Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.stsci.edu/ftp/instrument_news/FOS/pub/fos_isr088.txt Дата изменения: Wed Oct 26 00:08:16 1994 Дата индексирования: Sun Dec 23 02:46:50 2007 Кодировка: Поисковые слова: http www.badastronomy.com bad tv foxapollo.html

FOS FLATS FROM SUPER SPECTRA

D. Lindler, R. Bohlin, G. Hartig, and C. Keyes

FOS Instrument Science Report CAL/FOS-088
March 29, 1993



ABSTRACT:

A new algorithm for computing the FOS detector non-uniformities
(flat field response) uses spectra of stars taken in 9 different
positions in the 4.3 arcsec aperture. Despite some "ringing" at
frequencies corresponding to the constant offset of the star in
the dispersion direction, the new blue flat fields achieve our
accuracy goal of about 1% and are appropriate for FOS BLUE side
spectra taken in any aperture in 1992.

Ringing at a higher level of 1-2 percent in the RED data is
caused by the loss of two-thirds of the G191B2B data due to
observing problems. These RED side flats should be used only
for blemish location or for visual verification of potential
features in observed spectra.

Future flat field data should be collected with a newly
recommended set of locations of the star in the FOS 4.3 arcsec
aperture.


INTRODUCTION:

In order to derive the FOS flat field corrections for small
scale instrumental artifacts, these pixel-to-pixel variations in
the photocathode and diode responses must be distinguished from
spectral features in the calibration source. The strengths of
the spectral lines in the stars are not known at FOS resolutions
of 1-10 Angstroms. Better FOS flat field calibrations require
determinations of small scale variations in the intrinsic
stellar flux distribution. A new technique uses high S/N
observations of stars to simultaneously compute both the flat
field and a precise stellar "super spectrum." Flat fields at
other epochs can be derived simply from the ratio of the
observed count rate to the super spectrum of the same star.

The new technique that was executed in proposal 2821 requires
stellar observations at nine locations in the FOS 4.3 arcsec
aperture (Figure 1). Moving the star in the X (dispersion)
direction moves spectral features to a different photocathode
and diode position in the observed data. Detector granularity
features will not move, as illustrated by the spectra in Figure
2, which shows a portion of the G191B2B (WD0501+527) data
observed at aperture positions 1 (solid), 2 (short dashes), and
3 (long dashes). The slew step size in the X-direction (1.79
arcsec) results in a shift of 4.75 diodes (19 quarter stepped
data points with an uncertainty of 1 point) in the spectral
features between data points 1800 and 1870. Most of the
structure in the data does not move and can be attributed to the
 Page 2


detector non-uniformities.

To separate the spectral flux distribution from the FOS flat
field granularity we create a non-linear system of equations:

Let: C(i) be the unknown count rate spectrum.
F(i) be the unknown flat field vector.

We observe the star at three different X locations in the 4.3
arcsec aperture to obtain observations O1(i), O2(i) and O3(i).
The spectral features are shifted by k data points between
observations. These observations lead to the system of
equations:

O1(i) = F(i) * C(i) i=1,n
O2(i) = F(i) * C(i+k) i=1,n
O3(i) = F(i) * C(i+2k) i=1,n

In our case, n is 2064 and k is 19. This leads to a system of
3n (6192) equations with only 2n + 2k (4166) unknowns. By
moving the star in the vertical direction in the 4.3 arcsec
aperture and observing at the photocathode location of the upper
and lower position of the FOS paired entrance apertures, the
number of unknowns increases by 4128 (two additional granularity
vectors). The stellar flux distribution remains the same and
increases our system to 9n (18,576) equations with only 8294
unknowns. If a second star is observed the number of equations
is doubled and the number of unknowns is only increased by n+2k
(2102). The second star will have a new flux vector but will
share the same flat field granularity vectors.

An iterative method for solving this large system of equations
is described in a later section.


