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FOC Instrument Handbook Version 7.0 81
Figure 44. Photometric calibration of the NUVOP. This plot compares the NUVOP
spectrum of the spectrophotometric standard HZ4 (solid) with the comparií
son spectrum from the calibration library(dotted).
Figure 45. Calibration of FaríUV Objective Prism (FUVOP) spectrum of the spectroí
photometric standard HZ4.

80 FOC Instrument Handbook Version 7.0
Figure 43. (a) Dispersion curve and (b) dl/dx relation for the NUV objective prisms,
and (c) dispersion curve and (d) dl/dx relation for FUV objective prisms.
NUV Prism FUV Prism

FOC Instrument Handbook Version 7.0 79
Table 13: Energy fractions for spectra as a function of the extraction width.
The energy fractions given in Table 13 are mean values based on measurements of the Sandí3
and HZ4 calibration observations. The 3s errors reflect the variations in the energy fraction
induced primarily by the effects of breathing and linearity in the spectrum and represent the range
of variations that can be expected in wellíexposed science observations.
The position of the undispersed target can also have a severe effect on the fluxícalibration of
the extracted spectrum, an effect that increases toward the longer wavelengths due to the noníliní
ear dispersion of the prisms. The dispersion curves provide the relation between a feature's posií
tion in the image to a wavelength, however, the wavelength range covered in a pixel determines
how the observed counts are distributed across the wavelength range spanned by each pixel. Both
relations, the dispersion curve and the dl/dx relation (wavelength covered by each pixel), are
shown in Figure 43. As a result, care must be taken to accurately determine the position of the tarí
get in the objective prism image.
Taking both of these effects into account, the calibration of the prisms has been improved coní
siderably over that provided in previous cycles. The final dispersion curves, shown in Table 6, had
rms errors in the fit of 0.86 pixels for the FUVOP dispersion curve and 3.43 pixels for the NUVOP
dispersion curve. These errors translate to 4Š at 1600Š and 60Š at 3500Š for the NUV OP and
1.3Š at 1150Š and 22Š at 2000Š for the FUV OP. The synphot package was also used to calculate
the apparent magnitudes for different passbands (including the U and B bands) using both the calí
ibrated spectra and the spectrum from the calibration spectra library. These calculations indicate
that the photometry of the NUVOP was within ~0.1 magnitudes from 1600Š í 4000Š and ~0.4
magnitudes from 4000í6000Š, while the FUVOP spectrum was within ~0.1 magnitudes of the
catalog spectrum between 1240Š to 3000Š. A comparison of the reduced spectrophotometric
standard's spectrum with the catalog spectrum in Figures 2 and 3 shows the close agreement for
both the NUVOP and the FUVOP respectively. The disparity in the flux from 1600í1800Š may be
due to reduced transmission in the NUV prism relative to the expected throughput. This should be
taken into account when performing spectrophotometry in that wavelength range with the NUV
prism.
Extraction Width
(pixels) NUVOP Error (3s) FUVOP Error (3s)
5 0.554 0.074 0.480 0.080
7 0.627 0.069 0.557 0.079
9 0.680 0.065 0.616 0.073
11 0.720 0.059 0.660 0.058

78 FOC Instrument Handbook Version 7.0
the extraction that is needed. This energy fraction was determined from background subtracted,
single source images by dividing spectra of varying extraction widths by the spectra of a 140 pixel
wide extraction. This provides some consistency with the DQE determinations for the FOC since
the energy fraction of a point source has been defined to be 1.00 for an aperture with a radius of 70
pixels (see FOCí085 for more details). The energy fraction for a spectrum of a given extraction
width was determined for each prism, with the results given in Table 13.
0 500 1000 1500
0
0.02
0.04
0.06
Time Since HV Turníon (Minutes)
Figure 42. F/48 camera background measured in three areas (A: arc í solid line; B: flare í dotted
line; C: background ídashed line) during the latest test, and plotted as a function of
time after camera switchíon. The relay showed this same basic behavior during each
observation run.

FOC Instrument Handbook Version 7.0 77
already noticed in the previous run. In Figure 42, the background is measured in three sample
regions (flare, arc, background) in the images taken during the December 1995 observations, and
is plotted as a function of time. This program had a duration of approximately 1200 minutes. The
measurements taken after 1000 minutes show that the intensity of the flare and arc continued to
decrease with time after turníon, converging to nominal values. The camera is demonstrated to be
operational and quite stable, within the background limits mentioned.
Due to these positive results, a decision was taken in Cycle 6 to make the F/48 camera
available to the users, limited to LONG SLIT SPECTROSCOPY ONLY. This offer is coní
tinued in Cycle 7. At the moment of writing, the long slit facility is unique on board the HST,
although after the refurbishment mission planned for 1997, STIS will be able to replicate, more
efficiently, all the features of the F/48 long slit spectroscopy (see STIS Handbook for additional
details).
6.14 OBJECTIVE PRISM SPECTROPHOTOMETRY
Analysis of objective prism images to produce a fluxí and wavelengthícalibrated spectrum not
only requires knowledge of the dispersion curve (given in Table 5), but also proper extraction of
the spectrum from the image. The calibrations carried out to determine the dispersion curves
given in Table 5 were based on objective prism observations of a emissioníline star and a spectroí
photometric standard source. Reduction of the spectra relies on preserving the Yíposition of feaí
tures and, for the calibrations, used the twoídimensional spectra software in IRAF to extract 7í
pixel wide image sections along the core of the observed spectra.
In order to insure that the extracted spectra can be fluxícalibrated, the percent of the total
observed flux contained in the extraction must be known. This is equivalent to knowing the encirí
cled energy fraction for photometry of a pointísource, only in this case it is an energy fraction of
Figure 41. Mosaic of F/48 Images taken ordered by time after switchíon during the Novemí
ber 1994 test. Earliest image is on the left. All are displayed with respect to the
same count rate scale, to show how the flare actually tended to subside over time
since switchíon. The regions of the flare and arc are marked in the center image.
Arc
Flare

76 FOC Instrument Handbook Version 7.0
Due to problems observing with the F/48 relay since the deployment of COSTAR, the prelimí
inary plate scale of 0.02825 arcsec pixel í1 remains the only value available, with an error of
‘0.0002 arcsec pixel í1 based solely on the preíCOSTAR calibrations. Observations of a field of
stars already observed prior to COSTAR deployment were used to determine the new plate scale
for the F/96 relay. The derived plate scale for the F/96 relay is 0.01435 arcsec pixel í1 (‘0.0002).
This value has been verified using astrometric observations.
Calibration programs have shown that these plate scales will provide separations between
close pairs of stars to within 0.4 pixels (or about 0.0057 arcsec for the F/96), while the separations
between widely spaced stars are good to within 0.25%. This is due to a combination of ef fects
including centroiding accuracy . However, the main error comes from the stabilization of the FOC
image after it is turned on for an observation run. Early calibrations (discussed in Instrument Scií
ence Report FOCí045) showed that the plate scale and geometric distortion varies for several
hours after initial highívoltage turn on. The plate scale, for example, only changes by about 0.25%
in the first few hours then remains relatively stable afterwards. This variation can be important to
an observer requiring the same astrometry for all their images, in which case, comments should be
made in the Phase II proposal stating that the visit shouldn't start immediately after HV turníon.
6.13 CURRENT F/48 PERFORMANCE
The first failure of the F/48 camera to turn on occurred in September 1992. The high v
oltage
tripped during its ramping up, at the beginning of an observation sequence. The F/48 camera was
switched on again successfully in October 1992, and a number of darks and flat fields were taken
which confirmed background values more than ten times higher than nominal. The next switch on
attempt (January 1993) failed, but the F/48 was again successfully switched on December 22,
1993, before the deployment of the COSTAR corrective optics. The camera remained on for the
duration of the observation. While the acquisition image showed a background level consistently
high with the previous dark count images, a preliminary analysis of the following frames showed
that the background increased dramatically with time, eventually reaching saturation levels
approximately two hours after HV switchíon. As a consequence, the F/48 was not made available
to GOs during Cycle 4 and 5, while extensive tests were carried out to establish its performance
and operational reliability.
After a long period of inactivity, the F/48 was switched on again in November 1994, for the
first time after the COSTAR deployment. Images and spectra of an extended target were successí
fully obtained, and showed a completely different behavior from the earlier tests.
A direct comparison of all nine spectra taken during the November test was made to determine
the characteristics of the background as a function of time after switchíon. The high background
was still localized in the central area of the image (flare), and in the upper arc across the top of the
images. The locations of these features can be seen in Figure 41, where all the images are disí
played with the same intensity contrast to allow direct visual comparison. But, it was clear from a
cursory comparison that instead of increasing in intensity over time, the flare actually tended to
subside over time since switchíon.
This finding was confirmed in the course of three additional successful turníons, on March 5
on March 30, and on April 18, 1995. In all cases the background decreased significantly as a funcí
tion of time, to reach a value lower than 10 í2 cts/sec/pix after approximately 250 minutes after
switchíon. The F/48 camera was switched on again in December 1995, to execute successfully the
first scientific program. The background behaved as expected, continuing the diminishing trend

