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HIGH SPEED SPECTROSCOPY USING THE
FOS IN RAPID MODE
William F. Welsh, Don Chance, Tony Keyes and Merle Reinhart
Space Telescope Science Institute
Instrument Science Report CAL/FOS 124
May 1994
Abstract
The HST Faint Object Spectrograph has the capability to record
spectra with time resolution better than 0.1 seconds. This makes the
FOS an extremely valuable tool for researchers studying rapid variabil­
ity, and even more so with the loss of the HSP. In this Report we give
formulae for computing live/dead times and present plots of duty cycle
versus READ--TIME so that the user can make an optimal choice of
time resolution. Various subtle points are noted to help the user obtain
the highest quality data possible.
1 INTRODUCTION
Numerous objects of astrophysical interest exhibit pronounced variability on
a timescale of seconds (e.g. flare stars, cataclysmic variables, X--ray bina­
ries, pulsating degenerate stars, occultation events, etc.). Very often these
fluctuations contain no preferred periodicity, so real--time phase folding us­
ing the FOS in PERIOD mode does not provide very useful information.
Rather, one can use the FOS in RAPID mode to record high speed spec­
trophotometry.
With the default parameters, the FOS in RAPID mode can record spec­
tra approximately every 6:2 seconds. By changing these default parameters,
the FOS can record several spectra per second. However, as higher time
resolution is demanded (i.e. shorter exposure times per spectrum), the ratio
of live time to READ--TIME decreases. At some level the trade--off becomes
so severe that efficient observing becomes impossible.
It is likely that once the FOS has been used several times in non--default
RAPID mode, there will be a much greater demand for the high speed
capabilities of the instrument, especially after the loss of the HSP. It is the
purpose of this report to help the user take full advantage of the unique high
speed spectroscopic capabilities of the FOS. The formulae given in section
2 should allow users to determine the live and dead time of their proposed
observations, and in section 3 figures are given to assist in the assessing the
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duty cycle (i.e., efficiency) of the observing scheme. Section 4 gives a few
vital suggestions on observing strategies that may be critical to the success
of a RAPID mode observing run with the FOS.
2 LIVE AND DEAD TIME
Before attempting to compute live and dead times, one should always consult
the current FOS Instrument Handbook for the general philosophy, defini­
tions, defaults and details of using the FOS in RAPID mode. In addition,
the FOS Handbook V1.1 (Ford & Hartig 1990) is of particular interest to
those attempting non--default RAPID mode observations. We note that the
formulae given in the FOS Handbook V4.0 (Kinney 1993) are accurate to
roughly a few tenths of a second, but for high speed work this is not accurate
enough.
For high speed observations with the FOS, the user defines the time reso­
lution via the parameter READ--TIME. READ--TIME is the time in seconds
between each recorded spectrum. READ--TIME consists of the sum of live
time plus dead time (internal to the FOS) plus the readout time required to
store the data,
READ--TIME = READOUT time + f (LT+DT) \Theta INTS \Theta SUB--STEP \Theta
OVERSCAN \Theta YSTEPS \Theta NPATT g,
where SUB--STEPjNXSTEP, OVERSCANjCOMBjMUL, YSTEPSjY--
SIZE and the other terms have their usual meaning. For high--speed RAPID
mode observations, INTS, NPATT, and YSTEPS should be equal to one.
The deadtime DT is by default 0.01 sec. Since there is relatively little
penalty in keeping OVERSCAN at the default value of 5 we recommend
the user do so. Only in cases where time resolution requirements exceed
data quality requirements should OVERSCAN be changed. We assume
throughout this Report that the minimum (LT+DT)=0.030 sec. Thus in
effect, the only free parameters are in SUB--STEP and in READOUT time.
SUB--STEP controls the sampling of the diode array, and hence the
spectral resolution. By default SUB--STEP=4 (quarter stepping). To satisfy
the Nyquist sampling theorem SUB--STEP must be – 2, though in some
cases SUB--STEP=1 (single stepping) may be tolerated.
2

The READOUT time depends upon the amount of data to be read out
and the speed at which it is read out. The READOUT time can be com­
puted by:
READOUT time=
(15/14)\Theta(1024/RAT E) \Theta NSEG(WORDS) \Theta SUB--STEP \Theta YSTEPS.