OBSERVED DATA:

The FOS was used to observe two stars, BD+28D4211 and WD0501+527
(G191B2B) at the nine locations in the 4.3 arcsec aperture shown
in Figure 1. Complete sets of data were obtained for the BLUE
detector in disperser modes H13, H19, H27, H40, L15 and the
prism during the period of March through July 1992 (Proposal
2821). For the RED detector, a complete set of data was
collected only for BD+28D4211 (Proposal 2821, June 1992). Data
were collected for only the 3 UPPER aperture locations with
WD0501+527 (February 1992). Observed RED detector disperser
modes included: H19, H27, H40, H57, L15, L65, and the prism.
The RED detector data for dispersers H19, H27, and L15 were
supplemented by seven sets of observations taken under the flat
field monitoring proposal 3975 during the period of January
through June 1992. Proposal 3975 observations contain data only
for the central position in the 4.3 arcsec aperture. All
observations analyzed were quarter stepped (XSTEPS=4) with
OVERSCAN=5.
 Page 3


FLAT FIELD COMPUTATION:

The following procedure was used to compute the flat field
vector and average count rate spectrum for each
detector/disperser mode. Initially, spectra taken at positions
1,3,4,6,7, and 9 (Figure 1) are assumed to have a spectral
offset of 19 data points (4.75 diodes) from the center positions
(2, 5, and 8). X offsets between the three center positions are
set to 0.

1) Partially reduce all observed data using CALFOS (the
standard FOS pipeline reduction routine). The reduction
consists of conversion to count rates, correction for
paired-pulse non-linearities, and correction for geomagnetic
image motion.

2) Initialize the flat field vectors for the three aperture
positions (UPPER, LOWER, and SINGLE) to 1.0.

Repeat steps 3 through 8 for 15 iterations. 15 iterations are
chosen, because the change in the flat fields from 10 to 15
iterations is on the order of 0.1%. In one test case, the
average change from 15 to 100 iterations is less than 0.2% with
most of that difference being low frequency variations.

3) Correct all observed count rate spectra using the present
flat field vectors (initially set to all 1.0's in step 2 for
the first iteration).

4) Shift to align wavelengths and average all flat fielded
spectra for each star.

5) Compute a normalization vector for each spectrum by fitting
a cubic polynomial (as a function of data point) to each
observation divided by the average stellar spectrum computed
in step 4. This is required because of the loss of light
resulting from YBASE errors and the loss of light in the
wings of the point spread function when the target is not
centered in the 4.3 arcsec aperture.

6) Divide each of the raw observed count rates (not flat
fielded) by the corresponding normalization vector from step
5.

7) Divide each normalized observed count rate spectrum from
step 6 by the appropriately shifted average stellar spectrum
from step 4. The results are the computed flat field for
each observation.

8) Average the results from step 7 at each of the three
aperture positions (UPPER, LOWER, and SINGLE) to give three
new flat field vectors. Repeat the iteration begining at
step 3 with the new estimate of the flat field response.

9) Remove low frequency variations in the computed flat field
vectors by dividing by a least squares cubic spline fit
(typically 13 nodes for 2064 data points) through the data.
 Page 4


Once this process has been completed, we have computed flat
field vectors for each of the three aperture positions (UPPER,
LOWER, and SINGLE) and an average flux rate distribution for the
stars. New spectral shifts (initially assumed to be 19) are
computed by cross correlation of the spectrum at the center of
the aperture (position 5 in Figure 1) with the other eight
positions in the 4.3 arcsec aperture after correcting by the new
estimate of the flat field vectors. The shifts are rounded to
the nearest integer. With these new, more precise offsets
between the spectra, the entire process (beginning at step 2) is
repeated. This process is repeated until no changes in the
shifts are required.

We have included in the above algorithm the ability to use three
types of data quality masks. The first type is used to flag
data as unusable (eg. telemetry errors). The second type of
mask is used to flag data that should be used in the computation
of the flat field vector but not in the computation of the flux
vector. This mask is used to flag large blemishes that change
significantly from one observation to another even though the
data was taken with the star in approximately the same
Y-position in the aperture. Flat field variations can result
from small changes in the position of the spectra due to target
acquisition errors, jitter, and temporal or thermal motion. The
third type of mask is used to flag data that should be used in
the computation of the flux vector but not in the computation of
the granularity vector. This type is used to flag sharp changes
in the flux distribution that may cause flat field artifacts
when alignment is not perfect (spectra are aligned only to the
nearest data point or 1/4 diode). Mask type 3 is also used to
flag spectral features that have a large contribution from the
sky spectra and can vary from one observation to the next.