FOC Instrument Handbook Version 7.0 75
ably flatter and outígassing should be very near stable. Consequently, effects on distortion are
much smaller and are taking longer to materialize. Based on our e
xperience;
a. The F/96 relay continues to be very stable, the geometric variation in the F/96 relay has
shown only about 1í2 pixels of movement since launch, (which theoretically should be the
worst time).
b. Although most of the variation in distortion resulting from the high voltage turníon has hapí
pened during the warmíup period where data is not normally taken, there is still some residual
variation over the next 2 hours. Those PIs needing the ultimate in geometric stability should
specify such on their proposal.
c. There are as much as 0.5% changes in effective plate scale between different high voltage
turníons.
d. The situation with the F/48 relay is somewhat less certain since monitoring of the preíCOSí
TAR F/48 relay has shown it to be considerably less stable, with several large, unexplained
changes in the geometric configuration. No systematic information exists for postíCOSTAR
data, due to the high voltage problems. All F/48 data must be considered to be poorly charací
terized with respect to geometric distortion.
6.12 PLATE SCALE
The plate scale (i.e., the pixel size in arcseconds) had been determined for both of the FOC
relays prior to the deployment of COSTAR. This was done by taking a series of images of a pair
of astrometric stars, moving the telescope between exposures by a predetermined angular offset.
The measured distances (in pixels) between the astrometric stars, combined with the known sepaí
ration (in arc seconds) then give us the plate scale. The effects of COSTAR on the focal ratio of
the image was then applied to these values to obtain preliminary plate scales.
200 400 600 800 1000
200
400
600
800
1000
PIXEL NUMBERS
LINE
NUMBERS
diff file : zlrg.tab
run entry : respos , dated Tue 13:50:59 05íAprí94 , history* V *
ref file : optref.tab
ref entry : optref , dated Tue 13:50:59 05íAprí94 , history* V *
magnif. : 2.
plotted : Tue 13:56:01 05íAprí94
Figure 40. The 512z ½ 1024 format distortion field for the F/96 relay.

74 FOC Instrument Handbook Version 7.0
ried out in a single step using a fluxíconserving algorithm which maps v
alues from the raw, disí
torted image into a geometrically corrected image. Figures 39 and 40 show as an example the
magnitude of the distortion field as determined for the preíCOSTAR F/48 and preíCOSTAR F/96
cameras using their 512z ½ 1024 formats, from iníflight calibrations (the differences arising from
the change in the new distortion and the optical distortion from the use of COSTAR amount to
only a few pixels at most; these figures are intended to show the global distortion effects).
The squares show where a regular grid of points on the sky (using a 60 pixel spacing) should
have appeared if there were no distortion; the ends of the line segments show where the grid
points actually appear in the distorted image. (The lines have been multiplied by a factor of 2 to
make them more easily visible,e.g., a line length of 50 pixels represents a distortion displacement
of 25 pixels). The pixel coordinates shown refer to normal, square pixels, rather than the rectanguí
lar, zoomed pixel mode the images were obtained in.
In order to carry out geometric correction of FOC data,i.e., to recover an image in which the
spatial relationships between objects are restored, a necessary requirement is that the geometric
distortion field, shown in Figures 39 and 40, must be stable. By this we mean that there must be no
significant change in the observed reseau positions with time.
Short term variation of the geometric distortion pattern occurs during the period immediately
following FOC high voltage switchíon. During this time the observed reseau positions show an
RMS deviation from the stable positions of approximately 1í2 pixels. This period however,
extends for only about 40 minutes, by which time the reseau position have stabilized to within 0.5
pixels, which is considered adequate for imaging purposes. In order to a
void this period of instaí
bility, the scheduling software automatically inserts a delay interval immediately following high
voltage switchíon which prevents exposures being taken during this time. Long term variations in
the geometric distortion were expected to occur as a result of desorption and outígassing in the
OTA and instruments, however given the time since launch, the desorption curve is now considerí
200 400 600 800 1000
200
400
600
800
1000
PIXEL NUMBERS
LINE
NUMBERS
diff file : dist75.tab
run entry : day835 , dated Tue 13:50:59 05íAprí94 , history* V *
ref file : optref.tab
ref entry : optref , dated Tue 13:50:59 05íAprí94 , history* V *
magnif. : 2.
plotted : Tue 16:34:47 05íAprí94
Figure 39. The 512z ½ 1024 format distortion field for the F/48 relay.

FOC Instrument Handbook Version 7.0 73
prism can work quite well. At that point, the only remaining problem is to insure that the o
verload
limit of the detector (described in Section 6.6) is not violated for the visible part of the image.
6.11 GEOMETRIC DISTORTION AND STABILITY
Because of the nature of the detectors, and the offíaxis location of the instrument, the raw
FOC data suffers from geometric distortion, i.e., the spatial relations between objects on the sky
are not preserved in the raw images produced by the FOC cameras. This geometric distortion can
be viewed as originating from two distinct sources. The first of these, optical distortion, is e
xternal
to the detectors and derives from the offíaxis nature of the instrument apertures. The second, and
much more significant source of distortion is the detector itself.
Geometric distortion is a fact of life when dealing with detectors containing image intensifií
ers, primarily because intensifiers rely on an electric field for accelerating, and a magnetic field
for focusing the photoelectrons. Any variation in the uniformity of either results in image distorí
tion within the intensifier. Photon positions are then further distorted in the process of ``readingí
out'' the TV tube's target, firstly because the readíout beam is performing an angular sweep across
a plane target, and secondly because of noníuniformities in the scanning rate of the beam. F
or this
reason, each video format has individual distortion characteristics, and so unfortunately, the disí
tortion measured for one format cannot be used to correct the distortion of an e
xposure taken in
another format.
In past cycles, the distortion correction model had been based on the measured location of the
reseau marks---fiducial reference points etched onto the first of the biíalkali photocathodes in the
intensifier tube. (Since these reseau marks only transmit about 10% of the incident light, for all
practical purposes they cannot be flat fielded out.) These reseau marks form an orthogonal grid of
17 rows and 17 columns with a separation of 1.5 mm (60 pixels), each reseau being 75 microns
square (3 ½ 3 pixels). The detector distortion was determined by illuminating the photocathode
with an internal light source, (i.e., an internal flat field). The observed positions of the reseau
marks, when compared to the expected positions, provide a map of the detector distortion across
the field. The optical component of the distortion is determined independently from rayítracing
models of the HST and FOC optics, and is applied to the reference reseau grid to gi
ve the
`expected' positions.
Unfortunately, the detector distortion for the FOC clearly has variations on spatial scales
smaller than the spacing of these reseau marks (particularly near the scan line beginning), and as a
result, models based only on the reseau marks do not adequately represent the true distortion. A
new method of determining distortion was developed which is based on overlapping observations
of crowded starfields to determined the net distortion (the optical distortion is naturally included
in this method of determining the distortion). These observations were then used to determine a
twoídimensional spline distortion model which in turn was used to generate the new geometric
correction files. The improvement in quality is most apparent for smaller formats where the small
number of visible reseaux prevented the determination of a good model. The new geometric corí
rection files have been used in the calibration pipeline for F/96 data since 19 March 1995 (F/48
geometric correction files are still based on reseau marks). As an aside, only those who desire sub
pixel accuracy in position measurements or those who have used the 256X256 format should even
consider reprocessing data taken prior to this date with the new geometric correction files. For
most, the improvements will not have a significant effect on their positions or photometry.
Although the geometric distortion arises from several sources, the correction of images is carí

