Gibion Makiwa,1,*
David A. Naylor,1
Marc Ferlet,2
Carl Salji,3
Bruce Swinyard,2,3
Edward Polehampton,1,2
and Matthijs H. D. van der Wiel1
1Institute for Space Imaging Science, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4, Canada
2RAL Space, Rutherford Appleton Laboratory, Didcot OX11 0QX, UK
3Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
Gibion Makiwa, David A. Naylor, Marc Ferlet, Carl Salji, Bruce Swinyard, Edward Polehampton, and Matthijs H. D. van der Wiel, "Beam profile for the Herschel–SPIRE Fourier transform spectrometer," Appl. Opt. 52, 3864-3875 (2013)
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile.
Günter Wiedemann, D. E. Jennings, R. H. Hanel, V. G. Kunde, S. H. Moseley, G. Lamb, M. D. Petroff, and M. G. Stapelbroek Appl. Opt. 28(1) 139-145 (1989)
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Observation Details of the Data Used to Determine the SPIRE Beam Profilea
Source
OD
OBSID
Res
Reps
DOO ()
Raster Grid Size
Step Size (″)
SS (″)
Neptune
210
MR
2
17260
9
2.24
742
LR
6
20983
7
2.26
Uranus
410
MR
2
16528
7
3.50
767
HR
4
17036
Cross ()
7.5
3.46
767
HR
4
17036
Cross ()
7.5
3.46
OD, operational day from the launch of the telescope; OBSID, OBServation IDentification number; Res, spectral resolution; LR, low resolution; MR, medium resolution; HR, high resolution; Reps, number of repetitions; DOO, duration of observation; SS, source size at the time of observation. More information about some of these parameters can be obtained from the SPIRE Observer’s Manual [7].
Table 2.
Comparison of the Waist Radii for the Beam Profile at a Few Frequencies in the SPIRE SSW Band Before and After Correcting for the Finite Size of Neptunea
Frequency (GHz)
Uncorrected
Corrected
1349
14.43
14.34
1379
14.40
14.44
1409
14.27
14.22
1439
14.18
14.28
1469
14.06
13.98
1499
14.15
14.05
Average errors for the uncorrected and corrected values are and , respectively.
Table 3.
Parameters Required to Generate the SPIRE FTS SLW Beam Profiles Using Eq. (1)a
(GHz)
FWHM
FWHM
442
24.01
0.55
0.643
0.021
0.192
0.013
0.164
0.016
39.5
0.3
449
24.68
0.43
0.642
0.015
0.219
0.008
0.139
0.012
42.3
0.3
457
24.90
0.34
0.646
0.012
0.230
0.006
0.125
0.009
43.1
0.2
464
24.80
0.32
0.652
0.011
0.231
0.005
0.116
0.008
42.7
0.2
472
24.45
0.32
0.659
0.012
0.228
0.005
0.112
0.008
41.6
0.3
479
23.91
0.32
0.663
0.012
0.224
0.005
0.112
0.008
40.4
0.3
487
23.31
0.30
0.662
0.011
0.222
0.005
0.116
0.008
39.3
0.2
494
22.79
0.28
0.657
0.011
0.221
0.005
0.121
0.008
38.6
0.2
502
22.44
0.26
