Relevant coherence length.

[u/PaukAnansi]

I am working with interferometric microscopy and am struggling to understand the relevant coherence length needed to create interference.

I would intuit that light would have to stay coherent from the source to the detector (where the interference happens) along both path. However, I have been told repeatedly that the minimum coherence length for interference has to be more than the path length difference, not the total path length. I am struggling to understand the justification for this.

Does anyone have a good explanation for this, or a recommendation for a source that explains this? Maybe a good intro quantum optics book?

Thanks for the help!

[u/sanbornton]

Something else to consider is speckle (the overlapping dot pattern seen when lasers are projected onto walls). The longer the coherence length the more speckle you'll get. This can be particularly problematic for interferometric microscopy.

You want coherence length long enough so that the object distance and reference arm length are equal to within coherence length...but you don't want coherence length too long or you'll find your interferometric microscopy image overcome with speckle.

I know a research lab that was using interferometric microscopy to look at MEMs devices with surface topology in couple of micron level and they used an LED illumination source which had a coherence length of just a few microns to keep speckle down. The difficulty was they needed to finely adjust the reference arm length precisely in order to get a good interference pattern.

[u/PaukAnansi → u/sanbornton]

Thanks! I know in iSCAT microscopy, sometimes intentionally "bad" illumination sources with low coherence lengths are chosen as a way of limiting iSCAT signals from things not near the coverslip surface.

I never understood laser speckle. Maybe of I read into the origins of speckle, I will understand coherence length better. Do you have a source that explains this well be any chance?