Subject: Thoughts on an improved spectral extraction procedure Hello all: Here are some thoughts on how to implement an improved spectral extraction procedure. niels ***************** New spectral extraction for JEM-X Niels Lund, 050806 Each event is characterized by a telemetry position, (RAWX, RAWY), a telemetry pulseheight PHA, and three gain correction values: - the correction applied on-board to compensate for the nonlinearities of the capacitive readout (the "curtain effect"). [IbLR] - the correction for the detector spatial nonuniformity. [Carl] - the correction for the time variations of the global detector gain. [CAO] Furthermore the detection of each event is characterized by a particular set of on-board selection criteria. In our analysis we will use two signal quantities derived from the above ones: PI: the "pulseheight" expressed in a scale directly related to the photon energy in keV. (as used until now). D_PHA: the discriminator-PHA which is the PHA value un-corrected for the curtain effect. This is still not exactly the signal acting on the on-board discriminator because the discriminator input is connected to the "fast" signal chain and the PHA-value comes from the "slow" signal chain, but it is our best estimate of the discriminator signal. To introduce D_PHA in our ISDC software we need to include an additonal table in our Instrument Characteristics, namely a table containing the position dependent correction factors applied by the on-board software. (I will discuss with Ib how we extract this table). Soren has performed an analysis on the countrate from the Fe-55 calibration sources in JEM-X1 as function of the gain (the time variable part of the gain). This analysis demonstrates that the efficiency for detecting the 5.9 keV photons depends on the gain in a gradual way - the discrimination is not sharp but extends over about a factor two in signal. This analysis was done using the PHA values (without removing the curtain effect) so the actual discriminator may perform better - and we should also recall that PHA is not the signal actually feeding the discriminator. Also the detector efficiency above 20 keV have during some periods been less than nominal due to the effect of the upper threshold for D_PHA we have introduced on-board to reduce the telemetry load. We should take care to include this effect now when we anyway begin to redesign the spectral extraction. Our current spectral extraction assumes that we can associate a given PI value with a detection efficiency through the instrument response function. But if the detection efficiency is related to PHA (or better: D_PHA) rather than PI, then this assumption breaks down, because the distributon of D_PHA for a given PI-value is quite broad (FWHM 30 % or more). A large contribution to the width of the distribution of correction factors going from D_PHA to PI comes from the spatial gain variations of the microstrip detector. Thus different positions within the field of view will sample different parts of the detector and will be associated with different response functions. And different science windows corresponding to different global gain situations will have different response functions even if the source position within the field of view is the same. So, to extract the spectrum from a given source, we will as before need to extract a source count spectrum and a background spectrum from each science window, but in addition we will need to calculate a response function corresponding to the specific position of the source for this science window. This response function need to be carried along in the analysis and combined with response functions from other science windows where this source has been observed. The response function for a given source should be calculated using the source illumination model - i.e. summing contributions from all the pixels selected as "source on" pixels. It should not be calculated by summing over the events actually observed in the science window, because this would make the response function sensitive to the unknown ratio of source counts to background counts. The response functions for the different science windows must be added with a weight factor for each function corresponding to effective observation time for the associated science window. The response functions can include the effective number of cm2 illuminated by the specific source, or the response functions can be normalized to unity and the number of cm2 must then be carried as a separate parameter. *** Consequenses for sky images Until now it has been assumed that the sky image from a single science window was characterized by a unique vignetting function independent of the energy band (apart from a possible energy dependent radius limit for the event positions in the detector). Now we must calculate new vignetting maps for a sequence of energy intervals. For each sky pixel the vignetting must take into account also the detection efficiency for the energy band. Such average efficiencies can only be calculated when the energy spectrum is specified, and this problem becomes more acute when considering wide energy intervals. I estimate that about a dozen basic energy intervals may achieve a reasonable coverage for the variable efficiency problem for sky images. A suggested list off energy intervals are given at the end. At the present time we have delivered 51 different vignetting maps corresponding to 51 different radius selections. This is probably an overkill - 99 % of the users will never even consider to change the radius limits from their default values. So we can probably reduce the number of radius values to maybe 8 and then introduce 12 energy bands (making for 8x12 maps). It will have to be seen if 12 energy bands is enough, but the effects we are considering are only important at the low and the high end of our energy range. Suggested energy intervals for vignetting maps to be used for skymaps: keV PI 0 2.96 to 3.52 45 to 51 1 3.52 to 4.24 52 to 60 2 4.24 to 5.12 61 to 71 3 5.12 to 6.08 72 to 83 4 6.08 to 7.52 83 to 101 5 7.52 to 9.52 102 to 123 6 9.52 to 12.48 124 to 143 7 12.48 to 17.38 144 to 168 8 17.38 to 22.32 169 to 187 9 22.32 to 26.24 188 to 199 10 26.24 to 30.20 200 to 210 11 30.20 t0 34.52 211 to 222