# Theoretical Description of Single-dish Imaging in CASA

A theoretical description of single-dish image generation and data gridding

For single-dish observations, ALMA uses on-the-fly mapping.  The technique is described in Mangum et al. (2007) .

Converting single-dish observations into an image or cube is done almost entirely in the image domain. After taking and calibrating the data, the process follows three steps:

1. Forming the image grid
2. Populating the image grid
3. Smoothing the image data

The fundamental parameter relevant to image quality is the sampling interval. There are a number of sampling functions that need to be considered: the sky sampling function, the image grid sampling function, and the response function of the single-dish beam. These functions all convolve against each other to yield an effective image resolution somewhat poorer than the actual theoretical FWHM of the telescope primary beam.

The dimensions and extent of the image grid are determined by the mapped area on the sky. The gridding pixel size must be at least one half the size of the theoretical beam when convolved with the sky-sampling function. Since the sky sampling function is typically 1/3 to 1/5 of the primary beam, and the effective FWHM of the telescope and sky sampling function is close to that of the telescope anyway, it's safe to use a pixel dimension that is 1/3th the width of the primary beam.

For example, a 30" telescope beam with a 6" sky sampling function has an effective FWHM of $\sim \sqrt{(30^2+6^2)}\simeq$ 30.6". Therefore, computing an image pixel size that is 30"/3 = 10", is appropriately oversampling the effective beam FWHM and sampling interval.

After the coordinates of the data are transformed into sky coordinates, the image grid is formed with dimensions either consistent with the user specifications, or so that the image fully encompasses the observed sky positions.

For each pixel in the grid (e.g. in RA-Dec space), the gridding process searches through the data for measurements taken within some cutoff radius (specified by convsupport). Depending on their distance from the grid coordinate, the observation is weighted according to the kernel type and added together in the spatial domain (i.e. entire spectra are added together). If the clipminmax function is invoked, the maximum AND minimium data in the ensemble (prior to weighting) are rejected before summing. This process is repeated iteratively for each element in the grid.

Citation Number 1 Mangum, et al. 2007, A&A, 474, 679-687 (ADS)