We can classify the correction steps per reduction level they can be applied on. Almost all the correction steps in PIA can be freely chosen. Each reduction step takes the data from one level to the next.

In this section we are going to describe briefly the processing algorithms used in PIA per reduction level, putting the emphasis on the meaning of the parameters, which are accessible from the graphical I/F. Please note that we are neither going to discuss the physical origin of the effects to be corrected for, nor the accuracy of the methods applied. For this subject please refer to the ISO Baseline Requirements Document for Off-line Processing (BRD).

The linearity correction factors are given in 20 mV intervals, from -1.2 V to 1.2 V, thus covering the full CRE dynamic range. Typical corrections are in the order of a few percent. When applying the correction every read-out voltage is corrected by adding the value resulting from linear interpolation between the correction factors in the corresponding 20 mV interval. A keyword 'PR_LINE' is written on the measurement header indicating that linearity correction has been performed, and avoiding it being done again by mistake, then PIA checks before applying the correction for the existence of the keyword.

Note: the linearity corrections are NOT applied looking for 'more' linear ramps. In general they have ramps which consequently fit better to a straight line, but in individual cases they could lead to the opposite effect.

*Main PIA routine: lin_voltages*

One of the most common effects following is a local 'jump' between 2 read-outs, or even 3 read-outs, and an immediate relaxation. Thus the general observation is of normal ramp behaviour, a jump in-between, coming back to the same behaviour as before the jump, leaving us with two perfect parts of a ramp with a gap between the parts.

Since the normal operational read-out frequency of the PHT detectors ranges from 8 to 64 Hz, depending on the detector used, the information redundancy on voltage differences between read-outs allows us to easily pick out those anomalous jumps and to correct the ramps affected.

Algorithm: the individual voltage differences between consecutive read-outs are computed in every ramp with at least a given number (MINP) of read-outs. Average and distribution standard deviation of all the differences but the highest one are calculated. The voltage differences, which are larger by a given number of standard deviations (FSIG) are determined. Every outlyer and the following value is replaced by the average difference found. This process is iterated for every ramp a given number of times (ITER). The processing has three parameters, MINP, FSIG and ITER, which can be changed. The measurement header gets the three keywords 'PR_DGLP', 'PR_DGLF' and 'PR_DGLI' with their corresponding values attached, at the time of performing the correction.

*Main PIA routine: ramp_deglitch*

Algorithm: for a read-out distribution corresponding to an expected constant signal, the voltage differences for all read-out pairs is computed, except for the ones corresponding to the destructive read-outs and the first read-out of the following ramp. Since this distribution generally shows transient behaviour and this can affect the statistical analysis, a normalisation is performed dividing this distribution by the result of its median filtering. A running window for median filtering with PR_MEDW elements is used, which should be sufficiently large to preserve local fluctuations but also give the general transient behaviour. This baseline corrected distribution is then used for computing average value and standard deviation. All points lying away from the average value by PR_THR1 standard deviations are flagged as main glitches, and not used for the next computation of a new average and standard deviation. This is repeated PR_ITER times. All the normalised voltage differences following a main glitch are flagged as bad points, until the first one is within PR_THR2 standard deviations to the average value. All the points flagged are then not used when computing the slope of a ramp. Again the parameters are quoted into the header of the measurement.

*Main PIA routine: pair_deglitch*

Algorithm: all read-outs with voltages above a certain value (MAXVOLT) are flagged as bad, and also all voltages below a certain value (this has nothing to do with saturation, but allows control of the dynamic ranges accepted, the parameter is MINVOLT). In addition if a negative gradient is found for read-out values above 0.6 Volt, all the read-outs following this gradient within a ramp are bad flagged. The parameters MAXVOLT and MINVOLT are changeable. The keywords 'PR_LVOLT' and 'PR_FVOLT' with the corresponding values are added to the measurement header.

