Phase anomalies in Fourier-transform spectrometers: an absorbing beam splitter is neither sufficient nor necessary

Recently it has been a topic of some discussion that the phase associated with part of the self-emission of a Fourier-transform spectrometer may differ neither by 0 nor by pi rad from the phase of an external target if there is absorption in the beam splitter. The conventional interpretation of this has been to separate the self-emission into three terms: instrument emission from the input port, in phase with the external target; emission from the secondary input port, pi rad from the target; and emission from an absorbing beam splitter with an anomalous phase (neither 0 nor pi rad with respect to the target). There is another necessary condition that has not received much attention, that the instrument not be isothermal. For polarized radiation there is an additional condition that suppresses the anomalous phase, and for unpolarized radiation there is a way to produce an anomalous phase without beam-splitter absorption.