0.652
0.011
0.223
0.005
0.125
0.008
38.2
0.2
509
22.24
0.26
0.650
0.010
0.226
0.005
0.124
0.008
38.1
0.2
517
22.12
0.26
0.653
0.011
0.230
0.005
0.118
0.008
38.0
0.2
524
21.98
0.29
0.659
0.012
0.233
0.005
0.108
0.009
37.6
0.2
532
21.78
0.34
0.666
0.014
0.237
0.006
0.097
0.010
37.2
0.3
539
21.52
0.36
0.669
0.015
0.241
0.006
0.090
0.011
36.8
0.3
547
21.25
0.36
0.668
0.015
0.245
0.006
0.088
0.011
36.5
0.3
554
21.01
0.33
0.664
0.014
0.247
0.006
0.089
0.010
36.3
0.3
562
20.82
0.32
0.662
0.014
0.248
0.006
0.090
0.010
36.1
0.3
569
20.68
0.31
0.663
0.014
0.247
0.006
0.090
0.010
35.7
0.3
577
20.55
0.31
0.669
0.014
0.244
0.006
0.087
0.010
35.3
0.3
584
20.44
0.33
0.676
0.015
0.241
0.006
0.082
0.010
34.7
0.3
592
20.35
0.36
0.682
0.016
0.240
0.006
0.078
0.011
34.4
0.3
599
20.29
0.36
0.684
0.016
0.241
0.007
0.075
0.011
34.2
0.3
607
20.23
0.36
0.684
0.016
0.242
0.006
0.074
0.011
34.2
0.3
614
20.14
0.36
0.683
0.016
0.244
0.006
0.073
0.011
34.1
0.3
622
20.01
0.36
0.682
0.017
0.246
0.007
0.072
0.011
34.0
0.3
629
19.81
0.36
0.683
0.017
0.247
0.007
0.070
0.011
33.7
0.3
637
19.60
0.35
0.683
0.016
0.248
0.006
0.069
0.011
33.3
0.3
644
19.41
0.33
0.684
0.016
0.248
0.006
0.068
0.010
33.0
0.3
652
19.30
0.31
0.684
0.015
0.247
0.006
0.069
0.010
32.7
0.3
659
19.26
0.30
0.685
0.015
0.244
0.006
0.070
0.009
32.6
0.3
667
19.21
0.30
0.687
0.014
0.243
0.006
0.071
0.009
32.4
0.3
674
19.10
0.30
0.688
0.015
0.241
0.006
0.071
0.009
32.1
0.3
682
18.90
0.32
0.689
0.016
0.241
0.006
0.069
0.010
31.8
0.3
689
18.68
0.33
0.691
0.016
0.242
0.007
0.067
0.010
31.4
0.3
697
18.58
0.33
0.694
0.017
0.242
0.007
0.063
0.010
31.1
0.3
704
18.73
0.34
0.702
0.017
0.239
0.007
0.059
0.010
31.1
0.3
712
19.23
0.36
0.715
0.018
0.232
0.008
0.053
0.010
31.4
0.4
719
19.99
0.41
0.729
0.019
0.223
0.008
0.048
0.011
32.0
0.4
726
20.73
0.43
0.734
0.019
0.218
0.009
0.048
0.011
32.9
0.4
734
21.18
0.41
0.725
0.018
0.221
0.008
0.054
0.010
34.0
0.4
741
21.34
0.38
0.710
0.016
0.229
0.006
0.061
0.010
34.9
0.4
749
21.33
0.35
0.699
0.015
0.236
0.006
0.065
0.009
35.4
0.3
756
21.22
0.33
0.694
0.014
0.239
0.005
0.067
0.009
35.4
0.3
764
21.08
0.32
0.693
0.014
0.241
0.005
0.066
0.009
35.3
0.3
771
20.95
0.32
0.693
0.014
0.242
0.005
0.065
0.009
35.2
0.3
779
20.85
0.32
0.690
0.014
0.245
0.005
0.065
0.009
35.2
0.3
786
20.75
0.32
0.683
0.014
0.250
0.005
0.067
0.009
35.4
0.3
794
20.63
0.31
0.673
0.014
0.257
0.005
0.070
0.009
35.7
0.3
801
20.46
0.29
0.661
0.013
0.264
0.005
0.075
0.009
36.0
0.3
809
20.28
0.27
0.651
0.012
0.269
0.005
0.080
0.009
36.2
0.2
816
20.09
