# Revisiting Hybrid Interferometry with Low-Frequency Radio Astronomy Arrays

## TL;DR

This paper extends radio interferometry theory to hybrid arrays with different antenna designs, providing a new interferometry equation involving vector inner products, useful for calibration and sensitivity measurement.

## Contribution

It introduces a novel interferometry equation for hybrid antenna arrays, expanding the mathematical framework beyond identical antenna assumptions.

## Key findings

- Derived a new interferometry equation involving vector inner products.
- Applicable to calibration of diverse antenna arrays using compact sources.
- Enhances sensitivity measurement techniques for hybrid arrays.

## Abstract

Radio interferometry most commonly involves antennas or antenna arrays of identical design. The identical antenna assumption leads to a convenient and useful mathematical simplification resulting in a scalar problem. An interesting variant to this is a "hybrid" interferometer involving two designs. We encounter this in the characterization of low-frequency antenna/array prototypes using a homogenous low-frequency array telescope such as the Murchison Widefield Array (MWA). In this work, we present an interferometry equation that applies to hybrid antennas. The resulting equation involves vector inner products rather than scalar multiplications. We discuss physical interpretation and useful applications of this concept in the areas of sensitivity measurement and calibration of an antenna/array under test using a compact calibrator source.