*Main PIA routine: acc_volt*

The reduction voltages to signal per ramp is done by the fitting of
a first to third order polynom to the read-out voltages of a ramp versus
the corresponding times (the 'normal' reduction is done by using the first
order polynomial, then all the calibration applies for this case only).
The fitted slope of the polynomial (in V/s) becomes the signal of the ramp,
and the uncertainty computed on this parameter by the fitting procedure
becomes the signal uncertainty. Both signal and uncertainty are accomodated
for every ramp and every detector pixel into the phtsrd
structure, together with the initial time of the ramp. In addition
a flag is set for every signal, coded bitwise and containing several informations,
partly depending on the number of valid read-outs used for fitting the
slope. If the number is exactly 2, a flag bit ("2 readouts/ramp")
is set indicating that the uncertainty is not completely valid **(*),**
and if less than 2, the value and the corresponding uncertainty are set
to 0 and another flag bit ("1 readout/ramp") set. In this last case the
fitting procedure is not applied, of course. The invalid read-outs are
given not only by the saturation recognition explained above, but also
by the read-out selection criteria applied. In addition if all the read-outs
corresponding to a ramp are "Not on target", another flag bit is set. This
makes possible to accept on the ERD level the "Not on target" read-outs
for deriving signals but rejecting the signals from further processing
(default choice).

The other ERD variables are reduced by the medians of their values within each ramp. The only exceptions are the variables STIM (slope time), which is taken as the initial time of every ramp, and TEMP (detector temperature), which is interpolated to the central point of every ramp, taking into account that this variable is not read in with the same frequency as the read-outs, but with a 2 second sampling.

The keyword 'PR_NDEG' appended to the measurement header indicates the degree of the polynomial fitted for reducing the data to the SRD level.

**(*) **In case of a ramp with only two read-outs the signal uncertainty
cannot be derived from the ramp slope uncertainty. PIA looks for the whole
distribution (all the signals corresponding to the same chopper plateaux)
and artificially creates an uncertainty depending on whether the distribution
contains several ramps with more than two read-outs or not. In the first
case, with points with valid signal uncertainties, all those which cannot
be derived get an uncertainty which is set to four times the median of
the valid ones. In the second case the uncertainties are set to four times
the median of all individual differences between neighbouring signals.

A special treatment: ramp sub-division

A better time resolution on the signal level can be reached by using the method of ramp sub-division. The user can define a pseudo-ramp with fewer read-outs [] than the original one [N_p] (this makes sense ifN_o). If so, the original ramps are separated into several pieces ofN_p <= N_o / 2read-outs (the possible remaining read-outs of an original ramp after definition of all theN_ppieces are taken as an extra pseudo-ramp if its number is larger thanN_p) and a signal is derived for each of these pseudo-ramps.N_p / 2

An important reason for ramp sub-division is that in some cases with a very low number of ramps per chopper plateaux, its statistical treatment is at least dubious, and significances and probabilities can hardly be derived. The disadvantage of sub-dividing ramps is that the high frequency read-out noise is less band-pass filtered. Measurements reduced using ramp sub-division quote this by a keyword 'PR_SEPAR' set to the number of read-outs taken per pseudo-ramp.

This is a special procedure developed for reducing PHT-C and PHT-P data,
taken in one of the chopper modes (rectangular, triangular or sawtooth)
excepting P32 data. Basically all the data from the on-source chopper plateaux
are compressed to one on-source and all the off-source chopper plateaux
are compressed to one off-source chopper plateau, both of them with an
**n
**number
of pseudo-ramps (by default 4 ramps on and 4 ramps off), independently
of the original number of ramps per chopper plateau.

This is done in the following way: pairs of valid read-outs are taken
and their voltage differences computed (the differences between a destructive
read-out and the first read-out of the next ramps are not taken). All the
voltage differences are then grouped into **n **logical ramps (n/2 off
and n/2 on), depending on the time difference to the begin of each corresponding
chopper plateau. The **n **averages are then the signals. In this way
a very high signal to noise ratio is reached, while the dominating "pattern"
per chopper plateau (induced mainly by the flux change when chopping between
on and off) is maintained. All the other variables are reduced in the same
way and accomodated into the phtsrd structure.
A
keyword ("PR_PATT") is added to the header of the measurement to indicate
that it was reduced under this scheme and for steering further data reduction.
The procedure is complemented on the SRD level, as explained under next
section in Processing to the SCP level, Ramps Pattern.

