ALS calibration: Analytic expressions for the antenna gains of a two and three element east-west interferometer

Studying a simple problem first, for which an analytic solution exists, can greatly improve our understanding of a complex problem. An undesired result of calibrating with an incomplete sky model is calibration systematics. Studying the systematics contained in the antenna gains of a simple east-west interferometer could aid us in understanding the artefacts associated with calibration in general. This paper aims to derive analytic expressions of the antenna gain vectors that were obtained during the calibration (using an incomplete sky model) of a two and three element east-west interferometer.