be done from estimates of the test antenna and probe far-field

patterns, from one-dimensional centerline tests, and from estimates or meas- urements of the random error in the measured data. Each of these will now be

described in more detail.

The first case considered is the most conservative one where data point

spacings of slightly less than x/2 are used. An effective band limit is produced in this case from the exponential attenuation of evanescent waves, and

random measurement errors are the source of the aliasing error spectrum. The

true spectra as previously defined can be considered as composed of two parts.

F(K) = D(K)e lYd

+ e(K), ( 3 )

the first term corresponding to the coupling product of probe and test antenna

spectra, and the second arising from noise and other sources of error in the

measured data. Since y is defined by the relation,

Y

= /k2 -(k? Vkp-, (9)

y becomes purely imaginary when k

2 + k

2 > k

2

, and the measured spectrum is

exponentially attenuated by the factor e^ yd in eq (8). An effective band

limit arbitrarily close to zero on the first term of eq (8) can therefore be

obtained by choosing 6 X and 6^ so that

16
The amount of attenuation or band limiting at the boundary of the k-space

domain is

20 log (e

1yd

) ~ -54.6 (^)AD/TOkF - 1 dB (ID

where

k

b^7^ »

or

J f- x y

For instance, if d = 3x, and 6 X

= 5^

= 0.4 x, D(_Kg) is attenuated by at least

122 dB on the scan plane from its magnitude at the antenna surface. Since

these evanescent modes are small for most antennas, there is an effective band

limit for the first term in eq (8) if the data point spacing is slightly less

than x/2.

The second term in eq (8) arises from errors in the measured data; most

of these are slowly varying at a function of x and y, and therefore also have

band limits. It is generally the random errors, due to receiver noise, vibration of the probe, etc., which produce an error spectrum that does not have a practical band limit. It is this noise spectrum that generally sets a lower

limit to the aliasing error effects. The magnitude of the noise level in the

computed spectrum F(_K) can be estimated from a knowledge of the random errors

in amplitude and phase, along with certain other antenna and measurement

parameters. A recent study [6] has shown that the ratio of the noise level in

the spectrum to the peak value of the antenna spectrum is

2 18(o 2 + o 2(N/N ))

< —* r

a-__.A_ t 1 7 e

e (K)

where

e(_K) = noise spectrum,

D(jg = peak value of antenna spectrum,

N = total number of measurement points,

N 0

= number of points within the effective area of the test antenna,

a

a = standard deviation of linear amplitude random error,

a

= standard deviation of random phase error in radians.

17
For typical measurements where a

a

< 0.5 percent, a

^

< 0.5 deg, the noise spectrum is on the order of 55 to 65 dB below the peak of the antenna pattern and

will have little effect on either peak gain or moderate sidelobes of -30 to

-40 dB.

To use eq (12), the standard deviations of the random amplitude and phase

distributions are required. These can be obtained by measuring or estimating

the contributions of such sources as resolution in analog-to-digital con- verters, receiver noise, scattering within the room, and random position

errors. An alternate method makes use of near-field centerline data at spacings much less than x/2 which allow calculation of the spectrum for values of

either k x /k or ky/k beyond +1 as shown in figure 11. These data were taken at

a z-distance of about 6 X, and from eq (11) any actual evanescent modes are attenuated to such a low level they could not possibly be detected. The calculated spectrum in the evanescent region therefore represents the effect of errors in the measurement, and the relatively constant floor level in this

region is a direct observation of the effect of random errors in the measured

data. From this direct measure of the si gnal -to-noi se ratio in the one- dimensional spectrum the correspondi ng signal -to-noi se ratio for the twodimensional data may be inferred. For instance, let the 1-D measurement be

taken in the x-direction over a length i x with the data point spacings 5 X

. The correspondi ng 2-D data will involve data point spacings 6 X

, 6y and scan lengths z

x and it . The noise level for the 2-D measurement will then be

e(K) e(K)

°<5T 2-D tfl^T

/

l r

6 6 x y x

t _TTr' x y x (13)

The next case considered is one where pattern results for a narrow-besm

antenna are required only over a limited region centered on or near K_ = CL

The data point spacings may then be increased beyond the value specified by

the sampling criteria, producing large aliasing errors outside the region of

interest while limiting the errors within. For example, if the far-field

region of interest is bounded by

only the evanescent spectra

Ik | < k , 1 k 1 < k , ym’ 1 xl xm

will al i as into this region if

( 14 )

18
20

log

i

Fourier

transform

of

B(x,0)

0.0000

- 10.0000

- 20.0000

- 50.0000

Multiple reflection lobes

- 40.0000

- 50.0000

- 60.0000

- TO . 0000

- 80.0000

- 90.0000

- 4.00 - 3.20 - 2.40 - 1.60 -.80 0.00 . 80 1.60 2.40 3.20 4 .00 k x /k

Figure 11. Spectrum resulting from measurements at data spacings Vs-, v ;• A/2 showing noise spectrum in region where k x

> k.

19
S (15) x * (1 + k /k) ’ sy

< (1 + k 7kT’

as illustrated in figure 12. Measurement and data processing time can, therefore, be reduced by using the larger spacings with little change in accuracy

within the region of interest.

The final situation is similar to the last one in that the data point

spacing is larger than prescribed by the sampling criteria. In this instance,

however, we are interested in estimating the errors in regions of the farfield where there is significant aliasing. One example of this situation is

the region where |k^| > k m

in figure 12, or all of the far field in figure 13

where a spacing of X has been used. These situations generally arise where

some accuracy can be sacrificed for measurement speed, but it is important to

know how much error is incurred.

As before, this error is estimated from some knowledge of the antenna and

probe patterns which together determine D(J<_), and the data point spacing which

determines the amount of overlap or aliasing. Either a graphical representation such as figures 12 and 13 or numerical values substituted into eq (6) can

be used. The errors can also be estimated from centerline near-field measurements where initially spacings on the order of x/ 10 are taken. The far field

is calculated from these data representing the approximate antenna pattern.

Similar far fields are then calculated using subsets of the data composed of

every nth point. As the spacing increases, changes in far-field parameters

such as gain, side-lobe level, etc. give a measure of aliasing errors. This

technique is also very useful in determining or verifying the adequacy of a proposed spacing.

The analytical and measurement techniques described in the last two sec- tions have been derived for arbitrary antennas and have been used successfully

on a wide variety of types as shown previously in table 1. They should work

just as well on the offset-reflector, shaped-beam antennas used on communications satellites.

20
RELATIVE

POWER

PATTERN

IN

D0

Figure 12. Data spacing greater than x/2, with no aliasing error within the region |k x | < k^

m

.

SPECTRAL RELATIVE WAVE NUMBER k /

k

X Figure 13. Overlapping spectra for data spacing of x.

21
4. Development of Diagnostic and Design Assist Methods Which Make Use

of Untransformed Near-Field Data

The intent of this approach is to try to reduce the time involved in both

the development and antenna performance verification test programs. The idea

is to compare the directly measured data with an expected or prescribed standard field distribution over the measurement plane, infer the reasons for differences, and effect corrections, changes, or repairs in the antenna system.

We will now consider the various aspects of this approach.

4.1 Specification of a Standard Near-Field Pattern

It was not within the scope of this research to develop the capability

for calculating such standard near-field patterns, but this capability does

exist both within INTELSAT and with the various contractors working on the

antenna developments. From a specification of the feed array and the reflector position, shape, and orientation, the electric field on a plane coincident

with the measurement plane can be specified. This assumes of course that the

relative positions and orientations of the test antenna coordinates and the

measurement plane are known. The near-field system does not in general measure electric-field components, since the probe's directivity and polarization

will influence the measurement to some extent. For small probes with high

polarization purity, the near-field data is very nearly the same as the electric field. However, for larger probes the field is smoothed by the integrating effect of the probe aperture causing the near-field data to differ from

the actual field. It is not difficult to include the effect of the probe in

the calculation of the standard pattern however since its receiving spectrum

will in general be known. We will therefore assume that a standard pattern

which specifies the expected relative near-field data can be calculated and

denote it as

B

$

(P) = a

$

(P)e

i*

s (P).

(16)

22
4.2 Comparison of Measured and Standard Data

The first point to keep in mind is that generally the complete near-field

data over the full measurement area will be required before reliable comparisons can be made. Since the far field in each direction is determined from

all the near-field data, complete near-field data will also be required for

comparison. There may be some cases where single centerline data could identify major discrepancies, but if the differences are small, complete data are necessary.

