Subsections

• 8.3.1 Read SPD header
  • Ancillary data required:
• 8.3.2 Read SPD record
  • Ancillary data required:
• 8.3.3 Determine celestial coordinates of each pixel in record
  • 8.3.3.1 Overview
  • 8.3.3.2 Extracting pointing data from IRPH
  • 8.3.3.3 Inclusion of chopper information
• 8.3.4 Determination of the equatorial offsets of the detector centre
  • Ancillary data required:

8.3 Common Processing Steps

8.3.1 Read SPD header

Operation:  Extract all relevant data from the SPD header.

The keywords from the SPD FITS header are read and stored internally for processing. The information is eventually passed to the AAR product headers. The following items are extracted from the SPD, the symbols in parenthesis will be used in the remainder of this chapter:

• General SPD header keywords:
  • EOHAAOTN, AOT name (e.g. P03)
  • ATTYPE, type of attitude operation (P, T, or R for single pointing, tracking or raster observation, respectively)
  • DETECTOR, detector used
  • NMEAS, number of measurements
  • PTOREXT, point or extended source expected
  • FPCMODE, chopper mode used
  • FPCAMP, chopper amplitude [arcsec]
  • CALSEQU, calibration sequence
• Spacecraft attitude data:
  • CINSTRA, corrected reference instrument J2000 right ascension in degrees (${\alpha}_c$)
  • CINSTDEC, corrected reference instrument J2000 declination in degrees (${\delta}_c$)
  • CINSTROLL, corrected reference instrument J2000 roll angle in degrees ($\phi$)
  • in case a raster mode was executed:
    • ATTRNPTS, number of raster points (M)
    • ATTRNLNS, number of raster lines (N)
    • ATTRDPTS, increment between points (dM)
    • ATTRDLNS, increment between lines (dN)
    • ATTRROTA, raster rotation angle ${\phi}_{raster}$
• Chopper mode information if FPCMODE is not staring:
  • FPCNSTEP, number of chopper steps
  • FPCINCR, increment between steps
• Spectrophotometric mode information if PHT40 used; for each pixel:
  • LAMBDA, LUNC, the central wavelengths and uncertainty
  • if point source: RESPP, RPUNC, point source responsivity and uncertainty -
    ( $C_{phts,pixel}$, ${\Delta}C_{phts,pixel}$)
  • if extended source: RESPE, REUNC, extended source responsivity and uncertainty -
    ( $C^E_{phts,pixel}$, ${\Delta}C^E_{phts,pixel}$)
  • CALDATE, date of production of spectral response function
• Results of SPD aperture photometry analysis, if PHT04 used:
  • BACKSRSS, (logical) true if SPD aperture photometry analysis could be applied
  • NORMCALC, (logical) true if sufficient S/N
  • FILTCORF, (logical) true if empirical aperture correction factor was available
  • NRMSIG$i$, relative background subtracted source flux ratio for aperture $i$
  • NRMSIGU$i$, uncertainty in ratio for aperture $i$
• Information for remaining AOTs; for each filter:
  • FILTER, filter identification
  • EXFLUX, expected flux density
  • UNCFLX, uncertainty in expected flux density
  • MXBACK, maximum expected background
• Detector responsivity related flags from SPD:
  • RESPDEF, (logical) true if default responsivity was used.
  • FCSDRIFT, (logical) true if signal of FCS measurement contained a residual drift.

Ancillary data required:

SPD product

8.3.2 Read SPD record

Operation:  Extract necessary information from an SPD record.

The following data are taken from each SPD record:

• Instrument time key (ITK)
• Raster point identifiers
• Filter identifier
• Aperture identifier
• Polariser identifier
• Number of destructive readouts
• Chopper plateau length (chopper dwell time) [1/128 s]
• Chopper step number
• Chopper position
• Measurement time [s]
• Measured powers plus uncertainties in [W] if PHT-P, PHT-C
• Measured flux densities plus uncertainties in [Jy] if PHT-S
• Plateau length [1/128 s]
• Data quality flags

For PHT-C and PHT-S, power, uncertainty, plateau length, and quality flags refer to each pixel separately. The chopper step number is used to check that an on-source and off-source pair are available for each chopped measurement in the AA processing.

Ancillary data required:

SPD product

8.3.3 Determine celestial coordinates of each pixel in record

Operation:  For all SPD records, derive:
(1) the sky position (in RA and Dec) of the detector origin, and
(2) the RA and Dec offsets (in arcsec) for each detector pixel with respect to the raster centre.

8.3.3.1 Overview

For a given SPD record, the position of a pixel on the sky is determined by:

• the pixel's position in the detector array;
• a deflection of the focal plane chopper, by design the deflection is only in the spacecraft Y direction;
• application of the raster mode, the raster mode can be defined either in spacecraft reference coordinates (i.e. raster increments only in Y and Z directions) or equatorial coordinates (raster increments in RA and Dec directions).

All three instances can occur during the same measurement in case of AOT PHT32 where the chopper is performing a saw-tooth scan using one of the C-arrays while the spacecraft is rastering in spacecraft reference coordinates.

For single pointing photometry the pointing keywords in the SPD product header (Section 8.3.1) are used.

For raster maps the PHT OLP software will determine for each SPD record the equatorial coordinates of the PHT centre field of view thereby considering the raster position as well as a possible chopper deflection. Subsequently, the RA and Dec offsets in arcseconds with respect to the centre of the map or image coordinates are computed. The map centre has been provided by the observer. Finally, the image coordinates for each pixel are derived taking into account the individual pixel offsets and the spacecraft roll angle.

