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WFPC2 Instrument Handbook for Cycle 10

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Linear Ramp Filters


The linear ramp filters are designed for narrow-band absorption and emission line imaging of moderately extended objects. Each filter is divided into four parallel strips where the central wavelength across each strip varies by approximately 6%. Each CCD pixel is mapped to a unique central wavelength with a FWHM bandwidth of approximately 1.3% of the central wavelength. The maximum size of an object which can be imaged at a given wavelength is approximately 13" and is determined by the width of the strips and the image size at the filter. The cumulative wavelength range of the four linear ramp filters is 3710Å to 9762Å. Originally intended for a four WFC configuration, the linear ramp filters require partial rotation of the SOFA wheels to +15°, -18° and -33° from their nominal positions, to recover wavelength regions which would fall on the PC camera or otherwise be lost. There will be vignetting at some wavelengths for these partial rotations.

Spectral Response

A JPL Memorandum (DFM #2031, 1992) gives the results of a prediction scheme to locate and quantify the passbands of the four WFPC2 ramp filters, FR418N, FR533N, FR680N and FR866N. The results are summarized here.

Laboratory (room temperature) measurements of the passbands of the four ramp filters were made at five equally spaced intervals on each of the four ramp stripes on each filter for a total of 80 passband measurements. The laboratory measurements were made with a narrow beam and were then integrated over an annular area of the filter to simulate the beam profile. The radius of the beam is 3.7 mm, or 13". The integration was carried out by assuming the nominal linear shift in wavelength with position, and that no significant changes in the passband shape occur across the beam. The integration makes the shape of the passband quite symmetrical.

The resulting spectral response can be fitted to within a few percent with a Munson function:

where a, b and c are shape parameters, and 0(a,b,c)1; T0 is the peak transmission of the passband, T=T0 at x=0; x is related to wavelength by x=(-0)/H, T=T0/2 at x=1 (so H is the half width at half maximum).

The parameters, (0, T0, H, a, b, c) were then fitted to polynomial functions of position Y (which starts at 0 inches at the lower wavelength edge of each strip) to predict the filter response for areas of the filters between the tested points. Good quadratic fits are available for all the parameters except for T0 which requires a cubic. The results are given in Table 3.3 through Table 3.6, which give the polynomial fit coefficients for the ramp filter parameters. The table entries, except for the first line, are used as parameter=A0+A1Y+A2Y2+A3Y3. The short wavelength side of the filter is opposite for alternate ramps. The first line in each table gives the Y position as a function of . If the polynomial fit predicts a, b, or c < 0 or > 1 then the quantities are set to 0 or 1, respectively.

Use of these fits should be restricted to objects near the center of the ramp, otherwise the beam will combine light from adjacent ramps. The fit should also not be used within 13" of the end of the ramp. There is enough wavelength overlap between ramps that the extreme ends need not be used, except at the very lowest and highest wavelengths. Figure 3.2 shows the fit parameter T0 as a function of 0 for all 16 ramp filter strips. Figure 3.3  shows 2H/0.

Table 3.3: Ramp Filter FR418N Parameters.
Quantity A0 A1 A2 A3
Ramp 1 Position
-26.1083
0.00713888
0.0000
Wavelength
3657.7
138.7
0.6178
Peak transmission
-0.01667
0.2188
0.04138
-0.03489
Half width at half max
21.95
-0.8347
2.143
a
0.2120
0.002857
0.002596
b
1.181
-0.8138
0.3535
c
0.3301
-0.3715
0.3825
Ramp 2 Position
-24.2554
0.00625704
0.0000
Wavelength
3876.9
158.6
0.5472
Peak transmission
0.1660
0.2288
-0.1080
0.004005
Half width at half max
21.50
3.315
-0.7079
a
0.1592
-0.003687
-0.0008497
b
0.7938
0.2355
-0.09124
c
0.9306
0.01366
0.007458
Ramp 3 Position
-24.7145
0.00598254
0.0000
Wavelength
4130.5
168.8
-0.7389
Peak transmission
0.1352
0.6200
-0.5226
0.1529
Half width at half max
22.09
1.306
-0.1181
a
0.2300
0.05586
-0.03044
b
1.096
-0.3185
0.1396
c
1.276
-1.279
0.5721
Ramp 4 Position
-23.4440
0.00536340
0.0000
Wavelength
4371.3
185.8
0.2913
Peak transmission
0.3189
0.1287
-0.01160
-0.001712
Half width at half max
25.62
1.015
0.1161
a
0.3123
-0.2055
0.09535
b
0.9222
0.1167
-0.04673
c
1.033
-0.1356
0.05660