The second point is that with the current state of development the com- parison process will not be completely automatic. The i nterpretati on of differences between measured and expected patterns will require a good deal of

evaluation and judgement to determine the likely causes. For instance, a difference could be due to a translation in x, y, or z of the measurement plane

relative to the chosen reference plane, and such possibilities should be

explored before considering possible antenna problems.

One of the best methods for presenting the comparison data in a way that

can identify even small differences and also present large amounts of data is

a contour plot of phase difference or amplitude ratio. In most cases, the

phase is the most sensitive indication of antenna problems. Some examples are identified below.

4.2.1 Beam Alignment

A phase difference which varies linearly with either x or y is an indication of the beam's being shifted in the far field. The amount of beam shift

is given directly from the phase slope. If there is a linearly varying phase

difference between the standard and measured patterns of Aij> over a distance

then the beam will be shifted by the amount aE, where

Ai|> A A 360

y

Ak—-- = sin(AE).

k (17)

4.2.2 Feed Alignment

If the feed is not at the focal point of the reflector, the near-field

phase will show a quadratic character as shown in figure 14.

23
Figure 14. Quadratic phase error due to feed misalignment.

4.2.3 Reflector Surface Errors

If the feed is operating properly, the near-field phase data can identify

surface errors in the reflector. This was shown very graphically in measurements on a compact-range reflector using a planar near-field scanner [7]. The

phase contours shown in figure 15 identify the location and magnitude of a misadjusted support. When this support was properly aligned, the phase was much more uniform as shown in figure 16. In this case, the phase was supposed

to be uniform across the reflector and so the measured phase was a direct

indication of departure from the desired. In more complex antennas such as shaped-beam types, it will be necessary to compute the phase differences

before presenting the data.

4.3 Diagnostic Methods Involving Some Data Processing

In some cases, the feed may be the source of problems, and it would be

desirable to do some processing of the data to locate faulty elements in a feed array. With this in mind, a more extensive study was initiated to

24
Panel - support

X (-— 120 cm —]

Figure 15. 10 deg phase contours for reflector with misaligned panels.

^

oo e c*:o •TO

Figure 16 Phase contours after panels correctly aligned.

25
determine the utility of doing some processing of the near-field data to

identify feed or reflector problems. This study compared the potential

information obtained and the amount of data processing required with that

already used in computing far-field patterns. This study involved a brief

preliminary investigation into the following questions:

A. Given a desired far-field pattern, is it possible to predict probe output

on a near-field measurement plane for subsequent comparison with measured

near-field data?

B. For an antenna (or feed) with approximately planar aperture, is it possible to perform near-field measurements on a given plane and transform

back toward the aperture to determine whether the aperture excitations

are correct?

C. For an offset reflector antenna, is it possible to perform near-field

measurements in front of the reflector and transform back toward the feed

via the reflector to determine whether the aperture excitations are cor- rect?

Discussion: A. Direct Near-Field Comparison , expressed everywhere in the forward hemisphere (z >

[ 8 ],

£(r_) =

2“ / / exp( ik*_r)

—co

dK-

= dk dk , x y»

A A -

K = k x + k y,

x y

ATrvtr, k > K

y = k = { z uW-'k7

, k < K

where b_(k_) is the plane-wave transmitting spectrum,

have

:

(18)

Asymptotically, we also

The electric field may be

0) by the relationship

dK,

~ !(l) exp(ikr)/(ikr),

where f is the far-field pattern.

(19)

26
Using the relationship,

f(k) = Y k b(k), (20)

we may write E in terms of the far-field pattern:

1 dk_

E_ = ! f l.(k) exp(ik_»r) -y.

-oo

In principle, eq (21) allows the determination of the field everywhere in

the forward hemisphere, given the complex far-field. In practice, computed

results are not valid in areas where evanescent (storage) modes dominate (the

reactive zone). There is seldom any measurable error, however, as long as one avoids the region within several wavelengths of the aperture. The backward

transform implied by eq (21) is a classic example of an ill -posed problem in

which small errors, which arise in the measurement of the far field, result in

exponentially large errors in the extreme near field. Even when the far-field

pattern is supplied analyti cal ly , errors due to the truncation of the integration region and finite precision arithmetic eventually doom any numerical

calculation of eq (21) as the aperture region is approached. However, using

an exactly solvable model (a two-dimensional slit), Hamada and Yeh [9] have

shown by example that the near field (beyond the reactive region) can be ac . i- rately reproduced numerically from the far field.

While the probe, of course, does not actually measure the electric field

directly, the coupling between probe and AUT may be described in terms of ‘ h Kerns transmission formula,

«> dk

b'(r) = F / {s_(k )

• f ( k ) exp(ik-r) -=,

—oo

where b' is the probe output, F is a known mismatch correction between ,>r , and detector, and s_is the probe's receiving pattern (which is simply r-'

to the far-field pattern if the probe is reciprocal). Equation (22) ii n

•

numerically viable in the reactive zone, as discussed above. However, •

is a more stringent limitation related to the assumption that inu

1 tiple

tions between the probe and AUT may be ignored. In order to meet thi

tion, the probe and AUT must be separated by an experiment 1 ly

tance, which usually places the probe well outside the react/- / • .

27
Equation (22) makes it possible to predict the output of a given probe on

a near-field scan plane if the far field of the AUT is known. Efficient algorithms have been implemented to numerically evaluate the integral (basically a 2-D Fourier transform), and the computed output is produced on a rectangular

grid on as fine a mesh as desired. Therefore, it is currently feasible, and

possibly quite useful, to make real time comparisons between measured and predicted field distributions from the feed array. It should be noted, however,

that the ultimate test is whether or not the far-field pattern meets specifications. Of course, the far-field pattern may also be obtained from the measured near-field data and the probe-recei vi ng pattern, and with currently

available capabilities, the necessary processing is inexpensive and requires

only a few additional minutes on the computer. (The far-field pattern of an offset reflector may be accurately determined, using physical optics, from the

far-field pattern of the feed array [see ref. 10].)

Using a direct near-field comparison, Repjar and Krerner [7] were able to

adjust a millimeter-wave compact range reflector to obtain an acceptably uniform phase front. Hamada et al . [10] have used near-field data to fine tune

an array feed for an offset reflector. Also, on at least one occasion, a standard near-field pattern measurernervt performed at NBS was used to-pinpoint

bad elements in an array which was known to have a pathological far field

behavior [11].

Discussion: B. Transformation from Near Field to Aperture . As implied

above, it is difficult to extract useful information on evanescent modes from

a near-field measurement. While posing no difficulty if only the far field is

to be computed, this is an obstacle if fields are required closer to the AUT,

for evanescent waves become increasingly important as the aperture is

approached.

It should be emphasized that far-field and near-field patterns theoretically contain the same information and that any technique which reconstructs

an aperture field from the far field can be adapted for use with near-field

data.

One approach in calculating approximate aperture fields is to simply perform the transformation (1), setting z = 0, and ignoring contributions from

the nonpropagating part of the spectrum. While the result may not be totally

28
correct, it is certainly not devoid of information either and might be quite

useful in gauging deficiencies in the feed-array excitation. Similar methods

have actually been used to study surface i rregul ari ti es in large dish antennas

[12-14], where it has proven feasible to plot accurate surface contours using

phase information from a projected aperture field.

Discussion: C, Transformati on from Near Field to Aperture via

Ref 1 ector. This point takes us beyond the plane-wave theory discussed so far

in that it is no longer possible to relate the field near the feed to the

field beyond the reflector with the simple transformati on [10], It might at

first seem feasible to trace the rays in the measured spectrum back to the

reflector, and then onto the feed region, but it is known that geometrical

optics breaks down at caustics. An example of a caustic is the focal point of

the reflector, the approximate location of the feed array.

An appropriate way to handle this problem uses the physical optics approximation, and procedures that can determine an appropriate feed excitation

given a desired far field [15] have been devised. These procedures begin by

bracketing the optimum pattern in an envelope of acceptability. The solution

ultimately obtained is not a true inversion of the problem but is a likely

candidate, being an aperture distribution which produces a far field which

lies within the specified envelope and which may satisfy other constraints

(e.g., on stored energy), as well.

Again, an aperture field constructed in this manner might provide useful

diagnostic information.

Concl usions . We conclude that useful information is provided by any of

the three methods A through C discussed above. A and B may be accomplished

using software that already exists at NBS. C would require code that is

probably best obtained from other sources. Each of the three approaches

provides roughly the same information content, though in different forms.

While the practical utility of A and B has been demonstrated in certain

instances, ultimately, the determination of the best attack in a given

situation depends on an experimental, and subjective, evaluation.

