Antenna mirror-surface measuring system

A positioner supports an antenna at an optional rotating angle and the mirror surface of the antenna at different rotating angles is measured. A computer expands the measured value into series using polar coordinates system associated with the measuring system, whereby the intrinsic deformation of the mirror surface under the zero-gravity condition and the deformation due to gravity are separately measured.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to an apparatus and a method for measuring the 
accuracy of a mirror surface of a reflecting mirror antenna or the like 
which are mounted on a satellite. 
2. Description of the Prior Art 
An example of apparatus of this type in the prior art is shown in FIG. 1. 
The arrangement shown in FIG. 1 is disclosed in the "Antenna Engineering 
Handbook" edited by the Japanese Institute of Electronics, Information and 
Communication Engineers, p. 458, Jun. 20, 1988, published by OHM Co., Ltd. 
In FIG. 1, the numeral 1 denotes an antenna, 2 denotes a theodolite for 
measuring the mirror surface of the antenna by the triangulation method, 
and 3 denotes a controller for measuring the mirror surface with the 
theodolite 2. 
The operation of the apparatus shown in FIG. 1 is as follows: The antenna 1 
is fixed in a horizontal position so that the mirror surface of the 
antenna can be seen from the theodolites 2. A plurality of theodolites 2 
face to the mirror surface from different positions and measure the 
configuration of the mirror surface in the three-dimensional coordinates 
system. A controller 3 controls the theodolites 3 to automatically measure 
points on the mirror surface directed by the theodolites and record the 
measured results. Therefore, the configuration of the mirror surface can 
be measured in the three-dimensional coordinates system. 
Another apparatus of this type in the prior art is shown in FIG. 2. This 
arrangement is also described in the "Antenna Engineering Handbook" edited 
by the Japanese Institute of Electronics, Information and Communication 
Engineers, p. 449, published by OHM Co., Ltd. on Jun. 20, 1988. In FIG. 2, 
the numeral 4 denotes a probe for measuring the electric field 
distribution in the vicinity of antenna 1, 5 denotes a scanner for 
plane-scanning the probe 4, and 6 denotes a transceiver. The beam axis of 
the antenna 1 is defined as the axis z, and thereby the coordinates 
associated with the antenna are defined as the x-y-z orthogonal 
coordinates system and the coordinates associated with the scanner as the 
X-Y-Z orthogonal coordinates system. Moreover, the antenna 1 is placed so 
that the x-y plane and X-Y plane are parallel. With the arrangement, the 
electric field distribution in the vicinity of the antenna is measured and 
the deviation from the phase distribution of the ideal mirror surface is 
obtained from the measured phase distribution, thereby an error of the 
mirror surface can be obtained. 
Since conventional antenna mirror surface measuring apparatuses were 
constituted as explained above, the measurement was made under the 
condition that an antenna is deformed by the influence of-the gravity. 
Accordingly, here rises a problem that the intrinsic deformation of the 
mirror surface in such a condition that a satellite is set on an orbit, 
namely under the zero-gravity condition cannot be separated from the 
deformation due to the gravity. 
SUMMARY OF THE INVENTION 
The present invention has been proposed to solve the problems explained 
above and it is therefore an object of the present invention to provide an 
antenna mirror surface measuring apparatus and a measuring method for 
separately measuring the intrinsic deformation of a mirror surface under 
the zero-gravity condition and the deformation of the mirror surface due 
to the gravity for an antenna mounted on a satellite. 
In accordance with the first aspect of the invention, an antenna mirror 
surface measuring apparatus comprises a distance and angle measuring 
means, a positioner for supporting an antenna to be measured, rotating the 
antenna around the main beam of this antenna and stopping the antenna at 
predetermined rotating angles to measure the configuration of the antenna 
mirror surface at each position of a plurality of different rotating 
angles, and a computer for executing an arithmetic operation of the series 
expansion of the measured values and separating the configuration of tile 
mirror surface which is independent of the rotating angles from the 
deformation of the mirror surface which is dependent on the rotating 
angles. 
