A. Internal Lamp-Flats

To determine the pixel-to-pixel sensitivity variations in the detector, one would ideally want to uniformly illuminate the detector — that is, expose each pixel to the same number of photons. Moreover, one would want the total counts per pixel to be close to the capacity of the detector, in order to maximize the signal-to-noise ratio of the exposure. In practice, such uniform illumination is impossible even for imaging. In the case of 2-D spectroscopy, one must also account for the dispersion of the light along one axis of the detector. As light sources do not have flat spectral energy distributions, this will lead to a wavelength term in the illumination of the detector even in the absence of any spatial nonuniformity in illumination.

A standard strategy for dealing with this problem is to include some sort of continuum light source inside the spectrograph, and use this to collect a set of images with maximum count-rates approaching the linearity limit of the detector. The SBIG spectrograph was designed for the amateur market, and thus does not include a broad-band internal continuum source. However, the design does include an internal red LED as a tool for determining the proper focus of the slit-plate assembly. In summer 2004, Mike Peters removed the stock red LED and switch unit, and replaced it with a red/green LED and a three-point switch. We made this improvement because the green LED provides a broader coverage of the optical bandpass than does the red LED. In the discussion that follows, all exposures were made with the green LED. The red LED is likely to be useful for high-dispersion work done in the red end of the spectrum.

The result of an exposure of the internal LED will be dominated by the dispersion in the x-direction and by non-uniformities in illumination in the y-direction. In order to assess the pixel-to-pixel variation in the detector sensitivity, these large-scale non-uniformities must be filtered out. The typical technique for doing this is to apply a spatial median filter to the exposures. One must take some care to choose a filtering scale that removes as much of the large-scale structure as possible, but retains the small-scale sensitivity variations. Below, I discuss a series of tests conducted to determine the strategy for obtaining and reducing internal lamp-flats for our spectrograph.

        Lamp-Flat Test Procedure
        Reduction of Lamp-Flat Frames
        Analysis of the Lamp-Flat Tests
        Strategy for Obtaining Lamp-Flat Frames

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Updated: 2005 October 10 [pbe]