29
5. Development of Beam Alignment Techniques

5.1 Introduction

One result of any antenna measurement, whether it involves far-field,

anechoic chamber, compact range, or near-field techniques, is a far-field pattern such as figure 17. In these patterns, the transmitted or received power

is specified as a function of angle, and these angles are defined with respect

to a measurement coordinate system. In far-field, compact range, or anechoic

chamber measurements where the antenna under test is mounted on a two-axis

rotator, the measurement coordinate system is fixed to and defined by the

rotator as shown in figure 18. The angles in plots such as figure 17 are obtained directly from the angle encoders on the two-axis rotator. It is

implicitly assumed that the two axes of rotation are mechanically aligned

orthogonal to each other, and they therefore represent the theta and phi

angles of a spherical coordinate system. In evaluating beam pointing ac- curacy, any mechanical misalignment of the rotator or errors in the encoders

will produce correspondi ng errors in the measured angles.

The precise definition of the measurement coordinate system is only one part of the requirements for accurate beam-alignment determination. Since the

AUT will in most cases be removed from the measurement system for actual use,

we need to know how these measured angles are defined in the antenna coordinate system. In the case of the rotator this would involve the relative

orientation and displacement of the AUT and the rotator coordinates.

In general, for any system the steps required in antenna boresight or beam alignment measurements are as follows:

A. Define the measurement coordinate system, denoted Cm

, and the techniques used to prescribe its location and/or orientation.

B. Define the methods for measuring directions relative to the measurement system and the estimates of uncertainty caused by the various sources of error.

C. Define the AUT coordinate system, denoted C

a

, and the methods used to

prescribe it in a known, fixed location on the antenna.

30
Relative

Power

In

dB

Azimuthal Angle in Degrees

Figure 17. Sample far-field pattern from antenna measurements.

IS) X

<

-eFigure 18. Schematic of far-field rotator showing neas in-cn* : : antenna coordinates.

31
D. Prescribe methods for aligning the AUT such that there is a known re- lationship between C m

and C

a

, and determine the relationship between

directions measured in C and correspondi ng directions with respect

to C

a

.

E. Determine the uncertainties in step 4, combine them with those in

step 2, and obtain an estimate of total uncertainty.

F. Perform alignments and measurements to demonstrate the validity of

estimated errors.

Each of these steps will now be described in detail as it applies to a planar

near-field measurement system. Even for this specific system, there are a number of ways by which these steps could be implemented, and we will describe

the approach used at NBS as one example.

5.2 Alignment Adjustments

The alignment process makes use of a variety of instruments for measuring

position, displacement, and angular rotation, and since these will be referred

to throughout this discussion they will each be described.

5.2.1 Theodolite Autocoll imator

One of the most useful alignment instruments is a precision theodolite

with the additional features of an optical autocollimator and optical micrometer. The basic theodolite consists of a high-power telescope and precision

scales to measure azimuth and elevation angles defining the orientation of the

telescope in the theodolite coordinate system. The zero for the azimuthal

angles can be set at any arbitrary direction, but the elevation angles are measured with respect to vertical using an internal electronic level. Both

angular scales have a resolution of 1 arc second and an estimated uncertainty

of ±2 arc seconds. The autocol 1 imation feature is used extensively and con- sists of a small, internal light source which projects an image of the crosshairs to a mirror located along the telescope's line of sight. If the mirror

is perpendi cul ar to the optical axis, the projected crosshairs will be

reflected by the mirror and appear superimposed on the original crosshairs.

In this way, the optical axis of the transit can be transferred to the optical

normal of the mirror. If the front and back surfaces of the mirror are

32
parallel, the axis is further transferred to the mechanical mounting surface.

If the mirror is mounted in a rigid fixture in a permanent location in the

laboratory, it will permanently retain a definition of a particular axis which

can be reestablished after the theodolite has been removed. For instance, in

the alignment of the planar scanner a mirror is permanently mounted behind the scanner and adjusted so that its surface is parallel to the x-y measurement

plane. In subsequent antenna alignments the autocollimator is aligned to the

mirror and then used to align the antenna to that same reference. Under

normal operating conditions the uncertainty in the colli mat ion of the transit

to the mirror is ±5 arc seconds.

5.2.2 Optical Micrometer

The optical micrometer is attached to the objective end of the telescope

and utilizes prisms to produce an apparent translation of the crosshairs relative to the target without actually moving the theodolite. The amount of

translation can be measured to within ±0.002 cm.

5.2.3 Laser Interferometer

A laser i nterferometer is used in many ways both in the operation of the scanner and in the alignment and definition of the scan plane. The interferometer is capable of measuring relative changes in displacement either along

or normal to the axis of the laser beam. To accomplish this the laser produces two orthogonally polarized beams at frequencies f and f . The electronics compares the frequency difference before they are radiated and after

the two beams have been directed along separate paths and reflected back to

the detector. Any difference in the Doppler shift of the two beams due to

relative movement of any of the optical components is converted to a corresponding position change and displayed by the electronics. For instance, in

the displacement mode where the position is measured along the axis of the

laser beam, the optical arrangement is shown in figure 19. The reference v<-

at frequency f is reflected back to the detector by the reference interpreter while the measurement beam at f

1 continues on to the cube corner r ^’

tor where it is also reflected back to the detector. Any relative mov-- i

‘

along the axis of the beam between the reference i nterferometer and the corner reflector will produce a change in the frequency difference and

33
Reference

Figure 19. Schematic of laser i nterferometer distance measurement system.

interpreted as a relative position change. However, identical movement of

both optical pieces along the beam, their translation normal to the beam, or rotation of the optics will have no effect on the position reading.

In the straightness mode different optics are used as shown in figure 20.

In this case the straightness i nterferometer separates the two beams by equal

and opposite angles 0^. The straightness reflector is composed of two flat

mirrors which are also rotated from a plane by the same angle 9^, and therefore reflect the two beams back to the i nterferometer and then to the

detector. Movement of either the i nterferometer or the reflector normal to

the beam and in the plane defined by the two diverging beams will produce a relative Doppler shift and correspond!’ ng change in measured displacement. If

the mirrors are flat, motion of either optical component along the beam or normal to the plane of the two beams will produce no position change. The

reference line or "straight-edge" for the straightness measurements is not the

laser beam, but the direction defined by the bisector of the angle between the

two mirrors. This means that the straightness reflector should not move during the measurement since we cannot distinguish between transverse motion and

rotation of the reflector. It also means that if displacement is to be measured relative to a specific axis, such as a horizontal or vertical line, the

bisector of the straightness reflector must be aligned along that precise

direction. Conversely, if straightness is measured for some arbitrary orientation of the reflector and we then need to define or transfer that direction

34
Figure 20. Schematic of laser interferometer straightness measurement system.

to a mirror or to the theodolite an auxiliary device must be used. Generally,

that auxiliary device is the optical autocollimator. By collimating alternately on the two mirrors in the straightness reflector, as illustrated in

figure 21, the location of the bisector can be determined and defined by a particular set of theodolite angles. That bisector or strai ght-edge ref-reline can then be rotated into any desired location, or the direction o

e the

theodolite axis transferred to a permanent reference such as a reference

mirror. If the autocoll imator has to be located more than 2 to 3 m away frj

the straightness reflector in the above process, the small size )

c the nirro

produces a very faint image and makes collimation di f ficult. This diffic/*..

can be overcome by a two-step process that transfers the location of toe

bisector to a larger flat mirror placed on the front of the stra i ghtnes - reflector mount as shown in figure 22. The theodolite is placed close t ; straightness reflector, and rotated to place its optical axis c o i n c i > -

'

the bisector axis as previously described. A flat mirror is then pit

the front of the reflector mount as shown in figure 22, tne theodolite

limated on the mirror, and the change in transit angles noted. If i‘ . where the transit is located farther away from the reflector, the 1 ir . mirror is used to provide a better image for collimation, and trv r--’-- *

rotated by the measured offset angles to place the stra i ghi

•• •

line parallel to the transit axis.

35
Theodolite with

Autocollimator

Straightness

Reflector

Figure 21. Method for locating straightness reference line on straightness reflector.

Figure 22. Method for transferring straightness reference direction to

flat mirror on surface of mirror mount.
5.2.4 Electronic Level

The fourth instrument used extensively in the alignment process is an electronic level or tilt meter which measures angular rotations with respect

to a vertical axis. It has a resolution of 1 arc second and can measure

changes in rotation as a function of position or determine the deviation of a surface from a horizontal or vertical plane.