Table 3.4: Ramp Filter FR533N Parameters. 
Quantity A0 A1 A2 A3
Ramp 1 Position
-26.7670
0.00572115
0.0000
Wavelength
4677.7
177.3
-1.125
Peak transmission
0.5450
-0.3612
0.3623
-0.1281
Half width at half max
25.67
0.3168
0.8873
a
-0.009839
0.4644
-0.2039
b
0.31511
0.9473
-0.4516
c
-0.3379
2.788
-1.346
Ramp 2 Position
-24.6600
0.00498393
0.0000
Wavelength
4948.4
199.2
0.6484
Peak transmission
0.4546
0.4188
-0.5456
0.1548
Half width at half max
32.10
-1.204
3.171
a
0.1678
-0.02726
0.09521
b
0.9345
0.1935
-0.1224
c
0.9571
0.02919
-0.009393
Ramp 3 Position
-24.5038
0.00465985
0.0000
Wavelength
5257.3
217.9
-1.481
Peak transmission
0.4944
-0.1714
0.1890
-0.0631
Half width at half max
34.03
5.078
-1.347
a
0.3851
-0.06264
0.003163
b
0.5605
0.6642
-0.2751
c
0.9665
0.05543
-0.03654
Ramp 4 Position
-25.5182
0.00455886
0.0000
Wavelength
5596.9
220.9
-0.6938
Peak transmission
0.5058
-0.2715
0.3203
-0.1230
Half width at half max
35.06
-2.856
2.382
a
0.06553
0.2253
-0.08275
b
1.043
-0.1190
0.02889
c
1.162
-0.4910
0.2059

Table 3.5: Ramp Filter FR680N Parameters.
Quantity A0 A1 A2 A3
Ramp 1 Position
-21.8962
0.00370137
0.0000
Wavelength
5916.0
269.4
0.3460
Peak transmission
0.1198
1.005
-0.4015
-0.00162
Half width at half max
41.50
-5.873
4.038
a
0.1743
-0.05050
0.06481
b
0.8320
0.3326
-0.1858
c
0.9682
-0.09110
0.05122
Ramp 2 Position
-22.6919
0.00360750
0.0000
Wavelength
6290.8
275.6
0.7184
Peak transmission
0.7918
-0.02034
0.1086
-0.05945
Half width at half max
39.48
2.120
0.3703
a
0.05596
0.3034
-0.1333
b
1.017
-0.27026
0.04560
c
0.7244
0.8326
-0.5107
Ramp 3 Position
-22.0719
0.00330755
0.0000
Wavelength
6673.5
301.6
0.3321
Peak transmission
0.9494
-1.008
1.161
-0.3777
Half width at half max
42.81
0.8193
0.4269
a
0.1038
0.09020
-0.02747
b
0.8415
0.3045
-0.1930
c
1.017
-0.1732
0.07463
Ramp 4 Position
-24.7447
0.00346462
0.0000
Wavelength
7141.9
289.3
-0.2999
Peak transmission
0.4823
0.4479
-0.07484
-0.05868
Half width at half max
44.72
0.8952
-0.0756
a
0.1612
-0.01167
0.01355
b
0.2708
1.077
-0.4757
c
0.9941
-0.02694
0.01685