0.25
0.644
0.011
0.273
0.005
0.084
0.008
36.2
0.2
824
19.94
0.24
0.638
0.011
0.275
0.004
0.087
0.008
36.3
0.2
831
19.82
0.23
0.632
0.011
0.278
0.004
0.090
0.008
36.3
0.2
839
19.74
0.23
0.627
0.011
0.281
0.004
0.092
0.008
36.5
0.2
846
19.65
0.23
0.621
0.011
0.286
0.005
0.093
0.008
36.7
0.2
854
19.54
0.23
0.616
0.011
0.290
0.005
0.094
0.009
36.8
0.2
861
19.38
0.23
0.612
0.011
0.293
0.005
0.094
0.009
36.7
0.2
869
19.21
0.22
0.609
0.011
0.296
0.005
0.095
0.009
36.6
0.2
876
19.05
0.21
0.605
0.011
0.299
0.005
0.097
0.008
36.5
0.2
884
18.94
0.20
0.597
0.010
0.303
0.004
0.099
0.008
36.7
0.2
891
18.88
0.20
0.585
0.010
0.311
0.005
0.104
0.008
37.3
0.2
899
18.87
0.19
0.567
0.010
0.323
0.005
0.110
0.008
38.2
0.1
906
18.88
0.19
0.549
0.010
0.336
0.005
0.115
0.008
39.3
0.1
914
18.88
0.19
0.536
0.010
0.346
0.005
0.118
0.009
40.0
0.1
921
18.86
0.19
0.531
0.010
0.351
0.005
0.118
0.009
40.2
0.2
929
18.82
0.19
0.533
0.010
0.352
0.005
0.116
0.009
40.1
0.2
936
18.78
0.20
0.535
0.010
0.352
0.005
0.113
0.009
39.9
0.2
944
18.72
0.20
0.533
0.010
0.355
0.005
0.112
0.009
39.9
0.2
951
18.65
0.20
0.524
0.011
0.362
0.005
0.113
0.010
40.2
0.2
959
18.57
0.21
0.510
0.011
0.373
0.006
0.117
0.010
40.7
0.2
966
18.50
0.20
0.496
0.011
0.383
0.006
0.121
0.010
41.3
0.2
974
18.47
0.19
0.489
0.010
0.388
0.006
0.123
0.010
41.6
0.2
981
18.48
0.18
0.492
0.010
0.386
0.005
0.123
0.009
41.5
0.2
989
18.54
0.17
0.501
0.009
0.379
0.005
0.120
0.008
41.1
0.1
, frequency; , waist radius; , error in ; , coefficients of Hermite–Gaussian terms; , error in , FWHM: full width at half-maximum; FWHM, error in FWHM. These parameters were derived from the central detector, SLWC3.
Table 4.
Parameters Required to Generate the SPIRE FTS SSW Beam Profile Using Eq. (1)a
(GHz)
FWHM
FWHM
936
17.36
0.27
1.000
0.016
20.4
0.3
944
17.35
0.16
1.000
0.010
20.4
0.2
951
17.34
0.13
1.000
0.008
20.4
0.2
959
17.28
0.12
1.000
0.007
20.3
0.1
966
17.17
0.12
1.000
0.007
20.2
0.1
974
17.01
0.12
1.000
0.007
20.0
0.1
981
16.83
0.12
1.000
0.007
19.8
0.1
989
16.65
0.12
1.000
0.007
19.6
0.1
996
16.53
0.12
1.000
0.007
19.5
0.1
1004
16.47
0.12
1.000
0.007
19.4
0.1
1011
16.45
0.12
1.000
0.007
19.4
0.1
1019
16.42
0.11
1.000
0.007
19.3
0.1
1026
16.35
0.11
1.000
0.007
19.2
0.1
1034
16.23
0.11
1.000
0.007
19.1
0.1
1041
16.08
0.11
1.000
0.007
18.9
0.1
1049
15.94
0.11
1.000
0.007
18.8
0.1
1056
15.84
0.11
1.000
0.007
18.6
0.1
1064
15.78
0.11
1.000
0.007
18.6
0.1
1071
15.74
0.11
1.000
0.007
18.5
0.1
1079
15.68
0.10
1.000
0.007
18.5
0.1
1086
15.60
0.10
1.000
0.007
18.4