5.2.5 Optical Square

In cases where it is necessary to obtain a precise 90 deg rotation in an optical axis an optical square is used. It is composed of two mirrors mounted

in a fixure with a 45 deg angle between them. An incoming beam is rotated by

90 deg regardless of the orientation of the fixture to the incoming beam.

These five instruments, along with the laser sources, optically flat and

parallel target mirrors, and other auxilliary mounting and adjustment devices

are used in a variety of combinations to carry out the alignments and measurements necessary for antenna boresight measurements.

5.3 Definition of the Measurement Coordinate System, Cm

In planar near-field measurements, the x-y plane of C mis defined by the

"best fit" plane of the mechanical scanner. We want to determine the orientation of that plane in the laboratory and place a target mirror in a convenient location with its surface parallel to the measurement plane. The target

mirror can then be used in future alignment of antennas.

In the box-frame design of the mechanical scanner shown in figure 23, the

top and bottom horizontal rails along with the two vertical rails on the movable tower are the guides for the probes and therefore define the measurement

plane. We will assume that these rails have previously been aligned to provide almost planar motion of the probe and that this plane is close to a vertical plane. The details of this alignment will not be described here since

the current task is to locate and define the measurement plane once the scanner has been aligned.

In principle, the scan plane can be defined by using either a dual theodolite system or a single theodolite and the optical micrometer. In the t,;'

theodolite system, the two theodolites are located at opposite ends o

f too

37
X-Drive

Motor

Wall

Reference

Mirror

Figure 23. Schematic of box frame near-field scanner.

38
horizontal axis, approximately centered in the vertical direction, and collimated on each other. Azimuth and elevation readings are taken with each theo

dolite focused on a tooling ball placed at the probe location. Readings are repeated at each (x,y) position and are then converted to Az(x,y). In a similar way, an optical micrometer is attached to a single theodolite and

direct readings of Az(x,y) are recorded. In both of these procedures, the

setting of the probe and reading of the theodolites are manual and require

long measurement times. As the probe is moved away from the theodolites the

accuracy of setting decreases. Most of these problems are overcome by using

the laser i nterferometer and electronic level to perform and digitally record

the measurements.

The laser measurements begin by mounting the reference mirror shown in

figure 23 on a very stable support behind the scan plane, and initially align

ing it to the leveled autocollimator so that its surface is vertical and approximately parallel to the scan plane. The laser i nterferometer with the

straightness optics is configured to measure the z-deviation of the bottom

rail as a function of scanner x-position as shown in figure 24. This deviation is denoted Az

g (x

s ), where x

$

denotes the scanner's x-reading. The

straightness reflector is then rotated about its vertical axis, thereby rotat

ing the straightness reference line until there is no linear variation in the

z-deviation and this final data is denoted Az

g (x

s ). A sample set of data is

shown in figure 25. The straightness reference line is now parallel to the

best-fit line of the bottom rail, and the next step is to transfer the orientation of this line to the reference mirror. The theodolite is first collimated through the optical square to the direction of the straightness reference line and then the reference mirror is readjusted for collimation in the

azimuthal direction as shown in figure 26. The mirror's elevation adjustment

is kept constant, and the plane of the mirror is now parallel to a surface

defined by the best-fit line of the bottom rail and a vertical line. This

plane is not necessarily parallel to the scan plane since the top horizontal

rail and the vertical rails also affect the probe motion, but it serves as an intermediate reference plane.

39
Figure 24. Straightness i nterferometer used in measurement of bottom rail of

planar scanner.

40
DELTA-Z

ERROR

IN

MM

STRAIGHTNESS ERROR OF X-RAILS

Figure 25. Deviation of bottom rail of scanner from straightness

reference line.

41
Figure 26. Theodolite and optical square arrangement used in transferring

straightness reference line to measurement system reference

mi rror.

42
DELTA

Z

ERROR

IN

CM

The vertical tower of the scanner is next placed in the position where

x

s = 0. Using the theodolite with its axis horizontal, and the optical square

to redirect that axis vertically, the reference line of the straightness re- flector is oriented vertically. The straightness i nterferometer is then moved

in the y-direction by the probe carriage and the z-deviation, Azj.(0,y

s

) is

measured as a function of the scanner y-position, y $. A sample set of data is

shown in figure 27.

In principle, the measurement of Az^. with the laser could be repeated at

a sequence of x-positions; however, the vertical alignment of the straightness

reflector at each x-position is time consuming. If the vertical tower is

rigid, the rails will have the same relative straightness at each x-position

and only the tilt of the tower about the x-axis will produce a change in z. This tilt change can be measured quickly and accurately with the electronic

level as shown in figure 28. The tilt meter is set to zero at x

$ = 0, and at

closely spaced x-positions, 9 (x ) is recorded.

X s

0 100 TOO

‘ Y- POSH ION IN CM

Figure 27. Deviation of vertical rails from vertical reference 1

i

r -.

43
Figure 28. Schematic of tilt meter on scanner to measure rotation of tower

about the horizontal x-axis.

44
These three measurements are finally combined to give Az'(x,y) over the

complete measurement plane using the relation

The primes indicate that these data are measured with respect to a vertical reference plane. Fitting these values of z'(x,y) to a linear equation in

x and y will give the plane that best fits the data and indicates the rotation

of that plane in azimuth and elevation to the plane defined by the current

orientation of the reference mirror. Once these rotations have been determined the reference mirror can be rotated, placing it parallel to the best-fit

pi ane.

In using eq (23) to calculate the z-error, rotations of the tower and the

probe transport about their y-axes have been neglected. Since the z-error

produced by the y-axis rotations are proportional to the cosine of the rotation, and the angles are small, this is a good approximation.

The estimates of uncertainty in the angular location of the z-axis of the

measurement plane are summarized in table 2. In combining each of the individual errors, we assume that they are independent, uncorrelated, and the

estimated errors are upper bounds.

Table 2. Estimate of error in defining scan plane using straightness laser.

4z'(x,.y) = 4z g(x

s

) + Az^(0.y

s

) + y

$

si n ( e x

( x

s ))- ( 23 )

Source of error Estimate of error (arc seconds)

in azimuth or elevation

Reference mi rror alignment to

straightness reference line

Definition of straightness line 10

Optical square error 2

Collimation error

To straightness reflector 5 To reference mirror

Mathematical fitting error

Final alignment of mirror to

best-fit plane

Reference mirror stability

5

6

5

3 Root Sum Square 15

45
Y

Figure 29. Antenna with fiducial marks to define x- and y-axes.

Figure 30. Mirrors on antenna to define its coordinate system.

46
5.4 Defining Antenna Coordinates

There are a number of possible ways to define the antenna coordinates,

and each will require different methods for aligning to the measurement system. The most frequently encountered will be described. In one method shown

in figure 29, fiducial marks define the x- and y-axes and three points on the

surface define the x-y plane. Another method is illustrated in figure 30

where mirrors attached to the antenna define the x- and z-axes. By definition, the y-axis is then orthogonal to both of these. The translational location of the axes can be identified with fiducial marks or, if the translational location is not critical, it can be arbitrarily defined during the

measurement by the (x,y) zero setting of the laser. Finally, a method

frequently used on far-field ranges is to specify the location of the z-axis

with a boresight scope attached to the antenna or its mounting bracket. The

angular location of the x- or y-axis can then be fixed with an orthogonal

mirror, a level attached to the antenna, or by fiducial marks.

5.5 Aligning the Antenna Under Test (AUT) to the Measurement Coordinates

If the antenna coordinates are defined by fiducial marks and three points

on the surface, the alignment is accomplished using mechanical means as illustrated in figure 31. The micrometer is fitted temporarily to the end of the

probe and brought sequentially into contact with the three reference surfaces.

The antenna is then rotated about its x- and y-axes until the micrometer reading (corrected for the Az error) at each of those points is the same. The

antenna is then rotated about its z-axis until its x-axis is parallel to the

x-axis of the scanner.

If the antenna axes are defined by mirrors or by the boresight scope, the

theodolite autocoll imator is used and the antenna is rotated until the optica 1

axis is parallel to the reference mi rror which defines the measurement system

z-axis. Since the reference mirror is fixed in a certain location, and the

AUT is generally at a different height, we must effectively transfer the

reference mirror to a new location. This can be done by using two theodolites, one positioned to collimate on the reference mi rror and one pos i t i oned

to collimate on the antenna. As shown in figure 32 the two theodolites ar*

collimated on each other and the azimuth scales are set to 0 and 130 deg, ' • -

pectively, making the two coordinate systems parallel. Collimating the ‘

•

47
Figure 31. Micrometer used to align antenna mechanically to

reference scan plane.