*Main PIA routine: process_erd_to_pattern.pro*

Since this correction has being applied for generating the calibration files, which are of course affected by this effect, its application is mandatory for a correct calibration of the analysed data.

*Main PIA routine: corr_reset_int*

Algorithm: for every chopper position, a 'running mean' method is applied. A signal average is computed using a region composed by a pre-determined number of valid signals (NSIG). The individual signals with their uncertainties in this region are compared to the region average and its standard deviation, and those signals which are far away by a number of sigmas (SIGMA) are flagged as suspicious. A new signal region is taken, moving by a number of signals (NJUMP) and the same procedure is applied with the signals corresponding to the new region. All the signals flagged a number of times (NFLAG) as being suspicious are flagged as bad. The method is therefore controlled by four parameters, NSIG, SIGMA, NJUMP and NFLAG, which are accessible and changeable by the corresponding test interfaces.

The keyword 'PRS_DEGL' is written to the measurement header indicating that this correction has been performed.

*Main PIA routine: deglitch_all*

When applying the dark current subtraction to a measurement, the keyword 'PRS_DARK' is written to the measurement header indicating that this correction has been performed, and avoiding it being done again by mistake, then PIA checks before applying the correction for the existence of the keyword.

*Main PIA routine: darkcur_orb*

When applying the dark current subtraction to a measurement, the keyword 'PRS_DARK' is written into the measurement header indicating that this correction has been performed, and avoiding it being done again by mistake, then PIA checks before applying the correction for the existence of the keyword.

*Main PIA routine: darkcur*

A dependence of the detectors response on the illumination level has
been established. Since all measurements are affected by this effect (also
the ones used for establishing the Responsivity, the FCS measurements)
the linearization of the detector response is better handled by a linearization
of all signals, as recorded by the detectors. Tables for normalizing signals
to a default central detector response are used for correcting for this
effect. Since several calibration files have been produced using this normalization
**this
correction is mandatory,** but **the level on which has to be applied
depends on the data reduction type.**

By the correction an input signal is just replaced by an output signal,
which should be the one seen if the detector responsivity would be constant
for all signal levels.

This correction should be applied **on the SRD level only by chopped
measurements** which are processed by the **"Ramp Pattern" procedure
**(since
the files derived for calibrating this mode used signal linearized data).
By **all other data** it should be first applied **on the SCP level**.
The reason is given by the fluctuations by normal signal distributions,
which are minimized when averaging over large number of signals (a special
worst case is given by very low illumination, when some signals in the
distribution are negative).

In order to be able to recognize the total or partial validity of a measurement (and thus, have confidence in main signals and uncertainties quoted), a stability analysis was introduced into PIA, which should tell us if a measurement has been completely stable, partially stable or not stable at all, and, depending on this, make a selection of signals for obtaining a valid region before performing the reduction to the SCP level.

Algorithm: based on the 'Mann method' for trend recognition in a data sample, PIA looks for an upward or downward trend in the slopes distribution within a staring measurement, per raster point. The trend is given with a certain level of confidence (parameter DCLV). If the distribution shows no trend, it is considered stable and all the slopes are valid. If not, the 'last' portion of the distribution is taken, according to the parameter INTDIV (from 1 to 3), through deselection of the first 1/2^DINT part of the distribution under analysis. This processing is repeated until either a stable part of the distribution is found, or not more than a given number of points is left (DMNP), which should be a number at least large enough to perform this kind of statistical analysis (~ 10). The region taken for the last iteration then determines the valid part of a distribution, invalidating all the signals before this cut-off for obtaining signal means, medians, etc. The parameter set used for the analysis is written into the measurement header through the keywords 'PRS_DCLV', 'PRS_DINT' and 'PRS_DMNP' respectively.

For statistical analysis (and also for better judgement of the drift behaviour and its influence on the values quoted), at the time of performing this analysis a text file is produced, which quotes the stability level (total, partial, or inexistent) per raster point, the number of points accepted and the signal variation per minute in the accepted region, relative to the signal average in this region (in [%/minute]). For this, a linear fit only is applied to the accepted signals, and its slope (and uncertainty) is divided by the mean signal.

