  Axion haloscopes search for dark matter axions from the galactic halo, most
commonly by measuring a power excess sourced by the axion effective current
density. Constraining axion parameters from detection or lack thereof requires
estimating the expected signal power. Often, this is done by studying the
response of the haloscope to a known, but different, source current density,
for example via a reflection measurement. However, only in the special case
when both sources induce the same electromagnetic fields, do the quantities
derived from a reflection measurement adequately describe the setup during an
axion measurement. While this might be valid for the traditional resonant
cavity haloscope, new broadband or open designs like dish antennas or
dielectric haloscopes cannot make this assumption. A more general relation
between axion- and reflection-induced fields is needed. In this article, we use
the Lorentz reciprocity theorem to derive an expression for the axion signal
power which instead of the unmeasurable axion-induced fields depends on the
measurable reflection-induced fields. This entirely circumvents the need to
know the response of the haloscope to the unknown axion source. It applies to a
wide variety of haloscopes including resonant cavities, dielectric haloscopes,
and broadband dish antennas.