0.1
1094
15.49
0.10
1.000
0.007
18.2
0.1
1101
15.37
0.10
1.000
0.007
18.1
0.1
1109
15.27
0.10
1.000
0.007
18.0
0.1
1116
15.20
0.10
1.000
0.007
17.9
0.1
1124
15.15
0.10
1.000
0.007
17.8
0.1
1131
15.09
0.09
1.000
0.007
17.8
0.1
1139
15.02
0.09
1.000
0.007
17.7
0.1
1146
14.93
0.09
1.000
0.007
17.6
0.1
1154
14.84
0.09
1.000
0.007
17.5
0.1
1161
14.76
0.09
1.000
0.007
17.4
0.1
1169
14.71
0.09
1.000
0.007
17.3
0.1
1176
14.67
0.09
1.000
0.007
17.3
0.1
1184
14.63
0.09
1.000
0.007
17.2
0.1
1191
14.55
0.08
1.000
0.006
17.1
0.1
1199
14.45
0.08
1.000
0.006
17.0
0.1
1206
14.35
0.08
1.000
0.006
16.9
0.1
1214
14.29
0.08
1.000
0.006
16.8
0.1
1221
14.31
0.08
1.000
0.006
16.8
0.1
1229
14.40
0.08
1.000
0.006
17.0
0.1
1236
14.53
0.07
1.000
0.006
17.1
0.1
1244
14.64
0.07
1.000
0.005
17.2
0.1
1251
14.71
0.07
1.000
0.005
17.3
0.1
1259
14.71
0.07
1.000
0.005
17.3
0.1
1266
14.68
0.07
1.000
0.005
17.3
0.1
1274
14.65
0.07
1.000
0.005
17.2
0.1
1281
14.63
0.07
1.000
0.005
17.2
0.1
1289
14.63
0.07
1.000
0.005
17.2
0.1
1296
14.64
0.07
1.000
0.005
17.2
0.1
1304
14.63
0.07
1.000
0.005
17.2
0.1
1311
14.59
0.07
1.000
0.005
17.2
0.1
1319
14.53
0.07
1.000
0.005
17.1
0.1
1326
14.47
0.07
1.000
0.005
17.0
0.1
1334
14.43
0.07
1.000
0.005
17.0
0.1
1341
14.42
0.07
1.000
0.005
17.0
0.1
1349
14.43
0.07
1.000
0.005
17.0
0.1
1356
14.44
0.07
1.000
0.005
17.0
0.1
1364
14.45
0.07
1.000
0.005
17.0
0.1
1371
14.43
0.06
1.000
0.005
17.0
0.1
1379
14.40
0.06
1.000
0.005
17.0
0.1
1386
14.37
0.06
1.000
0.005
16.9
0.1
1394
14.33
0.06
1.000
0.005
16.9
0.1
1401
14.30
0.06
1.000
0.005
16.8
0.1
1409
14.27
0.06
1.000
0.005
16.8
0.1
1416
14.24
0.06
1.000
0.005
16.8
0.1
1424
14.22
0.06
1.000
0.005
16.7
0.1
1431
14.21
0.06
1.000
0.005
16.7
0.1
1439
14.18
0.06
1.000
0.005
16.7
0.1
1446
14.16
0.06
1.000
0.005
16.7
0.1
1453
14.13
0.06
1.000
0.005
16.6
0.1
1461
14.09
0.06
1.000
0.005
16.6
0.1
1468
14.06
0.06
1.000
0.005
16.6
0.1
1476
14.06
0.06
1.000
0.005
16.5
0.1
1483
14.07
0.06
1.000
0.005
16.6
0.1
1491
14.11
0.06
1.000
0.005
16.6
0.1
1498
14.15
0.06
1.000
0.005
16.7
0.1
1506
14.16
0.06
1.000
0.005
16.7
0.1
1513
14.14
0.06
1.000
0.005
16.6
0.1
1521
14.10
0.06
1.000
0.005
16.6
0.1
1528
14.07
0.06
1.000
0.005
16.6
0.1
1536
14.11
0.06
1.000
0.005
16.6
0.1
1543
14.26
0.07
1.000
0.005
16.8
0.1
1551
14.56
0.07
1.000
0.005
17.1
0.1
, frequency; , waist radius; , error in ; , coefficients of Hermite–Gaussian terms; , error in , FWHM: full width at half-maximum; FWHM, error in FWHM. These parameters were derived from the central detector, SSWD4.
