Subsections

• • Ancillary data required:
• 7.10.1 Default responsivities
  • Ancillary data required:
• 7.10.2 Determination of in-band power from FCS measurement
  • Ancillary data required:
• 7.10.3 Signal to in-band power conversion for P detectors
  • Ancillary data required:
• 7.10.4 Signal to in-band power conversion for C detectors
  • Ancillary data required:
• 7.10.5 In-band power for PHT-P and PHT-C chopped observations
  • Ancillary data required:
• 7.10.6 In-band power for raster and sparse maps
  • Ancillary data required:
• 7.10.7 Dependencies on mission dates
  • Ancillary data required:

7.10 In-band Power Calibration

Detailed description: Chapter 5, Section 4.5.4

The steps described in this section are applied to all measurements both in staring and chopped mode except those collected with PHT-S.

The detector responsivity varies from revolution to revolution, and along a revolution, in particular the long wavelength detectors P3, C100, and C200 show significant variations. To ensure proper photometric calibration, all PHT AOTs except PHT40 contain at least one FCS measurement per detector used during an AOT. The FCS measurement determines the responsivity of the detector at approximately the same time as the sky is observed.

The derivation of the target's in-band power using the FCS calibration requires important instrumental corrections to ensure the best photometric calibration. The related processing steps are described in the following sections.

Ancillary data required:

None

7.10.1 Default responsivities

Detailed description: Section 4.2

The in-orbit calibration observations of the FCS on celestial standards were also used to analyse the properties of the detector responsivity, see also Section 4.2. The FCS calibration observations were frequently performed throughout the mission enabling a statistical assessment of the responsivities as a function of orbital phase. This analysis showed that the responsivities scatter around a mean value which is a function of orbital phase due to ionising radiation. The time dependent mean responsivity provides a first order estimate of the detector responsivity and is used as default responsivity $R_{default}(i,t)$ in W/A, where $i$ indicates the detector pixel and $t$ the orbital dependence.

The default responsivity for the P and C detectors is applied in case:

• FCS measurements are missing or are of insufficient quality for the derivation of reliable detector responsivities. Such an event occurs e.g. in case all ramps/signals during the FCS measurement were rejected due to saturation or glitches.
• Chopped observations with detector P2 were obtained. The responsivity of P2 was extremely constant throughout the mission, and using the default responsivity provides more accurate photometry than the responsivity determined from the chopped FCS measurement.
• The FCS heating power is outside the calibrated range. The FCS heating powers were calibrated using a range of astronomical standards covering a finite flux range. Some FCS measurements were commanded with heating powers yielding fluxes outside this range.

For each measurement the orbital phase is read from ERD keyword TREFCOR2 which gives the orbital phase corresponding to the mid point of an AOT. The default responsivity is determined by linear interpolation in the Cal-G file which contains the default responsivity versus orbital position for a given detector.

Derive_SPD also computes the FCS1 responsivity from the FCS measurement and the results are stored in the designated Cal-A file. To give the observer some information on the discrepancies, the ratio:

$$r(i) = \frac {R_{FCS}(i)}{R_{default}(i,t)},$$ (7.80)

is stored for each pixel $i$ in the SPD header with keyword RESPRi.

Ancillary data required:

Orbit dependent default detector responsivities are stored in Cal-G files PPRESP, PC1RESP, and PC2RESP for the P, C100 and C200 subsystems, respectively, see Section 14.13.

7.10.2 Determination of in-band power from FCS measurement

Detailed description: Chapter 5

The electrical heating power $h$ applied to the FCS directly corresponds to an FCS power on the detector $P_{FCS}$. The conversion is obtained from dedicated in-orbit FCS calibration observations where the signal of a celestial calibration source is directly compared with the signal of the FCS for a given heating power $h$. However, the calibration observations could only cover a limited range in $h$ due to limited availability of suitable calibration targets. FCS measurements with values for $h$ outside the range, which can be calibrated, will get less reliable $P_{FCS}$ based on extrapolations.

In Derive_SPD the value for $h$ is checked. In case the value of $h$ is outside the valid range, the default responsivity (Section 7.10.1) is used.

Ancillary data required:

The valid heating power ranges are included in the FCS power calibration Cal-G files PPxFCSPOW ($x$=1,2,3) for the P detectors, and PCxFCSPOW ($x$=1,2) for the C100 and C200 detectors, see Section 14.12.

