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Astronomical Data Analysis Software and Systems IV
ASP Conference Series, Vol. 77, 1995
R. A. Shaw, H. E. Payne, and J. J. E. Hayes, eds.
Modeling Scattered Light in the HST Faint Object
Spectrograph
H. Bushouse
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218
M. Rosa and Th. Mueller
Space Telescope--European Coordinating Facility, European Southern
Observatory, Karl­Schwarzschild­Str. 2, D--85748 Garching, Germany
Abstract. We describe the software tool bspec which models the dis­
persion and diffraction of light in the HST Faint Object Spectrograph.
The bspec program is available in both the MIDAS and IRAF environ­
ments.
1. Introduction
The HST Faint Object Spectrograph (FOS) uses blazed, ruled gratings and
detectors that are sensitive over wide wavelength ranges. Therefore the FOS
is subject to scattered light which has its origin in the diffraction patterns of
the gratings and the entrance apertures, as well as the micro­roughness of the
ruled gratings. This becomes a significant problem when red stars are observed
at short wavelengths where the spectrum is often dominated by scattered red
photons.
The analysis of laboratory and in­flight FOS data indicates that the instru­
ment is very close to the performance anticipated from ideal optical surfaces.
Therefore, the contamination of observations by scattered light can be predicted
with reasonable accuracy.
The program bspec has been developed to model the dispersion and diffrac­
tion of light in the FOS with an accuracy sufficient for the estimation of scattered
light contamination in observed FOS data. The program was developed and is
maintained in the MIDAS environment and it was recently ported to the IRAF
environment. bspec takes an input spectral distribution and disperses it into
the most significant spectral orders---using the equations of blazed gratings and
the grating parameters for the FOS---and convolves this multi­order spectrum
with a model of the instrumental line spread function (LSF). It is light from the
wing of order zero that constitutes a significant portion of the scattered light
level seen in the blue wavelength end of first­order FOS spectra.
The spectra produced by bspec, which includes the intrinsic spectrum of
the source as well as the predicted intrinsic plus scattered light spectrum, can
be compared with FOS observations in order to determine the relative amount
of scattered light contained in observed spectra.
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2. The Details
The bspec program takes as input a spectral distribution of count rates which
is dispersed into the most significant spectral orders (e.g., \Gamma5 to +5) using the
equations of blazed gratings and the known parameters of the FOS gratings.
Light from the wing of order zero constitutes a significant component of the
scattered light in the blue part of the first order spectra imaged onto the detector.
The amount of zero order light is determined in bspec as the residual flux not
being distributed into higher orders. By comparison with more rigorous models,
we find it sufficient to include orders up through 5. Even for stellar spectra as
late as M5, the fractional improvement of including higher orders is below 10 \Gamma4 .
The spectral shape in each order is the product of the input spectrum and
the blaze function for a given order. The resultant multi­order spectrum is
convolved with a model of the line spread function (LSF) which represents the
effects of diffraction at the entrance aperture, the collimator, the grating and the
detector faceplate, and includes a flat component to simulate micro­roughness
and dust particle scatter.
In order to ensure that all significant light is collected and redistributed by
both the grating equations and the convolution with the LSF, the computation
is performed over a range of diffracted angles much larger than that seen by the
actual detector. The red and blue FOS detectors both cover the range \Gamma1:47 to
+1:47 degrees from the grating normal. The computations in bspec typically
cover the range \Gamma10 to +35 degrees in diffracted angle, which includes all orders
from zero to five.
3. Using BSPEC
In practice, correcting observational data for scattered light must be done before
the count rate spectra are transformed to absolute fluxes. The bspec program is
therefore intended to produce output data that are in units of counts per pixel,
which then requires that the input data also be in this form. Calibrated spectra
must be prepared for use in bspec by scaling by the sensitivity and transmission
of all the HST and FOS optical components, except for the grating blaze function
which is computed and applied within bspec. In particular the conversion from
flux per unit wavelength to counts per pixel has to be made before using in
bspec.
To make this job easier a program called countspec has been developed in
IRAF/STSDAS which will convert a flux calibrated spectrum of any object into
a count rate spectrum. The countspec program uses the known throughputs
and sensitivities of the HST and FOS optical components---as contained in the
HST Calibration Data Base System (CDBS)---to perform this conversion.
The bspec program, in both the MIDAS and IRAF environments, uses
tables for all input and output data. The countspec program (only avail­
able in IRAF/STSDAS) also uses tables. The input and output tables for
countspec and the input table to bspec are simple two­column tables of wave­
lengths and fluxes (or counts). The output table produced by bspec contains
several columns of data including wavelengths and dispersed counts, both with
and without scattered light, and the grating blaze function.

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4. Example Calculations
For illustration let the target spectrum be the model atmosphere for the the
solar­like star 16 Cyg B, which we wish to compare with an observed spectrum
of this star obtained using the FOS blue detector, the G190H grating, and the
1: 00 0 round aperture.
First, we prepare the model spectrum---which is in absolute flux units---
using the countspec task to convert the model data to a count rate spectrum.
The calibrated model data are contained in table cyg16b.tab and the count rate
spectrum will be written to table counts.tab. We run countspec as follows:
cl? countspec cyg16b fos,1.0,g190h,blue counts.tab
The second argument, ``fos,1.0,g190h,blue'', specifies the desired instrument ob­
serving mode.
Second, we run bspec, using the table counts.tab as input, to compute
a predicted scattered light spectrum. The output from bspec will be written
to table scatter.tab. It is only necessary to specify the input and output
table names and the detector and grating names. Appropriate default values
for the grating and LSF parameters will be chosen based on the selected detec­
tor/grating combination. We run bspec as follows:
cl? bspec counts.tab scatter.tab blue g190h
5. Results
Figure 1 shows the results of bspec computations for the star 16 Cyg B as
observed with the FOS blue detector and G190H grating. The lower curve in
Figure 1 shows what would be an ``ideal'' spectrum as observed by an unphys­
ical instrument that relates wavelengths one­to­one with diffracted angles. The
upper curve (offset vertically by a factor of 10) shows the ``model observations''
computed by bspec, i.e., the intrinsic spectrum dispersed by the blazed grating
and further convolved with the scattering imposed by the entrance aperture, the
ruled surface of the grating and a minute amount of dust on the optical surfaces.
Orders \Gamma5 to +5 were computed but only orders 0 to 2 are shown in the figure.
Note that the real detector covers only the wavelength range indicated by the
horizontal bar near 2000 š A.
The shape of the zero order peak in Figure 1 reflects the actual LSF. The far
wings of this LSF carry light from the peak of the original spectral distribution
into regions where the target spectrum, filtered by the total throughput of the
optical elements and the detector efficiency, produces few intrinsic counts. In
addition, this LSF moves photons from the zero order peak into the adjacent
parts of the first order seen by the detector.
Figure 2 shows an actual observed FOS spectrum of 16 Cyg B overlaid
with the ``ideal'' and the ``model'' observations from Figure 1. The observed
spectrum is offset vertically for clarity. For a solar­like spectrum, the scattered
light component ranges between 1--99% of the observed signal in the FOS blue
G190H mode.

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Figure 1. FOS blue G190H count rate spectra for a G5V model at­
mosphere.
Figure 2. FOS blue G190H data for the G5V star 16 Cyg B.