Optical 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 degrees , -18 degrees and -33 degrees 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.

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; T_0 is the peak transmission of the passband, T=_T0 at *x*=0; *x* is related to wavelength lambda by *x*=(lambda-lambda_**0**)/H, *T*=*T_*0/2 at *x*=1 (so *H* is the half width at half maximum).

The parameters, (lambda_0, *T_*0, *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 *T_*0 which requires a cubic. The results are given in Tables 3.3 through 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=*A_*0+*A_*1*Y*+*A_*2*Y_*2+*A_*3*Y_*3. 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 lambda. 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 *T_*0 as a function of lambda_0 for all 16 ramp filter strips. Figure 3.3 shows 2*H*/lambda_0.

**Table 3.3: Ramp Filter FR418N Parameters.**

**Table 3.4: Ramp Filter FR533N Parameters.**

**Table 3.5: Ramp Filter FR680N Parameters.**

**Table 3.6: Ramp Filter FR868N Parameters.**

**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.**

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 degrees 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.**

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.

**Table 3.7: Aperture Locations and Wavelengths for
Ramp Filters.**

**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 diamter
(in arcseconds).**

**3.3.1**- Spectral Response**3.3.2**- Target Locations**3.3.3**- LRF Photometric Calibration