*Main PIA routine: pia_mann*

*Main PIA routines: pia_drift_mod, drift_mod_proc*

**Chopper Plateau by Chopper Plateau:**

Processing from SRD to SCP means performing averages and medians over
the signals per chopper plateau or per raster point (or over the whole
measurement for the staring case and a unique pointing). In addition all
the accompanying variables in the SRD level are also reduced to values
per chopper plateau or raster point.

[For chopped raster measurement divided into chopper plateaux (P32
case): chopper plateaux and raster positions are in this case not synchronized.
It is necessary therefore to provide for the case of a chopper plateau
beginning in one raster position and continuing in the next one, after
the on raster flag is ON again. If this happens, all the signals from a
raster point are valid until the on raster flag is OFF, from that point
until end of the chopper plateau all signals are considered invalid, despite
their raster flags. ]

Algorithm: the 'weighted mean' method is
used for averaging the signals, unless it is disabled or the number of
signals is too low (< 15). Every mean computed by two or more elements
(N > 1) is considered completely valid. Those chopper plateaus or raster
points containing only one valid element get ** <S>=S
**and

In addition medians, first and third quartiles are calculated, per chopper plateau or raster point, using all the valid signals. Also the medians of all the other variables are taken, except for the time, for which the central time of the valid points is computed, and the raster point IDs, for which the unique raster point is taken.

**Ramps Pattern:**

The obtained "signals" in the "Ramps Pattern" reduction from ERD to
SRD are used for deriving one on and one off signal, corrected with calibration
tables for signal losses due to chopping. The user has no influence on
the choice of which signals are taken in this case (the choice is fixed
independently for each detector).

*Main PIA routine: process_tmpsrd*

"**Dynamic Calibration":**

As explained in section 3.3.8. this method
is based on a comparison of the temporal evolution of signals per
ramp corresponding to a sky measurement with parametrised signals corresponding
to a set of calibrators. Each calibrator is covering (for a given detector
pixel) a certain flux range. The calibration is based on the fact that
the transient behaviour of a PHT-S detector pixel (operated in the P40
staring mode) depends mainly on the flux it is seeing. Due to the dark
current measurement at the begin of the P40 observation template the starting
conditions are always very similar. The characteristic transient behaviour
changes slowly with increasing flux, and so it is possible to have a good
quality calibration by interpolating between the fluxes of known calibrators,
which show the most similar transients behaviour. The output is calibrated
data in Jy / MJy/sr, thus AAP level.

*Main PIA routine: calib_dynsrd*

When applying this correction, a keyword 'PRC_VIGN' is written into the measurement header.

*Main PIA routine: vignet*

A (very!) first order approximation can be given by multiplying the signal value from the celestial background contribution by the straylight factor, and subtracting this value from the FCS signal, prior to the responsivity calculation. The user can change the straylight factor manually.

Please note that this is a very crude approximation and should give the PIA user just a hint about whether or not the straylight level could be important for the responsivity determination. In the future a better assessment of the straylight problem will surely be followed by the creation of a new calibration file, according to the parameters on which this correction depends.

*Main PIA routine: pia_get_strayl*

The mean and median valid signals are substracted. Normal uncertainty propagation is calculated for the means (using the signals uncertainties) for every subtracted signal, e.g. every point belonging on the SCP level to the 'source' step. The differences calculated are accomodated within a new structure, and the mean of the valid mean differences and the median of the valid median differences are computed.

Valid points are those with a flag value of less than 2. The subtracted values get a flag 0 for the case where both involved values in the subtraction are 0, 1 if at least one of them has an assigned flag 1 and 2 if at least one of them has an assigned flag 2. In this case the subtraction is declared as invalid and the subtracted value is set to 0.

The reason for performing the subtraction this way instead of directly subtracting the means per chopper step is given by the influence of the general signal drifts on the subtracted mean uncertainty, which in this case is minimized. Also computing all subtracted values individually allows for a control on the stability of the signal difference, and this is exploited fully by the PIA graphical I/F.

