the grammatical structure?

No, CARS is a nonlinear, optical imaging system

In my opinion, there should have been a comma after "Photobleaching"

You could rewrite it thus

To capture the cellular images, the interdisciplinary UB team of biologists, chemists and physicists, led by Prasad, utilized an advanced biophotonic approach that combines three techniques to measure dynamics of proteins: (1) a nonlinear, optical imaging system (CARS or Coherent anti-Stokes Raman scattering), (2) TPEF (two-photon excited fluorescence), which images living tissue and cells at deep penetration and (3) Fluorescence Recovery after Photobleaching.

It seems to have been written hastily and inconsistently - for example the third method is not introduced with an abbreviation (e.g. FRAP) yet it is named in title case.

no, it's an acronymy for Two-Photon Excited Fluorescence, which is some sort of imaging techniques which is seen by a non-linear optical imaging system, somewhat analagous, possibly to x-rays being seen by the film in an x-ray machine. The TPEF would be analgous to the X-rays.

Yes, the third caused the problem of understanding.

Thank you both.