48
Figure 32. Dual theodolites used in optical antenna alignment.

49
on the reference mirror and setting the angles of both to the same value

orients both theodolites normal to the reference mirror. The AUT can then be

rotated to collimate its mi rror on the second theodolite and hence align its

z-axis parallel to the reference coordinate system. Similar techniques can then be used with the theodolite collimated on a second mirror (see fig. 30)

as the AUT is rotated about its z-axis to complete the alignment.

Assuming that the collimation technique has been used, the estimates of

uncertainty in the alignment are itemized in table 3.

Table 3. Estimates of uncertainty for antenna alignment.

Source of error Alignment error (arc seconds)

Definition of reference axes (from table 2) 15

Collimation errors

Two theodolites

To reference mirror

To antenna

Angle measurement

Alignment resolution

Root sum of squares (RSS)

5

5

5

5 _5

19

5.5.1 Far-Field Angle Measurement

In the near-field measurements , angles to define directions for far-field

patterns are not measured directly. Measured quantities are the x- and ypositions, and the amplitude and phase of the near fields at each of these

positions. Through the Fourier transform the far-field spectrum, which is

given as a function of the wave numbers k x and ky, is derived. Angles are then derived through the relations

X (i c

- N /2)

k /k =

ij-5

- = cosE sinA

x NS , (24)

k /k

y

x (i r

- N

r /2)

NTr y

= SinE. (25)

50
where i c and N

c are the column index and number of near-field columns, with

similar definitions for the row parameters i r and N

p

.

Angle errors are then related to errors in the dimensions of the scan lengths l_ x and L , and wavelength; namely

aA

1 cosE cosA

(26)

where L

x

aE

cosE

,AX

y

al

L2

y

N

c

<$ x and L = N

p 6y.

(27)

5.6 Measurement Errors Affecting Boresight Errors

There are certain errors in the amplitude and phase data that can cause

errors in boresight. These errors produce an artificial offset in the farfield spectra that are independent of the alignment errors previously

discussed. From analytical studies, computer simulation, and tests during

near-field antenna measurements, the following have been identified as primary

contri butors

:

1. z-position errors

2. Linear phase errors due to flexing of cables;

3. Phase errors due to receiver nonlinearity;

4. x- or y-position errors;

5. Truncation;

6. Multiple reflections, and

7. Phase drift during measurement due to temperature change.

The magnitude of each of these errors will depend on the particular measurement system, the frequency of operation, and the character of the AUT. For

instance, if the AUT is a wel 1 -col 1 imated antenna with the main beam along

z-axis, the near-field phase is essentially constant as a function of x and

y. In this case, x-y position errors and receiver linearity will have little

effect. If the beam is not well collimated, or if it is steered oft a<is,

both of these will have a significant effect since the phase will changrapidly as the probe moves over the scan plane. In some cases, errjr

51
equations are available to estimate the magnitude of the beam alignment errors

[16] and in other cases, special tests must be performed to identify their

effect. One such test is to compare beam pointing results from two different

measurements on the same antenna. In the two measurements, the antenna has

been rotated about the z-axis by 180 deg and precisely aligned in each case. Other similar comparisons can identify individual errors. An example of

results for such tests is summarized in table 4.

Table 4. Estimates of uncertainty for beam poi nti ng.

Beam pointing error (arc seconds

)

Source of error Narrow beam antenna Broad or steered beam

z-position errors 20 100

Cable flexing or rotary joints 20 20

Receiver phase nonlinearity 20 50

x-y position errors 5 60

Truncati on 10 30

Multiple reflections 10 60

phase dri ft 5 5 Antenna alignment (from table 3) li 19

Estimated total uncertainty

root sum square combination

43 146

6. Development of Near-Field Swept-Frequency Measurement Techniques

6.1 Introduction

Swept-f requency measurements of the complete satellite system including

transmitter, receiver, and the associated antennas are an important part of

pre-launch testing of communication satellites. "Holes" in the frequency re- sponse of any part of the system cause degradation or loss of performance in

some of the channels, and therefore reduce the value and usefulness of the

satellite. Each part of the system is tested separately and the total system

is also evaluated to detect any problems arising from system interactions. In

the past, these measurements have been performed using far-field techniques.

If near-field testing is to be used on these systems, methods must be

52
developed to provide equivalent information. In this section we will describe

the development of such techniques and give sample results. Some aspects of

the far-field testing are discussed first and establish a basis both for com- parison and to define requirements.

6.2 Analysis

The potential amount of data required for complete frequency characterization of a satellite system is massive, and therefore some choice is always

made to obtain a practical and yet adequate data subset. The total potential

data set is viewed as a three-dimensional volume in figure 31 where the farfield angles are two dimensions, and frequency is the third. Covering the

complete volume requires fine increments in all three dimensions. Testing

time is prohibitive for such complete characterization, and therefore either

the angular or frequency coverage must be reduced. The usual choice is

complete patterns at a few (10-20) frequencies across the operating band,

represented by the horizontal slices in figure 33. The patterns are then supplemented with continuous swept-f requency measurements at important or representative key angular locations as illustrated by the vertical lines. These

locations are typically the peak of the beam where gain variation is obtained,

and the edge of coverage where isolation between beams is measured. It is

implicit that these limited tests represent typical performance at similar

angular locations of the pattern, and therefore complete angular coverage is

not necessary.

Swept near-field measurements yield results similar to the far-field

tests, but measurements at one near-field point do not directly represent the

frequency response in any one far-field direction. They require further

analysis and interpretation and will be used as a guide and supplement to the

complete near-field measurements at fixed frequencies. In the following, we

will describe how they are used first to specify the required frequency increments and also to give an approximate far-field frequency response.

We begin with a hypothetical case based on three assumptions; it illustrates the desired information, the measured data, and the problems to be

solved. (1) The pattern, gain, and polarization of the AUT are required onl> over a limited angular region in the far field. For the satellite antennas

under consideration this is a region of approximately 20 deg in both a z i .*

53
Figure 33. Schematic representing three-dimensional data volume.

and elevation. (2) Within this angular region of interest the far-field frequency response is required at a few (three to five) specific locations. The

K_ values specifying these angular locations are denoted as _K ^

. A sample of a typical swept measurement is shown in figure 34 where the peak gain of an antenna at =

0_ has been measured over the operating frequency band. (3) At

each of these locations the frequency response curves are accurately

represented by stepped frequency measurements with increment Af(K^). In general, the required frequency increments may depend on the part of the

pattern being measured; sidelobes and cross-polarization require smaller

increments than the peak of the beam. In the example of figure 34, the

smallest measured period is 350 MHz, and the corresponding Af(K^) is

175 MHz. The Af(K^) essentially define frequency sampling criteria for the

far-field measurements and guarantee that, if measurements are made at increments of Af ( K. ) or less, the complete response can be reconstructed. The

measured data at 175 MHz increments will not have the fine resolution of the curve in figure 34, but since we have determined a minimum period in the

measured data, Fourier analysis will produce complete reconstruction. The

54
Gain

in

dB

Frequency in Ghz

Figure 34. Sample swept-gain results.

55
first two assumptions are realistic for the satellite antenna systems being

measured and they also assist in a practical solution to the measurement

problem. The third is not generally known; in fact it is one of the objects

of the measurement, but once it is determined the remainder of the approach is

strai ghtforward.

The first assumption reduces the magnitude of the problem because it

reduces the near-field data necessary to characterize the far field. As

already noted for fixed frequency measurements, the size of the scan area is

reduced and the data point spacing increased for these limited angular

regions. Especially for the peak gain frequency data, only the near-field

region where the amplitude is relatively large and the phase smoothly varying

will make a significant contribution.

The second assumption means that there may be rapid frequency variations

in wider angular regions or at selected locations within the angular region of

interest. However, if these variations are not at any of the selected locations, they do not have to be considered in determining the minimum frequency

sampling interval.

The third assumption is the key one. If by some means these frequency

sampling intervals can be determined, the remaining measurements are routine.

Given that the Af(K^) are known, complete near-field data at these frequency

increments produce complete far-field parameters by the usual Fourier transform of each data set at a given frequency.

D

1 (K,fj)

e -iyd

47T 7^

-iK.P

e

' “dP. (28)

For polarization information, similar data with a cross-pol ari zed probe is

necessary and requires similar processing.

D"(K,fj) e -iyd

4tt F

11 f

-i KP

e

- "dP. (29)

In the above,

f

j * f o

+ <5i>.

(30)

where f Qis specified.