Table 3.6: Ramp Filter FR868N Parameters.  
Quantity A0 A1 A2 A3
Ramp 1 Position
-23.2685
0.00308029
0.0000
Wavelength
7555.5
320.4
1.906
Peak transmission
0.7524
-0.3328
0.4543
-0.1343
Half width at half max
49.32
1.742
0.4914
a
0.2958
-0.3877
0.2465
b
1.321
-0.9156
0.3666
c
0.3762
1.668
-0.9499
Ramp 2 Position
-22.9766
0.00286673
0.0000
Wavelength
8014.3
350.5
-0.7500
Peak transmission
0.8204
-0.3368
0.3815
-0.1057
Half width at half max
54.17
1.579
0.2196
a
0.05832
0.7525
-0.3625
b
0.4582
0.8433
-0.4350
c
0.6422
0.3247
-0.1593
Ramp 3 Position
-22.6085
0.00265657
0.0000
Wavelength
8510.7
375.6
0.3706
Peak transmission
0.5817
-0.1920
0.4517
-0.1627
Half width at half max
55.19
-0.7459
1.433
a
0.5422
-0.2444
0.03545
b
1.420
-1.176
0.4814
c
0.4257
-0.2522
0.1777
Ramp 4 Position
-23.2142
0.00256976
0.0000
Wavelength
9034.3
387.2
0.8722
Peak transmission
0.6241
0.2403
-0.1230
0.02829
Half width at half max
59.69
2.167
-0.1996
a
0.2376
-0.01879
-0.00864
b
0.9670
0.02456
-0.00477
c
0.7829
0.03750
0.02393

Figure 3.2: Ramp Filter Peak Transmission. The four line types correspond to the four different filters (each containing four ramps).
 
Figure 3.3: Ramp Filter Dimensionless Widths.
 

Target Locations

In Figure 3.4 and Figure 3.5 we show the correspondence between central wavelength and location in the focal plane for the nominal and rotated filter positions. The selection of filter and aperture for the linear ramp filters is transparent to the user who is required only to specify the linear ramp filter name LRF and a central wavelength. Each central wavelength is assigned to a unique filter and CCD location.

Following on-orbit testing of WFPC2 a revised table of linear ramp filter wavelengths has been compiled and is shown in Table 3.7. For each wavelength listed, there is a minimum 10" diameter unvignetted field-of-view. Some wavelengths can be obtained with several different settings of the ramps, however, for simplicity, the redundant wavelengths have been removed from the table. Note that this table supports observation with the PC and a new +15° rotation of the filter wheel. Table 3.8 lists wavelengths which are available, but with some compromise in data quality, so as to avoid gaps in wavelength coverage. Most of these wavelengths are observed slightly off the central wavelength of the passband. This implies a slightly reduced throughput (see estimates of the light reduction in the table), and some additional difficulties in flattening the data to remove variations in the passband across the target. A few other wavelengths are observed slightly off the unvignetted centerline of the ramps, and these are indicated by note "FOV" in Table 3.8. Again, this vignetting will present some additional complications when calibrating the data. Further details regarding the ramp filter wavelengths and apertures will be made available in a separate instrument science report.

We note that an interactive tool is available on the WFPC2 WWW pages which will compute target locations for LRF observations. The user inputs either the central wavelength or the target location in the field-of-view, and the other quantity is returned.

Figure 3.4: FR418N and FR533N Wavelength Mapping.
 
Figure 3.5: FR680N and FR868N Wavelength Mapping.
 

LRF Photometric Calibration

As of this writing, the preferred method of flat fielding LRF data is to use a narrow band flat observed nearby in wavelength. This will remove pixel-to-pixel effects, as well as effects of distortion and vignetting in the cameras, while avoiding the complications of pinholes on the LRFs and spurious variations due to the spectrum of the flat field light source.

Conversion of counts to source flux is best achieved by using the SYNPHOT synthetic photometry package. An LRF filter setting is simply specified by including "LRF#xxxx" in the OBSMODE, where xxxx is the central wavelength specified on the Phase II proposal.

