Often a simple test, like taking the average of each column, shows that the bias frame is not flat. In practice, there is often a slow variation of the read-out level along the row direction of the detector. Over 10 observing runs at ESO, with four different detectors, the difference between bias frames taken during a same run could be represented by a level offset varying in the same way linearly along all rows. This variation was only seen with the TEK CCDs, and is presumably due to the use of the system before the configuration was stable, as a stronger gradient occurs preferentially in the start of a run, and may reappear (less strong) in the start of the next nights. These variations and lack of flatness are easily corrected, and from now on, it will be assumed that such effects have been eliminated. More information on the bias frames of these observing runs can be found in De Cuyper & Hensberge (2000).
All 24 bias frames of the 92.04 observing run show striped patterns at the level of the read-out noise. Two examples are shown in Figure 1a, giving an idea of the observed range of pattern from frame to frame. Decisive progress in understanding how such patterns build up followed from the recognition that we see a one-dimensional periodic function that is phase-shifted from row to row.
The function is multi-peaked (Figure 2) with a semi-amplitude of 10 and repeats after 439 pixels. Hence the period is not much shorter than the time needed to read a row. The phase-shift from one row to the next is nearly one-third of the period and generates in combination with the 3 peaks the visual pattern present in Figure 1a. A slight, smooth variation in the phase shift from row to row produces stripes that are curved rather than straight.
The periodic function was actually reconstructed by estimating its periodicity from an initial FFT analysis, after which the phase-shifts were iteratively improved by cross-correlation with subsequent approximations of this periodic function. These approximations were iteratively obtained by averaging phase-shifted rows of all bias images.
The multi-peaked function shown in Figure 2 is represented by a Fourier series with 16 terms and its phase variation between rows is parameterized by a polynomial of degree 7 (suitable to describe the variation over the rows of all bias frames). On all but the bias frames, the phase parameters had to be determined from trustworthy overscan pixels (6 up-scan rows and 40 pre-scan columns were used). This was done by a least-squares algorithm with initial estimates for the phase shifts being obtained again from cross-correlation of individual rows with the systematic function. For each calibration or science frame, the range in phase shift from row to row and the mean value of this shift are shown in Figure 3.
Figure 1b shows the bias frames of Figure 1a corrected for the periodic pattern using only the information in the selected overscan pixels. Figure 1c shows the difference between this model and the one derived using the information over the whole bias frame (Note that the scale differs by a factor of 10). A check over all bias frames indicates that the rms in images as shown in Figure 1c lies below 0.5 and that local differences may reach 4 . This shows that the procedure applied to the overscan pixels results in good estimates of the phase shifts. Moreover, the fact that the parameter space covered by all frames is already covered by the subsample of the bias frames adds confidence that no spurious results were produced.
This research was carried out in the framework of the project ``IUAP P4/05'' financed by the Belgian Federal Scientific Services (DWTC/SSTC). We thank H. Van Diest for help with the data handling. This work is based on observations obtained at the European Southern Observatory (E.S.O.), La Silla, Chile.
De Cuyper, J.-P. & Hensberge, H. 2000, in Optical Detectors for Astronomy, Proceedings of the ESO CCD Workshop held in Garching Germany Sep. 13-16 1999, eds. P. Amico & J.W. Beletic, ASSL Series Kluwer Academic Publisher, in press