8.3.3.2 Extracting pointing data from IRPH

The instrument reference pointing history (IRPH) contains pointing information expressed in quaternions (see `ISO Handbook, Vol. I: ISO - Mission & Satellite Overview', [20]). The quaternion $Q_{raster}$ that defines the position of the PHT central field of view for a given raster point in the J2000 inertial frame can be computed from:

$$Q_{raster} = Q_{str} \cdot Q_r \cdot Q_{str/qss} \cdot Q_{qss/pht} \cdot Q_{cor},$$ (8.1)

where quaternions

• $Q_{str}$ defines the J2000 pointing of the ISO star tracker,
• $Q_{r}$ defines the raster point relative to the raster centre of the scan,
• $Q_{str/qss}$ describes the misalignment between the star tracker and the quadrant star sensor (QSS),
• $Q_{qss/pht}$ describes the QSS to instrument aperture alignment; there is one value for $Q_{qss/pht}$ per PHT subsystem and is listed in the focal plane geometry Cal-G file IFPG.FITS (see `ISO Handbook, Vol. I: ISO - Mission & Satellite Overview', [20]),
• $Q_{cor}$ gives a fine pointing correction to the star tracker calibration; since this correction depends on the position of the guide star in the star tracker field of view, a different correction is given for each raster position.

The following records are read from the IRPH:

• ATTMISQ(1:4), = $Q_{str/qss}$, star tracker to QSS misalignment quaternion
  
  
  
• ATTINSQ(1:4), = $Q_{qss/pht}$, QSS to instrument aperture misalignment quaternion

A more detailed description on the contents of the IRPH is given in  `ISO Handbook, Vol. I: ISO - Mission & Satellite Overview', [20]. Note: due to different conventions adopted for the misalignment, Q(str/qss) as given in the IRPH should be converted to the PHT OLP convention:

$Q^{PHT}_{str/qss}(2) = -Q^{IRPH}_{str/qss}(2)$


$Q^{PHT}_{str/qss}(3) = -Q^{IRPH}_{str/qss}(3)$

For each raster record in the IRPH, the following parameters are extracted:

• raster point ID (RPID)
• $Q_r$, raster point quaternion (RPQ)
• $Q_{str}$, star tracker quaternion (STRQ)
• $Q_{cor}$, raster point correction quaternion (CORQ)

With this information the quaternion $Q_{raster}$ in Equation 8.1 can be derived.

8.3.3.3 Inclusion of chopper information

We define the detector origin to be the centre of the aperture in case of a P detector, the centre of the central pixel 5 in case of C100, and the centre of the array in case of C200.

Assuming a perfect alignment between chopper and spacecraft y-axis, the quaternions representing the rotations of the detector origin with respect to a given raster point are:

$$\begin{eqnarray*} Q_{1} = & (0, 0, sin(y_{det}/2), cos(y_{det}/2))\\ Q_{2} = & (0, sin(-z_{det}/2), 0, cos(-z_{det}/2)),\\ \end{eqnarray*}$$

where $y_{det}$ is the chopper deflection and $z_{det}=0$ is the spacecraft z-offset.

The quaternion of the detector origin for a given chopper position in a raster can now be computed via:

$$Q_{chop}= Q_{raster} \cdot (Q_1 \cdot Q_2),$$ (8.2)

where $Q_{raster}$ is the raster point quaternion as derived in Equation 8.1. $Q_{chop}$ can be converted to RA ($\alpha$), Dec ($\delta$), and Roll-angle ($\phi$) according to standard quaternion transformation:

$$\begin{eqnarray*} sin(\delta) & = & 2Q(1)Q(3)-Q(2)Q(4)\\ sin(\alpha)cos(\delt... ...-Q(3)Q(4)\\ sin(\phi)cos(\delta) & = & 2Q(1)Q(4)-Q(2)Q(3).\\ \end{eqnarray*}$$

8.3.4 Determination of the equatorial offsets of the detector centre

We define the detector centre to be the centre of the aperture in case of PHT-P or the centre of a detector pixel in case of PHT-C. Note that for PHT-P the detector origin and centre are identical.

Based on the position of the detector origin the detector centre is obtained. For a given record the sky position in RA and Dec of the detector origin is converted into offsets ( ${\Delta}\alpha$ and ${\Delta}\delta$) with respect to the centre of the raster (${\alpha}_c$, ${\delta}_c$). The offsets are aligned with the RA and Dec axes in the equatorial coordinate system.

For each pixel the RA and Dec offsets with respect to the detector origin are computed from the detector roll angle and the relative pixel positions. It is assumed that the pixels are positioned in an idealized configuration:

• the pixels in the C100 array are arranged in a regular $3{\times}3$ grid with $46''$ spacings in spacecraft Y and Z direction and with the centre of pixel 5 in the origin at ($0'',0''$);
• the pixels in the C200 array are arranged in a regular $2{\times}2$ grid with $92''$ spacings in Y and Z direction. The origin is at the centre of the array;
• in case of PHT-P the detector centre is the detector origin.

Adding the offsets of the detector origin this will give the map offsets in arcsec for any raster position, detector pixel, and chopper plateau combination.

Ancillary data required:

1. SPD product
2. IRPH product