In accordance with the second aspect of the invention, an antenna mirror 
surface measuring apparatus comprises a probe for measuring the electric 
field distribution, a scanner for scanning this probe, a transceiver for 
transmitting and receiving a signal between an antenna to be measured and 
the probe, a positioner for supporting the antenna to be measured, 
rotating the antenna around the main beam of this antenna and stopping the 
antenna at predetermined rotating angles to measure the configuration of 
the mirror surface of the antenna at each position of a plurality of 
different rotating angles, and a completer for executing an arithmetic 
operation of the series expansion of the measured values and separating 
the configuration of the mirror surface which is independent of the 
rotating angles from the deformation of the mirror surface which is 
dependent on the rotating angles. 
In accordance with the third aspect of the invention, an antenna mirror 
surface measuring apparatus comprises a rotating base supporting an 
antenna to be measured arid having two or more rotating axes, a 
transceiver for transmitting and receiving a signal to and from the 
antenna to be measured a positioner for supporting the antenna to be 
measured, rotating the antenna around the main beam of this antenna and 
stopping the antenna at predetermined rotating angles to measure the 
configuration of the mirror surface of the antenna at each position of a 
plurality of different rotating angles, and a computer for executing an 
arithmetic calculation of the series expansion of the measured values and 
separating the configuration of the mirror surface which is independent of 
the rotating angles from the deformation of the mirror surface which is 
dependent on the rotating angles. 
Further, in accordance with the fourth aspect of the invention, an antenna 
mirror surface measuring method includes the steps of measuring 
two-dimensional electric field distribution in the vicinity of a 
reflecting mirror antenna, executing arithmetic operation of the measured 
values based on the plane wave expansion, converting the values for the 
measured position to values for a position different from the measured 
position, and obtaining the configuration of the mirror surface from the 
phase item of the electric field distribution. 
Moreover, in accordance with the fifth aspect of the invention, an antenna 
mirror surface measuring method includes the steps of measuring 
two-dimensional electric field distribution in the vicinity of the range 
narrower than the aperture of an antenna to be measured, executing 
an-arithmetic operation of the measured values based on the least squares 
method and the series expansion, separating the configuration of the 
mirror surface which is independent of the rotating angles from the 
deformation of the mirror surface which is dependent on the rotating 
angles, and obtaining the configuration of the antenna to be measured. 
With the first aspect of the invention, the antenna mirror surface 
measuring apparatus can separately measure the intrinsic deformation of 
the mirror under the zero-gravity condition and the deformation of the 
mirror surface due to the gravity, because the positioner stops the 
antenna to be measured at optional rotating angles, the distance and angle 
measuring means, a controller measure the mirror surface of the antenna at 
different rotating angles and the computer expands a configurational value 
into series at a predetermined point on the mirror surface using the polar 
coordinates associated with the measuring system. 
With the second aspect of the invention, the antenna mirror surface 
measuring apparatus can measure electrical characteristics under the 
zero-gravity condition and separately measure the intrinsic deformation of 
the mirror surface under the zero-gravity condition and the deformation of 
the mirror surface due to gravity, because the positioner stops the 
antenna to be measured at optional rotating angles, the two-dimensional 
electric field distribution are measured by the probe, the scanner and the 
transceiver at the different rotating angles of this antenna and the 
computer expands the phase distribution of predetermined points on the 
mirror surface into series using the polar coordinates associated with the 
measuring system. 
With the third aspect of the invention, the antenna mirror surface 
measuring apparatus makes outdoor measurement, easier since a scanner is 
not used. As a result, the measurement of a large diameter antenna can be 
made easily. Further, the intrinsic deformation under the zero-gravity 
condition and the deformation of the mirror surface due to gravity can be 
measured separately, because the positioner stops the antenna at optional 
rotating angles, the rotating base enables spherical scanning or 
cylindrical scanning by using the two or more rotating axes, the electric 
field distributions at different rotating angles of the antenna are 
measured by using a probe and a transceiver, and the computer obtains the 
electric field distribution in the vicinity of the antenna from the 
measured values and expands the phase distribution of predetermined points 
on the mirror surface using the polar coordinates associated with the 
measuring system. 
With the fourth aspect of the invention, the antenna mirror surface 
measuring method eliminates the influence of a primary horn or 
sub-reflecting mirror other than the main reflecting mirror and separately 
measures the intrinsic deformation of the mirror surface under the 
zero-gravity condition and the deformation of the mirror surface due to 
gravity, because the measured values of the two-dimensional electric field 
distribution of the reflecting mirror antenna for the measured position 
are converted to values for a position different from the measured 
position. 
