4.4.2 Horizontal Smearing

During readout of a badly overexposed image, there is spurious charge detected by the readout electronics. The apparent brightness of the stellar halo is higher to the right of the saturated columns. This is particularly obvious at the bottom of the image in Figure 4.3 which is a region in the shadow of the pyramid edge.

The horizontal "smearing" seen in highly saturated images can be modeled as an exponential function which decays over a few rows after a saturated pixel is encountered. The effect itself temporarily saturates after about ten saturated pixels (subsequent saturated pixels have no effect). The effect is twice as bad with gain 7 e^- DN^-1 than with gain 14 e^- DN^-1. This model only works on very highly saturated stellar images.

In Figure 4.3, the image to the right side of the saturated columns is brighter than the left side; and the brightness increases as the number of saturated columns increases. This effect appears to be a signal which starts at a saturated pixel and decays over the next few rows, wrapping around as it does so. The signal is additive with each successive saturated pixel. Jumps are obvious when the number of saturated columns changes. The problem is a known characteristic of the amplifier electronics, and an effort was made to minimize it during design. The increase in signal in rows with saturated pixels is also seen in the over-scan region (the over-scans are provided in ".x0d" files from the pipeline).

An approach to calibrating out the horizontal smearing is described here. An exponential function fits the effect reasonably well. An appropriate algorithm creates an array to contain the signal model. It searches through the uncalibrated image (with the over-scan region included) in the sequence in which the pixels are read out. When it encounters a saturated pixel, it adds an exponential function to the model array, beginning at that pixel. The function has the form s(x)=Ae^-x/h, where x is the offset from the saturated pixel and only positive x values are included. The half-width, h, and amplitude, A, appear to vary from frame to frame and must be determined on the image itself. As more saturated columns are encountered in a row, the signal intensity builds up in the model image. The image can then be "improved" by subtracting the model from the raw image.

The amplitude and half-width parameters can be obtained by trial and error. The typical parameters vary slightly for each chip. The amplitude per saturated pixel is typically 1.75 DN (gain 7) or 0.2 DN (gain 14). On the other hand the half-width at a gain of 14 is larger (h=1800) than at 7 (h=350). So the total integrated effect is about twice as bad at gain 7. A straightforward application of the above algorithm cleaned up most of the signal in rows which had a few saturated columns, but over-subtracted in rows with a large number. The algorithm can be modified to saturate by making the parameter A, which gives the peak contribution from a single saturated pixel, depend on the current level of the effect: A=A₀*(1-C/C_max). This implies that the correction is never larger than C_max no matter how many saturated pixels are encountered. C_max is approximately 14 DN for a gain of 7 and 10 DN for a gain of 14.

The algorithm gives improvement only on highly saturated stellar images (where the star is saturated to 3 or 4 columns at the edges of the chip). On less saturated data, it over-subtracts significantly. This indicates that the problem is nonlinear, and therefore a general algorithm applicable to all data will be difficult to develop.