Tables (4)
Table 1.
Observation Details of the Data Used to Determine the SPIRE Beam Profilea
Source
OD
OBSID
Res
Reps
DOO ()
Raster Grid Size
Step Size (″)
SS (″)
Neptune
210
MR
2
17260
9
2.24
742
LR
6
20983
7
2.26
Uranus
410
MR
2
16528
7
3.50
767
HR
4
17036
Cross ()
7.5
3.46
767
HR
4
17036
Cross ()
7.5
3.46
OD, operational day from the launch of the telescope; OBSID, OBServation IDentification number; Res, spectral resolution; LR, low resolution; MR, medium resolution; HR, high resolution; Reps, number of repetitions; DOO, duration of observation; SS, source size at the time of observation. More information about some of these parameters can be obtained from the SPIRE Observer’s Manual [7].
Table 2.
Comparison of the Waist Radii for the Beam Profile at a Few Frequencies in the SPIRE SSW Band Before and After Correcting for the Finite Size of Neptunea
Frequency (GHz)
Uncorrected
Corrected
1349
14.43
14.34
1379
14.40
14.44
1409
14.27
14.22
1439
14.18
14.28
1469
14.06
13.98
1499
14.15
14.05
Average errors for the uncorrected and corrected values are and , respectively.
Table 3.
Parameters Required to Generate the SPIRE FTS SLW Beam Profiles Using Eq. (1)a
(GHz)
FWHM
FWHM
442
24.01
0.55
0.643
0.021
0.192
0.013
0.164
0.016
39.5
0.3
449
24.68
0.43
0.642
0.015
0.219
0.008
0.139
0.012
42.3
0.3
457
24.90
0.34
0.646
0.012
0.230
0.006
0.125
0.009
43.1
0.2
464
24.80
0.32
0.652
0.011
0.231
0.005
0.116
0.008
42.7
0.2
472
24.45
0.32
0.659
0.012
0.228
0.005
0.112
0.008
41.6
0.3
479
23.91
0.32
0.663
0.012
0.224
0.005
0.112
0.008
40.4
0.3
487
23.31
0.30
0.662
0.011
0.222
0.005
0.116
0.008
39.3
0.2
494
22.79
0.28
0.657
0.011
0.221
0.005
0.121
0.008
38.6
0.2
502
22.44
0.26
0.652
0.011
0.223
0.005
0.125
0.008
38.2
0.2
509
22.24
0.26
0.650
0.010
0.226
0.005
0.124
0.008
38.1
0.2
517
22.12
0.26
0.653
0.011
0.230
0.005
0.118
0.008
38.0
0.2
524
21.98
0.29
0.659
0.012
0.233
0.005
0.108
0.009
37.6
0.2
532
21.78
0.34
0.666
0.014
0.237
0.006
0.097
0.010
37.2
0.3
539
21.52
0.36
0.669
0.015
0.241
0.006
0.090
0.011
36.8
0.3
547
21.25
0.36
0.668
0.015
0.245
0.006
0.088
0.011
36.5
0.3
554
21.01
0.33
0.664
0.014
0.247
0.006
0.089
0.010
36.3
0.3
562
20.82
0.32
0.662
0.014
0.248
0.006
0.090
0.010
36.1
0.3
569
20.68
0.31
0.663
0.014
0.247
0.006
0.090
0.010
35.7
0.3
577
20.55
0.31
0.669
0.014
0.244
0.006
