Each image has ZERO-FLUX PATTERN NOISE, that is the image you would get observing with zero flux on the array with the same on-chip integration time (FRAME TIME in this document), readout speed, number of A/D samples per frame, and number of resets per frame as are used for imaging. The number of images coadded for a single observation, which gives the INTEGRATION TIME, should not matter if the result is scaled by the number of coadds. The pattern noise includes pixel and multiplexer channel voltage offsets in the array and in the signal processing electronics. The pattern noise will depend on frame time because of the dark current. It will also depend on the method and number of resets. In general, a single reset will not set each pixel to a hard reset value, but will leave a residual depending on the flux level and the properties of that pixel.
To obtain a useful image, it is necessary to subtract the pattern noise. For an optical CCD this is what is done when a dark slide exposure is obtained and subtracted from the sky image.
If there is substantial background flux in the sky image, as is the case in the mid-IR, this will leave a pattern due to the gain variations from pixel-to-pixel resulting from differences in the detector, in the array read-out multiplexer, and in the the signal processing electronics. To correct for this you need to divide by a GAIN MATRIX, which gives the relative gain for each pixel.
For the mid-IR, when you beam-switch with secondary chopping or telescope nodding, the flux level and the camera settings will be the same in both beams and the pattern noise and the sky-plus- telescope flux should be effectively subtracted out when the images are subtracted in processing, leaving no zero-flux pattern noise or gain related pattern. However, as soon as there is an astronomical object imaged on the array, a gain matrix is required to provide a valid image of the object.
If there were no pattern noise and the detector and readout were completely linear, then a single image of a uniform background, suitably shifted so a pixel value of zero means zero flux, would represent a gain matrix and could be divided into the sky image to ``flatten'' it. This is often done in the near-IR. However, this is not the case in the mid-IR. Also there is no practical source of a single uniform background illuminating the array the same as the sky. The telescope, which dominates the background, will in general illuminate the array differently from the sky.
So it is necessary to form a gain matrix for a given spectral filter, camera magnification, and focal ratio from two flux levels, both of which contain the same flux from the telescope. The varying part should pass through the telescope in the same manner as flux from the sky. The methods for this that have been used with MIRAC are 1) the sky at one and two airmass, 2) the off-source beam during observing at what ever range of airmass occurs, and 3) the closed dome and the sky (with the same telescope orientation).
The first two methods are nice because they make the measurement at the same flux level as the astronomical observations, hence are not so sensitive to array non-linearity. But they suffer from small signal and great sensitivity to changing sky conditions. It is even possible to get negative gain matrix elements with those methods. Also, they can be affected by changing flexure between the telescope and the camera optics and array with changing telescope orientation.
The third method has been found to give large signal-to-noise in the difference, is least sensitive to sky vagaries, and is most reliable. However, care must be taken to chose the frame time so the dome flux is within the linear range of the array and is similar to the level the array is operated at during astronomical observations. This will be shorter that the frame time used for the astronomical observations because of the higher flux from the closed dome. With burst-mode readout of the camera, where the readout is a fixed time and the frame time is determined by a delay between readouts, this difference in frame time has little effect on the gain properties of the array. This is not likely to be the case for continuous readout, for which the frame time is changed by changing the read time. The linear range is not, in general the same as the A/D range! For the Rockwell HF-16, the linear range goes from the zero flux level to about .69 of full well.
In any case, it is essential that the zero-flux pattern noise be the same for both flux levels by using the same camera settings. Also, since residual pixel levels after reseting once will be dependent on flux level, it is best if the camera has the capability of multiple resetting at the start of each frame.
The gain matrix, which is divided into the image, is formed from the difference of the images at the two flux levels, normalized to a mean of unity. The reciprocal of this is an ``inverse'' gain matrix which should be multiplied times the image.
It goes without saying, that the astronomical images must also be obtained within the linear range of the array, or all this is for naught.
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