7.2 Nonlinearity

If the count rate from a point-like target is in the nonlinear regime, you should take special precautions when determining its brightness. For example, you might consider measuring the flux in the wings of the PSF and scaling them to a linearly exposed PSF. Unfortunately, no reliable and robust method exists for correcting nonlinearity in the FOC. There are, however, a couple of useful approaches for correcting some of the nonlinearity in calibrated FOC images, depending on whether the intensity distribution uniform or point-like.

Nonlinearity is introduced at the last stage of the FOC imaging process, so you should apply any nonlinearity corrections before geometrically correcting and flatfielding the image. The correction to apply to a given pixel depends on both the count rate in the pixel and the rates in neighboring pixels. If the count rate remains relatively constant over scales of 10-20 pixels or so, then the nonlinearity will be more severe than for a single pixel with the same count rate surrounded by pixels with a lower rate, such as in the center of a stellar PSF.

This procedure was extended by Greenfield in FOC ISR 074. He hypothesized that the actual flux distribution within a given aperture was not as important as the mean count rate. By looking at pre-launch test FOC images he was able to determine that convolving images of PSFs with a circular aperture with radius 5.5 pixels yielded a nonlinearity correction very similar to what a flatfield would give. A more detailed discussion of this procedure is beyond the scope of this manual, but readers are referred to FOC ISRs 074 and 073 for some suggestions on how to deal with nonlinearity for stellar fields.

If the count rate for a uniform source is in the nonlinear regime, but below the saturation value, it is possible to correct the pixel values for nonlinearity using the fflincorr task in the STSDAS foc.focphot package. The fflincorr task uses the FOC linearity curve which has been derived for uniform sources from internal lamp flatfields. The linearity curve follows the formula , where is the observed count rate, a is the uniform source saturation count rate as given in Table 7.2, and r is the true count rate. This correction can be applied only for small or moderate nonlinearity; it is not valid for high nonlinearity. Users should beware that these methods are somewhat preliminary, and they are not guaranteed to correct (or even improve) all types of data. Do not apply this correction blindly.