0.087
0.010
35.3
0.3
584
20.44
0.33
0.676
0.015
0.241
0.006
0.082
0.010
34.7
0.3
592
20.35
0.36
0.682
0.016
0.240
0.006
0.078
0.011
34.4
0.3
599
20.29
0.36
0.684
0.016
0.241
0.007
0.075
0.011
34.2
0.3
607
20.23
0.36
0.684
0.016
0.242
0.006
0.074
0.011
34.2
0.3
614
20.14
0.36
0.683
0.016
0.244
0.006
0.073
0.011
34.1
0.3
622
20.01
0.36
0.682
0.017
0.246
0.007
0.072
0.011
34.0
0.3
629
19.81
0.36
0.683
0.017
0.247
0.007
0.070
0.011
33.7
0.3
637
19.60
0.35
0.683
0.016
0.248
0.006
0.069
0.011
33.3
0.3
644
19.41
0.33
0.684
0.016
0.248
0.006
0.068
0.010
33.0
0.3
652
19.30
0.31
0.684
0.015
0.247
0.006
0.069
0.010
32.7
0.3
659
19.26
0.30
0.685
0.015
0.244
0.006
0.070
0.009
32.6
0.3
667
19.21
0.30
0.687
0.014
0.243
0.006
0.071
0.009
32.4
0.3
674
19.10
0.30
0.688
0.015
0.241
0.006
0.071
0.009
32.1
0.3
682
18.90
0.32
0.689
0.016
0.241
0.006
0.069
0.010
31.8
0.3
689
18.68
0.33
0.691
0.016
0.242
0.007
0.067
0.010
31.4
0.3
697
18.58
0.33
0.694
0.017
0.242
0.007
0.063
0.010
31.1
0.3
704
18.73
0.34
0.702
0.017
0.239
0.007
0.059
0.010
31.1
0.3
712
19.23
0.36
0.715
0.018
0.232
0.008
0.053
0.010
31.4
0.4
719
19.99
0.41
0.729
0.019
0.223
0.008
0.048
0.011
32.0
0.4
726
20.73
0.43
0.734
0.019
0.218
0.009
0.048
0.011
32.9
0.4
734
21.18
0.41
0.725
0.018
0.221
0.008
0.054
0.010
34.0
0.4
741
21.34
0.38
0.710
0.016
0.229
0.006
0.061
0.010
34.9
0.4
749
21.33
0.35
0.699
0.015
0.236
0.006
0.065
0.009
35.4
0.3
756
21.22
0.33
0.694
0.014
0.239
0.005
0.067
0.009
35.4
0.3
764
21.08
0.32
0.693
0.014
0.241
0.005
0.066
0.009
35.3
0.3
771
20.95
0.32
0.693
0.014
0.242
0.005
0.065
0.009
35.2
0.3
779
20.85
0.32
0.690
0.014
0.245
0.005
0.065
0.009
35.2
0.3
786
20.75
0.32
0.683
0.014
0.250
0.005
0.067
0.009
35.4
0.3
794
20.63
0.31
0.673
0.014
0.257
0.005
0.070
0.009
35.7
0.3
801
20.46
0.29
0.661
0.013
0.264
0.005
0.075
0.009
36.0
0.3
809
20.28
0.27
0.651
0.012
0.269
0.005
0.080
0.009
36.2
0.2
816
20.09
0.25
0.644
0.011
0.273
0.005
0.084
0.008
36.2
0.2
824
19.94
0.24
0.638
0.011
0.275
0.004
0.087
0.008
36.3
0.2
831
19.82
0.23
0.632
0.011
0.278
0.004
0.090
0.008
36.3
0.2
839
19.74
0.23
0.627
0.011
0.281
0.004
0.092
0.008
36.5
0.2
846
19.65
0.23
0.621
0.011
0.286
0.005
0.093
0.008
36.7
0.2
854
19.54
0.23
0.616
0.011
0.290
0.005
0.094
0.009
36.8
0.2
861
19.38
0.23
0.612
0.011
0.293
0.005
0.094
0.009
36.7
0.2
869