RESULTS:

Figures 3 to 28 show the average stellar count rate spectra for
each detector/disperser mode observed. The estimated one sigma
uncertainty (percent) in the mean is plotted below each
spectrum. This uncertainty is computed from the scatter of the
computed count rate vectors C(i) of the individual observations
from the average. Figures 29 to 67 show the average flat field
response for each aperture position (lower, single, upper) along
with the one sigma scatter about the average. The scatter about
the mean includes both counting statistic errors and actual
changes in the granularity among the observations. The counting
statistics is the lesser of the two causes of scatter. Regions
with abnormally large sigmas indicate blemishes which change
significantly from one observation to the next.

A 1-2 percent "ringing" is seen in some of the flux
distributions and is particularly evident in the region below
2400 Angstroms in the RED H27 BD+28D4211 spectrum (Figure 17).
Compare this region to the BLUE H27 data in Figure 8. The major
contribution to the ringing occurs at frequencies of
approximately 19.0 and 9.5 pixels and can be explained by the
sampling method used to observe the data. Data were collected
with the star shifted in the aperture such that the spectral
 Page 5


features move 19 pixels to the left or right of the positions
observed in the X-center of the aperture. Any component of the
granularity vector and flux vector at the frequency of 19 cannot
be properly retrieved and can be visualized by the following two
cases.

1) The flat field is uniformly 1.0 except at every 19th pixel
which has a value of 0.9. The stellar flux rate is uniformly
1.0 at all wavelengths.

2) The flat field is uniformly 1.0 at all locations. The
stellar flux rate is uniformly 1.0 at all wavelengths except at
every 19th pixel which contains a value of 0.9.

In both cases, the observed data will be identical. It is not
possible to determine if the 10% features are in the flat field
or the flux array.

A better method for collecting data is to vary the step (slew)
sizes in the 4.3 arcsec aperture. Figure 68 shows the computed
spectrum from a simulation using the 19 pixel pattern. The
ringing is clearly evident at the 1 to 3 percent level. Figure
69 shows the simulation in which the spectra were taken with
shifts of (17,0,-12) in the upper aperture position, (18,0,-14)
in the single aperture position, and (19,0,-8) in the lower
aperture position. No ringing is evident in these results. We
recommend that these varying steps sizes be used for future data
collection.

The actual results for the FOS show that the level of ringing
varies with detector/disperser modes. Some modes have better
results because of small 1 to 2 pixel positioning errors due to
target acquisition centering errors and geomagnetic image
motion. These 1 to 2 pixel errors result in the spectral
offsets varying from 17 to 21 pixels. When larger variations in
the offsets are present, the ringing is decreased. The ringing
on the BLUE detector modes (which had a full set of data for
both stars) appear to be less then 0.5% except for H40 and
isolated spectral regions where it approaches 1%. The ringing
varies from 1 to 2% for the RED results except for the RED L65
where it is under 0.5%.


CONCLUSIONS/RECOMMENDATIONS:

We recommend that the results for the RED detector not be
implemented in the routine reduction of FOS data because of the
level of 19-pixel ringing present within the data. The plots of
the RED flat fields included in this report are still valuable
to visually determine if an observed feature is at a blemish
location in the flat field vector.

The BLUE detector flat fields are appropriate for current data
observed in the A-1 aperture. The spatial extent of the
spherically aberrated telescope point spread function causes the
flat field response to vary with aperture size. As the aperture
size increases, the spectral profile perpendicular to the
dispersion becomes broader. As the profile becomes broader,
 Page 6


smoothing of the granularity occurs, as illustrated in Figure
70. Data taken in the B-3 (1.0 arcsec circular) aperture and
C-2 (0.25 x 2 arcsec) slit show a more pronounced photocathode
blemish than the same blemish illuminated by a star in the A-1
(4.3 arcsec) aperture.

Figures 71 to 83 show the comparison of the new A-1 flat field
vectors with the B-3 aperture flat fields computed using Science
Verification (SV) data (Anderson 1992). Ratios of the two sets
of flat fields show variations by as much as 5 percent. Some of
the variation may be the result of the different aperture sizes.
Other possible causes include actual changes in
photocathode/diode response and changes in the y-position of the
observed data. Changes in the y-position can result from target
acquisition errors, filter grating wheel non-repeatability, and
temporal or thermal motion.