72 FOC Instrument Handbook Version 7.0
through the entire OTA+COSTAR+FOC system is shown by the curve marked F231M. The actual
observed count rate in this configuration, of course, corresponds to the integral of this curve.
If the F231M filter alone is used in this endeavour, the contribution of the flux within the band
2330 ‘ 115Š is only @ 18% of the total of 39 counts sec í1 . The counts originating from the region
l > 2580Š represent, in contrast, 71% of the total. In this admittedly extreme case, the thus
derived UV brightness would be highly suspect, to say the least. Solutions to this problem are not
easy to find but, at least for the F/96 relay, one simple device would be to introduce a second cleví
erly selected filter into the beam in addition to the original one. This selection should be geared
towards maximizing the suppression of the visible leak while minimizing absorption in the UV
bandpass of interest.
In the case worked out in Figure 38, for example, the F220W filter on FW#2 is ideal as shown
by the curve marked F231M+F220W. Now, the iníband fraction of counts amounts to 69% while
the visible leak is only 5% or less of the total. The e
xposure time required to reach a S/N=10 in
this case increases by a factor of six mainly because of the effective suppression of the visible
counts.
Unfortunately, the F/48 relay with its much smaller filter complement has f
ar less flexibility in
this regard than the F/96 relay. In this case, another possible solution to the problem is to use the
objective prisms to physically separate the UV from the visible. This technique works best for
point or, at least, compact sources where spatial and spectral overlap is minimized. But even for
extended sources, appropriate positioning of the target with respect to the dispersion axis of the
Figure 38. The expected monochromatic count rate as a function of wavelength for the F/96
relay and the F231M filter or the F231M+F220W filters in the beam for an e
xtended
source whose spectrum varies as the curve marked SOURCE SPECTRUM. The
source flux units are photons cm í2 sec í1 Š í1 .

FOC Instrument Handbook Version 7.0 71
Unsmoothed flat fields are available from the FOC WWW pages or the STScI ftp directories
(see Chapter 9 for more details), and by using them, it is often possible to improve the flat fielding
by the appropriate registration of the flat field to the science image. But this requires scientific
judgment and must be applied on a caseíbyícase basis.
One final effect should be mentioned. Although it is not a flat field issue, it appears to many at
first glance to be one, and so it will be e
xplained here. Many observers see a fringe or fingerprint
type of pattern in the background of their calibrated images where the fringes are of relatively low
spatial frequency---usually of periods of 20 or more pixels. It is a result of the geometric correcí
tion applied to the data. It does not appear in the raw data. What is being seen is not alternating
areas of darker and brighter background, but rather, alternating areas of higher and lower variance
in the poissonian noise of the background. This effect arises from the resampling algorithm used
in the geometric correctionííessentially what one is seeing is the effect of the pixels in the output,
geometrically corrected image drifting in and out of phase with the corresponding pixels in the
input, distorted image. Those pixels mapping directly to the center of a pixel in the input image
result in little or no effective smoothing, while those which map to a point in between pixels in the
input image will be an average of the input pixels and thus have smaller variance in the noise. A
small amount of further smoothing to the geometrically corrected image will virtually eliminate
the effect. The pattern is identical in all images as long as they use the same geometric correction
file.
The achievable relative photometric accuracy depends on many factors, of course, and no simí
ple rule of thumb will apply to all analyses. In many cases the accuracy depends on the amount of
work an observer is willing to do to calibrate his data. For RSDP calibrated files, one should not
expect the large scale accuracy to be better than 3í5% over the central region of the format, and
should expect errors as large as 10% closer to the edges (much higher very close to the edges).
Fine scale features can introduce large pixelítoípixel errors (i.e., scratches and reseau marks).
Scratches and blemishes can be dealt with by careful flat fielding. It is sometimes possible to
remove the pattern noise with special techniques. Most important is to a
void placing targets on or
near areas with serious photometric problems if possible. That is, k eep targets of interest way
from the edges of the format, burníin regions, A/D glitches and known blemishes if more accurate
photometry is desired.
6.10 VISIBLE LEAKS
Although the FOC narrow and medium band filters are as good as the technology of 15í20
years ago could provide, they do exhibit a residual transmission of@ 10 í3 í 10 í4 between 5000 and
6000Š where the detectors are still relatively sensitive. Consequently, indiscriminate use of these
filters to isolate faint UV features from a bright visible background can lead to serious errors. The
magnitude of the error is, of course, very sensitive to the precise shape of the spectrum of the
source to be observed throughout the sensitive range of the FOC. Thus, it is not always sufficient
to know only the expected flux of the source in the rangel 0 ‘Dl/2 in order to estimate the
expected count rate.
A striking example of a possible observing scenario that can be e xpected when imaging a
bright visible source in the UV is shown in Figure 38. In the example shown in this figure, the
source spectrum is assumed to increase sharply with increasing wavelength in the manner
expected from an M supergiant star. If this source is fed into the F/96 relay with the F231M filter
on FW#3 in the beam, the resulting monochromatic count rate as a function of wavelength

70 FOC Instrument Handbook Version 7.0
patternsííunfortunately not fixed. Although not always easily seen in low count extended areas or
flat fields, there are two different patterns always present. The more noticeable one is an approxií
mately sinusoidal pattern with the peaks and troughs oriented at an approximately 45 degree posií
tion angle and a period of 3.35 pixels for the F/96 relay. It is believed to originate from a moirù
effect between a TV tube grid and the diode array on the target. The RMS amplitude of this patí
tern is approximately 5% for the F/96 relay and 2.5% for the F/48 relay (the peak deviations from
a flat response due to this pattern are at least twice these v
alues). This pattern becomes intensified
when count rates are in the nonlinear regime and thus is much more easily seen. In f
act, it is a
quick way of recognizing serious nonlinearity in an image. The pattern noise disappears at v
ery
low count rates.
A second pattern arises from some form of interference with an FOC digital timing waveform
that has a 4 pixel period. It shows up as vertically striped patterns on the flat fields. Although very
coherent in nature with regard to orientation and frequency, the details of the modulation do not
appear to remain constant from image to image. The RMS amplitude of this pattern is approxií
mately 2.5% for both relays.
There also appears to be an intrinsic granularity in the fine scale response,i.e., effectively raní
dom pixelítoípixel variations in response which has not yet been well characterized.
Some comments on flat field calibration are in order, especially with regard to the routine
pipeline calibration. Small drifts in distortion of the order of a pixel result in misregistration of
fine scale features such as scratches between the flat field and the science image. Flat fielding the
data in this case actually worsens the effects of the fine scale features by correcting the wrong pixí
els. For this reason and because FOC flat fields are of relatively low signal to noise (typically 300í
500 counts per pixel), the flat fields used in RSDP are heavily smoothed to eliminate most of the
fine scale features. As a consequence, they are not corrected for in the calibrated outputs of RSDP.
a. b.
Figure 37. Contour plot of the ratio between external UV flat field and internal LED flat field for
the F/48 relay (a) and the F/96 relay (b) based on preíCOSTAR data. The expected
effects of vignetting on the ratio for the F/48 relay are not included. The center of
each plot has been normalized to 1 with the contours at intervals of 2.5%.