Comparisons between the SYNPHOT predictions and on-orbit observations of standard stars suggest that the current photometric calibration is only accurate to about 10% for the LRF filters. This is rather poorer than normal WFPC2 filters (typically 1% - 2% accuracy). The cause is not understood at this time, but is under study (May 2000).
Table 3.7: Aperture Locations and Wavelengths for Ramp Filters.
Start (Å) End (Å) Filter CCD / Aperture x1 (pix) y1 (pix) x2 (pix) y2 (pix)
3710
3800
FR418N WF4-FIX
750
736.8
161 .5
737.7
3800
3878
FR418N33 WF3-FIX
669.5
559.2
395.1
128.9
3881
3907
FR418N18 PC1-FIX
402.3
225
515.4
579.5
3907
3929
FR418N33 WF2-FIX
128.4
286.7
250.1
209.9
3929
4008
FR418N18 WF2-FIX
562.7
233
130.1
367.1
4008
4038
FR418N PC1-FIX
541.3
632.7
543.3
256.5
4038
4100
FR418N18 WF3-FIX
425.3
130.8
532 4
469.9
4100
4177
FR418N WF4-FIX
309
276.2
750.3
275.5
4186
4210
FR418P15 WF4-FIX
596.5
515.9
469.4
482.1
4210
4308
FR418N WF3-FIX
248.2
665.9
252.7
128.5
4308
4337
FR418P15 PC1-FIX
690.2
264.6
598.4
599.9
4337
4446
FR418N WF2-FIX
127.9
247.6
725.4
255.7
4446
4550
FR418N WF2-FIX
691.7
716.2
180.6
709.2
4550
4571
FR418P15 WF2-FIX
230
253.8
130.7
225.8
4593
4720
FR418N WF3-FIX
713.7
125.6
708.5
749.9
4746
4863
FR533N WF3-FIX
689.3
748.9
694.4
135.5
4884
4900
FR533P15 WF2-FIX
128.3
205.1
209
227.9
4900
5013
FR533N WF2-FIX
153.6
689.6
745.9
697.7
5013
5020
FR533N18 WF2-FIX
693.4
642.4
662.9
651.8
5020
5153
FR533N WF2-FIX
737.3
236.6
130
228.4
5153
5176
FR533P15 PC1-FIX
637.9
614.9
698.6
393.3
5188
5310
FR533N WF3-FIX
233.5
127.4
228.8
684.7
5310
5335
FR533P15 WF4-FIX
482.8
505.5
593.1
534.9
5339
5450
FR533N WF4-FIX
750.9
294.7
277.2
295.5
5450
5528
FR533N18 WF3-FIX
504.4
445.3
404.1
127.6
5528
5566
FR533N PC1-FIX
585.3
277.5
583.4
632.3
5566
5671
FR533N18 WF2-FIX
124.1
348.8
552.3
216.1
5671
5700
FR533N33 WF2-FIX
224.8
203.2
122.3
267.7
5700
5741
FR533N18 PC1-FIX
558.8
577
444.9
220.1
5743
5910
FR533N33 WF3-FIX
370.8
126.5
745.9
714.9
5910
6007
FR533N WF4-FIX
333.8
747.6
738.8
746.9
6007
6192
FR680N WF2-FIX
750.3
706.9
122.9
698.4
6192
6208
FR680P15 WF2-FIX
177.1
228.4
124.9
213.6
6238
6409
FR680N WF3-FIX
703.6
128.1
698.8
708.2
6409
6584
FR680N WF3-FIX
237.8
705.6
242.6
127
6590
6631
FR680P15 PC1-FIX
699.1
315.3
620.9
601.2
6631
6800
FR680N WF2-FIX
125.9
237.5
684.5
245.1
6800
6921
FR680N18 WF2-FIX
480.1
248
129.9
356.6
6921
6976
FR680N PC1-FIX
563.3
639.2
565.3
274.6
6976
7061
FR680N18 WF3-FIX
413.2
126
490.8
371.7
7061
7241
FR680N WF4-FIX
203
286.4
748.3
285.6
7251
7420
FR680N WF4-FIX
749.6
743.5
213.3
744.3
7420
7600
FR680N33 WF3-FIX
688.9
608.4
381.6
126.4
7605
7658
FR680N18 PC1-FIX
427
230
538.9
580.6
7658
7690
