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4.5 Flat-Fields

The flat-field can be defined as the relative response of different pixels of the detector to a source with uniform brightness distribution within the field of view. For ISOCAM it is useful to distinguish between the detector flat-field and the optical flat-field. The detector flat-field can be defined as the relative response of different pixels to a uniform illumination of the detector, while the optical flat-field can be defined as the relative flux falling onto different pixels when a source of uniform brightness distribution occupies the field of view. The observed flat-field results from the product of the detector flat-field and the optical flat-field. The need to separate the two arises because the position jitter of the ISOCAM wheels (described in Section 4.11) means that the optical flat-field can move slightly over the detector. While the detector flat-field is strictly related to the relative sensitivity of the detector pixels to incoming flux, the optical flat-field measures the vignetting due to the optical components of the camera, in particular the aperture stops near the filters. The vignetting profile is a function of the angular distance from the optical axis, and with different lens magnifications the detector sees different parts of the vignetting profile. Even with the same lens, different optical flat-fields may arise, as mentioned above, because of the wheel jitter (see Section 4.11). In practice, the detector flat-field is not directly observable. So, by convention, the flat-field at 1.5 $^{\prime \prime }$ is defined to be the detector flat-field for any given filter, because it suffers less than other pfov flat-fields from vignetting effects. The optical flat-fields at any pfov are obtained by dividing the observed flat-fields by the appropriate filter detector flat-field. As a consequence, the optical flat-field at 1.5 $^{\prime \prime }$ is a matrix with 1's everywhere. Flat-fielding is a crucial step in the data processing, in particular in the infrared, where the brightness of the background is very often comparable to (or higher than) the brightness of the target source. Therefore, the generation of flat-fields is a very important step in the overall calibration strategy of ISOCAM. It must be noted, however, that many observations in raster and beam-switch mode allow the observer to directly build a flat-field from his data, depending on the brightness of the background, and the relative extension of the target source(s) with respect to the raster (or beam-switch) steps. In all staring mode observations, as well as in a few cases of raster and beam-switch observations, particularly of very extended sources or crowded fields, the use of a flat-field library is nevertheless unavoidable. There have been two kinds of flat-field observations:

observations of the Zodiacal Background, which we will refer to as `ZB flat-fields' in the following;
observations of the Internal Calibration Device, which we will refer to as `ICD flat-fields'.

The targets for ZB observations were chosen as close as possible to the sun-viewing constraint of ISO in order to maximise their flux. The choice of the raster strategy for observation allows the minimisation of possible non-uniformities in the zodiacal background, since a given pixel of the detector sees different sky pixels during the raster, and a flat-field image can be constructed from the median of all raster-position images. A total of $\sim$ 100 ZB raster observations were executed in the available ISOCAM calibration time. In Figure 4.13 we show four examples of ZB flat-fields in the LW3 (15 $\mu$ m) filter, with 1.5 $^{\prime \prime }$ , 3 $^{\prime \prime }$ , 6 $^{\prime \prime }$ and 12 $^{\prime \prime }$ pfov, respectively. It can be seen that only the central part of the array is illuminated when the 12 $^{\prime \prime }$ pfov is chosen. The pixel dependent stabilisation times generate a pattern across the images which increases the spatial noise. Low frequency noise levels can be observed for several minutes after a flux step. The main problems are for pixels located at the edges of the array, and on a line in the lower left hand quadrant of the array which has a slightly lower responsivity than the average (and it is usually nicknamed: `the hair'). The flat-fields have been normalised so that the mean of the central 11 $\times$ 11 pixel sub-array is one. This definition has the advantage that vignetted outer pixels do not alter the normalisation factor, causing the flat-field to directly contribute to the photometric calibration factor for the system. (Ideally, the flat- field should only adjust spatial fluctuations, it should not affect the average signal level for the array.)

**Figure 4.13:** Four examples of zodiacal background flat-fields in the LW3 filter. From top-left in clockwise order: 1.5 $^{\prime \prime }$ , 3 $^{\prime \prime }$ , 6 $^{\prime \prime }$ , 12 $^{\prime \prime }$ pfov, respectively. Note that in the case of the 12 $^{\prime \prime }$ pfov, only part of the array is illuminated.
$\resizebox {14cm}{14cm}{\includegraphics{ffzb4.ps}}$

Even with a careful choice of the brightest zodiacal positions, the zodiacal background does not provide enough illumination for a proper calibration of all ISOCAM configurations. This is the case for the shorter-wavelength, small-pfov, configurations of CAM LW, and for all of the SW configurations. For LW a solution was adopted to replace the flat-field of configurations with low zodiacal background with the ZB flat-field of a corresponding configuration nearest in wavelength. The only solution for CAM SW was to use the ICD as the calibration source. This choice has the drawback that the ICD does not provide a uniform illumination of the field of view of ISOCAM, and considerable vignetting is seen at the edges of the detector. (See Section 2.7). It is important to stress again that most raster and beam-switch ISOCAM scientific observations can provide independent flat-field estimations. The idea behind these observing modes was indeed to beat the pixel-to-pixel response variation by observing the same sky region with different pixels. Observers using these observing modes do not need to be particularly concerned about the quality of the calibration flat-fields. The calibration flat-fields are however necessary for staring observations (or when the source is very extended with respect to the raster dimensions, or the observed field is very crowded). Imperfect flat-fielding induces two kind of error:

photometric error arising from the uncertainty in the responsivities of the pixels that see each source; and
the photometric error arising from the background subtraction.

As the source will be usually located at the centre of the array, the former error will always be relatively low, of the order of a few percent, even when no sky flat-field is available, since one can safely use the ICD flat-field near the array centre. On the other hand, identifying faint sources over a high-brightness background requires a very accurate flat-field. As an example, the currently achieved median accuracy of 0.5% in the LW10 6 $^{\prime \prime }$ flat-field means that with an average background flux of 50 ADU/G/s in this configuration, the 1- $\sigma$ limit for the detection of a faint source per pixel is $\sim$ 60 $\mu$ Jy (using the ADU/G/s to Jy conversion factors from Blommaert 1998, [10]). On the other hand, the poor accuracy of only 6% that we have reached for the LW2 1.5 $^{\prime \prime }$ flat-field gives a 1- $\sigma$ limit per pixel of $\sim$ 20 $\mu$ Jy for a typical background flux of 0.8 ADU/G/s in this configuration (note however that in this low background configuration one needs a long measurement to reduce the readout noise). In other words, in the configurations where the background flux is high we need a higher flat-field accuracy, but if the flux is high, a higher ZB flat-field accuracy is easier to achieve. The typical flat-field accuracy is about 1-3%.

Next: 4.6 Point Spread Function Up: 4. Calibration and Performance Previous: 4.4 Transients

ISO Handbook Volume II (CAM), Version 2.0, SAI/1999-057/Dc