7.10.3 Signal to in-band power conversion for P detectors

Detailed description: Section 5.2.5

From the electrical power (in mW) applied to the FCS, an in-band power on the detector P$_{fcs}$ normalised to the aperture area (in Wmm$^{-2}$) is obtained using FCS calibration tables, see Chapter 5. The FCS measurement taken with detector $det$ provides the detector responsivity:

$$R_{det} = \frac{{\langle s_{fcs} \rangle}\cdot{C_{int}^{det... ...dot}A(a){\alpha}(f,a) {\chi}_{det}(f)}~~~~~~~~~~{\rm [A/W]},$$ (7.81)

where

• $f$ is the filter and $a$ the aperture selected for the measurement,
• $\langle s_{fcs} \rangle$ in V/s is the weighted mean signal of the FCS measurement,
• $C_{int}^{det}$ in F is the integration capacitance associated with detector P1, P2, or P3,
• $P_{fcs}(f,h)$ in Wmm$^{-2}$ is the in-band power on the detector from the FCS due to heating power $h$ in mW,
• $A(a)$ in [mm$^2$] is the area of aperture $a$,
• ${\alpha}(f,a)$ is a dimensionless correction for inhomogeneous illumination in aperture $a$ by the FCS,
• ${\chi}_{det}(f)$ the relative filter-to-filter correction for a given detector $det$ (P1, P2, or P3) to obtain the same responsivity independent of filter.

Although filter transmissions were measured in laboratory, and instrumental geometry was well known, correction factors to adjust the photometry were necessary. The resulting detector responsivities were found to vary from filter to filter. The calibration factors to achieve a filter independent responsivity are stored in ${\chi}_{det}(f)$.

The in-band power $P_{target}$ from the source is obtained from:

$$P_{target}(f') = \frac{\langle s_{target} \rangle C_{int}^{det}} {{R_{det}}{\cdot}{\chi}_{det}(f')}~~~~~~~~~{\rm [W]},$$ (7.82)

and

$${\Delta}P_{target}(f') = \frac{{\Delta}\langle s_{target} \... ...langle s_{target} \rangle} P_{target}(f')~~~~~~~~~{\rm [W]},$$ (7.83)

where $f'$ indicates a filter available for the same detector as for which the responsivity $R_{det}$ has been derived.

Caveat:  In principle, inhomogeneous illumination by the FCS (see Section 7.10.4) affects the calibration involving apertures. The FCS power on the detector is not proportional to the aperture area for a given electrical power applied to the FCS. Although a provision for correction has been implemented, the present version of the Cal-G files provides no correction i.e. $\alpha(f,a)\,=\,1$.

Ancillary data required:

• The PHT-P FCS calibration tables $P_{fcs}(f,h)$ in units of Wmm$^{-2}$ are stored in Cal-G files PP1FCSPOW, PP2FCSPOW, and PP3FCSPOW for the three P detectors, see Section 14.12.
• The values of the FCS aperture area $A_{fcs}(a)$ in mm$^2$ from the aperture ID are hardcoded in the software. The values used are listed in Section A.1.2. These areas were obtained from on-ground measurements of the instrumentation.
• The filter-to-filter correction factors ${\chi}_{det}(f)$ for a given detector $det$ are stored in the Cal-G file PPFTOF (see Section 14.16).
• The correction method for inhomogeneous FCS illumination of the apertures ${\alpha}(f,a)$ assume the following Cal-G files (see Section 14.15): PP1FCSAP, PP2FCSAP, and PP3FCSAP.

7.10.4 Signal to in-band power conversion for C detectors

Detailed description: Section 5.2.5

First, the FCS measurement is used to determine the responsivity of each pixel $R(i)$ for the filter in which the FCS measurement is taken:

$$R(i) = \frac {\langle s_{fcs}(i,f) \rangle \cdot C_{int}^{d... ...s}(f,h) \cdot {\Gamma}(i,f) \cdot {\chi}(i,f)}~~~{\rm [A/W]},$$ (7.84)

where

• $f$ indicates the filter, $i$ the pixel number,
• $\langle s_{fcs}(i,f) \rangle$ in V/s is the FCS signal per chopper plateau,
• $C_{int}^{det}$ is the detector capacitance,
• $P_{fcs}(f,h)$ is the in-band power (in W/pixel) for a given FCS heating power $h$,
• ${\Gamma}(i,f)$ is the FCS illumination matrix, and
• ${\chi}(i,f)$ the relative filter-to-filter responsivity correction for a given detector pixel $i$ (C100 or C200) to obtain the same responsivity independent of filter.

The values of ${\chi}(i,f)$ (see Section 7.10.3) are not the same for different pixels of the same detector array. These differences are suspected to be due to spatial filter inhomogeneities which are projected onto the array.

The illumination matrix ${\Gamma}(i,f)$ is needed to correct for the fact that the FCS illumination is not flat but varies from pixel to pixel in the C100 and C200 arrays. This correction is applied to each pixel in the array (Section 4.5.4).

