In the emission theory of light, light waves can move at any speed. We can still apply the Doppler effect, but to the best of my knowledge, only the frequency changes, not the wavelength. The pattern for a diffraction grating only depends on the wavelength right? And we have observed redshifts and blueshifts using a diffraction grating. Although emission theory has long been discredited, is the existence of diffraction redshift a valid reason to discard emission theory?