With the fifth aspect of the invention, the antenna mirror surface 
measuring method enables the range for measuring the electric field 
distribution off the antenna to be narrowered than the aperture diameter. 
As a result, the probe is scanned by tile scanner over the range narrower 
than the aperture diameter for obtaining the configuration of the mirror 
surface of a large diameter antenna and the intrinsic deformation of tile 
mirror surface under the zero-gravity condition and the deformation of 
mirror surface due to gravity are separately measured.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIG. 3, there is shown the first embodiment according to the 
present invention. In FIG. 3, the reference numerals 1 to 3 denote the 
elements similar to those of the conventional apparatus shown in FIG. 1. 
The numeral 7 denotes a positioner which supports an antenna 1 and rotates 
the antenna around the one axis, 8 denotes a base rack which supports the 
antenna 1 and the positioner 7 at a predetermined height, 9 denotes a 
computer which executes arithmetic calculation for coordinates of the 
mirror surface measured at different rotating angles of the antenna 1. 
In the operation, the coordinate systems associated with the antenna 1 are 
defined using the x-y-z orthogonal coordinates system and r-.theta. polar 
coordinates system and the coordinates systems associated with the 
measuring system are defined using the X-Y-X orthogonal coordinates system 
and r-.phi. polar coordinates system. A rotating angle .PHI. 
(.phi.=.theta.+.PHI.) is a value according to the polar coordinates system 
of the measuring system. The positioner 7 rotates the antenna 1 by a 
predetermined rotating angle and fixes it at this angle. The theodolite 2 
measures the mirror surface of the antenna 1 in three dimensions, that is, 
the roughness of the surface at the rotating position directed by the 
controller 3. Next, the positioner 7 is rotated to measure the mirror 
surface in three dimensions at a different angle. Thus, the 
three-dimensional coordinates of the mirror surface when the rotating 
angle is .PHI..sub.i can be obtained by repeating such measurements. A 
deviation in the normal direction from the ideal mirror surface, namely a 
mirror surface error f.sub.i (r, .theta.) for each point is obtained from 
such measured values. The intrinsic deformation component of the mirror 
surface under the zero-gravity condition is separated from the deformation 
component of the mirror surface due to gravity by obtaining the series 
expansion of the measured mirror surface error. First, in the case of 
measuring the mirror surface by continuously changing the rotating angles, 
a measured value f (r, .theta., .phi.) of the mirror surface error can be 
expanded as follows by using the Fourier series for the angle component 
.phi.: 
##EQU1## 
The Fourier coefficients a.sub.o (r, .theta.), a.sub.n (r, .theta.), 
b.sub.n (r, .theta.) are determined at each point (r, .theta.) . In the 
case where the number of times of measurement N (.gtoreq.2) executed at 
different rotating angles is not sufficiently large, the number of 
expansion terms must be reduced to a Finite number. When the rotating 
angles are selected at equal angular intervals, the following relationship 
can be obtained. 
EQU .PHI..sub.i =2.pi.i/N, (i=1, 2, . . . , N) (2) 
Therefore, the following Fourier series can also be obtained. 
