Mach-Zehnder interferometer has been used, among other things, to measure phase shifts between the two beams caused by a sample or a change in length of one of the paths. My simple question is: What is the intensity distribution behind the first beam splitter on an observation screen at the same distance like behind the second beam splitter?
If the beam splitters are all 50% reflectors and perfectly flat, etc. then whatever spatial energy profile the incoming beam has will be seen in both paths behind the first splitter. A typical interferometer is set up so that the paths are short enough that self-interference/diffraction does not happen. Assuming your "second splitter" is the recombiner, then the intensity pattern there is the combination of the interference effects with the input spatial intensity pattern. That is, if you had a "dim" region in the input beam, you'd see the same fringe pattern as elsewehre in the beam but with lower peak intensity.