56
Without knowing the frequency sampling criteria, many more near-field scans

are required. This illustrates the importance of determining Af(K^) before

making any near-field measurements. In a near-field system the far-field frequency response cannot be measured directly, and we must therefore develop

equivalent tests and analysis to determine the frequency sampling criteria.

The test proposed and studied is one where swept-f requency measurements

at very closely spaced frequency increments are performed at a few selected

locations in the near field. The combinations of these data will have the same frequency sampling requirements as the far fields in the prescribed locations. If we determine the sampling requirements from the near-field data,

the far-field requirements are therefore known.

The near-field swept-f requency tests are performed as illustrated schematically in figure 35. The generator and load ports are first connected

together, the frequency is varied in very small increments, and the amplitude

and phase are recorded at each frequency. These data serve as the reference

curve that defines the variation of input signal and measurement system

response. The generator is then connected to the AUT, the load to the probe,

and the probe is placed at some point in the near field P . The frequency is

again varied over the same range, with the same increments, and again the

amplitude and phase are recorded. The ratio of these two measurements is the

near-field frequency response of the AUT/probe combination for that particular

x,y,z probe position. A sample of one such measurement is shown in figure 36.

Fourier analysis of this single swept measurement, as shown in figure 37,

shows a pulse width of approximately 50 ns corresponding to a frequency sampling requirement of 20 MHz.

Before describing data analysis techniques further, we will consider the

mechanisms that produce frequency variations in the antenna system and how

these influence the choice of probe type and probe location for swept tests.

There are a group of components that affect all far-field directions and,

therefore, every near-field location equally. These include the electronics

of the transmitter/ recei ver, the transmission lines between the electronics,

and any switches, couplers, connectors, etc., common to all antenna ele . Frequency variation caused by these components are detected by placin'; t.

n

(

.

probe at any location.

57
Figure 35. Schematic of two parts of swept near-field measurement illustrating generator-to-1 oad and antenna-to-probe measurements.

58
Ratio

of

probe

output

to

AUT

Input

In

dB

- 25.00

- 30.00

- 35.00

- 40.00

- 45.00

- 50.00

- 55.00

- 60.00

- 65.00

- 70.00

- 75.00

2.50 2.65 2.80 2.95 3.10 3.25 3.40 3.55 3.70 3.85 4 c

Frequency In GHz

Figure 36. Sample results from swept near-field measurements.

59
relative

amplitude

in

dB

.0000

- 5.0000

10.0000

- 15.0000

- 20.0000

- 25.0000

- 90.0000

• 95.0000

- 40.0000

45.0000

50.0000

.00 10.00 20.00 90.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

time in nanoseconds

TIME DOMAIN RESPONSE OF ANTENNA FOR

PROBE AT X- "0. 1 L^, Y 0

Figure 37. Time-domain representation of swept near-field measurement data.

60
If the feed or the antenna itself is composed of individual elements,

there is another group of transmission lines, connectors, and possibly electronics associated with individual elements. In the case of a phased array,

the probe would have to be near a particular element to detect the complete

frequency characteristics of that individual element. If the probe is very

close to the array surface, and not near the element, swept measurements will

not detect its effect. If the probe is moved farther from the array, the

effect of a single element becomes less, but the probe will "see" some effect.

In the far field the effect of the single element is likewise smoothed out.

The above all indicate that the probe should be placed at z-distances as far

away as possible for swept-f requency tests within the constraints of the measurement facility.

If the feed of a reflector antenna is composed of individual elements,

each element produces an approximate plane wave, and within the collimated

region the probe responds to the combined effect of each feed element. In a particular direction in the far field one element may have a larger effect

than the others, and this will not be apparent in the near-field data. Techniques will be described later to process the swept data in a way that tends

to focus on a specific direction, and either emphasize the contribution of a particular feed element or reduce the effect of variations not associated with

that direction.

Scattering from the reflector, the feed, and other structures produces

frequency variations with minimum periods corresponding to the size or distance between structures. For a dimension i in the radiating or scattering

system, the corresponding period in the swept-f requency data is

for single reflection

Af = J

(31) or

for multiple reflections

where c is the velocity of light. An estimate of Af(K.) can therefore he

based on mechanical dimensions.

61
Taking each of these factors into account, the following guidelines are established for the near-field swept-f requency tests.

A. The probe should have a relatively smooth frequency response over the

measurement band since the measured frequency response is a combination of

both system and probe characteristics.

B. The separation distance between the AUT and the probe should be as large as possible within the facility size constraints.

C. The probe pattern should be relatively constant over the angular

region of interest. This will generally be required for the regular near- field tests.

D. Swept measurements are then taken at a few representati ve points in

regions where the amplitude is the largest. This is generally the collimated

region correspondi ng to the antenna's physical area for the main component

data. Typical positions are along the two centerlines and in the region of

the four quadrants. For the cross component, the field is often very low

along the centerlines and the region of the four quadrants is better. Typically, a two-dimensional scan such as figure 38 is obtained to aid in choosing

representative regions where the amplitude is significant.

There are two approaches for choosing the Af(K.) frequency increments.

In the simplest, each individual swept measurement is analyzed separately to

determine the required sampling increments. The minimum frequency increment

from all of the measurements is used for all _K^ directions. The second

approach is suggested by the Fourier transform analysis of the near-field data

in eq (28). The individual swept measurements are combined by the relationship

G

1 (f . ,K

.

) =v J ’-r n=l,N

b ' (P ,f .) -i K. -

P

o -n j

; e

-l - a (f .

)

o

v j

(33)

where G

1 ( fj

,JCj ) is the approximate gain variation in the given direction.

This produces a swept-f requency curve that corresponds to a particular location in the far field. In this processing, lower amplitude measurements are automatically given less weight, and frequency variations that are not phase

62
Probe

x-position

in

cm

Probe y-position in cm

Figure 38. Contour plot of near-field cross component data.

63
coherent at the different measurement points will tend to average out. As the

number of swept measurements increases, the validity of this approach also

increases. Experience and further study will indicate the most effective

tradeoff between the number of measurement points and the accuracy of the

results.

Figure 39 shows an example of combining swept data using eq (33). Preliminary results have been very promising. Further testing will be pursued

during Phase II.

7. Specification of Hardware Requirements for Planar Near-Field Testing of

Satellite Antenna Systems

7.1 Introduction

A typical near-field measurement system is shown schematically in

figure 40. The specifications of the measurement system will be discussed in

terms of the five subsystems: (1) the mechanical probe positioning system,

sometimes referred to as the scanner; (2) the rf source that produces the

stable measurement signal; (3) the receiver with any associated preampl ifiers

that converts the probe output signal to a digital record of the amplitude and

phase; (4) the rf probe used to sample the radiated field, or in the case of a receiving antenna, to illuminate the test antenna, and (5) the computer that

controls the measurement process and in some cases performs the numerical

analysi s.

There are two types of specifications for the measurement system. The

first defines the requirements for any measurement on a given antenna system.

Examples of these are the frequency coverage of the source and receiver, and

the size of the scanner. The second type determines the accuracy of a given

measurement, and these will receive the primary attention. The process for

specifying the requirements of each of the sub-systems uses as input data the

information about the antenna system being measured, the accuracy requirements, and the kinds of final results needed. For each of the final results,

we then construct an error budget that allocates a portion of the error to

each of the known sources of error. Using the equations developed from

studies of the error sources [3], the subsystem specifications can be determi ned.

64
Relative

Magnitude

of

Sum

In

- 1«.00

-19.00

-24.00

^ -29.00

-54.00

-59.00

-44.00

-49.00

-54.00

-59.00

-54.00

2.50 2.65 2.80 2.95 5.10 5.25 3.40 3.55 3. TO 3.85 « X

Frequency In GHz

Figure 39. Combination of swept frequency curves for on-axis direction

response.

65
RF.FERfJiCE

SIONAL

66

Figure

40.

Schematic

of

near-field

measurement

system.
7.2 Antenna System Measurement and Accuracy Requirements

For this study, the antenna system considered is the Intelsat VI shown in

figures 41 and 42. It is composed of offset reflector antennas operating in

the frequency ranges of 3.4 to 4.2 and 5.8 to 6.6 GHz. These antennas are circularly polarized and produce shaped beams referred to as Hemi or Zone

beams. The two-spot beam reflectors operate in the frequency band from 10.7

to 14.5 GHz. In addition, there are a cluster of global horns operating in

the frequency range from 4.035 to 6.425 GHz.

