Reconstructing CCD flat fields using nonuniform background-illumination sources

Abstract Precision CCD photometry over large fields-of-view and detection of faint and diffuse objects demand great care inthe acquisition of flat-field frames. Variations in the illuminated field will introduce spatial variability in the flat field.Small angular displacements of the CCD, telescope, and instrument, with respect to the external light source yields acorresponding linear translation of the image on the CCD with respect to the true flat-field function, so that a functionalequation relates the flat field to these shifted data sets. In two-dimensions an elliptic partial differential equation relating theoffset CCD measurements to the flat-field function can be derived enabling relaxation solution techniques to be used. Asimulation is presented and discussed. Introduction The process of generating a uniform photometric response for large format CCD cameras resides in the acquisitionof a good high-quality flat-field frame, particularly over the scientifically interesting regions of the array. Attention must begiven to the many issues such as vignetting and shadowing in the optical train, to visual and sub-visual clouds in the sky,sky polarization effects (Buil 1991) and twilight and moon-induced sky gradients, etc. High quality flat field data isnecessary for unambiguous detection of very faint and distant sources (Tyson 1989), photometry of distant supernovae andgravitational lenses, detection of faint reflection nebulae and circumstellar disks, and microlensing in rich star fields. Forplanetary landers using CCD cameras good flat fields are important to detect tenuous sky phenomena, i.e., thin clouds, haze,ice crystals, etc., and enable better characterization of minerals in the soil and rock via multi-color imagery. For planetarylanders and many spacecraft imagers a flat field screen is not readily available so alternative methods to create a flat field areneededRecently Chromey and Hasselbacher (1996) and Chromey (1996) discussed the various issues associated with skyflats in wide-field astronomical images, and note that illumination variations in the sky will introduce gradients in the flat-field frames on the several percent level. Furthermore, for example, the Hubble Space Telescope (HST) must obtain flatfield frames using uniquely different and often cunning approaches such as using the shifting illuminated Earth surface as asource, and great pains have been expended to guarantee well calibrated flat-field frames over most of the array (Biretta 1995).This paper summarizes work presented by Wild (1997). Kuhn et a! (1991) independently (and six years earlier)developed a practical least-squares methods based on the same functional equation; Snyder et a!. (1996) have also looked atthe problem using estimation-based methods. Wild (1997) looked more at the mathematical structure of the functionalequation in two dimensions and developed a direct solution technique, a matrix formulation, and an elliptic partial differentialequation method. Another (unpublished) method is to solve the functional equation in Fourier space using the convolutiontheorem. The partial differential equation technique is used here in a simulation. The present paper is a reduced version ofour PASP paper. Evidently, while several teams have been, or are currently, active in this discipline, from the response toour PASP paper it appears that few researchers and instrumentation specialists are familiar with the quantitative techniquesthat underlie the principle of flat field estimation from shifted frames. The work of Kuhn et al. (1991) has a very elegantleast-squares approach and has been demonstrated with experimental data, and is the seminal paper in this field. Our workpoints out some new mathematical directions, but it is unclear if there are any advantages to the approaches laid out in Wild(1997). Pure matrix techniques coupled with optimal estimation theory are often the best methods, but due to the large sizeof the CCDs the matrix approach remains embryonic because of the intense demands made on computing memory. We alsopoint out some of the issues associated with the flat field reconstruction task.