19.21
0.22
0.609
0.011
0.296
0.005
0.095
0.009
36.6
0.2
876
19.05
0.21
0.605
0.011
0.299
0.005
0.097
0.008
36.5
0.2
884
18.94
0.20
0.597
0.010
0.303
0.004
0.099
0.008
36.7
0.2
891
18.88
0.20
0.585
0.010
0.311
0.005
0.104
0.008
37.3
0.2
899
18.87
0.19
0.567
0.010
0.323
0.005
0.110
0.008
38.2
0.1
906
18.88
0.19
0.549
0.010
0.336
0.005
0.115
0.008
39.3
0.1
914
18.88
0.19
0.536
0.010
0.346
0.005
0.118
0.009
40.0
0.1
921
18.86
0.19
0.531
0.010
0.351
0.005
0.118
0.009
40.2
0.2
929
18.82
0.19
0.533
0.010
0.352
0.005
0.116
0.009
40.1
0.2
936
18.78
0.20
0.535
0.010
0.352
0.005
0.113
0.009
39.9
0.2
944
18.72
0.20
0.533
0.010
0.355
0.005
0.112
0.009
39.9
0.2
951
18.65
0.20
0.524
0.011
0.362
0.005
0.113
0.010
40.2
0.2
959
18.57
0.21
0.510
0.011
0.373
0.006
0.117
0.010
40.7
0.2
966
18.50
0.20
0.496
0.011
0.383
0.006
0.121
0.010
41.3
0.2
974
18.47
0.19
0.489
0.010
0.388
0.006
0.123
0.010
41.6
0.2
981
18.48
0.18
0.492
0.010
0.386
0.005
0.123
0.009
41.5
0.2
989
18.54
0.17
0.501
0.009
0.379
0.005
0.120
0.008
41.1
0.1
, frequency; , waist radius; , error in ; , coefficients of Hermite–Gaussian terms; , error in , FWHM: full width at half-maximum; FWHM, error in FWHM. These parameters were derived from the central detector, SLWC3.
Table 4.
Parameters Required to Generate the SPIRE FTS SSW Beam Profile Using Eq. (1)a
(GHz)
FWHM
FWHM
936
17.36
0.27
1.000
0.016
20.4
0.3
944
17.35
0.16
1.000
0.010
20.4
0.2
951
17.34
0.13
1.000
0.008
20.4
0.2
959
17.28
0.12
1.000
0.007
20.3
0.1
966
17.17
0.12
1.000
0.007
20.2
0.1
974
17.01
0.12
1.000
0.007
20.0
0.1
981
16.83
0.12
1.000
0.007
19.8
0.1
989
16.65
0.12
1.000
0.007
19.6
0.1
996
16.53
0.12
1.000
0.007
19.5
0.1
1004
16.47
0.12
1.000
0.007
19.4
0.1
1011
16.45
0.12
1.000
0.007
19.4
0.1
1019
16.42
0.11
1.000
0.007
19.3
0.1
1026
16.35
0.11
1.000
0.007
19.2
0.1
1034
16.23
0.11
1.000
0.007
19.1
0.1
1041
16.08
0.11
1.000
0.007
18.9
0.1
1049
15.94
0.11
1.000
0.007
18.8
0.1
1056
15.84
0.11
1.000
0.007
18.6
0.1
1064
15.78
0.11
1.000
0.007
18.6
0.1
1071
15.74
0.11
1.000
0.007
18.5
0.1
1079
15.68
0.10
1.000
0.007
18.5
0.1
1086
15.60
0.10
1.000
0.007
18.4
0.1
1094
15.49
0.10
1.000
0.007
18.2
0.1
1101
15.37
0.10
1.000
0.007
18.1
0.1
1109
15.27
0.10
1.000
0.007
18.0
0.1
1116
15.20
0.10
1.000
0.007
17.9
0.1
1124
15.15
0.10
1.000
0.007
17.8
0.1
1131
15.09
0.09