##STR1## 
Moreover, measurement errors caused by other factors can be analyzed more 
easily by expanding the respective coefficients a.sub.o (r, .theta.), 
a.sub.n (r, .theta.), b.sub.n (r, .theta.) using the Fourier series for 
the angular component .theta. associated with the mirror surface as 
follows: 
##EQU2## 
FIG. 4 is a diagram for explaining a deformation caused by gravity that the 
mirror surface would be subjected to. An intrinsic configuration of the 
mirror surface under the zero-gravity condition is indicated by a solid 
line 1a, while a deformation due to the gravity that the mirror surface 
would be subjected to is indicated by a broken line 1b. In the case where 
the deformation due to the gravity to the mirror surface is very small and 
linear, a displacement vector .delta. in the normal direction of the 
gravity is expressed as follows: 
EQU .delta.(r, .theta., .phi.)=[C(r, .theta.)G.multidot.n]n (5) 
Where the vector n is a normal unit vector of the mirror surface, the 
vector G is a vector of the gravity and C (r, .theta.) is an unknown 
scalar coefficient depending on the deformation of each point on the 
mirror surface. The component .delta..sub.n in the normal direction of the 
vector .delta. can be summarized as follows: 
EQU .delta..sub.n (r, .theta., .phi.)=A.sub.o (r, .theta., C)+A.sub.1 (r, 
.theta., C) cos .phi.+B.sub.1 (r, .theta., C) sin .phi. (6) 
Thus, if the intrinsic deformation of the mirror surface under the 
zero-gravity condition is defined as q (r, .theta.), a mirror surface 
error f (r, .theta., .PHI.) is given by 
EQU f(r, .theta., .phi.)=q(r, .theta.)+.delta..sub.n (r, .theta., .phi.)(7) 
The intrinsic deformation q (r, .theta.) of the mirror surface under the 
zero-gravity condition and the deformation due to gravity .delta..sub.n 
(r, .theta., .phi.) can be obtained at each point by comparing 
coefficients of the equations (1) to (8) and the equation (7) and solving 
these simultaneous equations. 
Thus, the intrinsic deformation of the mirror surface under the 
zero-gravity condition and the deformation of the mirror surface due to 
gravity can be separately measured by expanding the configuration at a 
predetermined point on the mirror surface into series using the polar 
coordinates associated with the measuring system. 
In this embodiment, a theodolite is used, but meritorious effects similar 
to those of this embodiment can also be attained even by using other 
mechanical measuring apparatus such as a photographic measuring apparatus, 
laser holography or the like. Moreover, an antenna to be measured may be 
any type of antenna such as a parabolic antenna, offset type antenna, dual 
reflecting mirror antenna or the like in such a manner that similar 
meritorious effects can be obtained. 
FIG. 5 is a schematic structural diagram indicating the second embodiment 
according to the present invention. The elements 1, 4 to 6 in FIG. 5 
denote elements similar to those in the conventional apparatus shown in 
FIG. 2. The numerals 7 to 9 denote the elements same as those of the first 
embodiment of the present invention shown in FIG. 3. The beam axis of the 
antenna is defined as the axis coordinates system associated with the 
antenna is defined by the x-y-z orthogonal coordinates system, while the 
coordinates system associated with the scanner 5 is defined by the X-Y-Z 
orthogonal coordinates system, wherein the axes z and Z are aligned. The 
antenna i is placed so that the x-y plane and the X-Y are set in parallel. 
The positioner 7 rotates the antenna 1 up to an optional rotating angle 
.PHI. (.phi.=.theta.+.PHI.) and fixes it in this condition. A probe 4 is 
driven by a scanner 5 so as to scan to measure two-dimensional electric 
field distribution of the fixed antenna 1. Next, the positioner 7 is 
rotated and is fixed a different rotating angle to measure the 
two-dimensional electric field distribution. The two-dimensional field 
distribution when the rotating angle is .PHI..sub.i can be obtained by 
repeating such measurement. A deviation from the phase distribution of an 
ideal mirror surface, namely a phase error F.sub.i (r, .theta.) for each 
point can be obtained by the phase distribution of the measured values. 
The obtained phase error values thus obtained are expanded into series 
using the equations (1) to (4). Moreover, the deformation due to gravity 
is indicated by .delta. of the equation (5). When the component in the 
direction z of .delta. is defined as .delta..sub.z, a phase error 
.delta..sub.p [rad] can be expressed as follows: 
EQU .delta..sub.p (r, .theta., .phi.)=.delta..sub.z (r, .theta., .phi.)(1-cos 
.THETA.)(2.pi./.lambda.) (8) 
Thereby, .delta..sub.p can be summarized with respect to .phi. similar to 
the equation (6). When a phase error generated by the intrinsic 
deformation of the mirror surface under the zero-gravity condition is 
defined as p (r, .theta.), a phase error F (r, .theta., .PHI.) can be 
expressed as follows: 
EQU F(r, .theta., .phi.)=p(r, .theta.)+.delta..sub.p (r, .theta., .phi.)(9) 
Thus, the intrinsic deformation p (r, .theta.) of the mirror surface under 
the zero-gravity condition and the deformation .delta..sub.p (r, .theta., 
.phi.) due to gravity can be obtained. In addition, in the present 
invention, since the intrinsic deformation of the mirror surface under the 
zero-gravity condition and the electric field distribution of the antenna 
to be measured can be measured, an electric characteristic under the 
zero-gravity condition can be obtained and the performance of antenna can 
be evaluated simultaneously. 