The expression NSEG(WORDS) is evaluated as:
NSEG = 1 if WORDS ! 51
NSEG = 1 + NINTf 0.499 + ((WORDS -- 50) / 61)g if WORDS – 51
where WORDS = (NCHNLS + OVERSCAN -- 1) and NCHNLS is the num­
ber of diodes to be read out (516 for full array with OVERSCAN=5). The
NINTfg function rounds to the nearest integer, e.g., NINTf0.499g=0,
NINTf0.500g=1, NINTf0.515g=1, and NINTf8.138g=8. RATE is the
data telemetry rate and is either 32,000 or 365,000 bits/sec. The slower
value (32 kbit/sec) is the default. If the amount of time spent on read­
ing out data (READOUT time) exceeds 20% of READ--TIME, the high
telemetry rate (365 kbit/sec) automatically is enabled. Note that at the
high telemetry rate, a maximum of ¸ 18 minutes of data can be
recorded due to onboard data storage capabilities. NOTE: Previous
FOS Instrument Handbooks claim a limit of 20 minutes, but due to over­
heads associated with starting and stopping the tape, the actual available
time is only ¸ 18 minutes. Once the onboard science data tape is filled, no
more science can be done until the data is dumped to the ground (but see
the last suggestion of section 4). While the telemetry rate cannot be speci­
fied by the user on the logsheet, a special request can be made to override
the default telemetry rate. This is accomplished via a comment entry in the
exposure logsheet. Be sure to explicitly state this request in the ``description
of special sheduling requirements'' and also in the ``description of proposed
observations'' sections of your proposal.
For SUB--STEP=4, OVERSCAN=5, NCHNLS=512 and the 32 kbit/sec
telemetry rate, the minimum READOUT time is 1.2343 sec. This drops
to 0.3086 sec for SUB--STEP=1. To remain at the 32 kbit/sec rate, the
minimum READ--TIME for quarter stepping is 6.18 sec. For SUB--STEP=2
this drops to 3.09 sec and to 1.55 seconds for SUB--STEP=1. READ--TIMEs
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less than these will force the FOS to use the high telemetry rate.
For the high telemetry rate (called the 1MHz rate in the FOS Hand­
book), the READOUT times drop to 0.1082 and 0.02705 sec for SUB--
STEP=4 and 1. The minimum READ--TIMES for the above parameters
are then 0.7082 and 0.1771 sec for SUB--STEP=4 and 1, assuming a mini­
mum (LT+DT)=0.030 sec. If OVERSCAN is set to 1, using SUB--STEP=1
can give a minimum READ--TIME of 0.057 sec.
By changing the number of diodes to be read out, substantially shorter
READ--TIMEs can be used. For example, the absolute minimum READ--
TIME possible can be obtained by reading out 50 or less diodes (NCHNLS!50),
with OVERSCAN=1 and SUB--STEP=1. This results in a READOUT
time of 0.0030 sec, and thus a a minimum READ--TIME of 0.033 sec. Note
that reading out less than 50 diodes does not reduce the READ--TIME as
NSEG cannot be less than 1. We caution that for very short exposures the
amount time actually spent collecting data may be only a small fraction of
the READ--TIME; one should compute the duty cycle.
3 DUTY CYCLE
We define the ``duty cycle'' as the amount of time spent actually accumu­
lating data divided by the READ--TIME. (Note that this is not the same
as LT/DT.) For many applications it is the optimization of the duty cycle
rather than the S/N ratio per spectrum that will determine the READ--
TIME.
For fixed NCHNLS and OVERSCAN the duty cycle will depend on the
number of SUB--STEPs and the telemetry rate. Because there are 2 values
of the telemetry rate and 3 SUB--STEP options, a total of 6 possible duty
cycles exist for a given READ--TIME.
It is instructive to look at the functional form of the duty cycle equation
for a moment. For a given set of optional parameters (i.e., holding SUB--
STEP, OVERSCAN, NCHNLS, and telemetry rate fixed), the duty cycle has
the form f(x) = x\Gammaconst:
x
, where x = READ--TIME and const: = READOUT
time + total dead time. The constraint that (LT+DT)?0.030 sec manifests
itself as a lower limit to the READ--TIME.
In figures 1 and 2 we show the duty cycle plotted as a function of READ--
TIME. Six curves are plotted, each corresponding to a different value of
SUB--STEP and telemetry rate. In each case NCHNLS=512, YSTEP=1,
and OVERSCAN=5. The curve studded with dots represents the SUB--
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STEP=4 case, the diamonds represent the SUB--STEP=2 case and the boxes
are for the SUB--STEP=1 case. The lower three curves (dashed) are for
the 32 kHz telemetry rate, the upper (dotted) curves represent the 1MHz
rate. The default telemetry rates are shown as the dark curves. Sharp
transitions occur when the default telemetry rate changes (when READOUT
time exceeds 20% of the READ--TIME). (Note that the transition criterion
does not account for the 0.01 seconds of DT, hence the transitions occur
below the 80% duty cycle level.)
From the figures one can multiply the READ--TIME by the duty cycle
fraction to get the true exposure time. For example, for SUB--STEP=4,
using the default telemetry rate, and a READ--TIME=10 seconds, one can
expect to be collecting photons for ¸ 85% of the time, or about 8.5 seconds.
