## Computing the pixel coordinates

Given the actual position of the derotator, MRTCAL can compute the pixel position on sky from the current telescope position. This position has been pre-computed using the radio projection (LONGOFF and LATOFF columns in the IMB-FITS), only the per-pixel offsets are to be added. MRTCAL checks first if it knows the offsets for the current receiver (as found in the column RECNAME in the frontend table). The pixels offsets are not self-described in the IMBFITS: they must be hardcoded in the program, with a correct correspondance between the pixel number found in the backend table and the hardcoded offsets3.4. Once the offset of the current pixel is found, the strategy is the following.

- The current position (reference + position offset) is unprojected to absolute spherical coordinates.
- The pixel position angle on sky is computed, given the pixel position in the array and the derotator angle.
- The spherical distance from the array center is added using an inverse Haversine formula, i.e., the pixel position in absolute spherical coordinates is found by adding an arc of great-circle towards the correct direction.
- The resulting position is reprojected again as a reference + position offset in the current projection system.

The deprojection, offset in spherical coordinates, and reprojection are done by the Gildas internal engines.