Accordingly, the intrinsic deformation of the mirror surface under the 
zero-gravity condition and the deformation due to gravity can be 
separately measured by expanding the phase distribution of the 
predetermined point on the mirror surface into series using the polar 
coordinates system associated with the measuring system. 
Here, it is noted that even if a transmitter and a receiver are integrated 
as a transceiver, of these are separately disposed, similar merits can be 
obtained. 
FIG. 6 is a schematic diagram illustrating a structure of the third 
embodiment of the present invention. In FIG. 6, the numerals 4 to 6 denote 
elements similar to those of a conventional apparatus shown in FIG. 2. The 
numeral 7 to 9 denote elements similar to those of the first embodiment of 
the present invention shown in FIG. 3. In FIG. 3, an antenna 10 is a 
Cassegrain antenna, 10a denotes a main effecting mirror consisting of an 
axial symmetrical parabola having the focal length or distance F.sub.1, 
10b denotes a subreflecting mirror consisting of a hyperboloid of 
revolution having the focal distances F.sub.1 and F.sub.2, 10c denotes a 
primary born having the phase center at the point F.sub.2. Measurement off 
the electric field distribution by placing a probe 4 nearer the main 
reflecting mirror 10a than the subreflecting: mirror 10b is obvious from 
the figure. Therefore, the electric field distribution must be measured at 
a position such as a plane I--I. At the plane I--I, an electromagnetic 
wave radiated from the primary horn 10c is partly reflected by the 
subreflecting mirror 10b and goes to the main reflecting mirror 10a and is 
then reflected again thereby to propagate after being converted into the 
plane wave. On the other hand, a portion of the electromagnetic wave 
radiated from the primary horn 10c departs from the subreflecting mirror 
10b and the spillover propagates as a spherical wave. FIG. 6, such plane 
waves and spherical waves are respectively indicated by a broken line and 
a dotted line. Therefore, interference fringes are generated by 
interference of these waves. It is noted that the measured phase 
distribution does not accurately represent the actual mirror surface. In 
order to eliminate the influence of such a spillover, the electric field 
distribution measured at the plane I--I is converted to that of waves 
which would exist at the plane II--II. Here, such a positional conversion 
of electric field distribution is made using a plane wave expansion 
method. When z=z.sub.1 at the plane I--I, the field distribution vector 
E(r) can be expanded as follows: 
##EQU3## 
Where the vector b (1, K) denotes the spectrum of the plane wave of the 
electric field component of TM wave in regard to the axis z, the vector b 
(2, K) denotes the spectrum of the plane wave of the electric field 
component of TE wave in regard to the axis z, .gamma. is a propagation 
constant, k is the number of free space waves, .omega. is a propagation 
angular frequency, .mu. is the permeability, and .epsilon. is the 
dielectric constant. Moreover, in the coordinates system of FIG. 7, the 
vector r means the positional vectors (x, y, z.sub.1), (r, 74 , .THETA.), 
while the vector R means the vector r, the vectors e.sub.x, e.sub.y, 
e.sub.z are unit vectors of the component perpendicular to the axis z of 
the positional x, y, z coordinates system, respectively, and b (m, k) is 
expressed as follows by the inverse Fourier transformation: 
EQU b(m,K)=e.sup.-j.gamma.z.sbsp.1 /(2.pi.)K.sub.m .multidot..intg.E.sub.t 
(R.sub.1 z.sub.1)e.sup.-jK.multidot.R dR, (m=1,2) (12) 
Here, E.sub.t is the component of the electric field distribution 
perpendicular to the axis z. Therefore, when z=z.sub.o in the plane 
II--II, the electric field distribution in the plane II--II can be 
obtained under the condition, z=z.sub.o, by substituting the plane wave 
spectrum b (m, K) of the equation (12) into the equation (10) . Thus, a 
phase distribution which accurately represents the mirror surface can be 
obtained and the deviation from the phase distribution of an ideal mirror 
surface, namely the phase error F.sub.i (r, .theta.) can be obtained at 
each point. In addition, from the equations (8) and (9) , the intrinsic 
deformation of the mirror surface under the zero-gravity condition and the 
deformation of the mirror surface due to gravity can be separately 
obtained in the same manner as the second embodiment of the present 
invention. 