FOC Instrument Handbook Version 7.0 69
All previous indications are that the relative variations in large scale response as a function of
wavelength between 1300 and 6000Š are weak; generally speaking, the large scale response does
not change more than 10% at all pixels except at the edges and corner of the full format. Figure
37a and 37b show contour plots of the ratio of the Orion Nebula derived flat fields to those
obtained from the onboard LEDs for the F/48 and the F/96 relays respectively.
Beyond 6000Š, the flat fields be gin to change significantly, generally with poorer relative sení
sitivity towards the corners. Although the changes in the large scale response with wavelength are
relatively minor, the changes in the fine scale features is more pronounced. Scratches and other
small scale defects deepen in the far UV; for the F/96, some scratches exhibit as much as a 30%
decline in sensitivity in the far UV. Another source of fine scale nonuniformity is the presence of
Figure 35. a. Contour plot of the smoothed flat field for the F/48 relay, including the effects of
vignetting. b. Contour plot of the smoothed flat field for the F/96 relay.
a. b.
a. b.
Figure 36. Plots across row 300 of the UV flat field for the F/48 relay(a) and the F/96 relay(b).
The effect of vignetting has not been included in plot(a).

68 FOC Instrument Handbook Version 7.0
the right edge, especially at L=256, 512, 768, are due to noise glitches on the scan coil driver
caused by changes in the most significant bits of the line counter. For both relays, the center 512½
512 is seen outlined in larger formats. This effect is due to a burníin of that heavily used format in
the camera target so that a charge discontinuity at the edges of the format has appeared. The edges
of a square baffle located just in front of the detectors limit the e
xtended field of the F/96 relay at
the upper and lower left corners, the extended image field of the F/48 relay on the upper left corí
ner. The broad vertical bands (bright and dark) seen near the beginning of the scan line arise from
ripples at the beginning of the scanning sawtooth waveform. The bands occur as a result of the
varying pixel size which is a consequence of the varying scan rate at the beginning of the scan. If
they were only an effect of geometric distortion, a proper geometric correction would remove this
effect; however, the new geometric correction files for F/96 do take scan line variations into
account, and do not seem to remove the effect entirely. It will be possible to remove residual
effects with format dependent flat fields, but at the moment they are not applied by the normal
pipeline calibration (the normal pipeline calibration of the images always uses the appropriate
section of a full format flat field to flatten images obtained in all formats).
The remaining features fall into two categories, large scale and small scale features. The large
scale variations are due either to vignetting (significant only for the F/48 relay) or detector
response. The expected vignetting for the full the F/48 full field format is shown in Figure 34a as
a contour plot. Contours are shown as percentage transmission. The expected vignetting has not
been included in the flat field for the F/48 relay shown in Figure A1 so that features closer to the
edge can be better seen. Figure 34b shows the vignetting function along the long slit.
Contour plots of smoothed flat fields, including the effects of vignetting for the F/48 relay, are
shown in Figure 35. A gaussian with a FWHM of 9 pixels was used to smooth the image and the
result was normalized to 100 at the center. Figure 36a and 36b show a plot of row 300 of a UV flat
field for the F/48 relay and the F/96 relay respectively to give a better idea of the size of the flat
field variations.
a. b.
Figure 34. a. Contour plot of the vignetting function for the F/48 relay across the entire photoí
cathode, with the location of the primary 512½ 512 imaging format shown (dotted
line). b. Plot of the vignetting function along the spectrographic slit.

FOC Instrument Handbook Version 7.0 67
to FOC mechanisms are required, the time interval between exposures can be reduced to 23 secí
onds total. This is the fastest rate at which the FOC presently can be run provided the telescope
can be slewed to a new position on the detector quickly enough to permit it.
All the overhead times reported here are to be considered approximated, and should not be
used for an accurate calculation of the required time (See the Proposal Instructions for a detailed
and accurate description of all the relevant overheads).
6.8 GUIDING MODES WITH THE FOC
The FOC will default to fine lock (estimated RMS jitter 0.005 arcseconds out of day/night
transitions) for all configurations. Users may not specify coarse track for their observations since
it has been determined that guiding in this mode has a detrimental effect on the FGSs. Similarly,
gyro hold may not be used because the large pointing and stability uncertainties are not conducive
to optimization of the science.
Occasionally, it will be found that two guide stars are not available for an observation. In that
case, STScI will notify the PI and offer the possibility of single guide star observing. For relaí
tively short exposure times (<2000s), the impact on performance is very small. The observation
will not be executed in this mode unless the PI gives approval.
Sometimes the FGSs fail to achieve fine lock for an observation. In this case, the Take Data
Flag comes down, the shutter is not opened, and the users are notified of what happened.
6.9 UNIFORMITY OF RESPONSE (FLAT FIELDING)
The extended format (512z ½ 1024) geometrically corrected flat fields for both of the new
relays are shown in Figures A1íA2. The F/48 image shows the approximate location of the new
default 512 ½ 512 format, which is no longer at the center, but close to the upper right quadrant.
The flat fields were obtained from overlapped observations of the inner region of the Orion Nebí
ula and are at 3727 and 1360Š respectively. The flat fields show a number of various types of feaí
tures, some more subtle than others. The more evident features are the occulting fingers for the
F/96 relay, the slit finger for the F/48 relay (used as a fiducial reference to the spectrograph slit)
and the reseau marks. Because of the geometric correction, the edges of the original raw images
can be seen as curved edges in these images, mainly on the left and right sides.
Because of the large amount of time necessary to obtain external flat fields for the FOC, these
two UV flat fields (one for F/96 and one for F/48) are currently the only UV flat fields for the
FOC. We obtained another UV flat field at about 2200Š, which has been analyzed, although its
quality assessment has not been completed yet.
In all images, regardless of format, a number of pixels at the beginning of the scan line (i.e.,
starting at S=1) are corrupted by defects in the beginning of the scanning sawtooth waveform. The
number of pixels corrupted depends on the detector and format. Generally it is about 5% of the
scan line for the F/96 relay and relatively independent of format, whereas for the F/48 relay it gets
progressively worse with smaller formats (for the 128½ 128 format it is as much as 25% of the
scan line). The faint horizontal stripes seen at small L values are due to a ripple instability of the
coil drivers at the beginning of a frame.
The narrow line running from the bottom left corner to the upper right corner is due to the read
beam not being completely blanked when it is forced to fly back to S=0, L=0 at the end of the
frame. This feature is more noticeable with the smaller formats. The narrow horizontal features at

66 FOC Instrument Handbook Version 7.0
brightness 10 magnitudes arcsec í2 viewed through the F430W filter with the F/96 relay. Targets
brighter than this limit can still be observed by the FOC, provided that 1) sufficient filters are
selected, so that a linear countrate is observed by the FOC, 2) the filter configuration is checked
prior to the observation [Special Requirement CHECKíFILTER = YES].
Currently, we cannot estimate the long term effects on the camera of exposures to high count
rates (> 100 cts/sec/pix). We therefore require that, for ALL FOC observations, the filter configuí
rations be fine tuned so that the observed countrate is maintained within the linear regime, even in
cases where the targets are fainter than the aboveímentioned safety limit. In very special cases, the
Instrument Scientist can waive this requirement, upon presentation of a compelling scientific jusí
tification.
6.7 OVERHEAD TIMES AND MULTIPLE EXPOSURES
Assuming that the standard science data dump operations at the 32 kHz rate apply, it will take
a constant 3.9 minutes plus a variable component to transition from the absolute time tag to stop
an exposure to the absolute time tag to start the next one. The variable component depends on the
mode change required and can be up to another 3.5 minutes for the worst case with the F/96 relay
(4 filter wheels) to 1.9 minutes for the worst case with the F/48 relay (2 filter wheels). Thus, it
could take up to a total of 7.4 and 5.8 minutes of time between successive exposures with an averí
age of approximately, 6 and 5 minutes for the F/96 and the F/48 relays, respectively. If no changes
1000 2000 3000 4000 5000 6000
Figure 33. The Earth daylight radiance for an average orbit of CVZ observing in Rayleighs Š í1
as a function of wavelength. This corresponds to a background of about 22 V magnií
tudes arcsec 2 and assumes the sun is providing most of the stray light.

