[alma-config]comparison of the boone's and kogan's compact configurations
Leonia Kogan
lkogan at aoc.nrao.edu
Sun Jan 27 11:22:35 EST 2002
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Dear Dave and Frederick,
I want to return back to the comparison of the boone's and kogan's compact configurations presented at the recent CDR meeting.
You both do not see the side lobes of ~13% at the boone's configuration
and I am strongly sure that they are there.
I think the difference is that we are looking at something different.
To clarify the situation I made another test yesterday:
I wrote the fortran task (beam.f) which calculate the worst side lobe inside of the circle of the given radius (RADIM) at the beam using the direct
Fourier transform of configurations.
The configurations I used are at the attached files BOONE_PREC.COMP and
ME.COMP
The comparison result is given at the following tables:
BOONE's CONFIGURATION
Radius of the circle || 8 | 10 | 15 | 20 | 25 | 30 |
----------------------------------------------------------------------------|
Worst sidelobe, % || 2.7 | 4.5 | 6.4 | 9.3 | 10.8 | 12.4 |
----------------------------------------------------------------------------|
at NX0 || 5.2 | 9.2 | -9.2 | -14.6 | -8.4 | -18.2 |
at NY0 || 3 | -1.6 | -8.2 | 9.8 | -22.4 | -22.8 |
KOGAN's CONFIGURATION
Radius of the circle || 8 | 10 | 15 | 20 | 25 | 30 |
----------------------------------------------------------------------------|
Worst sidelobe, % || 1.4 | 4.9 | 5.1 | 5.1 | 5.1 | 5.1 |
----------------------------------------------------------------------------|
at NX0 || 0 | 10 | 11.6 | 11.6 | 11.6 | 11.6 |
at NY0 || -7.2 | 0 | -5.8 | -5.8 | -5.8 | -5.8 |
The Radius and NX0, NY0 are given at the number of resolutio element lambda/D
Comparing the two tables we arrive to the conclusion that:
----------------------------------------------------------------------------|
The kogan's configuration has lower side lobes than the boone's one
inside of any circle.
For the radius >22 the kogan's configuration give more than factor 2
advantage at side lobes
----------------------------------------------------------------------------|
I see only one reason that both of you do not see the large sidelobes
at the Boone's configuration: You look at the small radius near the center
How big the radius should be chosen?
It depends on the primary beam width.
Consider the circle dish with flat illumination.
The one side width of the such dish beam (at the zero level) is
1.2*lambda/d, where d is the dish diameter
For a tapered illumination the primary beam will be wider.
The radius of the side lobes optimization shoud be at least twise bigger
(check this statement with Mark Holdaway)
So :
Radius *lamda/D > 2.4*lambda/d => Radius >2.4 * D/d {D=150, d=12} = 30
I am looking forward to here you
Leonia
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C calculate the beam shape to check BOONE
C Report maximum value of the side lobes
INTEGER I, K, IANT, NPOINT, NANT
REAL XARR(100), YARR(100), D, NX, NY, NX0, NY0, X, Y, RE, IM, ARG,
* TWOPI, RADI, RADIM
open(unit=8,file='BOONE_PREC.COMP')
C
TWOPI = 2 * 3.141592
C D is diameter of the array
D = 200
C The beam size is NPOINT*NPOINT