Thus, the influence of the primary horn or auxiliary reflecting mirror- 
other than the main reflecting mirror can be eliminated by converting the 
measured two-dimensional electric field distribution into the electric 
field distribution at the position nearer the mirror surface. Further, the 
intrinsic deformation of the mirror surface under the zero-gravity 
condition and the deformation of the mirror surface due to gravity can be 
separately measured. 
FIG. 8 is a schematic diagram illustrating a structure of the fourth 
embodiment of the present invention. The reference numerals 4 to 6 denote 
elements similar to those of a conventional apparatus shown in FIG. 2. The 
numeral 7 to 9 are elements similar to those of the first embodiment of 
the present invention shown in FIG. 3. The numeral 11 denotes a large 
diameter antenna. FIG. 9 shows the aperture plane of the antenna 5 
projected in the scanning surface off the scanner 5 and the range of 
scanner in such a case that the rotating angles are given at the intervals 
of 90.degree.. In this figure, the scanning range when the rotating angle 
is 0.degree. is indicated by solid lines and oblique solid lines, the 
scanning range when the rotating angle is 180.degree. is indicated by 
broken lines and oblique broken lines, the scanning range when the 
rotating angle is 90.degree. is indicated by a dot-and-dash chain line, 
and the scanning range when the rotating angle is 270.degree. is indicated 
by a two-dots-and-dash chain line. Here, the scanner 5 does not scan the 
entire part of the aperture plane. When the rotating angle is .PHI..sub.i, 
the scanning range is set to S.sub.i and the measured value of the phase 
distribution is set to F.sub.i (r, .theta.) and the Fourier coefficient of 
the equation (1) is obtained by the least squares method. First, the least 
square error e (r, .theta.) is defined as follows: 
##EQU4## 
From this equation, e (r, .theta.) is minimized for each point (r, 
.theta.). Namely, the Fourier coefficients a.sub.o (r, .theta.), a.sub.n 
(5, .theta.), b.sub.n (r, .theta.) can be obtained by solving the 
following equation: 
##EQU5## 
Therefore, the Fourier coefficients can be solved in a manner similar to 
the second embodiment of the present invention by comparing them with the 
coefficients of the equation (9). 
Thus, since the range for measuring the field distribution of an antenna by 
scanning the probe with the scanner is narrowed more than the aperture 
plane of the antenna, the intrinsic deformation of the mirror surface 
under the zero-gravity condition and the deformation of the mirror surface 
due to gravity can be separately measured even for a large diameter 
antenna. 
In this embodiment, the electric field distribution of an antenna to be 
measured is measured, but the similar effect can also be ensured by a 
mechanical measurement of the configuration of the mirror surface with a 
theodolite as in the case of the first embodiment. 
FIG. 10 is a schematic diagram illustrating a structure of the sixth 
embodiment of the present invention. The reference numerals 4 to 6 denote 
elements similar to those in the conventional apparatus shown in FIG. 2. 
The numerals 7 to 9 denote elements similar to those off the first 
embodiment of the present invention shown in FIG. 3. A positioner 7 is set 
to rotate around the axis orthogonal to the direction vector of the 
gravitational force, making parallel the aperture plane and the scanning 
surface of the scanner. When the orthogonal unit vector (i, j, k) 
depending on the measuring system is defined, the vector G of the gravity 
is defined as follows: 
EQU G=-gi (15) 
Moreover, when the mirror surface is rotational symmetry, the normal unit 
vector n of the mirror surface is expressed as follows from the unit 
vector (e.sub..rho., e.sub..THETA., e.sub..theta.) of the spherical 
coordinates system: 
EQU n=Ae.sub..rho. +Be.sub..THETA. (16) 
The deformation .delta..sub.p (r, .theta., .phi.) can be expressed as 
follows by substituting the equations (5), (8) into the equations (15) and 
(16): 
EQU .delta..sub.p (r, .theta., .PHI.)=A.sub.1 (r, .theta., .phi.) cos .phi.(17) 
When the coefficients are compared with those of the equation (1) after 
substituting the equation (17) into the equation (9), the Fourier 
coefficient a.sub.o (r, .theta.) corresponds to the intrinsic deformation 
p (r, .theta.) of the mirror surface and a.sub.1 (r, .theta.) cos .phi. 
corresponds to the deformation .delta..sub.p (r, .theta., .phi.) caused by 
gravity. 