FOC Instrument Handbook Version 7.0 65
`LOW SKY' requirement, which forces the observation to be taken only when the background
can stay within 30% of the minimum obtainable levels. The `LOW SKY' requirement can not be
used with CVZ observations, unlike the `SHADOW' requirement. These requirements should be
considered for all observations requiring low background levels, especially background from
stray light, and included in the Phase II proposal if deemed necessary. These considerations can
dramatically improve the detection of faint targets.
6.6 DETECTOR OVERLOAD AND BRIGHTNESS LIMITS
The FOC detectors described in Section 4.6 may be damaged by illumination levels exceeding
10 7 photons s í1 pix í1 at the photocathode due to point sources and by an a
verage illumination
from a diffuse source over the whole photocathode exceeding 10 4 photons s í1 pix í1 . Because of
this danger, the 36 kV HV power supply on the 3 stage image intensifier is set to trip off when the
point source illumination exceeds the value given above or if the average illumination from a difí
fuse source exceeds 200 photons s í1 pix í1 . Thus, for safety reasons, no point source delivering
more than 10 6 photons s í1 pix í1 at the photocathode or a diffuse source delivering more than an
average rate of 100 photons s í1 pix í1 over the whole photocathode will be allowed to be imaged
by the FOC. These values correspond to an 9th magnitude blue star or a diffuse source of surface
Figure 32. Stray light illumination in V magnitudes arcseconds í2 at the OTA focal plane due
to the Moon and daylit Earth as a function of offíaxis angle determined from iní
orbit observations. Limits on zodiacal light contribution are also given.
0 10 20 30 40 50 60 70 80 90
10
15
20
25
30
35
40
Angle to limb

64 FOC Instrument Handbook Version 7.0
½ 10 í4 counts pixel í1 s í1 in the detector for the F/96 relay and 10 í2 counts pixel í1 s í1 in the detector
for the F/48 relay (see also Section 6.13 for current F/48 performance). Upward fluctuations of a
factor ¨3 from these minimum values are, however, seen throughout the HST orbit. The minimum
iníorbit background rates are, respectively, factors of ¨5 and ¨3 higher than the background rates
measured during ground testing implying that the bulk of detector background counts are particle
induced.
6.5 STRAY LIGHT
Normally, the FOC background is dominated by the detector, by zodiacal light in the visible
and by geocoronal Lyman alpha and diffuse galactic light in the far UV (see Chapter 7 for detailed
calculations of these components). When a bright object such as the Sun, Moon or the bright
Earth limb is nearby, however, it may be dominated by stray light reaching the OTA focal plane
due to scattering from the baffle system, the OTA tube and dust on the mirror. The observed
brightness of stray radiation at the OTA focal plane due to the proximity of the Moon or bright
Earth limb in the daytime part of the orbit in V magnitudes arcsec í2 as a function of the angle
between the Moon or the limb and the OTA axis is shown in Figure 32. These iníorbit calibrations
of the baffle attenuation were performed by P. Bely for angles above 30Ú, while the attenuation for
angles less than 30Ú were derived by D. Elkin. The spectral shape of the stray radiation in the case
of the Earth has been assumed to be, for most practical purposes, that of the Earth's daylight radií
ance given in Figure 33. This data used anad hoc earth albedo published by R. R. Meier (
Space
Sci. Reviews, 58, 1, 1991).
The average zodiacal light background of 120 S10 corresponding toV @ 23 magnitudes arcí
sec í2 is reached at angles greater than 80Ú to the limb, approximately. For viewing configurations
in which the angle is less than this value, stray light will dominate in most situations. One of the
most interesting of these is that encountered when observing in the continuous viewing zones
(CVZ) which, in principle, allows for long uninterrupted integrations of very faint sources. Due to
the altitude of the spacecraft and the depression of the horizon, the offíaxis angle to the Earth limb
in the CVZ will be in the range 20Ú í 44Ú, approximately. From Figure 32, the expected stray light
illumination in this configuration in the visible will be between 20 th and 23 rd magnitudes arcsec í2 .
This means that observations in the visible will be limited mainly by this source of background.
Below 3400Š, ho wever, this effect will be negligible, as shown in Figure 33, providing an opporí
tunity to use the CVZ for the detection of f
aint sources with the minimum level of background
light.
It is of more than passing interest for observers to pay some attention to the maximum allowí
able background they can tolerate for their specific observation. The most heavily affected obserí
vations are those of faint extended sources, where the background can have comparable count
rates. For example, a spiral galaxy with B=20.5 magnitudes arcsec í2 could be observed with the
F430W filter and achieve a S/N of 10 over a 0.1''x0.1'' region in 57 minutes under average observí
ing conditions. Generally this would require a CVZ observation since most orbit viewing periods
are only about 50 minutes long (on average). However, in the CVZ, the stray light can be as bright
as V=21 magnitudes arcsecond í2 , which would require a 83 minute exposure to obtain the same
S/N. This situation can be remedied by specifying the Special Requirement `SHADOW' to force
the observations to be taken only during Earth shadow. For the CVZ observations, this would coní
strain the observations to be scheduled for orientations of low stray light insuring the best possible
S/N. Another special requirement that can be used to limit the amount of bacground light is the

FOC Instrument Handbook Version 7.0 63
Table 12: FormatíDependent Sensitivity Ratios.
6.4 DETECTOR BACKGROUND
The detector background arises primarily from thermal electrons at the first photocathode and
high energy particles. In the 600~km altitude, 28Ú inclination orbit of HST, substantial fluxes of
magnetospheric electrons and protons are encountered in the South Atlantic Anomaly (SAA). The
more energetic of these particles are capable of generating intense flashes ofC ^ erenkov radiation
in the MgF 2 faceplate of the FOC intensifiers. Since this noise source originates as photons at the
very front end of the detector, the Video Processing Unit of the FOC is not able to distinguish
between real celestial photons striking the cathode and C ^ erenkov generated photons.
The threshold energy for C ^ erenkov radiation in MgF 2 is E>220~keV for electrons and
E>400~MeV for protons. Shielding of 4 mm aluminum or more was built into the design of the
FOC in order to prevent electrons of energies E < 3í5~MeV from reaching the detectors from any
direction.
The effects of the SAA on the FOC were extensively mapped during the commissioning
phase. The FOC turned out to be considerably less sensitive to SAA electrons than had been
feared. This is presumably due to the additional shielding to electrons provided by the rest of the
HST spacecraft. The response of the FOC to SAA protons on the other hand is in good qualitative
agreement with the expectationsíalthough the sensitivity of the two FOC detectors differs someí
what.
The highest background rates (0.2~counts pixel í1 s í1 in the F/48 during nominal operations
and 0.02 counts pixel í1 s í1 in the F/96) are encountered over South America within the peak of the
SAA proton density distribution. Since these rates are not high enough to cause damage to the
FOC detectors, the FOC is kept fully operational during SAA passages. However, such high backí
ground rates do exclude useful scientific observations. A groundítrack contour delineating the
observed region of high background has been installed within the HST ground system in order
that FOC observations not be scheduled within it. Users of the FOC need therefore not concern
themselves with avoiding the SAA under normal circumstances (i.e., periods not having unusually
high solar activity). The typical detector background rates experienced well outside the SAA are 7
Camera
Format
(F½L) Relative Sensitivity
F/96 512z½1024 1.25
512z½512 1.45
512½512 ¡1.0
256½256 1.20
128½128 1.23
F/48 512z½1024 1.44
256z½1024 1.28
512½1024 1.02
512½512 ¡1.0
256½256 0.85

62 FOC Instrument Handbook Version 7.0
6.3.1 Formatídependent Effects
It has been found that the DQE is a function of detector format (see Instrument Science Report
FOCí075). The cause of this is not known. The relative sensitivities for each format are given in
Table 12, where the 512X512 format is set to 1.0 by definition. The DQE v
alues given in Table 11
and Figure 30 refer to the 512X512 format. Typical uncertainties in these numbers are approxií
mately 5%.
1000 2000 3000 4000
0
0.005
0.01
0.015
0.02
CIII
CN270
FOC Filters
STIS Filters
Figure 31. Comparison of FOC + NUV filters to STIS + NUV MAMA + filters.