FR680N33 WF2-FIX
126.2
276.1
212.1
222
7690
7830
FR868N WF4-FIX
711.5
751.3
316.5
751.9
7830
8072
FR868N33 WF3-FIX
728.2
705.8
360.9
129.7
8077
8140
FR868N18 PC1-FIX
471.5
231
589.7
601.5
8140
8300
FR868N18 WF2-FIX
527.6
213.2
126.2
337.6
8300
8362
FR868N PC1-FIX
605.4
644.1
607.3
287.9
8362
8460
FR868N18 WF3-FIX
393.1
126.1
470.6
371.7
8460
8661
FR868N WF4-FIX
196.9
305.7
724.7
304.9
8661
8910
FR868N WF3-FIX
218.3
731.6
223.4
125.3
8945
8980
FR868P15 PC1-FIX
701.1
467.5
651.9
647.3
8980
9200
FR868N WF2-FIX
142.7
218.5
678.2
225.8
9200
9415
FR868N WF2-FIX
668.4
686.5
162.2
679.6
9415
9456
FR868P15 WF2-FIX
219.9
220.5
127
194.2
9501
9762
FR868N WF3-FIX
684.3
135.4
679.2
750.2
Table 3.8: Vignetted Wavelengths for Ramp Filters. The right column gives the maximum throughput reduction (in %) for these settings where the target must be placed away from the optimal location on the filter glass. "FOV" denotes settings where transmission is optimal, but the usable field-of-view is reduced below 10" to the indicated diameter (in arcseconds).
Start (Å) End (Å) Filter CCD / Aperture x1 (pix) y1 (pix) x2 (pix) y2 (pix) Max %
Light Loss
3878
3881
FR418N18 PC1-FIX
402.3
225.0
402.3
225.0
2
4177
4182
FR418N WF4-FIX
750.3
275.5
750.3
275.5
3
4182
4186
FR418P15 WF4-FIX
596.5
515.9
596.5
515.9
2
4571
4582
FR418P15 WF2-FIX
130.7
225.8
130.7
225.8
13
4582
4593
FR418N WF3-FIX
713.7
125.6
713.7
125.6
13
4720
4733
FR418N WF3-FIX
708.5
749.9
708.5
749.9
14
4733
4746
FR533N WF3-FIX
689.3
748.9
689.3
748.9
14
4863
4873
FR533N WF3-FIX
694.4
135.5
694.4
135.5
8
4873
4884
FR533P15 WF2-FIX
128.3
205.1
128.3
205.1
8
5176
5183
FR533P15 PC1-FIX
698.6
393.3
698.6
325.9
FOV~9"
5183
5188
FR533N WF3-FIX
233.5
127.4
233.5
127.4
2
5335
5337
FR533P15 WF4-FIX
593.1
534.9
593.1
534.9
1
5337
5339
FR533N WF4-FIX
750.9
294.7
750.9
294.7
1
5741
5743
FR533N33 WF3-FIX
370.8
126.5
370.8
126.5
1
6208
6221
FR680P15 WF2-FIX
124.9
213.6
124.9
213.6
8
6221
6238
FR680N WF3-FIX
703.6
128.1
703.6
128.1
11
6584
6587
FR680N WF3-FIX
242.6
127.0
242.6
127.0
1
6587
6590
FR680P15 PC1-FIX
699.1
294.3
699.1
315.3
FOV~9"
7241
7246
FR680N WF4-FIX
748.3
285.6
748.3
285.6
2
7246
7251
FR680N WF4-FIX
749.6
743.5
749.6
743.5
2
7600
7602
FR680N33 WF3-FIX
381.6
126.4
381.6
126.4
1
7602
7605
FR680N18 PC1-FIX
427.0
230.0
427.0
230.0
1
8072
8074
FR868N33 WF3-FIX
360.9
129.7
360.9
129.7
1
8074
8077
FR868N18 PC1-FIX
471.5
231.0
471.5
231.0
1
8910
8920
FR868N WF3-FIX
223.4
125.3
223.4
125.3
2
8920
8945
FR868P15 PC1-FIX
701.1
339.1
701.1
467.5
FOV~7"
9456
9478
FR868P15 WF2-FIX
127.0
194.2
127.0
194.2
13
9478
9501
FR868N WF3-FIX
684.3
135.4
684.3
135.4
13



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