While the measurement requi rements differ somewhat for the different

antenna systems, in general the following data are required:

A. peak gain at fixed frequencies in the center of each channel and at

band edges;

B. relative patterns for both main and cross-pol ari zed comonents over an angular region of +10 deg from the subsatellite point;

C. EIRP measurements on the transmitting system and Saturating Flux

Density measurements on the receiving system; and

D. swept measurements of peak gain, sidelobe levels, and polarization

isolation at a few (5-6) Earth station locations within each beam.

The specified accuracy of the peak gain and power parameter measurements is

0.25 dB, while the specified accuracy of the sidelobe, cross-pol ari zati on, and

isolation measurements is 0.75 dB.

Using the above measurement and accuracy requirements, table 5 lists the errors alloted to each of the individual sources affecting the peak gain

result.

67
10 4 rr.

Figure 41. Schematic of Intelsat VI satellite.

4.7m8.3m

6.1m

Figure 42. Schematic of Intelsat VI satellite antennas.

68
Table 5. Error budget for peak gain measurements.

Error source Error in dB

Probe relative pattern 0.00

Probe polarization ratio 0.00

*Probe gain 0.10

Probe alignment 0.02

*Normal i zati on constant (or power measurement) 0.10

Impedance mismatch 0.05

AUT alignment 0.00

Aliasing error 0.00

Measurement area truncation 0.05

*Probe x-y position error 0.01

*Probe z-position error 0.01

Multiple reflections 0.15

*Receiver amplitude nonlinearity 0.01

*System phase errors 0.00

Receiver dynamic range 0.02

Room scattering 0.05

Leakage and crosstalk 0.05

Random errors in amp and phase 0.00

RSS combination (dB) 0.23

*$ee discussion below.

The magnitudes have been chosen to meet the requirement of 0.25 dB uncer- tainty and to reflect typical and realizable situations. The error sources

are of two kinds. For those shown with an asterisk (*), there are error equations that give correspondi ng system specifications directly. For instance,

the relationship between gain error and z-position error is

. - 5

2 AG < -5- (-4) (in dB)

/n

( 34 )

where n is the aperture efficiency, 6 Z the magnitude of the z-position error,

and x the wavelength. Similar relations are available for the other para; -

eters. These equations, along with a detailed discussion of the error analysis, are supplied in [16]. Using these relations, the allowable system uncer- tainties for peak gain are:

69
probe gain uncertainty

normalization constant measurement

probe (x,y)-position

probe z-position

receiver amplitude nonlinearity

[16, eq. (63)]

system phase error

0.10 dB,

0.10 dB,

0.01 X,

0.01 X,

v = 0.002, and

2.0 deg.

For the remaining errors, tests must be performed on the actual

AUT/Probe/Measurement system to estimate their magnitude. The truncation test

has been discussed, and similar ones are described in the error analysis [14],

The magnitudes given in the above table are typical and should be realizable

for the types of antennas to be tested. For the above errors, the tests

should determine that the

truncation spectrum (similar to fig. 6) < -45 dB,

peak-to-peak multiple reflections < 0.15 dB, and

leakage and crosstalk < -45 dB.

In table 6, the same error sources have been itemized for a -30 dB sidelobe in the main component pattern. The analytical error analysis has shown

that when the errors vary sinusoidally in x and/or y, they have the most

effect on the sidelobe region and that a particular period is associated with

each direction in the far field. For instance, if the z-position error is of

the form

Az(x,y) = 6 z cos , (35)

the sidelobes in the directions

k-2- = + — = sin (elevation angle) (36)

K T

will be in error, but in all other directions the error will be essentially

zero.

70
Table 6. Error budget for -30 dB sidelobe measurement.

Error source Error in dB

Probe relative pattern 0.10

Probe polarization ratio 0.05

Probe gain 0.00

Probe alignment 0.20

Normalization constant (or power measurement) 0.00

Impedance mismatch 0.00

AUT alignment 0.00

Aliasing error 0.05

Measurement area truncation 0.15

Probe x- , y-position error 0.06

*Probe z-position error 0.21

Multiple reflections 0.30

*Receiver amplitude nonlinearity 0.07

System phase errors 0.23

Receiver dynamic range 0.20

Room scattering 0.05

Leakage and crosstalk 0.05

Random errors in amp and phase 0.00

RSS combination (dB) 0.56

*See discussion below table 5

The sidelobe region for the communication satellite antennas with aperture dimension a is bounded by the main beam with an approximate half-power

beam width

9 B ” T5a

radians 37

and the edge of Earth at approximately 10 deg off axis. The periods that will

produce errors in this sidelobe region are then bounded by

6 x < t < 10a.

This means that to satisfy the requirements for sidelobe accuracy, sinusoHil

errors in amplitude, phase, or x-, y-, z-positions whose periods are wit''

the range given by eq (38) must have magnitudes less than the following:

71
probe (x,y)-position 0.01 a, probe z-position 0.0005 A,

receiver amplitude nonlinearity y < 0.0004, and

system phase error 0.2 deg.

For the position errors, this implies a Fourier analysis of the position error data such as figures 25 or 27. The result of such an analysis on the z- position data is shown in figure 43. In this example, where f = 3 GHz, the

periodic variation with t = 100 cm affects the sidelobes in the directions

where the elevation angle is 5.7 deg. The amplitude of 0.08 mm (corresponding

to 0.0008 a) is slightly larger than the required specifications. In such

cases, the sidelobe error can be reduced by position error correction of the

measured data. For example, since the position error can be measured with the

laser to a resolution of at least 0.001 cm, and the primary effect of the error is on the phase, a simple correction that can be applied to the data is

Phase correction = Aij)(x,y) = k .a r_(x,y) (39)

where

= main beam propagation vector,

Ar(x,y) = Ax(x,y) e + Ay(x,y) e + Az(x,y) e . (40)

-x -y -l

With this correction the residual error is reduced to the specified level.

The requirement for measuring cross polarization ratio in the main beam

region is an accuracy of 0.75 dB. While there is no stated restriction that

this requirement applies to a nominal value for the polarization ratio, one must be assumed for practical application. For if the cross polarization

approaches zero in some direction, the ratio approaches -°° and uncertai nties

of 0.75 dB cannot be maintained at these levels. We therefore assume that the

nominal values are in the range of -30 to -35 dB. Table 7 shows an allocation

of the error for these nominal values. The error equations employed are the same as for peak gain, since the angular region of interest is in the main

beam region and the field component being measured is the main component for

the probe. Since the signals are lower, scattering, multiple reflections,

truncation, and dynamic range have a larger effect.

72
DELTA-Z SPECTRUM VERSUS ELEVATION ANGLES

Figure 43. Fourier analysis of z-position error data.

73
Table 7. Error budget for cross polarization ratio in main beam.

Error source Error in dB

Probe relative pattern 0.10

Probe polarization ratio 0.60

Probe gain 0.10

Probe alignment 0.02

Normalization constant (or power measurement) 0.20

Impedance mismatch 0.00

AUT alignment 0.00

Aliasing error 0.05

Measurement area truncation 0.20

Probe x- y-position error 0.01

Probe z-position error 0.01

Multiple reflections 0.25

Receiver amplitude nonlinearity 0.01

System phase errors 0.00

Receiver dynamic range 0.20

Room scattering 0.10

Leakage and crosstalk 0.10

Random errors in amp and phase 0.05

RSS combination (dB) 0.76

The uncertainty in the axial ratio and tilt angle of the probe used to measure

the cross component also contributes to the error, and has been included in

table 7. From the error analysis [16, eq (37)], the relationship between

probe errors and AUT results is

aAR^(K) = axial ratio error in dB

i2x. -i

2

t .I -t2t „ AR

t (K)e

L + AR

s „(K)e - AR

s

„ E (K)e - AR

t (K)

where

AR = axial ratio in dB,

t = tilt angle,

t = AUT parameters,

s" = actual probe parameters, and

Sg = probe parameters used.

74
For the 0.75 dB requirement, the probe parameters must be known to the

following uncertainties:

probe axial ratio error < 0.05 dB, and

probe tilt angle error < 20.0 deg.

Using the combination of system specifications from the gain, sidelobe,

and polarization ratio tables, we now can give the requirements for each part

of the measurement system.

7.3 Specification for Antenna Measurement System

In tables 8 through 10, specifications are given for the scanner, the

receiver, and the probe. The tables also identify the critical antenna meas- urements that determine the accuracy requirements.

Table 8. Mechanical probe positioner/scanner specifications.

