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First, what's so good about oxygen-releasing photosynthesis? It enables using something very common as an electron donor: water. That means that O2-releasers can support a very large biota, a biota that can include large populations and total masses of eaters of them and eaters of eaters of them etc.
There are photosynthetic organisms that can use other electron donors, organisms like the green and purple bacteria. They use electron donors like iron (Fe++ -> Fe+++), hydrogen, sulfides, and sulfur. These are much less common than water, making their users' biomass productivity much more limited.
As to looking for spectroscopic evidence of photosynthetic pigments, there are some problems. At first sight, it might be "Look for a spectral line of chlorophyll", but there are several problems with that approach.
Spectral lines of condensed-state materials are often much broader than gas-phase spectral lines: http://www.cbu.edu/~jvarrian/122/absspex.html of some photosynthetic pigments.
Organisms use a variety of photosynthetic pigments:
- Chlorophylls
- Carotenoids
- Phycobiliproteins
- Bacteriorhodopsin
So extraterrestrial photosynthesizers may use any of these, or some different ones.