- EXPOSURE is the exposure time per bin as found in the keyword in the calibrated data headers.
- intper is the integration period in 0.05 second intervals.
- 0.002 is the overhead required to read out the data.
- n
_{coadd}is the number of coadds to the bin. If any value contains fill, no exposure time can be computed and the entire bin is flagged as unusable. The values for n_{coadd}and intper are read from the extracted engineering file. If this step is omitted, then the paired pulse correction (PPC_CORR) will also be omitted, regardless of its setting.

The position of the individual substep bins are mapped into photocathode space using the following:

- SAMPLE is the sample position of the first diode.
- DELTAS is the spacing between sample positions.
- LINE is the line position of the diodes.
- XD is the X-deflection minus 2048.
- YD is the Y-deflection minus 2048.
- s0, b, c, and e are coefficients in table
`ccr2`, interpolated for the given Y-deflection. - L0, and A are coefficients in table
`ccr1`.

This DOP_CORR step computes the percentage of time spent at each Doppler offset in the original observation. These are computed by dividing the observation into time segments and computing the deflection offset for each segment. The SHP packet time is used as the start of the readout and the packet time of the first science packet is used as the ending time of the readout. This step is not applied in the pipeline because GHRS observations are interruptible. We may know the start time of the observation and that it was interrupted, but we have no way of knowing when the interruption began, so we don't know where we are in Doppler space.

This map is intended to have a granularity vector for multiple line positions. At each line position, the granularity is tabulated with a constant starting sample for all lines and a constant delta sample. To compute the response for a given line and sample, bilinear interpolation is used within the reference file. If Doppler compensation is specified (`DOP_CORR = `PERFORM'`), the response is smoothed by a weighting function describing the motion of the data samples along the photocathode.

The VIG_CORR routine removes the vignetting and low frequency photocathode response using a reference file that has a vignetting map, `vighfile`, when MAP_CORR is also performed. The vignetting map has a vector for multiple line positions and carrousel positions. At each line position the vignetting response is tabulated with a constant starting sample for all lines and a constant delta sample. To compute the response for a given line and sample, tri-linear interpolation is used within the reference file over carrousel position, line position and sample position. If doppler compensation is specified (DOP_CORR = `PERFORM'), the response is smoothed by a weighting function describing the motion of the data samples along the photocathode.

bin 1 D1.1 D1.2 D1.3 D1.4 ...The position of the data points in the two-dimensional data array mapped into a one-dimensional data array are . This routine maps the data into the output array for half-stepped data as:

bin 2 D2.1 D2.2 D2.3 D2.4 ...

...

...

bin 7 D7.1 D7.2 D7.3 D7.4 ...

D1.1 D2.1 D1.2 D2.2 D1.3 D2.3 ...And for quarter-stepped data as:

D1.1 D2.1 D3.1 D4.1 D1.2 D2.2 D3.2 D4.2 D1.3 ...

- NINT is the nearest integer.
- A, B, C are in table
`ccr5`. - a, b, and d are in table
`ccr5`. - carpos is the carrousel position.
- ydef is the Y-deflection adjusted for the proper aperture (LSA: 128 added to it, SC1: 128 subtracted from it). The wavelengths are computed by solving the dispersion relation for wavelength using Newton's iterative method. The dispersion relation is described by the following equation:
- m is the spectral order.
- l is the wavelength.
- a0,a1,... are the dispersion coefficients.
- s is the sample position.
The dispersion constants are calculated in one of two ways. If the switch GWC_CORR is set to PERFORM, then the dispersion coefficients are calculated from the
`ccrc`table's set of global coefficients which define a function based on carrousel position. If ADC_CORR is PERFORM but GWC_CORR is set to OMIT, then the dispersion coefficients are read from the`ccr6`table, which contains the dispersion coefficients for a few carrousel positions. Therefore, when GWC_CORR is OMIT, interpolation is performed between two sets of coefficients bracketing the required position, if that particular position is not in the`ccr6`table. If ADC_CORR is omitted, then many other switches relying on it are also omitted, namely: IAC_CORR, VAC_CORR, HEL_CORR, FLX_CORR, ECH_CORR, BCK_CORR, and GWC_CORR. The subject of wavelength calibrations and their improvement is treated in the next chapter.

If MDF_CORR is set to PERFORM, then a median filter is applied to the background. This size of the filter box is found in table ccr3 in columns SKY_MDFWIDTH and INT_MDFWIDTH. This switch is not normally applied in RSDP: it is provided as a recalibration option.

If MNF_CORR is set to PERFORM, then a mean filter is applied to the background. The size of the filter box is found in table `ccr3` in the columns SKY_MNFWIDTH and INT_MNFWIDTH. This switch is not normally applied in RSDP: it is provided as a recalibration option.