As a check on the stability of the flats over a shorter time
interval, the separate BLUE flats are computed for the
independent observations of G191B2B in 1992 March and of
BD+28D4211 in 1992 July. The typical differences between the
flats for these two epochs are less than 1 percent, in agreement
with the uncertainties in the average BLUE flats shown in
Figures 29-46. However, the differences are occasionally as big
as 2 percent. Therefore, any feature in a BLUE side FOS
spectrum that is weaker than about 2 percent could be spurious,
especially at wavelengths where the flat field correction itself
exceeds 5 percent.

In order to determine the applicability of the new flats over
the time period of January 1991 through October 1992, 70 BLUE
spectra are flat fielded with both the new A-1 flats and the old
SV B-3 flats. The results are:

1) Calibrations with the new A-1 BLUE flat field vectors are
better for both the B-3 and A-1 apertures for data taken
in 1992. Even though the A-1 aperture flat field vectors
are not perfect for the smaller apertures, applying the
A-1 Flat is better than leaving the data uncorrected.

2) Calibrations with the old SV B-3 BLUE flat field vectors
are better for 1991 data taken in the B-3 apertures.

3) Calibrations of 1991 A-1 BLUE data show mixed results with
the old SV flats giving better results the majority of the
time. A few of the observations showed regions where the
best results were obtained when no flat field correction
was applied.

Our recommendation for routine calibration of FOS data is to use
the SV B-3 flats for all BLUE side data taken in a SINGLE
aperture prior to January 1, 1992. Beginning on January 1,
1992, the new A-1 flats should be used to calibrate all BLUE
side data. BLUE side data taken in a paired aperture during
1991 should be corrected with the new A-1 flats computed for the
UPPER and LOWER aperture positions or should be left
uncorrected. In no circumstances should the SV B-3 flats be
used to correct data taken in a paired aperture. A review of
 Page 7


Figures 29 to 67 clearly shows significant differences in the
flat fields between the three aperture locations.

The FOS/BLUE A-1 flats described here have been delivered to the
Calibration Data Base System (CDBS) and installed in the Post
Observation Data Processing System (PODPS) pipeline. Observers
wishing to use CALFOS to re-calibrate data may obtain these new
flats via anonymous ftp from node stsci.edu in subdirectory
/cdbs/yref. Observers with access to the ST ScI VAX Science
Cluster can also find the files in the directory,
DISK$REFERENCE:[CDBSDATA.REFER.YREF]. Table 1 contains the
reference file names for particular instrument configurations.


FUTURE CALIBRATION:

We recommend that the failed RED side observations of WD0501+527
be repeated as soon as possible. The repeat should be with the
slew sizes in the X (dispersion) direction that are specified
above.

After the deployment of COSTAR, the computed flux vectors for
the two targets will no longer be applicable. A complete set of
new calibration data should be taken at the nine recommended
positions in the 4.3 arcsec aperture for both stars. The flat
field response vectors computed for post-COSTAR A-1 data should
be applicable to all FOS entrance apertures. The significant
suppression of the flux in the wings of the point spread
function will make the profile of the spectra perpendicular to
the dispersion direction nearly identical for all apertures.
This assumption should be verified by comparing the spectra
taken with the target in different apertures for at least one
grating mode. The time variability of the flat field vectors
can then be monitored by observing the star in a single location
in the aperture (or 3 locations if monitoring of the upper/lower
apertures is required). The flux distributions computed using
the 9 position data can be used to reduce all subsequent single
position data. In fact, the new flux distributions might be
smoothed to match pre-COSTAR data to obtain better pre-COSTAR
flats for archival research.