Second, for a measurement of the sky, the power on each pixel for any filter $f'$ of the same detector can be derived from the mean signal per chopper plateau $\langle s_{target}(i,f') \rangle$:

$$P_{target}(i,f')\,=\,\frac {\langle s_{target}(i,f') \rangle \cdot C_{int}^{det}}{R(i) \cdot \chi(i,f')}~~~~~{\rm [W]},$$ (7.85)

and

$${\Delta}P_{target}(i,f') = \frac {{\Delta}\langle s_{target... ...le s_{target}(i,f') \rangle} P_{target}(i,f')~~~~~{\rm [W]}.$$ (7.86)

Ancillary data required:

• The PHT-C FCS calibration tables $P_{fcs}(f,h)$ in units of W/pixel are stored in Cal-G files PC1FCSPOW and PC2FCSPOW. The tables give the mean in-band power from the FCS averaged over all pixels, see Section 14.12.
• The illumination matrices ${\Gamma}(i,f)$ which give the FCS illumination for each pixel normalised to the mean pixel illumination are stored in Cal-G files PC1ILLUM and PC2ILLUM, see Section 14.14.
• The filter-to-filter responsivity correction ${\chi}(i,f)$ for C100 and C200 are stored in Cal-G files PC1FLAT and PC2FLAT, see Section 14.17. For each filter the correction is normalised with respect to the filter yielding the largest responsivity for the C100 or C200 detectors.

7.10.5 In-band power for PHT-P and PHT-C chopped observations

Detailed description: none

The SPD product for chopped observations contains the in-band powers of the on-source position (i.e. source plus background power) and the off-source position (i.e. background power) plus the associated uncertainties. These are computed from the corrected signals $s_{on}^c$ and $s_{off}^c$ (derived in Section 7.5.5) using the expressions given in Section 7.10.3 for PHT-P and Section 7.10.4 for PHT-C.

The signal values of the generic pattern, the difference between the two intermediate patterns, as well as the derived uncertainties are stored in the header of the SPD product under keywords PFfPiLl, PDfPiLl, and PUfPiLl, where $f=1{\dots}$no. of filters, $i=1{\dots}$no. of pixels and $l\,=\,1{\dots}8$.

Ancillary data required:

None

7.10.6 In-band power for raster and sparse maps

Detailed description: None

In case of a raster or sparse map, two FCS measurements are collected (see Sections 3.10.1 and 3.10.2). For a raster map one FCS measurement is taken immediately before and one immediately after the map measurement. For a sparse map the FCS measurements are taken after the last measurement in the first AOT and after the last measurement in the last AOT of the sparse map chain.

In both cases the detector responsivity is obtained from the average responsivity $\overline {R(i)}$ of the two FCS measurements $R_1(i)$ and $R_2(i)$:

$$\overline{R(i)} = \frac{R_1(i)+R_2(i)}{2}~~~{\rm A\,W^{-1}},$$ (7.87)

with uncertainty^7.1:

$$\Delta\overline{R(i)} = \frac {\sqrt{\Delta^2R_1(i)+\Delta^2R_2(i)}}{2}. ~~~{\rm A\,W^{-1}}$$ (7.88)

The values of $\overline {R(i)}$ and $\Delta\overline {R(i)}$ are written to the SPD header. The index $i$ refers to the detector pixel in case of the C100 or C200 array. There are a number of exceptions for which the above computation cannot be performed:

1. if only one valid FCS measurement is available, then the responsivity from this FCS measurement is used;
2. if for raster mode observations the FCS heating power is out of the calibrated range for both FCS measurements, then the default responsivity (Section 7.10.1) is used;
3. if for sparse maps the heating power is out of the calibrated range for one of the FCS measurements, then the responsivity from the other valid FCS measurement is used;
4. if for sparse maps the heating power is out of the calibrated range for both FCS measurements, then the default responsivity (Section 7.10.1) is used;

If instances (2) and (4) occur, a warning message will be written in the SPD product header.

Ancillary data required:

None

7.10.7 Dependencies on mission dates

Detailed description: None

During the mission two main events took place which seriously impacted the ISOPHOT calibration:

• the change in FCS1/TRS2 emission properties (see Section 2.7) between revolution 93 and 94. This event caused the FCS emission for the long wavelength detectors (P3, C100 and C200) to become about a factor 2 higher than before for the same electrical power. Consequently, new uplink and FCS power tables had to be constructed after extensive in-orbit measurements of the FCS1/TRS2 properties.
• an extra curing procedure was introduced approximately halfway in the ISO science window for detectors P3, C100 and C200 as of revolution 150 onwards. The extra curing was performed during the handover period between the VILSPA and Goldstone ground stations. The procedure restored the nominal detector performance whereas, without the procedure, both detector noise and responsivity continue increasing.

As a consequence, the following calibration files have different entries depending on the revolution date:

• FCS power Cal-G files (PP3FCSPOW, PC1FCSPOW, and PC2FCSPOW see Section 7.10.2) are different before and after revolution 94.
• the Cal-G files giving the matrices of the PHT-C illumination by the FCS (PC1ILLUM, and PC2ILLUM, see Section 14.14) are different before and after revolution 94.
• orbit dependent default responsivities Cal-G files (PPRESP, PC1RESP, and PC2RESP see Section 7.10.1) are different before and after revolution 150.

Ancillary data required:

Information on the time dependence of ISOPHOT Cal-G files is stored in Cal-G file PTIMEDEP, a detailed description is given in Section 14.2.