PIA can handle the product of a subtraction as a new (pseudo-)measurement. In this case the measurement looks like a staring measurement, and its signal (mean or median) should correspond to a measurement of the source without any background. The other parameters are reduced just using the medians (temperature, FCS powers, etc.) except in the case of the time assigned, which is just the central time of the observation. This way the full use of the graphical I/F is given, and saving, restoring and further reduction are also possible. PIA recognizes from the internal name that this 'measurement' is the product of a subtraction and indicates this in the graphical I/F handling.

*Main PIA routine: subtr_bckg*

The same applies here as in the previous paragraph concerning accomodating the subtracted values as a new (pseudo-)measurement. The variables included in the corresponding buffer are derived from the source measurement exclusively in this case.

*Main PIA routine: subtr_meas*

*Main PIA routine: chop_freq_corr*

Algorithm: the SCP signals corresponding to an FCS illumination (with a given electrical power P_el) are multiplied with the capacity corresponding to the detector used and divided by the expected in-band power from the FCS illumination. This last value is derived from the FCS power tables (e.g. PPFCSPOW.FITS for the PHT-P detectors). The FCS power tables contain, for a set of optical powers, the FCS electrical powers necessary to illuminate the detector on such a level. PIA determines the optical power level, by interpolating logarithmically with the actual electrical power applied to the FCS. In the case of PHT-P detectors the in-band powers on the FCS power tables are quoted in units of [W/mm^2], and therefore have to be normalized by multiplying with the aperture used. For the C-arrays this is not necessary, since the unit is [W/pixel].

Correction for non-flatness of the FCS illumination: the FCS illumination onto the detectors is not flat. For the C-arrays a correction is applied via the so-called FCS illumination matrices, contained in the Cal G files P##FCSILL.FITS, and giving the asymmetry per pixel of the array. A similar correction should be applied for the different apertures used by PHT-P observations. This has not yet been implemented, pending calibrations results.

Responsivities obtained using both means and medians are computed within PIA, and the graphical I/F makes use of this, giving the user the possibility of choosing among them. The responsivities accepted are accomodated into a buffer with 'actual' responsivities, which can be used for the power calibration, as explained below.

*Main PIA routine: pia_respons*

Algorithm: same as for establishing the actual responsivity, but performed
for the two FCS measurements FCS1 and FCS2. The results ** R1 **and

(At the time of interpolating, the average of both R1 and R2 is computed as actual responsivity. Thus, performing power calibration using actual responsivity immediately after interpolation is an alternative to using the responsivity average.)

*Main PIA routine: respons_interpol.pro (in conjunction with process_scp.pro)*

PIA contains four different power calibration methods: a) using the default responsivities per detector pixel and orbital position (as contained in the Cal G files P#RES.PRO for the P (#=P) and C detectors (#=C1 or #=C2) in [A/W] or deriving them from PSPECAL.FITS for PHT-S), b) using the actual responsivities as obtained from a corresponding FCS measurement, c) the absolute photometry case and d) interpolating actual responsivities as obtained from two different FCS measurements.

The only conversion possible for PHT-S is using default responsivities, since there are no FCS measurements associated with PHT-S observations. The unit for the calibration values given in the corresponding Cal G file PSPECAL.FITS is basically [V/s / Jy], reflecting the fact that the conversion for PHT-S directly converts from signals into fluxes. In order to maintain a flat s/w architecture among the different PHT sub-instruments PIA does a pseudo-conversion into optical powers in Watts. For this purpose the calibration values are divided by the variables for the conversion from optical power into fluxes (internally coded as 'C1' variables), as given in Table 13 of the PHT-Observers manual (the same values are used again for flux extraction in the further reduction, therefore cancelling, thus the use of the term pseudo-conversion).

In the case of absolute photometry the individual signals per chopper plateau corresponding to the FCS signals are used for deriving an actual responsivity distribution. This distribution is then used point by point on the source signals.

The responsivities (per pixel) used for the conversion are quoted in the header of the measurement under the keywords 'PRC_R###' (### = pixel number). In the absolute photometry case, an average of the responsivities used per pixel is written into the header.

