# Coherent length measurement of a monochromatic laser source

i need to learn about how to measure coherent length of a monochromatic laser source. I know that I can use michelson interferometer or spectrometry. For laser which has long coherent length michelson interferometer is hard to use.we need to use spectrometry.But when should I use spectrometry? I mean up to what length it is suitable to use michelson? And which spectrometry should I use for long coherent length? And how can I measure the bandwith?

• It's actually the other way round. You can use a spectrometer for very short coherence but you need a very high Q system for long coherence, so that would be a Michelson or an Echelon. The most precise systems of this kind that were ever built are probably the interferometric gravitational wave detectors. Another possible way to measure coherence of laser sources is by mixing the light of two sources and by measuring the spectrum of the lower product signal. That will give you GHz absolute bandwidth, i.e. approx. 1e-6 relative bandwidth, which is better than an interferometer. Commented May 14, 2015 at 9:22
• This only works if the reference laser is almost absolutely monochromatic. Commented Nov 6, 2019 at 0:25

A very simple way to check would be a Fizeau interferometer. You'll need:

• a laser beam expander
• a clean piece of glass.

Say you want to check if your laser has >= 2 meters of coherence length. Expand your laser beam such that the diameter of the beam is 5-15cm at the 2 meter mark.

Now take the piece of glass and lean it against something, reflecting the expanded beam back towards the laser aperture, but a few degrees off to the side onto a piece of paper.

Like with the Michelson interferometer, the contrast of the fringes will indicate whether the light is still in phase. However, instead of concentric rings, you'll see a zebra stripe pattern.

You can repeat this for 2m, 5m, 10m, and so on to get a ballpark estimation of coherence length.

A michaelson interferometer can be arbitrarily long if one of the arms is, for example, in a rolled-up length of optical fiber. It is easy to get optical fiber many kilometers long, and easy to build an interferometer with a fiber arm.

Spectrometry is, in my opinion, more difficult to use for long coherence length measurement. Coherence length of 1 km would correspond to wavelength stability of roughly one part in $$10^{12}$$, which is not easy to measure spectroscopically.