33.1 Calculating Exposure Times

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• Start and end times (of the observation, or of the integration for a given group).
• Exposure time per pixel (i.e., the integration time which contributes to the counts in each pixel), for the whole observation, or a given group.

Timing Information for FOS

Type of Information	Source	Units
Observation start time	EXPSTART1	Modified Julian date
Group start time	FPKTTIME2 - group_elapsed_time	Modified Julian date
Group_elapsed_time	FPKTTIME (group 1) - EXPSTART	Seconds
Group exposure time per pixel	EXPOSUREb	Seconds
Group end time	FPKTTIMEb	Modified Julian date
Observation end time	FPKTTIMEb (last group)	Modified Julian date

¹ Header keyword

² Group parameter

33.1.1 Exposure Time Details

• LIVETIME: The fundamental unit of integration time. This is the time between opening and closing the 512 accumulators. The shortest time is 3 ms. The header keyword is LIVETIME.
• DEADTIME: Time required for housekeeping chores. It is normally 10ms. The header keyword is DEADTIME.
• Exposure time per pixel: This is the integration time per pixel that contributes to the counts observed in that pixel. This differs from the exposure time per spectrum because of substepping. The header keyword EXPOSURE gives the total exposure time for a non-edge pixel in seconds.
• Exposure time per group: This is the integration time for a given group, which is equivalent to the integration time per diode and is exclusive of instrument overheads. The exposure time of the group (exp_group) (units of seconds) using the header keywords is determined as -follows:
exp_group = EXPOSURE x NXSTEPS

This simple equation in terms of the basic FOS time and data acquisition terms is given to the full accuracy of the FOS clock by:

exp_group = LIVETIME x 7.8125E-6 xINTS x NXSTEPS x OVERSCAN x YSTEPS x NPAT

In this calculation we have not accounted for the deadtime because we are interested in calculating only the time over which the photons were collected.

• Elapsed time per group: This is the total time associated with an entire group. It is longer than the exposure time of a group because of the added deadtime. The following equation can be used to determine the elapsed time of a group for nearly all observations.
elapsed time_group = (LIVETIME + DEADTIME) x 7.8125E-6 x INTS x NXSTEPS x OVERSCAN x YSTEPS x SLICES x NPAT

This elapsed time can be used to determine theapproximate start and stop time of each group in the data. The procedure is as follows:

The FPKTTIME in the group parameters of the .d0h file is the time at which the FOS memory for that group was read out and is inclusive of all deadtime for the group. Unfortunately, it may also include an indeterminate additional interval of up to 0.13 second caused by HST SDF overheads. In the headers this time is given (to the accuracy of about 0.125 second) in units of modified Julian date, which is the Julian date minus 2400000.5. This time can be converted from modified Julian date to the standard notation using the epoch task. For many FOS datasets in the HST Archive obtained prior to January 1, 1995, the exposure start time is incorrectly populated. The time at which the integration was started is given by:

start time = FPKTTIMEgroup - elapsed time_group

Please note that the start time for each individual group should be calculated from the FPKTTIME of the relevant group and not simply by a recursive addition of group elapsed time to the start time of a previous group.

The group parameters can be determined by running the task grlist to determine all the groups in the d0h file and then finding the value of the necessary keyword using hedit. Note that the FPKTTIME is accurate only to approximately 1/8 second.

• Exposure time for the observation: This is the total time during which the FOS accumulated data for the observation and is given in the header keyword EXPTIME. This should be the exposure time given in Phase II instructions. This is given by the equation:
exptotal = EXPOSURE x NXSTEPS x NREADS x NMCLEARS

In the basic FOS data acquisition units, this is:

exp_total = LIVETIME x 7.8125E-6 x INTS x NXSTEPS x OVERSCAN x YSTEPS x NPAT x SLICES x NREAD x NMCLEARS

• Elapsed time for the observation: This is the total time spent by the FOS for a given observation, which includes the deadtime during which photons were not accumulated. Corresponding to the exposure time for the observation is the elapsed time for the observation. This is given by:
elapsed time_observation = (LIVETIME + DEADTIME) x 7.8125E-6 x INTS x NXSTEPS x O VERSCAN x YSTEPS x NPAT x SLICES x NREAD x NMCLEARS

33.1.2 Timing

Observation start and stop times are determined from the header information with a precision of +0.125 to -0.255 second, while exposure times are determined with a precision of 7.8125 microseconds. This has particular impact on certain RAPID mode timings as described in "RAPID Mode Observation Timing Uncertainties" on page 33-5.

Start and End Times

The end time of the integration for each group of data is given in modified Julian days in the group parameter FPKTTIME. The end time of an observation is the FPKTTIME of the last group of the observation. Again, in many FOS datasets obtained before January 1, 1995, the EXPEND keyword is incorrectly populated with LPKTTIME rather than FPKTTIME of the last observation group. You should insure that the FPKTTIME of the last group has been used for EXPEND.

To calculate the approximate group start time, subtract the group elapsed time from FPKTTIME. The group elapsed time (which will be nearly the same for all groups in a given observation) can be calculated in two ways: 1) for datasets obtained after January 1, 1995: as FPKTTIME for the first group of data minus EXPSTART, or 2) for any dataset: from the formula given in the previous section. The start time of each subsequent group is then given as FPKTTIME for that group minus the group elapsed time (see Table 33.1).

As noted earlier, an additional uncertainty of approximately 0.13 seconds exists since the HST Science Data Formatter can be delayed in issuing the command to read out the FOS memory, which is recorded as FPKTTIME.

Exposure Times

The exposure time per pixel, the integration time which contributed to the flux observed in a given pixel, differs from the exposure time for the spectrum whenever substepping is employed. The exposure time is divided among the NXSTEPS individual substepped spectra which together produce the single spectrum. The (typical) exposure time per pixel is therefore given by the exposure time divided by NXSTEPS. This quantity is contained in the group parameter EXPOSURE.¹

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¹ Note, however, that the actual exposure time for a given pixel may be different from EXPOSURE, either because the pixel did not receive input from OVERSCAN diodes (because it was an edge pixel or because it was fed by input from one or more disabled diodes), or because a particular readout was rejected by the onboard burst noise rejection algorithm. Thus EXPOSURE actually reports the maximum possible exposure time per pixel. The calfos task correctly calculates the count rate of each pixel, taking into account the number of diode readouts which contributed to the counts observed in each pixel, using the information in the disabled diode reference table to compensate for disabled diodes and the noise rejections tallied in the reject array (the .d1h file) to compensate for times when the counts from a particular diode were not accumulated into memory due to noise rejection.