*Main PIA routine: process_scp*

A special case: PHT-S chopped data using dedicated "dynamic calibration for chopped data"This calibration method is explained under Section 3.3.9. It's based on a calibration using a spectral response function (SPRF) obtained with calibration observations taken exclusively in chopped modes and applying a first order correction linked to the signal level.

Main PIA routine: calib_choppmeas_sl.pro

*Main PIA routine: subtr_bckg*

F_nu = P / (C1 * FPSF) for extracting the **flux density **in the
case of P1, P2 or P3 observations or

F_nu = P / C1 for extracting the **flux density per beam **in the
case of C100/C200 observations **(*)**

and

B_nu = P / (C1 * OBS * Omega) for surface brighntess extraction,

'P' being the optical power as the main SPD value, 'C1' a constant per detector (as given in the Cal G file 'PFLUXCONV.FITS' for PHT-P and PHT-C, and internal coded for PHT-S), 'FPSF' the point spread function corresponding to detector, filter and aperture used (extracted from the Cal G file 'PPSF.FITS'), 'OBS' an obscuration factor of the secondary mirror of the ISO telescope (OBS=0.91) and 'Omega' the solid angle of the aperture or array projected on the sky. It has been found, that the Omega values are not simple, but depend on filter and aperture. The calibration values are contained in the Cal G files 'P#OMEGA.FITS'.

The reason for the special treatment of PHT-S data is explained in the 'Power calibration' section. Here the same variables C1 are used as defined there.

**(*) **The Point Spread Function factors for C100 and C200 are defined
both for the whole array and for an individual pixel. However, they can
be used at first in the computation of the flux integration when performing
the final photometry in the astrophysical applications. By C200 staring
or chopped observations the detector array is pointing centrally at the
chosen object, thus in the intersection of all 4 pixels. Therefore in these
cases it is of no use the PSF factor for individual pixels. In observations
with the C100 detector the central pixel (#5) is pointing centrally at
the chosen object. PIA accounts for this by using this factor if only pixel
5 is chosen for final photometry, as explained further below.

*Main PIA routine: process_spd*

For general common processing there are two alternatives:

The possibilities for further data reduction diverge according to the different observation types. Multi-filter and multi-aperture photometry, polarimetry, mapping and spectro-photometry are the various possibilities. The only data correction which can be applied on this level is the colour corrections to the fluxes coming from multi-measurements observations.

The only real data reduction implemented on this level is mapping, since the others are in principle just combinations of several measurements' fluxes and/or brightnesses (photometry and polarimetry with the additional possibility of performing colour corrections) or lines and continuum fitting (spectro-photometry).

Mapping is possible with and without pointing information, which refers to the information on central pointing of every raster point position, as measured by ISO, and contained in the products 'IRPH######.FITS'.

Algorithm: fluxes and brightnesses are added (weighted by their uncertainties)
for every chopper plateau within one measurement. The addition of several
pixels (for the PHT-C-arrays) is done and the PSF correction applied in
this case (for PHT-P measurements it is already done by the flux extraction)
by dividing through the PSF factor for the whole array. Several measurements
(also from different detectors) can be processed together in the same way,
thus obtaining a flux/brightness spectral distribution. For this a normalization
is applied according to the apertures used in the case of PHT-P measurements.

C100 / C200 pixels can be selected/deselected for doing photometry.
By C200 observations is only allowed to deselect one pixel at once. Its
value is replaced by the average of the other 3 pixels before applying
the PSF correction. By C100 observations up to one corner pixel and one
side pixel of the 3x3 detector pixels can be deselected, their values replaced
by the averages of the pixels of the same type. As a special, very important
case, it is possible to deselect all but the central pixel (#5). In this
case, PIA will use the point spread function factor CPSF for an individual
C100 pixel for converting into flux.

*Main PIA routine: pia_multi_aap*

Algorithm: fluxes and brightnesses are added (weighted by their uncertainties) for every chopper plateau within one measurement. Several measurements (only from one given detector and filter) can be processed together in the same way, thus obtaining flux/brightness vs area distributions.

