**Authors:** Don Lindler, Gerhardt Meurer, George Hartig, Zlatan Tsvetanov

**Detector:** SBC, HRC

**Purpose:**
Compute the wavelength dispersion relations for the prism modes and check
the slope of the prism on the detector.

**Data:**
SBC Prism wavelength calibration observations were obtained on May 26, 1999
(Table 1)
using RASCAL with the 100 micron pinhole. RASCAL was fed by the CDS
(Calibration Delivery System). The Ball monochromator, housed within the CDS,
was used to isolate the positions of selected wavelengths on the detector. The
illuminating source was a Hamamatsu D_{2} lamp. The slits of the monochromator
were set to produce a spectral resolution of 90 Angstroms. The whole system
(CDS + RASCAL + ACS) was housed in a "tent" and purged with N_{2}. At the
beginning and end of each set of prism observations (PR110L and PR130L), an
undispersed observation of the 100 micron pinhole was obtained using the F115LP
filter to estimate the rate of image motion during the observation sequence.

A set of HRC PR200L prism data (Table 2) was obtained on May 19, 1999 using a Platinum/Neon lamp attached to the monochromator. The slit was much more narrow for these observations so that a single line at a time could be isolated. A scan of the 2145 Å Neon line on May 18, 1999 (entries 8664-8670) was used to determine the spectral resolution: 3 Angstroms, and an offset (the monochromator wavelength is 0.9 Angstroms less than the true air wavelength of the line). The 100 micron pinhole was used in all observations. Observations with filter F250W were obtained before, after, and once during the middle of the sequence of prism observations to measure image motion.

**Method:**
Wavelength calibration of the data was done with custom-made IDL routines
(PR110L.pro,
PR130L.pro,
PR200L.pro, and
prism_funct.pro).
Checks of the slope of the prism spectra were done using custom routines
PR110L_slope.pro,
PR130L_slope.pro, and
PR200L_slope.pro.

Preprocessing of the HRC CCD data included overscan trimming and overscan bias level subtraction. Multiple sequentially observed images at the same wavelength were combined with cosmic ray rejection using the routine ACS_CR. The CCD images (all taken with Amp C) were rotated to the Amp A readout orientation. No preprocessing of the SBC images was required.

Profiles (in the dispersion direction) of the 100 micron pinhole imaged onto the detector were constructed for each image by summing the rows in a 31 column by 13 row rectagular region of the image, centered approximately at the center of the spot (as measured by a cursor). The X-position of the center of the first profile (from the initial filter image) of each sequence was computed as the centroid of the intensity profile after subtracting 1/3 of the maximum value and clipping at zero. The centers for the remaining profiles in each sequence were then computed using the offset of the profile from the first profile determined by cross-correlation (IDL routine CROSS_CORRELATE). The same method was used for determining Y positions for slope computation using a 31 row by 13 column region of the image.

Each measured position was corrected for image motion as determined from the filter observations. A constant rate of motion was assumed between the filter observations. The computed image motion was compared to the image motion computed using the red pile-up of light (where it had sufficient signal and was not blended with the observed monochromator bandpass).

For each prism mode, the coefficients (a0, a1, ..., a5) for the following dispersion were determined using a non-linear least squares fit with the IDL routine CURFIT and the associated function prism_funct.

wavelength (Å) = a1 + a2 / x + a3 / x^{2} +
a4 / x^{3} + a5 / x^{4}

where: x = (pixel position - a0)

Pixel position is in the dispersion direction and starts at zero for the first pixel. For the HRC CCD, the pixel position is the position after trimming the overscan regions of the image.

A weighted fit was performed using the weights equal to one over the dispersion squared at each data point (where the dispersion was computed by an initial unweighted least squares fit). These weights were chosen to minimize the squares of the sample position residuals (in pixels) instead of the squares of the wavelength residuals in Angstroms (obtained with no weighting). Initial guesses for the dispersion coefficients were obtained by trying hundreds of randomly chosen initial guesses and picking the one giving the final best RMS residual.