C pixels. The pixel size is 0.2
NPOINT = 400
C RADIM is maximum radius at the
C beam plane
RADIM = 40
DO 100 I = 1, 100
READ(8,1000, END=200) X, Y
XARR(I) = X
YARR(I) = Y
PRINT 2000, X, Y
100 CONTINUE
200 CONTINUE
NANT = I-1
PRINT 2100, NANT
2100 FORMAT('NANT=', I3)
C calculate the beam
NX = -0.2 * (NPOINT/2)
BEMMAX = 0
DO 500 I = 1, NPOINT
NX = NX + 0.2
NY = -0.2 * (NPOINT/2)
DO 400 K = 1, NPOINT
NY = NY + 0.2
RADI = SQRT(NX*NX+NY*NY)
C take the point not more far
C than RADIM
IF (RADI .GT. RADIM) GO TO 400
C exclude the main lobe
IF ((ABS(NY) .LT. 5).AND. (ABS(NX) .LT. 5)) GO TO 400
RE = 0
IM = 0
DO 300 IANT = 1, NANT
ARG = TWOPI/D *(XARR(IANT)*NX + YARR(IANT)*NY)
RE = RE + COS(ARG)
IM = IM + SIN(ARG)
300 CONTINUE
BEAM = (RE*RE + IM*IM)
IF (BEAM .GT. BEMMAX) THEN
BEMMAX = BEAM
NX0 = NX
NY0 = NY
END IF
400 CONTINUE
500 CONTINUE
PRINT 3000, BEMMAX/(NANT*NANT), NX0, NY0
C-------------------------------------
1000 FORMAT (1X, 2F20.4)
1100 FORMAT (1X)
2000 FORMAT (2F20.4)
3000 FORMAT ('WORST SIDELOBE = ',F5.3, ' at NX0=', F5.1, ' NY0=', F5.1)
END
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8.8000 25.5000
21.9000 18.5000
19.7000 -17.0000
33.3000 4.0000
2.0000 6.5000
-12.5000 10.5000
10.4000 75.0000
8.8000 44.0000
42.7000 30.0000
-9.9000 -30.0000
-9.4000 103.0000
-9.3000 50.5000
-28.0000 20.5000
53.6000 0.0000
-8.8000 -13.5000
-46.1000 -27.5000
31.0000 44.0000
38.0000 -31.0000
53.3000 77.5000
34.8000 -46.5000
-30.2000 92.0000
-38.0000 -59.5000
55.1000 -43.0000
-13.4000 74.0000
-56.0000 -70.0000
31.9000 68.0000
-18.5000 -92.0000
20.3000 -117.0000
95.6000 44.5000
-61.7000 -12.0000
-50.2000 3.5000
89.6000 -19.0000
80.9000 -55.5000
-77.6000 45.5000
67.4000 38.0000
74.1000 -87.0000
34.2000 -99.5000
-53.3000 39.5000
-57.4000 -86.0000
60.8000 93.5000
-34.0000 70.5000
21.7000 -71.5000
-17.8000 -72.5000
-68.6000 64.5000
-84.5000 -47.0000
90.6000 -68.5000
86.5000 64.0000
106.8000 -9.0000
37.6000 109.5000
2.2000 -115.5000
104.3000 -33.5000
-67.8000 34.5000
102.7000 25.5000
-93.0000 -7.5000
79.4000 14.5000
48.7000 -109.0000
-89.4000 -29.5000
-28.2000 -105.0000
-45.5000 90.0000
22.0000 112.0000
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14.2265 7.4870
-0.4220 16.5627
-12.1719 7.1481
-13.6723 -7.8371
-0.6269 -15.3959
14.8396 -7.5614
32.9233 15.4204
23.0126 29.0508
4.1336 38.8459
-14.5751 35.3757
-25.4759 24.9646
-34.0368 9.3620
-35.7428 -9.2282
-24.7265 -24.4414
-13.4898 -37.0765
5.8720 -38.6858
25.6068 -28.5523
34.4240 -15.2932
51.4067 16.5135
40.7448 33.8753
27.0506 47.5831
8.0447 53.4102
-14.7077 53.0211
-32.6402 44.2188
-45.6393 28.3237
-52.6238 12.8971
-51.2437 -13.1306
-46.3939 -29.2189
-32.7927 -42.7468
-15.0102 -52.4185
9.4055 -53.9149
26.7383 -47.4250
41.0120 -35.2068
51.9974 -17.7205
71.1450 16.8261
64.9417 34.0098
55.0806 50.5427
42.0238 58.4340
26.2243 69.4841
10.1774 70.3779
-7.7999 73.6784
-21.8604 67.7796
-37.1165 63.9438
-49.7209 51.1936
-59.2943 39.3131
-68.6773 25.0682
-71.4957 6.8180
-72.4198 -8.2717
-69.2177 -25.2670
-59.3903 -40.5126
-48.8020 -51.4030
-35.3966 -64.2502
-20.7548 -68.4010
-6.2891 -73.3952
10.4747 -70.3164
28.4021 -66.7164
41.7221 -58.9202
56.5840 -46.9224
66.2943 -33.2410
71.7598 -18.4668
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