Accordingly, since the positioner rotates around the axis orthogonal to the 
direction vector of gravity force, the intrinsic deformation of the mirror 
surface under the zero-gravity condition and the deformation of the mirror 
surface due to the gravity can be separately measured. 
In this embodiment 5, an electric field distribution of an antenna to be 
measured is measured, but it should be noted that a similar effect can 
also be obtained even when a mechanical measurement of a shape of mirror 
surface is used with a theodolite. 
FIG. 11 is a schematic diagram illustrating a structure of the fifth 
embodiment of the present invention. The reference numerals 4 to 6 denote 
elements similar to those of the conventional apparatus shown in FIG. 2. 
The numerals 7 to 9 denote elements similar to those of the first 
embodiment of the present invention shown in FIG. 3. The numeral 12 
denotes a mesh antenna consisting of a metallic mesh 12a and a mast 12b, 
13 denotes a supporting means formed by a material having a high rigidity 
for fixing the mast 12b in order to suppress the deformation due to 
gravity to a small quantity when the antenna rotates. When the antenna is 
rotated by a positioner 7, if the mirror surface generates non-linear 
deformation, the component of high order Fourier coefficient becomes large 
in the equation (1) and the Fourier expansion becomes difficult in the 
case where the number of times of measurement becomes small. The solution 
can be obtained in the same manner as the second embodiment of the present 
invention by controlling a deformation of the mast to a linear deformation 
using the supporting means 13. 
Thus, since the supporting means formed by a material having a high 
rigidity fixes and rotates the mast for extending a metal mesh, the 
intrinsic deformation of the mirror surface under the zero-gravity 
condition and the deformation of the mirror surface due to gravity can be 
separately measured, even when the mirror surface generates extremely 
large deformation due to gravity. 
In this embodiment, the electric field distribution of an antenna to be 
measured is measured, but the similar effect can also be obtained by 
mechanical measurement of a shape of mirror surface using a theodolite as 
in the case of the first embodiment. 
Referring now to FIG. 12, there is shown a schematic diagram illustrating a 
structure o-F the seventh embodiment of the present invention. The 
reference numerals 1, 6, 7, and 9 denote elements similar to those of the 
first embodiment of the present invention shown in FIG. 3. The numeral 14 
denotes a transmitting antenna, 15 denotes a reference antenna, 16 denotes 
a rotating base for spherical scanning. A positioner 7 rotates around the 
beam axis of the antenna, stops at a predetermined rotating angle, 
measures the two-dimensional electric field distribution of the antenna by 
the spherical scanning at different rotating angles converts the measured 
values of two-dimensional field distribution into the field distribution 
at a position nearer the mirror surface with a computer in order to obtain 
the phase distribution corresponding to a predetermined position on the 
mirror surface. Such a positional conversion of electric field 
distribution can be obtained from the equations (10) to (12). Moreover, 
since the spillover by the primary horn and the diffraction wave by the 
subreflecting mirror give influence on a wide angle plane, this influence 
can be reduced by measuring the electric; field distribution at 
sufficiently far area. Here, when the two-dimensional electric field 
distribution at the distant position is defined as E.sub.i (.theta.', 
.PHI.') for the rotating angle .phi..sub.i and positional conversion is 
executed to the aperture surface of z=0, the electric field distribution 
E.sub.i(ap) (x, y) at the aperture surface is expressed as follows: 
EQU E.sub.i(ap) (x,y)=.intg..intg.E.sub.i (.theta.', 
.phi.')c.sup.-j(x.theta.'+y.phi.') d.theta.'d.phi.' (18) 
Thus, the phase distribution F.sub.i (r, .theta.) can be obtained and the 
solution can be obtained in the same manner as the second embodiment of 
the present invention. 