REFERENCES:

Anderson, S. F. 1992, FOS Spectral Flat Field Calibration
(Science Verification Phase Data), Instrument Science Report
CAL/FOS-075

 Page 8


TABLE 1

FOS/BLUE Flat Field Reference Files Derived
from Superflat Technique




APERPOS GRATING HEADERFILE DATAFILE

single h13 d2f1332py.r1h d2f1332py.r1d
single h19 d2f1332sy.r1h d2f1332sy.r1d
single h27 d2f1332ty.r1h d2f1332ty.r1d
single h40 d2f13331y.r1h d2f13331y.r1d
single l15 d2f1332ry.r1h d2f1332ry.r1d
single pri d2f13332y.r1h d2f13332y.r1d

lower h13 d2f1333dy.r1h d2f1333dy.r1d
lower h19 d2f1333gy.r1h d2f1333gy.r1d
lower h27 d2f1333iy.r1h d2f1333iy.r1d
lower h40 d2f1333jy.r1h d2f1333jy.r1d
lower l15 d2f1333fy.r1h d2f1333fy.r1d
lower pri d2f1333ly.r1h d2f1333ly.r1d

upper h13 d2f13334y.r1h d2f13334y.r1d
upper h19 d2f13336y.r1h d2f13336y.r1d
upper h27 d2f13338y.r1h d2f13338y.r1d
upper h40 d2f1333ay.r1h d2f1333ay.r1d
upper l15 d2f13335y.r1h d2f13335y.r1d
upper pri d2f1333cy.r1h d2f1333cy.r1d



NOTE:

APERPOS = single implies apertures A-1, B-1, B-2, B-3, and C-2.

APERPOS = lower implies apertures A-2, A-3, A-4, and C-1.

APERPOS = upper implies apertures A-2, A-3, A-4, and C-1.
 Page 9


FIGURE CAPTIONS




1) The nine locations where the stars were observed in the FOS
4.3 arcsec acquisition aperture. The location where the C-1
(1.0 arcsec square) paired aperture would fall is shown by
the dashed squares. Locations 1, 2, and 3 correspond to the
y-position of the lower aperture of the paired aperture,
locations 3, 4, and 5 correspond to the center location of
the single apertures, and locations 7, 8, and 9 correspond to
the upper aperture Y-position.

2) A portion of three spectra of WD0501+527 (G191B2B) taken with
the star at locations 1 (solid line), 2 (dotted line), and 3
(dashed line) in Figure 1. Spectral features move
approximately 19 data points between positions. Detector
non-uniformities remain at the same location.

3 to 28) The average count rates for the BLUE and RED (=AMBER)
spectra of WD0501+527 and BD+28D4211 computed using the
method described in this paper. Below each plot is the
estimated one sigma uncertainty in the super spectrum. The
wavelength range of all plots is limited to the region where
the typical flat field correction exceeds its typical
statistical uncertainty.

29 to 67) The average detector flat-field granularity vector
computed for each disperser mode and each of the three
aperture positions (LOWER, SINGLE, and UPPER). The one sigma
scatter from the average is plotted beneath each granularity
vector. The flat field is set to 1.0 in regions where low
counting statistics or sharp changes in the stellar flux
distribution give poor flat field calibrations.

68) Results of a simulation of the algorithm described in this
paper using the star pattern shown in Figure 1. The
simulated spectrum is smooth except for a sharp feature at
data point 420. The "ringing" is an artifact of the
observation technique.

69) The same simulation as Figure 68 except that the slew sizes
between the position of the star in the aperture were changed
to (17, 0, -12) data points in the upper aperture position,
(18, 0, -14) in the single aperture position, and (19, 0, -8)
in the lower aperture position.

70) A flat field feature shown in the spectrum of BD+75D325
observed in three different apertures; the A-1 (4.3 arcsec
square) is shown as the thick solid line. The B-3 (1.0
arcsec circular) and the C-2 (0.25 x 2 arcsec slit) spectra
are shown as the thin solid line and the dashed line for
spectra obtained on June 5, 1991.

71-83) A comparison of the flat field vectors computed with the
1992 A-1 data and algorithm described in this report (NEW,
top plots) and the ones computed from SV aperture B-3 data
 Page 10


(OLD, center plot). The bottom plot shows the ratio of the
two vectors. The simularity of the Old and New flats
demonstrates the validity of both results, since the
derivations are entirely independent. Gaps in the ratio are
where either flat field vector is set to 1.0, which is where
there is line contamination in the Old flats. The New flats
are set to 1.0 in regions where sigma is generally larger
than the actual flat field deviation from unity.