FOC Instrument Handbook Version 7.0 61
With COSTAR, the magnified plate scale means that such a large aperture size cannot be used
for DQE measurements, particularly since most of the measurements of spectrophotometric staní
dards were made using the 256X256 imaging format to improve the linearity performance. For
this reason, it was decided to define the encircled energy to be 1.0 at a radius of 1.0 arcsecond (70
pixels) and to define the background as that value which minimizes the scatter of the points in the
encircled energy curve with 0.9'' < r < 1.1''. In practice, this is equivalent to setting the backí
ground to the value measured at approximately 1.0'' radius, and it does give encircled energy
curves that are qualitatively in agreement with what such a curve would look like: the encircled
energy asymptotically approaches a constant value at the last measured points. Users should be
aware that there is some flux outside 1 arcsecond radius, especially in the ultraviolet, but this flux
is not considered ``useful'' and its contribution to the total DQE is not included.
A thorough discussion is given in FOC Instrument Science Report FOCí085.
The fluxes of the spectrophotometric standards within 1'' were compared with SYNPHOT
predictions. The spectrophotometric standards had been recalibrated using the best model of the
white dwarf star G191B2B to redetermine the IUE sensitivity calibration (a correction of several
percent in the 1200í2000 Š w avelength range). It was found that the observed/expected flux valí
ues depended on wavelength linearly for the reasons outlined in the previous paragraph, so the
DQE curve was transformed by this linear function to derive the new DQE curve.
The overall (OTA + COSTAR + FOC) central absolute quantum efficiency Q(l) in counts
photon í1 with no filters in the beam is plotted and tabulated as a function of wavelength in Figure
30 and Table 11 for the four FOC imaging and spectrographic configurations. The data represent
the product of iníorbit measurements for the F/96 relay+OTA absolute quantum efficiency, and
groundíbased reflectance calibrations of the COSTAR mirrors for the F/48. The predicted loss of
light from two reflections of MgF 2 coated aluminum COSTAR mirrors amounts to a 20% loss in
the visible and a 35% loss in the ultraviolet. The loss due to the COSTAR mirrors is more than
compensated by the improvement in image quality, since the encircled energy performance is
improved from 18% within a 0.1'' radius to@ 80% within the same area, based on theoretical
PSFs. This data also includes the obscuration of the OTA, unlike the curves in previous versions
of the Handbook. As a result, these data can be directly compared with the throughput tables proí
duced by SYNPHOT.
The spectrograph efficiency is shown for the four orders of the grating (I, II, III and IV) with
no order sorting filters in the beam. These measurements were made before launch; no oníorbit
calibration of the spectrograph sensitivity has been performed yet, although the observations that
have been made show that the groundíbased calibrations are consistent at the 50% level.
For the F/96 relay, uncertainties in the DQE curve are approximately ‘10% (1s), while for
F/48 errors in the 2000í6500Š range for the imaging modes should not exceed ‘ 20% and for
wavelengths below 2000Š the y are expected to be of the order‘ 50%. This latter uncertainty
should be applied to all the spectrograph data especially in the orders III and IV.
Comparing the FOC UV sensitivity to the STIS MAMA sensitivity, we find that while in the
range 1150Š í 2000 Š the FOC UV response is lo wer than the FUVíMAMA, in the range
between 2000Š and 3500Š the sensiti vity of the FOC is comparable to the NUVíMAMA. See
Figure 31 for a comparison plot of the FOC and NUVíMAMA UV response, for a number of corí
responding filters.

60 FOC Instrument Handbook Version 7.0
Figure 30. Baseline overall (OTA + COSTAR + FOC) absolute quantum efficiency in counts
photon í1 as a function of wavelength for the three imaging modes and the four long
slit spectrograph orders, including the obscuration of the OTA.

FOC Instrument Handbook Version 7.0 59
Table 11: Overall (OTA+FOC+COSTAR) Absolute Quantum Efficiency Q(l)
in 10 í3 counts photon í1
l(Š) Q(F/48) Q(F/96) Q(SPI) Q(SPII) Q(SPIII) Q(SPIV)
1150 1.45 1.00 0.20
1160 4.04 1.39 0.32
1170 6.52 2.30 0.40
1180 9.28 3.39 0.47
1190 11.47 4.62 0.61
1200 13.14 5.88 0.46 0.70
1250 19.95 9.11 0.63 0.95
1300 22.74 10.93 0.70 1.08
1400 22.68 12.37 0.88 1.26
1500 22.30 13.47 1.05
1600 20.13 12.92 1.15
1700 18.72 12.32 1.34
1800 17.84 11.72 2.04 1.55
1900 20.26 13.12 2.69
2000 26.41 16.86 3.32
2200 40.80 26.20 4.60
2400 51.59 35.44 5.33
2600 53.59 43.06 5.55
2800 55.43 51.36 5.47
3000 55.87 60.66
3400 56.62 67.65 10.48
3800 51.70 67.73 10.64
4000 47.28 61.51 10.58
4500 35.45 38.66 10.24
5000 21.27 22.06 8.45
5500 8.97 10.88 4.84
6000 3.95 4.90
6500 0.38 0.46

58 FOC Instrument Handbook Version 7.0
used to construct this figure was drawn from FOC postíCOSTAR F/96 512 ½ 512 images of the
center of the globular cluster w Cen taken through the F430W filter and combinations of ND filí
ters ranging from F1ND to F6ND+F1ND. Observed count rates for each stellar image, measured
inside a 5ípixel radius aperture, are expressed in terms of the corresponding peak count rate,
assuming a normal F430W pointíspread function. The expected peak count rates for each stellar
image were determined by measuring the stellar flux through the most opaque ND filter combinaí
tion in which the star is wellíexposed, then extrapolating to more transparent filters based on the
ND filter calibrations in Section 4.4.1. Above peak count rates of 2 counts/pixel/sec, the observed
peak count rate falls noticeably below expectations, indicating the onset of nonílinearity.
To put some hard numbers around these figures, note that a 20th magnitude A0V star will gi
ve
a total count rate with the F342W filter of 10.9 counts/sec. Referring to T
able 9, one can see that
for the F/96 relay, the central pixel contains ~8.7% of the total light, therefore the e
xpected count
rate for this star is 0.95 counts/sec in the central pixel, which is at the FOC linearity limit. To
observe stars brighter than 20th magnitude, it is necessary to either use a smaller format, neutral
density filters or a narrower filter (e.g. F346M).
Attempts to deal with nonílinearity corrections for preíCOSTAR FOC data are presented in
FOC Instrument Science Reports FOCí073 and FOCí074, which are a
vailable from STScI or can
be browsed from the FOC WWW pages.
6.3 ABSOLUTE QUANTUM EFFICIENCY
Spectrophotometric standard stars were observed during SMOV and Cycle 4 Calibration
using a variety of filters to allow measurement of both the PSF characteristics and the detector
quantum efficiency. These measurements were made after the COSTAR mirror tilts and DOB
focus were set to optimize the imaging performance at 4860 Š wavelength for the F/96 camera.
Since the characterization of the F/48 camera is still in progress, this section refers to the F/96
camera only.
The encircled energy and detector quantum efficiency are somewhat coupled since the PSF
does not have a wellídefined edge; instead the flux drops steadily with distance from the star cení
ter until it gets lost in the background noise. The flux in the wings is due to scattering by dust and
small imperfections in the OTA+COSTAR+FOC optical train, and is more pronounced at shorter
wavelengths. When constructing an encircled energy curve, which is the curve of the fraction of
light enclosed within a circular aperture of a given radius as a function of radius, one naturally has
to define how one measures the total flux. In the past, this was done by choosing an aperture size
that was large enough to include the spherically aberrated PSF, or about 3.5 arcseconds radius.
This aperture size could comfortably fit inside the workhorse 512X512 imaging format before
COSTAR was installed.

FOC Instrument Handbook Version 7.0 57
Figure 28. Flatífield linearity plots for the detectors in the preíCOSTAR F/48 and preíCOSTAR
F/96 relays, a and b respectively, based on 512 ½ 512 pixel flatífield images of the
internal LEDs at different intensities. The solid line in each plot is the bestífit solution
for the linearity function given in the text.
a. b.
0 2 4 6 8 10
0
2
4
6
8
10
Figure 29. Linearity relation for point sources within a 5ípixel radius aperture, based on
512 ½ 512 pixel images taken with the postíCOSTAR F/96 relay through the
F430W filter.