Accordingly, the intrinsic deformation of the mirror surface under the 
zero-gravity condition and the deformation of the mirror surface due to 
gravity can be separately measured by measuring the values at a far field. 
In the ease of this embodiment, an antenna to be measured is in the 
receiving operation. But, in the case where the antenna is in the 
transmitting operation, the similar effect can also be attained. In 
addition, in the embodiments 2 to 6, the transmitting and receiving 
operations are changeable and similar merits can be achieved in either 
operation mode. In the above embodiments, the electric field distribution 
is measured at the far field of the antenna to be measured, but similar 
merits can also be attained even when the electric field distribution is 
measured in the vicinity of the antenna. Moreover, in the above 
embodiments, the rotating base is capable of rotating around two or more 
axes for the spherical scanning, but similar merits can also be obtained 
even if the rotating base rotates around only one axis and the scanner 
scans the antenna or probe only in one direction for the cylindrical 
scanning. Further, similar merits can also be obtained even when the 
electric field distribution is converted to that in a different position 
as in the case of the third embodiment. In addition, similar merits can be 
obtained even if the rotating axis of the positioner is set within the 
horizontal plane as in the case of the fifth embodiment. Moreover, similar 
meritorious effects can also be achieved even if the supporting means is 
provided behind the antenna as in the case of the sixth embodiment. 
As explained above, the antenna mirror surface measuring apparatus 
according to the first aspect of the present invention provides the merits 
that the intrinsic deformation of mirror surface under the zero-gravity 
condition and the deformation of mirror surface due to gravity can be 
separately measured, because the positioner stops the antenna to be 
measured at a predetermined rotating angle, the distance and angle 
measuring means and a controller measure the shape of the mirror surface 
of the antenna to be measured at different rotating angles and the 
computer expands -the shape of a predetermined point on the mirror surface 
into series on the polar coordinates system fixed to the measuring system. 
Moreover, the antenna mirror surface measuring apparatus according to the 
second aspect of the invention provides the merits that the electrical 
characteristics under the zero-gravity condition can be measured and the 
intrinsic deformation of mirror surface under the zero-gravity condition 
and the deformation of mirror surface by gravity can separately be 
measured, because the positioner stops the antenna to be measured at -the 
predetermined rotating angle, the probe, scanner and transceiver measure 
two-dimensional electric field distribution of this antenna to be measured 
at different rotating angles, and the computer expands the phase 
distribution of predetermined point on the mirror surface to series on the 
polar coordinates system fixed to the measuring system. 
In addition, the antenna mirror surface measuring apparatus according to 
the third aspect of the invention provides the merits that the outdoor 
measurement is made easier since the scanner is not required, measurement 
is suitable for a large diameter antenna and the intrinsic deformation of 
mirror surface under the zero-gravity condition and the deformation of 
mirror surface by gravity can be separately measured, because the 
positioner stops the antenna at the predetermined rotating angle and 
realizes the spherical scanning or cylindrical scanning since the rotating 
base has two or more rotating axes, the probe and transceiver measure the 
electric field distributions at different rotating angles of the antenna 
and the computer obtains the electric field distribution in the vicinity 
of antenna from the measured values and expands the phase distribution of 
the predetermined point on the mirror surface into series on the polar 
coordinates system fixed to the measuring system. 
Furthermore, the antenna mirror surface measuring method according to the 
fourth aspect of the invention provides the merits that the influence of 
the primary horn or subreflecting mirror other than the main reflecting 
mirror can be eliminated and the intrinsic deformation of mirror surface 
under the zero-gravity condition and the deformation of mirror surface by 
gravity can separately be measured, because measured values of 
two-dimensional electric field distribution of the reflecting mirror 
antenna can be converted to positions different from the measuring 
position. 
Moreover, the antenna mirror surface measuring method according to the 
fifth aspect of the invention provides the merits that the shape of mirror 
surface of a larger diameter antenna is scanned with the probe which is 
driven by the scanner for the range narrower than the antenna diameter and 
the intrinsic deformation of mirror surface under the zero-gravity 
condition and the deformation of mirror surface due to gravity can be 
separately measured, because the range for measuring the electric field 
distribution off the antenna to be measured can be made narrower than the 
aperture plane.