Parameter Critical antenna measurement Speci f i cati on

Si ze Angular coverage L

x

> a

x + 2d tan 9X Ly > a^ + 2d tan 9y

Si ze Truncation error in:

Si delobes * < 0.15 dB error

Cross polarization * < 0.15 dB error

x-posi ti on Si del obe A < 0.01 X y-positi on Si del obe Ay < 0.01 X z-positi on Side! obe 6

Z < 0.01 X Scan plane stability Boresight Tilt change < 3 arc sec

d

L x’

Ly

a x’ ay

0 x> 9y

A

x * Ay

-

*Verify by

separation distance between probe and AUT

scan length in x-, y-di recti ons antenna aperture size in x-, y-directions

angular region of interest in x-, y-directions

position errors in x-, y-, z-directions

test on actual antenna.

75
Table 9. Receiver specifications.

Parameter Critical antenna measurement Specification

Dynamic range Sidelobe * 40 dB

Cross polarization * 40 dB

Amplitude linearity

Non peri odi

c

Gai n y < 0.002

Peri odi c Sidelobe y ( K) < 0.0004

Phase linearity

Linear error (x,y) Boresi ght M

>

< 2°/a ,a Nonperiodic (x,y) Gai n Aip < 2 deg ^ Periodic (x,y) Si del obe Ai|>(t) < 0.2 deg

y = receiver nonlinearity (see [16, eq (63)] for definition)

t = period for sinusoidal errors

Aty = receiver phase error

*Verify by test that dynamic range effect on results is within bounds of

tables 5-7.

Table 10. Probe specifications.

Parameter Critical antenna measurement Speci f i cati on

Gai n Pattern

Axial ratio

Tilt angle

Gain AGp

Sidelobe < 0.

Polarization ratio aAR

Polarization ratio AT <

< 0.10 dB

10 dB

< 0.05 dB

20 degrees

AGp = probe gain error

aAR = probe axial ratio error

aT = probe tilt angle error

This completes the summary of system specification. Although it applies

to the specific antenna systems under study, the same process can be applied

to any type of measurement requirements.

76
8. Summary

This report, along with Part 1 [1], completes the final report for

Phase I on the Development of Near-Field Test Procedures for Communication

Satellite Antennas. In this part, scan area and data point spacing requirements were analyzed to verify that the requi red parameters could be obtained

and that techniques to determine the scan parameters were available. The

results of both analysis and simulation demonstrate that the satellite antenna

requirements can be met with near-field scanning.

A study of diagnostic techniques that would use either direct near-field

data or various methods of processing to enhance the location of antenna

anomalies was made. Phase data tends to be the most sensitive, and transformation closer to the antenna can give better resolution, but care must be

exercised where evanescent modes are involved.

Techniques for the accurate alignment of the antenna to the mechanical

scan plane were described, and estimates for the uncertainty of boresight

measurement were derived.

Swept near-field techniques to define the required frequency spacing of

complete near-field scans were developed. These swept measurements can possibly give estimates of far-field frequency performance, but this will require

further development and verification.

Finally, the various parts of the study were combined, along with past

error analysis studies to derive the system specifications for satellite

antenna testing. These system specifications were developed using the

required accuracy statements on far-field ranges. It was found that the system requirements are achievable with current mechanical and electronic equipment.

9. References

[1] Newell, A. C.; Repjar, A. G. Development of near-field test procedures

for communication satellite antennas, Phase I, Part 1. Nat. Bur. Stani.

(U.S.) NBSIR 85-3031; 1985 September.

[2] Newell, A. C.; Crawford, M. L. Planar near-field measurements on hio

performance array antennas. Nat. Bur. Stand. (U.S.) NBSIR 74-380; :

j

' '• July.

77
[3] Yaghjian, A. D. Upper-bound errors in far-field antenna parameters

determined from planar near-field measurements. Part 1: Analysis. Nat.

Bur. Stand. (U.S.) Tech. Note 667; 1975.

[4] Grimm, K. R.; Hoffman, J. B.; Newell, A. C.; Francis, M. H. Final

report: results of near-field probe scanning tests for ultralow sidelobe

arrays, TSC-W41-406-kks. Technology Service Corporation Report; 1986

May.

[5] Kefauver, N. ; Cencich, T. ; Osborn, J.; Osmanski , J. T. Final report:

near-field testing of the 5-meter model of the tetrahedral truss

antenna. NASA Contract Report 178147; 1986 August.

[6] Newell, A. C.; Stubenrauch, C. F. Effect of random errors in planar

near-field measurements. IEEE Trans. Antennas Propagat., Special Issue

on Near-Field Scanning Techniques; 1988 June.

[7] Repjar, A. G. ; Kremer, D. P. Accurate evaluation of a millimeter wave compact range using planar near-field scanning. IEEE Trans, on Ant. and

Prop. AP-30( 3) ; 1982 May.

[8] Kerns, D. M. Plane-wave scatteri ng-matri x theory of antennas and

antenna-antenna interactions. Nat. Bur. Stand. (U.S.) Monogr. 162; 1981

June. 162 p.

[9] Hamada, S.; Yeh, Y. Computer reconstruction of near-zone field from

given far-zone data of two-dimensional objects. IEEE Trans. Antennas

Propagat. AP-25: 304-311; 1977 May.

[10] Hamada, S.; Ingerson, P. G.; Rush, W. V. T. Reflector radiation pattern

from planar near-field measurements of array feed. IEEE Trans. Antennas

Propagat. AP-28: 436-442; 1980 July.

[11] Newell, A. C. Nat. Bur. Stand. (U.S.), private communication, 1985.

[12] Mayer, C. E.; Davis, J. H.; Peters, W. L. Ill; Vogel, W. J. A holographic surface measurement of the Texas 4.9-m antenna at 86 GHz. IEEE

Trans. Instrum. Meas. IM-32: 102-109; 1983 March.

[13] Godwin, M. P. ; Whitaker, A. J. T. ; Bennett, J. C.; Anderson, A. P. Microwave diagnostics of the Chilbolton 25M antenna using the 0TS satellite. IEEE Conf. Pub. 195, Antennas and Propagation, Part I: Antennas.

1981 April; London, England. 232-235.

[14] Bennett, J. C.; Anderson, A. P. ; Mclnnes, P. A.; Whitaker, A. J. T. Microwave holographic metrology of large reflector antennas. IEEE

Trans. Antennas Propagat. AP-24: 295-303; 1976 May.

[15] Bird, T. S. Contoured-beam synthesis for array-fed reflector antennas

by field correlation. IEE Proc. 129(H): 293-298; 1982 December.

[16] Newell, A. C. Error analysis techniques for planar near-field measurements. IEEE Trans. Antennas Propagat., Special Issue on Near-Field

Scanning Techniques; 1988 June.

78
NBS-114A irev. 2 -ec) U.s. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

SHEET (See instructions)

REPORT NO.

NBSIR 87-3081 August 1988

4. TITLE AND SUBTITLE

Development of Near-Field Test Procedures for Communication

Satellite Antennas Phase I, Part 2

5. AUTHOR(S)

Allen C. Newell

6. PERFORMING ORGANIZATION (If joint or other than N BS. see in struction s) 7. Contract/Grant No.

national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gn i fi cant bibliography or literature survey, mention it here) The purpose of this program is to define and further develop the

capabilities of near-field antenna test techniques, specifically

for

. ,the requirements associated with the development and

verification testing of reconf i gurabl e, multibeam, frequency

reuse, commercial satellite antennas. This report. Phase I, Part 2, focuses on the planar near-field measurement method and covers the determination of sampling criteria and scan limits,

development of diagnostic and design assist methods, development

of beam alignment techniques, development of swept-f requency

equivalent tests, and specification of hardware requirements for

the measurement system. Phase I, Part 1, a previous report, gave

a general survey, definition, and description of near-field and

compact range measurement methods as they apply to satellite

antenna systems testing. Each of these methods was evaluated to determine how well they meet the measurement requirements.

Included for each technique was a summary of the measurement

method, discussions on probe correction and data processing,

measurement hardware considerations, a results available section,

and measurement accuracy and range certification considerations.'

The basis for the choice of the best measurement technique was established with the planar near-field measurement method

receiving the best score for the directive antennas considered.

It is for this reason that the planar near-field method is the

focus of this report.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper nomes; and separate V<-y , antenna alignment; antenna Foresight measurements; antenna diagnostics; ant'

measurements $ antennas; near-field measurements; near- field testing; planar n> scanning; satellite antennas; swept-frequency measurements

13. AVAILABILITY

fcxl Unlimited

| | For Official Distribution. Do Not Release to NTIS

i | Order From Superintendent of Documents, U.S. Government Printing Office, Washington. D.C. 20402.

14. NO. OF

PRINTED PAGES

84

IS. Price

jCX] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

-

u. S. GOVERNMENT PRINTING OFFICE: 1983 -674-153/ 5016