1.000
0.007
17.8
0.1
1139
15.02
0.09
1.000
0.007
17.7
0.1
1146
14.93
0.09
1.000
0.007
17.6
0.1
1154
14.84
0.09
1.000
0.007
17.5
0.1
1161
14.76
0.09
1.000
0.007
17.4
0.1
1169
14.71
0.09
1.000
0.007
17.3
0.1
1176
14.67
0.09
1.000
0.007
17.3
0.1
1184
14.63
0.09
1.000
0.007
17.2
0.1
1191
14.55
0.08
1.000
0.006
17.1
0.1
1199
14.45
0.08
1.000
0.006
17.0
0.1
1206
14.35
0.08
1.000
0.006
16.9
0.1
1214
14.29
0.08
1.000
0.006
16.8
0.1
1221
14.31
0.08
1.000
0.006
16.8
0.1
1229
14.40
0.08
1.000
0.006
17.0
0.1
1236
14.53
0.07
1.000
0.006
17.1
0.1
1244
14.64
0.07
1.000
0.005
17.2
0.1
1251
14.71
0.07
1.000
0.005
17.3
0.1
1259
14.71
0.07
1.000
0.005
17.3
0.1
1266
14.68
0.07
1.000
0.005
17.3
0.1
1274
14.65
0.07
1.000
0.005
17.2
0.1
1281
14.63
0.07
1.000
0.005
17.2
0.1
1289
14.63
0.07
1.000
0.005
17.2
0.1
1296
14.64
0.07
1.000
0.005
17.2
0.1
1304
14.63
0.07
1.000
0.005
17.2
0.1
1311
14.59
0.07
1.000
0.005
17.2
0.1
1319
14.53
0.07
1.000
0.005
17.1
0.1
1326
14.47
0.07
1.000
0.005
17.0
0.1
1334
14.43
0.07
1.000
0.005
17.0
0.1
1341
14.42
0.07
1.000
0.005
17.0
0.1
1349
14.43
0.07
1.000
0.005
17.0
0.1
1356
14.44
0.07
1.000
0.005
17.0
0.1
1364
14.45
0.07
1.000
0.005
17.0
0.1
1371
14.43
0.06
1.000
0.005
17.0
0.1
1379
14.40
0.06
1.000
0.005
17.0
0.1
1386
14.37
0.06
1.000
0.005
16.9
0.1
1394
14.33
0.06
1.000
0.005
16.9
0.1
1401
14.30
0.06
1.000
0.005
16.8
0.1
1409
14.27
0.06
1.000
0.005
16.8
0.1
1416
14.24
0.06
1.000
0.005
16.8
0.1
1424
14.22
0.06
1.000
0.005
16.7
0.1
1431
14.21
0.06
1.000
0.005
16.7
0.1
1439
14.18
0.06
1.000
0.005
16.7
0.1
1446
14.16
0.06
1.000
0.005
16.7
0.1
1453
14.13
0.06
1.000
0.005
16.6
0.1
1461
14.09
0.06
1.000
0.005
16.6
0.1
1468
14.06
0.06
1.000
0.005
16.6
0.1
1476
14.06
0.06
1.000
0.005
16.5
0.1
1483
14.07
0.06
1.000
0.005
16.6
0.1
1491
14.11
0.06
1.000
0.005
16.6
0.1
1498
14.15
0.06
1.000
0.005
16.7
0.1
1506
14.16
0.06
1.000
0.005
16.7
0.1
1513
14.14
0.06
1.000
0.005
16.6
0.1
1521
14.10
0.06
1.000
0.005
16.6
0.1
1528
14.07
0.06
1.000
0.005
16.6
0.1
1536
14.11
0.06
1.000
0.005
16.6
0.1
1543
14.26
0.07
1.000
0.005
16.8
0.1
1551
14.56
0.07
1.000
0.005
17.1
0.1
, frequency; , waist radius; , error in ; , coefficients of Hermite–Gaussian terms; , error in , FWHM: full width at half-maximum; FWHM, error in FWHM. These parameters were derived from the central detector, SSWD4.