56 FOC Instrument Handbook Version 7.0
internal LED calibration lamps. It was found that the intensity of the light from these lamps is
directly proportional to the commanded intensity level. The linearity curve was measured for seví
eral different formats to verify the format dependence of the saturation, and the dependence on
zoom mode was also investigated. A plot of the measured linearity relation for the 512½ 512 forí
mats of the preíCOSTAR F/96 and preíCOSTAR F/48 detectors is shown in Figures 28a and 28b,
respectively. Superposed is a curve that describes the behavior of the linearity relation for intení
sity values up to approximately 80% of the saturation value, originally suggested by Jenkins
(M.N.R.A.S., 226, 341 (1987)):
where r is the measured count rate,r is the `true' count rate anda is a fitting parameter that is
identified as the asymptotic measured count rate.
When the FOC is configured for zoomed pixels, the linearity performance is slightly different
from what would be expected from scaling the results for normal pixels by the ratio of frame scan
times. This is because the event sizes and the VPU detector logic are different for zoomed pixels.
However, once the linearity performance of one format is calibrated for each camera in zoom
mode, the performance at other formats in zoom mode can be derived by scaling by the ratio of
format areas, as is the case for normal pixels. The validity of the scaling assumption for both norí
mal and zoomed pixels was checked and found to be true.
Values of a for the most commonlyíused formats are given in Table 10. The values refer to
dezoomed data in the case of formats that were originally zoomed. In practice, the v
alue of a
depends somewhat on position in the image, since it is effectively a measure of the photon event
size, and this varies over the format due to slight focus quality variations. To ensure that noníliní
earity does not compromise the science data, users are advised to ensure that the count rate is k
ept
below N MAX , which is the count rate that would give 10% nonlinearity, as given in the third colí
umn of Table 10. Correct and quantifiable operation of the FOC at count rates e
xceeding N MAX
cannot be guaranteed.
6.2.2 NoníUniform Illumination
When the illumination comes from a star, the FOC is able to count at a much higher rate
before saturation occurs. This is because photon events centered on pixels close to the central
pixel of a star are much less probable than in the flatfield case.
During OV and SV it became clear that for the FOC preíCOSTAR F/96 camera when used in
the 512 ½ 512 format, the maximum obtainable count rate in the core of a star was approximately
3 counts/second/pixel. Variations on this level occur because of jitter, focus, etc. At count levels
higher than this, the core of the star turns into a dark `hole', and a bright crescent appears to one
side of the core. Comparison of PSF's taken with and without neutral density filters indicate that
there is no noticeable deviation from linear behavior for core count rates up to 1 count/sec in the
brightest pixel. This produces the simple guideline for observers: keep the count rate in the cení
tral pixel below 1 count/sec, and then any photometry method chosen will give results that are
not biased by nonílinearity effects. If the central count rate is above 1 count/sec, one will need to
use other methods to determine the brightness of the star (such as measuring the intensity in the
bright halo).
An example of the nonílinearity relation for point sources is shown in Figure 29. The data
r a 1 e r
-- a
/
( )
--
( )
=

FOC Instrument Handbook Version 7.0 55
cally 3 ½ 3 pixels). However, if the illumination comes from a perfect point source, then the phoí
ton event size does not matter, since there are no neighboring photon events, only those that arrive
in the illuminated pixel. For FOC images, no source is truly pointlike, but the linearity characterí
istics of astronomical point sources and flat fields are sufficiently different that they are discussed
separately. The situation for more complex image structure (i.e. just resolved or linear) will of
course be intermediate between these two limiting cases.
6.2.1 Uniform Illumination
Here `uniform illumination' refers to the case where the intensity v aries by less than 20% over
scales of 20 pixels. The frame scan time is given by
where z = 1 for normal andz = 2 for zoomed pixels. For the most widelyíused format (512½
512, normal pixels), this comes to 30 milliseconds. If, during a frame, more than half of the forí
mat area is occupied by photon events, a further event will overlap one or more existing events
and will not be counted as a detected photon. This would predict a maximum count rate for the
512 ½ 512 format of 0.05 counts/pixel in 30 milliseconds, or about 1.7 counts/sec/pixel. In prací
tice the saturation level is reached at a lower level, because most of the overlapping events are
much larger than a single photon event and are classified as ion events and rejected.
The flatfield nonlinearity was measured oníorbit during OV and SV using observations of the
Table 10: Calculated FlatíField Linearity Parameters
Camera
Format
(F½L)
Linearity Parameter
a
N MAX
(cs í1 )
F/96 512z½1024 0.11 0.04
512½1024 0.37 0.08
512½512 0.73 0.15
256½256 2.93 0.60
128½128 11.7 2.40
F/48 512z½1024 0.065 0.03
512½1024 0.26 0.05
512½512 0.52 0.10
256½256 2.09 0.40
128½128 8.37 1.60
F/48 SPEC 256z½1024 0.13 0.03
256½1024 0.52 0.10
T f
z S L
½
( )
8.8 6
½10
íííííííííííííííííííí sec
=

54 FOC Instrument Handbook Version 7.0
for the F342W PSF, see also Figure 26). This causes the central pixel to contain only 3.5% of the
total light in the PSF, compared to 10% for the F342W filter.
A selection of PSF images is available through the FOC WWW pages. The PSF images, and
other FOC information is accessible via anonymous FTP, gopher, or WWW's Mosaic interface at
stsci.edu (see Chapter 9 for more details).
6.1.1 Image quality and Field Dependence of the PSF
The FOC was designed to image the HST focal plane in an offíaxis position, 6.56 arcminutes
from the optical axis. At this distance, the focal plane is tilted with respect to the V1 axis by 10Ú.
It is this plane that the FOC cameras image onto their photocathodes. However, the focal surface
produced by COSTAR is tilted with respect to the plane that the FOC images. This results in a
fieldídependent focus variation of approximately 0.7mm over the full field of the F/96 relay. Simí
ilarly, the tangential and sagittal focal surfaces are tilted with respect to each other, and this introí
duces fieldídependent astigmatism. Both of these effects increase linearly with distance from the
fullyícorrected field point.
The fieldídependence of the PSF was investigated during SMOV, but the limited observations
do not allow detailed characterization of the performance as a function of field position. It is clear
from calibration observations that the PSF is visibly different away from the central field point
across the largest formats. However, this does not affect the encircled energy within 0.1 arcsec
radius by more than a few percent for any field position within the 512X512 aperture.
6.2 DYNAMIC RANGE
If two or more photon events overlap during a given frame, the VPU detection logic will only
count one detected photon. This `undercounting', or nonílinearity, sets a hard limit on the maxií
mum allowable photon rate for the FOC. This limit depends on the frame scan time, which is proí
portional to the area in pixels of the selected format. Users can improve the linearity performance
by choosing a smaller imaging format (but at the cost of field of view).
The linearity performance also depends on the image structure. If the illumination is nearly
uniform, then the nonílinearity depends on the frame scan time and the photon e
vent size (typií
Figure 27. Images of PSFs taken with the COSTARícorrected F/96 camera. a. F486N filter b.
F120M filter c. F372M filter.
a. b. c.