Using the default telemetry rate for SUB--STEP=1 and a READ--TIME
of 0.4 seconds, a duty cycle of ¸ 80% can be achieved. One can also see
that by forcing the telemetry to be at the slow rate, for SUB--STEP=2 and
READ--TIME=2, the duty cycle is ¸ 64%.
4 IMPORTANT USER CONCERNS
Below are a listing of various concerns to those using the FOS in RAPID
mode for time series analysis.
ffl The STSDAS calibration software (calfos) is designed to work with
data that has SUB--STEP=4, NCHNLS=512 and OVERSCAN=5. Other
combinations are not fully supported and it is possible that the standard
calibration pipeline will be inadequate. Users must be aware that they may
need to calibrate the data themselves, and that calibration files for non--
routine FOS observing modes may not be available. Likewise, we caution
that in--orbit calibration of the internal stability of the FOS in rapid mode
has not been established.
ffl In cases where the sampling rate (i.e. READ--TIME) needs to be
exactly set a priori, one must be absolutely sure to specify a total exposure
time (TIME PER EXP) that is an integral multiple of READ--TIME. If not,
the READ--TIME (not the TIME PER EXP) will be altered to make this
true.
ffl One should specify the NON--INTERRUPTIBLE special requirement if
a continous data set is needed (i.e. no gaps). For example, an exposure may
be broken up into two pieces due to an Earth occultation unless specifically
prohibited.
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ffl Avoid READ--TIMEs that are right on the transition from the 32kHz
to 1MHz telemetry rates. Small roundoffs or adjustments to READ--TIME
(see above) can have a drastic effect.
ffl To achieve maximum time resolution, the number of channels to be
read out must be restricted. This is done by using the WAVELENGTH pa­
rameter in the exposure logsheet. Note that for the G130H, G160L, G190H,
G650L, G780H, and PRISM dispersers, the background count rate can be
directly determined from regions on the diode array beyond the area where
the dispersed light falls. This ability is sacrificed if a wavelength range is
specified. In the case of the G160L grating the order zero light is also lost --
see below.
ffl Because of jitter in the spacecraft pointing induced by the light/dark
terminator crossing, etc., it is wise to use the largest aperture possible, and
perhaps omit data taken near the time of transition.
ffl The G160L grating is particularly useful because of its wide wavelength
coverage (–– 1150--2510 š A) and the (undispersed) zero order light also falls
on the diode array. For the blue camera, the order zero light corresponds
roughly to the U band (Eracleous, et al. 1994; note: this supersedes Horne
& Eracleous 1993). For bright objects, one must be careful not to exceed
the count rate limit per diode, since most of the order zero light falls on one
or two diodes (see Hartig 1988, also the tables of Kinney 1993). Note that
if a wavelength range is specified, the zero order data will not be recorded.
The maximum wavelength coverage possible with the FOS is achieved via
the PRISM and RED camera (–– 1850 to ¸8600 š A), though the calibration
of the (highly non--linear) wavelength scale is considerably worse than for
the gratings, especially in the optical (Sirk & Bohlin 1986).
ffl It may be possible to collect more than 18 minutes of data at the
high telemetry rate because an additional science tape recorder has become
available. There is still the physical limit of ¸ 18 minutes on each tape
recorder. However, one may be able to take 18 minutes of data in one
exposure, then on the next exposure switch to the other tape recorder giving
an additional 18 minutes. You must discuss this with an FOS instrument
scientist before attempting to do this as the full details have not been worked
out at this time. Note that in the event that HST goes into a safemode
situation, data on one of the science tape recorders may be lost.
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Acknowledgements
We wish to thank Anne Kinney for comments on an early draft. WFW
thanks the STScI Grad Student Program.
5 REFERENCES
Eracleous, M., Horne, K., Robinson, E.L., Zhang, E.--H., Marsh,T.R.,
& Wood, J.H., 1994 ApJ (in press --- 20 September 1994)
Horne, K., & Eracleous, M., 1993 Instrument Science Report
CAL/FOS--091
Sirk, M. & Bohlin, R., 1986 Instrument Science Report CAL/FOS--026
Hartig, G., 1988 Instrument Science Report CAL/FOS--047
Kinney, A. (ed.) 1993 Hubble Space Telescope Faint Object Spectrograph
Instrument Handbook V4.0
Ford, H. C. & Hartig, G. F. (eds.) 1990 Hubble Space Telescope Faint
Object Spectrograph Instrument Handbook V1.1
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Fig. 1. Duty cycle versus READ--TIME.
The boxes mark the SUB--STEP=1 case, the diamonds mark the SUB--
STEP=2 case and the dots mark the SUB--STEP=4 case. The upper three
curves (dotted) are for the high telemetry rate and the dashed curves are at
the low rate. The thick curves correspond to the default telemetry rate. In
all cases OVERSCAN=5 and NCHNLS=512.
Fig. 2. Duty cycle versus log READ--TIME.
Similar to Fig. 1, except now the abscissa is plotted on a log scale.
8