3. Projection onto the sky and extraction of sources
3.1. Projection onto the sky
The reduced cube (u) can now be flat fielded (FF). Notice that at this stage the FF only applies to values which are close to zero and that the precision for this FF is not critical. Actually, the method outlined above provides a natural FF for the data, namely the median of the fitted background (as given by the term applied to the central time of each raster) along all raster positions. By convention (ISOCAM Consortium), the FF is normalised to one in the central 144 pixels of the camera. A dark removal is required only for this FF (see Sect. 2.1); thus, no precise dark is really required in the entire reduction procedure. The dark level, even if it slowly fluctuates, is removed by the beam-switch technique. The FF is applied to both the data and the noise cubes (u and ).
The data are then projected onto a sky map (RA, DEC: epoch 2000) with a closest pixel method and fine sampled pixels (we use 1.5 arcsecond pixels on the sky for the 6 arcsecond lens, an integer multiple so that the method preserves fluxes). A projection of each CAM raster plane is done by using the raster central position (RA, DEC) and roll angle (ROLL) from the IIPH raster averaged values. Corrections are done for the slightly distorted camera field-of-view. A gnomonic projection type is used as with IRAS. Usually a pixel on the sky has been measured by different pixels of the camera. We use an optimised averaging of these different measurements with a weighting. A sky noise map is then also deduced from this optimised averaging. A scaling is applied to this sky noise map in order to take into account the correlation of noise in the oversampled sky pixel map across each camera pixel extension.
3.2. Detection of point-sources and photometry
So far, no bias has been introduced against positive or negative (if any!) flux sources, extended or point sources, except for sources more extended than the raster step for which the beam-switching reduction technique is not appropriate. A side effect of the method is to leave negative sources of half flux near any positive source along the raster direction at a raster step distance. Indeed, the fitting algorithm of Sect. 2.4 will find a negative signal of minus half the central value, on the raster positions that are adjacent to a strong positive signal position. A more sophisticated algorithm would be required near the confusion limit.
Point sources are searched for with a top-hat 2 dimensional wavelet. A 2D Gaussian of fixed width is then fitted (with a simple least square method) around the candidate position on the sky map in intensity and position along with a flat background (see a discussion by Irwin, 1985). For the HDF, we have used an 8 arcsecond (resp. 4) FWHM Gaussian for the 6 (resp. 3) arcsecond lens. This routine was implemented to deal with both the undefined values, which are scattered around because of the masking applied to the data cube and its projection onto the sky, and the non-uniform noise maps (affecting the weight of each pixel in the fit in the optimal way). The final flux of a source is given as the 2D Gaussian integrated ADUG. The error on the flux is deduced from the error sky map that was produced in the previous section. Fluxes in are obtained by dividing fluxes by the integration time per readout (ADUG/) and the conversion table in the ISOCAM cookbook multiplied with an efficiency factor which happens to be unity (the temporary absolute calibration for stabilised point sources quoted by Cesarsky et al. (1996) has since been revised upward). The fluxes are then scaled by a number 1.83 (resp. 1.87) for LW2 (resp. LW3) that was determined by simulating the ISO PSF, its modulation by the triple-beam method (that produces negative half-flux ghost sources on the sides) and the Gaussian fit with a fixed FWHM, in order to recover the whole camera efficiency. Fluxes are given at the nominal wavelength of 6.75 (resp. 15) with an assumed spectral dependence (IRAS convention). After the strongest source is found and its Gaussian flux removed from the map, one repeats the Gaussian fitting procedure to find the next source. It is then removed and one iterates the method in order to produce a catalog of candidate sources with position, flux and errors.
3.3. Detection of slightly extended sources
The Gaussian fitting allows going to the faintest level of point source detection but misses part of the flux if the source is extended. We can also compute a fixed aperture photometric flux in order to check for possible extensions with different apertures (although for the particular HDF ISOCAM data we have not done so because of the small raster steps). These fluxes are noisier but they allow a more appropriate measurement for extended sources. Geometric parameters can also be deduced following the methods of Jarvis & Tyson (1981) and Williams et al. (1996).
The redundancy factor (the number of times a sky pixel was seen by different pixels on the camera) is a key factor in deciding the reliability of sources. So far we have kept as reliable candidates those sources which have been covered during at least two raster positions by unmasked camera pixels. Quality criteria on the photometric consistency can then be given to each point-source candidate. For this purpose, we can independently project three subrasters made out of every third raster values of the u cube onto the sky. For each subraster, we measure the flux (, , ) and flux uncertainty (, , ) of each source s found in the total map (of flux and noise ) at the same position. We define the quality of a source as the highest ranking condition that it meets, according to:
where the condition must hold for all the 3 subraster index i (from 1 to 3). Clearly, the quality from 2 to 4 gives an increasing confidence in the source reliability. We added the level of 1 for strong signal-to-noise sources which can be otherwise dropped because the flux reproducibility (and not the statistical significance) is then more difficult to achieve: this source noise happens because of the ISO jitter, the errors in the projection process and the undersampling of the PSF. We define a secondary quality criterion for low redundancy surveys according to the same logic as Eq. 7 but keeping only the two flux values with the lowest noise out of the 3 subraster fluxes.
The reduction of several independent surveys of the same area (slightly shifted if possible) allows a control of systematics. The relative photometric accuracy is generally achieved at the ten percent level while the absolute photometric accuracy is not better than the thirty percent level (as deduced from weak calibrated stars and using the known linearity of the stabilised camera). It seems that stronger sources do not have better signal-to-noise (than say 30) because other errors (the source noise mentioned above is proportional to the signal) can occur. We found that sources in common in the different surveys agree well in position (say within a CAM pixel or two). At present, the comparison of various ISOCAM datasets with other surveys (in optical and radio) confirms the astrometric precision of 6 arcsecond radius at the level.
© European Southern Observatory (ESO) 1999
Online publication: February 22, 1999