FOC Instrument Handbook Version 7.0 53
sures 1.6í1.8 pixels (~0.08 arcsec). Compared to STIS, the FOC has better sampling, given the
pixel size of 0.05'' for the STIS CCDs and of 0.025'' for the STIS MAMAs.
The discrepant point in Figure 26 comes from the PSF using the F320W filter, which is signifí
icantly degraded in resolution to a FWHM of 0.09 by 0.035 arcsec.
Despite the outstanding performance of the OTA+COSTAR+FOC imaging system in terms of
encircled energy within small radii, the PSF appearance does not quite match a true diffractioní
limited simulation perfectly at all wavelengths. The PSF obtained using the F486N filter shows a
noníuniform azimuthal intensity distribution in the first diffraction ring (Figure 27a). There is also
a small amount of residual coma that possibly varies with time, possibly due to some slack in the
M1 tilt mechanism. This was removed for the most part by a small tilt of the COSTAR M1 mirror
in early August 1995.
In the ultraviolet, the PSF shows a fairly strong jetílike feature pointing approximately in the í
V3 direction (Figure 27b). The strength decreases with increasing wavelength but is still quite
noticeable at 4000Š. The cause of this feature and the asymmetry in the first diffraction ring is
unknown.
Several filters have been found to have artifacts. The F372M filter shows a strong linear feaí
ture in the PSF wings, at approximately 45Ú to the OTA spider (Figure 27c). The F501N and
F502M filters both show a faint ghost image 60 and 24 pixels respectively from the PSF center,
approximately 5 magnitudes fainter than the core. The PSF taken through the F320W filter is sigí
nificantly degraded, having a FWHM of approximately 6x2.5 pixels (compared to 2.5x2.5 pixels
F320W filter
Figure 26. Variation of FWHM with wavelength for the F/96 relay of the FOC

52 FOC Instrument Handbook Version 7.0
taken for the DQE measurement program typically allows measurement of the PSF profile to 25í
50% accuracy when azimuthally averaged over a 1ípixel wide annulus. Variations of the profile
will occur in the core as a result of OTA orbital variations, but outside 0.15 arcsec radius the PSF
profile is dominated by scattering from smallíscale irregularities in the OTA & COSTAR mirrors
and FOC optics. It is recommended that if observers need accurate characterization of the PSF for
their data (for example, if they are trying to detect lowísurface brightness features in the vicinity
of bright pointílike sources), then they should explicitly ask for such calibration time in their proí
posal. Again, it is stressed that characterization of the PSF interior to 0.1 arcsec is not possible,
because of its dependence on orbital variations in the focus.
The resolution provided by the HST+FOC combination is characterized in a simplistic way by
specification of the FWHM of the PSF as a function of wavelength. This was measured for a samí
ple of PSF observations using the raw (.d0h) images, so that there would be no degradation by the
geometrical correction resampling process. The FWHM was measured in both the X and Y direcí
tions by simply interpolating where in the 1ídimensional profiles the intensity dropped to half of
the peak value; no attempt was made to account for undersampling. The mean of X and Y FWHM
is plotted as a function of wavelength in Figure 26. It can be seen that the FWHM is less than 0.05
arcsec at all wavelengths, dropping to only 0.03 arcsec (2 pixels) below 3000Š. Users should
note for comparison that one PC pixel is 0.045 arcsec, and that the PC PSF typically meaí
Figure 25. The encircled energy fraction and PSF profile for the COSTARícorrected F/96 and
preíCOSTAR F/96 relays compared to those expected from a perfect diffraction limí
ited OTA.

FOC Instrument Handbook Version 7.0 51
how many counts one can expect to measure given the total count rate from FOCSIM or SYNí
PHOT, or from using the formulation in Chapter 7. For the most part, these numbers are believed
to be good to approximately 10% or so, but they are subject to variation due to the changes in the
effective focus of the OTA (`breathing'). This typically causes the fraction of the energy in small
apertures (with radius 3 pixels or so) to vary by ~10%, but with worst case variations of up to
50%, and is most severe in the 2000í4000 Š range. Taking PSF observations just before or after
one's science data will not help to improve the measurement of encircled energy, since the variaí
tion is orbital in nature.
The improvement in performance over the aberrated PSF is shown in Figure 25, where the
encircled energy curve is compared to that of the aberrated OTA and with a perfect diffractioní
limited image from a 2.4m circular aperture with a 0.33 central obstruction. It can be seen that the
COSTARícorrected FOC PSF approaches that of an ideal imaging system in both encircled
energy performance and in the FWHM of the PSF core.
The profile of the PSF itself is not characterized to v ery high accuracy, since this would
require long integrations at many different wavelengths. The signalítoínoise ratio of PSF images
Table 9: Measured Energy Fraction e(l) for the F/96 Relay
r Filter
n (arcseconds) F120M F140M F170M F210M F278M F346M F410M F486N F550M
1 0.007 0.039 0.061 0.055 0.094 0.093 0.087 0.071 0.064 0.054
9 0.024 0.214 0.294 0.319 0.415 0.452 0.409 0.385 0.380 0.345
21 0.037 0.315 0.421 0.463 0.555 0.621 0.528 0.543 0.548 0.532
37 0.049 0.393 0.499 0.558 0.626 0.712 0.601 0.627 0.613 0.611
69 0.067 0.491 0.577 0.652 0.688 0.774 0.722 0.744 0.697 0.670
97 0.080 0.536 0.619 0.696 0.722 0.802 0.773 0.799 0.769 0.727
137 0.095 0.578 0.657 0.739 0.768 0.832 0.809 0.830 0.831 0.807
177 0.108 0.599 0.682 0.763 0.798 0.858 0.833 0.844 0.855 0.851
225 0.121 0.626 0.703 0.781 0.821 0.886 0.856 0.858 0.870 0.870
293 0.139 0.653 0.724 0.798 0.841 0.909 0.877 0.877 0.886 0.881
349 0.151 0.664 0.736 0.808 0.851 0.919 0.896 0.888 0.897 0.888
421 0.166 0.682 0.749 0.819 0.859 0.928 0.916 0.905 0.909 0.898
489 0.179 0.696 0.762 0.829 0.867 0.934 0.927 0.922 0.917 0.906
577 0.194 0.712 0.777 0.841 0.873 0.942 0.938 0.934 0.928 0.915
665 0.209 0.723 0.790 0.850 0.877 0.948 0.944 0.941 0.941 0.921
749 0.222 0.734 0.799 0.855 0.883 0.951 0.948 0.945 0.950 0.929
861 0.238 0.747 0.810 0.863 0.889 0.954 0.952 0.950 0.955 0.942
973 0.253 0.750 0.821 0.871 0.896 0.958 0.956 0.953 0.958 0.949
1085 0.260 0.765 0.830 0.879 0.902 0.961 0.958 0.957 0.961 0.952
1201 0.281 0.774 0.839 0.886 0.909 0.964 0.959 0.961 0.964 0.955
1313 0.293 0.790 0.847 0.892 0.913 0.967 0.961 0.964 0.966 0.958
1457 0.309 0.803 0.856 0.900 0.917 0.970 0.964 0.967 0.969 0.961
1597 0.324 0.813 0.865 0.907 0.923 0.972 0.966 0.970 0.972 0.963
1741 0.338 0.822 0.875 0.914 0.929 0.974 0.968 0.973 0.975 0.964

50 FOC Instrument Handbook Version 7.0
6.0 INSTRUMENT PERFORMANCE
6.1 THE POINT SPREAD FUNCTION (PSF)
Before the installation of COSTAR, the HST+FOC PSF suffered from severe spherical aberraí
tion, which meant that a circular aperture of 0.1 arcsecond radius contained only 15í18% of the
light from a star instead of the expected 70%. The principal effect of the spherical aberration was
a loss in sensitivity, because most of the light in the halo of a f
aint star is effectively lost in the
background noise. COSTAR has restored much of the OTA capability, in that the COSTARícorí
rected PSF contains more than 75% of the light within a radius of 0.1 arcsecond at visible w
aveí
lengths while losing less than 20% of the light to the two reflections at the two extra mirror
surfaces. The net increase in sensitivity is a factor of approximately 3í4 at visible wavelengths.
The correction COSTAR made to the PSF is illustrated in Figure 24, which shows the radial proí
file of an aberrated PSF image and a COSTARícorrected image.
In Table 9, the encircled energy fraction e(l) is tabulated for various circular apertures against
the number of pixels in the aperture and the effective radius (defined as , with the defí
inition that the encircled energy is 1.0 at a radius of 1 arcsecond (70 pixels)). A more thorough
discussion of the definition of the encircled energy calculation and the rationale behind it is given
in the Detective Quantum Efficiency section, 6.3. These energy fractions are to be used to predict
Figure 24. Radial profiles of preíCOSTAR aberrated PSF (dotted) and COSTARícorrected PSF
(solid) at 4860Š.
#pixels p
/