*Main PIA routine: pia_multi_aap*

*Main PIA routine: pia_specphot*

Algorithm: for every chopper plateau, the theoretical position is calculated. This is derived from raster point ID, together with central map position, number of raster lines and raster points (all information present in the measurement header), combined with the chopper position and the pixel offset. Using all the positions calculated, a map is defined, according to the maximum resolution achieved by the number of raster points and chopper positions given. Brightnesses corresponding to the same position are co-added taking into account the dwell time on every position for obtaining the brightness value.

Pixels can be individually **selected or deselected**. Only the selected
pixels (by default all pixels) are used for producing the map.

*Main PIA routine: pia_mapw*

Algorithm: For every chopper plateau the real position is calculated,
by combining chopper position, raster position and pixel offset. **Binning**
of the map is user defined. The surface brightnesses which correspond to
a map cell are combined, taking into account the dwell time on every position
and the overlap factor. The overlap factor is given by the portion of the
detector pixel at a certain position falling into the map cell. The RA-DEC
positions for every map pixel are calculated using a coordinates transformation
matrix, defined by a reference sky position, a reference map point, the
pixel size of the map and the rotation of the map [x,y] axes relative to
the sky [-RA,DEC], the so-called ISO roll angle.

*Main PIA routine: pia_mapw*

Due to the observation redundance (same sky positions seen by different pixels, sometimes several times) mapping offers, a good possibility of correcting for the residual response differences between the different C100 and C200 pixels.

Various **flat fielding** options can be chosen:

**central FF:** individual maps are produced for every selected
pixel, and the central part of all the individual maps (common to all of
them), are used for deriving mean quotients per pixel to the first selected
pixel. These factors are then used for normalizing the pixels before general
map co-addition.

*Main PIA routines: ffmap and ffmap_simple*

**normalisation with median filtered distribution: **a baseline
correction is applied to the data, by dividing the original individual
pixel flux distributions by their median normalised distributions (using
a certain width for the median obtention). The map is co-added using the
baseline corrected distributions (and thus implicitely flat-fielded) and
then re-normalised to the total flux in the original distribution.

*Main PIA routine: ff_med_smooth*

**normalisation with partial distributions:** it is possible
to choose a part of the flux distribution for each pixel which should yield
in total the same flux level (eg. part of the background). Regions
thus chosen are averaged per pixel and pixel to pixel normalisation factors
obtained from the averages.

*Main PIA routine: ff_bck*
**normalisation using 1st Quartile:*** *this is a very simple
method of computing the 1st Quartile **QI **of
each detector pixel (as a value which could be representative for the background
measured) and normalising multyplying fluxes, brightnesses and uncertainties
of each pixel I with **FFI =** **<Q> /
QI**

It is specially useful by mini-maps, on which the other methods cannot
be applied.

The squares of the inverse uncertainties are used as weights for every
element: *w_i = 1
/ (unc_i)^2*

All elements with invalid uncertainties get lower weighted by taking as weight the median weight in the measurement multiplied by a factor 16.

The mean is computed by *<S>= SUM (S_i
*
w_i) / SUM (w_i)*

while the uncertainty is *<sig<S>> = SQRT (1/(N-1)
* SUM( (<S>-S_i)^2 * w_i^2)
/ SUM(w_i^2))*

with N as the total number of ** S_i **elements.
Eg, the uncertainty of a signal per chopper plateau is the standard deviation
of the mean value. In addition the standard deviation of the signals distribution
is quoted as

Date | Author | Description |
---|---|---|

15/06/1996 | Carlos GABRIEL (ESA VILSPA-SAI) | First Version |

10/06/1997 | Carlos GABRIEL (ESA VILSPA-SAI) | Update (V6.3) |

13/10/1997 | Carlos GABRIEL (ESA VILSPA-SAI) | Update (V6.5) |

16/02/1998 | Carlos GABRIEL (ESA VILSPA-SAI) | Update (V7.0) |

20/08/1999 | Carlos GABRIEL (ESA VILSPA-SAI) | Update (V8.0) |