**Results:**
The wavelength calibration results for PR110L are shown in Table 3. Image positions were computed using
cross correlation with the F115LP observation number 8831 whose
centroid was computed at pixel 499.18. Image motion was corrected for
by using the F115LP observation number 8846 taken at the end of the
sequence of PR110L observations. The rate of motion was 0.12
pixels/hour. This is close to a motion of 0.10 pixels/hour computed
by custom routine PR110L_motion.pro using the red
pile-up of light (fit shown in Figure
1). The least squares fit to the dispersion coefficients had an
RMS of 0.18 pixels. Results of the fit are displayed in Figure 2 where the diamonds show the
location of the measured points and the solid line shows the fit. The
slope of the PR110L spectrum, computed using the y-profiles, was -0.24
degrees (Figure 3, where the diamonds
show the y locations of the spots versus the x location and the solid
line is a linear least squares fit).

Table 4 shows the wavelength calibration results for PR130L. Image positions were computed using cross correlation with the F115LP observation number 8847. Image motion was corrected for by using the F115LP observation number 8872 taken at the end of the sequence of PR130L observations. The rate of motion was 0.3 pixels/hour. The rate of motion, computed using the red pile-up of light using custom routine PR130L_motion.pro (Fit shown in Figure 4), was 0.5 pixels/hour. The least squares fit to the dispersion coefficients had an RMS of 0.11 pixels. Results of the fit are displayed in Figure 5 where the diamonds show the location of the measured points and the solid line shows the fit. The slope of the PR130L spectrum, computed using the y-profiles (PR130L_slope.pro), was -0.13 degrees (Figure 6).

Table 5 shows the wavelength calibration results for PR200L. Image positions were computed using cross correlation with the combined F250W observation numbers 8693 and 8694. Image motion was corrected for by using the F250W observation number 8708 taken in the middle of the sequence of PR200L observations and the combination of images 8744 and 8745 taken at the end of the observation sequence. The rate of motion was computed to be 0.48 pixels/hour for the first part of the sequence and 0.64 pixels per hour for the remainder. The second part of the sequence extended over a period of almost 4 hours. Figure 7, computed with routine PR200L_motion.pro, shows that the rate of motion for the second part of the sequence, computed using the red pile up of light, was approximately constant over the 4 hours and has a computed slope of 0.58 pixels/hour (which is close to the slope computed with the filter observations). The least squares fit to the dispersion coefficients had an RMS of 0.13 pixels. Results of the fit are displayed in Figure 8 where the diamonds show the location of the measured points and the solid line shows the fit. The slope of the PR200L spectrum computed using the y-profiles (PR200L_slope.pro) was -1.59 degrees (Figure 9).

**Conclusions:**
The dispersion relations for the prisms mode can be modelled by:

wavelength (Å) = a1 + a2 / x + a3 / x^{2} +
a4 / x^{3} + a5 / x^{4}

where: x = (pixel position - a0)

and where the coefficients for each mode, determined by least squares fit, are:

Coefficient PR110L PR130L PR200L a0 339.33770 354.03448 870.12088 a1 1051.6163 1071.7806 1133.2426 a2 21150.558 -14967.555 82999.557 a3 9237490.7 1947999.0 -828929.38 a4 4.9340281e+08 54848094. -4653501.0 a5 1.2458532e+10 1.1163562e+09 1.6888817e+08

The measured slopes of the prism spectra were:

PR110L -0.24 degrees PR130L -0.13 degrees PR200L -1.59 degrees

**Tables:**

- SBC Prism Wavelength Calibration Observations
- HRC Prism Wavelength Calibration Observations
- PR110L Dispersion Results
- PR130L Dispersion Results
- PR200L Dispersion Results

**Figures:**

- PR110L Image Motion (GIF,PostScript)
- PR110L Dispersion (GIF,PostScript)
- PR110L Slope of spectrum (GIF,PostScript)
- PR130L Image Motion (GIF,PostScript)
- PR130L Dispersion (GIF,PostScript)
- PR130L Slope of spectrum (GIF,PostScript)
- PR200L Image Motion (GIF,PostScript)
- PR200L Dispersion (GIF,PostScript)
- PR200L Slope of spectrum (GIF,PostScript)

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Last updated 26 October 2000 08:40:26

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