[This followup replaces a poorly worded fourth paragraph in the
original. My apologies for the bungle.]
There are numerous experimental tests that purport to confirm Special
Relativity theory and/or refute what the testers and their reviewers
call emission theory, but those examining doppler shift all seem to
depend on the assumption that emission theory predicts wavelength
constancy even when source and observer are in relative motion.
That assumption is pretty thin. Any theory predicting so is falsified
by the very existence of doppler shift in light. There's no ground for
denying that; therefore no such theory is viable, and there's no reason
to bother with disproving it. Or even mentoning it, in my view.
The opposite assumption however, that emission theory predicts variable
wavelength when source and observer are in relative motion, is much more
interesting; the accepted definitions of frequency and wavelength wrt
streams of particles are intuitiuvely correct and are clearly congruent
with their waveform equivalents, but unlike SR with its FoR magic,
a potentially viable emission theory must account for the effect of
relative motion between the source and the observer explicitly. The
frequency definition does that, but the wavelength definition does not.
What the observer experiences is the objective wavelength altered by
the change in distance between source and observer while one wavelength
passes; in other words, changed inversely as the speed. It is given by