If PLY_CORR is set to PERFORM, then a polynomial is fit to the background and the function is subtracted. The order of the polynomial is found in table ccr3 in columns SKY_ORDER and INT_ORDER. Currently the order is set to 0 but can be modified in your own copy of the ccr3 table as a recalibration option.

It is possible to have all three filter options set, in which case, they are all performed in the order given above. However, if any of the above are set to PERFORM and BMD_CORR is set to PERFORM, then the background model correction is omitted.

There are three ways to calculate the background counts: the first involving resampling by linear interpolation and the other two internally measuring the background.

- Bscale is the background to subtract from the science.
- Bres is the resampled sky background.
- Naper is the normalization factor to compensate for the different sizes of the apertures.

- B
_{i}is the background at diode i. - a, b, c, d, are scattered light coefficients from table ccrb.
- U
_{i}is the upper inter-order background at diode i. - L
_{i}is the lower inter-order background at diode i. - N
_{i}is the net on-order count rate. - N
_{ave}is the average of N over all science diodes. N_{i}is determined by:Eq. 36.9 N

_{i}= D_{i}-0.5(U_{i}+L_{i}) ,and D

_{i}is the on-order count rate at diode i.The two internal methods differ in how the Ui and Li data are determined.

- The background can be measured from inter-order spectra. The background is measured by the science diodes by observing the photocathode above and below the science data. Ui is set to the upper background spectrum and Li is set to the lower background spectrum.
- The background can be measured from the corner diodes. There can be up to six substep bins sampling both the upper and lower background diodes. The background for each corner diode is the average of all measurements for that particular corner diode: Eq. 36.10

- corner is the corner diode identifier: UL - upper left, UR -upper right, LL - lower left, LR - lower right.
- B
_{corner}is the effective background measured by the corner diode. - B
_{ncorner}is the individual background measurement by the corner diode. - n is the number of measurements from the corner diode.
The Ui and Li vectors are then calculated by interpolating between the corner diodes as follows:
- U
_{i}is the upper background at diode i. - L
_{i}is the lower background at diode i. - B is explained above.
- C is the channel for diode i.
- C1 is the effective channel or diode for the left corner diodes.
- C2 is the effective channel or diode for the right corner diodes.
The observation can specify any combination of corner diodes using the substep bin identifications (
`BINID`) found in Table 36.1. If no specific corner diodes are specified, then all four corner diodes are used for each -science substep bin.

- The background can be calculated using a model. There are good reasons for doing this. Sometimes the number of counts accumulated in the background diodes is very small because the exposures are fairly short. When this occurs, the counting statistics limit the accuracy of the background correction. The model, on the other hand, is based on the cumulative experience of the GHRS in orbit. There are also reasons to avoid the model. In particular, if the observations span a range of orbital conditions, then the model's estimate of background may be significantly wrong. This is especially a problem in the region around the South Atlantic Anomaly. Also, for longer observations, the measured background may be well-measured anyway.
BMD_CORR is provided as a recalibration option; it controls the application of the background count rate model available in
**calhrs**v.1.3.11 (March 1997). When performed, the background model correction will calculate and subtract a model background based on location of the telescope in its orbit instead of using the background bins obtained with an observation. Because results from the background count rate model are not reliable in or near the SAA, the SAA Model 7 contour (defined in SAAHFILE) is used to issue warning messages per readout of an observation. The`ccre`table contains mean derived background count rates as a function of geomagnetic latitude and longitude. The model is actually the blue FOS model derived by Rosenblatt, et al. (1992) multiplied by a GHRS-detector-specific scaling factor. Header keywords in the table contain the multiplicative scaling factors required to scale the results from the model to the appropriate GHRS detector. See*GHRS ISR*084.

The `ccr8` table is searched for the correct grating, spectral order, aperture, and carrousel position to obtain two coefficients, A and B. Interpolation of the coefficients (in carrousel position) is used if an exact match is not found. These coefficients are then used to compute an offset using the following formula:

- l is the wavelength.
- A and B are coefficients from ccr8.
- s is the photocathode sample position.
- m is the spectral order.

Tables `ccr9` and `ccra` contain echelle blaze constants. This step performs the echelle ripple removal (if the data were taken with one of the echelle gratings) after the dispersion constants are applied (ADC_CORR is performed) by dividing the flux by the following echelle ripple function:

- m is the spectral order.
- samp is the photocathode sample position.
- r0, b, d, and f are grating parameters in the
`ccra`table. - a and b are coefficients from the ccr9 table. The blaze function is normalized to 1.0 as the center of the order. The center of the order is defined to be the center of the photocathode at the carrousel position 27492 for Echelle-A and 39144 for Echelle-B.

The nature and quality of the flux calibrations is treated in the next chapter.

_{obs}- is calculated by the dispersion correction (ADC_CORR).- V is the velocity of
*HST*in the direction of the target. - V
_{x},V_{y}, and V_{z }are computed from parameters in the SHP file. - and are right ascension and declination of the target.
- c is the velocity of light.

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