You can also measure spectrum of laser by spectrometer and then translate spectral width ∆λ into ∆f.

When coherence length defined by L=c/(n*∆f).

where c is the light speed, n is the refractive index of medium and ∆f is the is the bandwidth of the source.

1- For Spatial coherence length one can use double-slit experiment .

You could also do this numerically: let coherent light source is fiber coupled and S is the fiber radius,the separation distance between the fiber and theobject plane (or the plane you would like to measure the spatial coherence)  is R. Then the spatial coherence then = 1.22*lambda*R/S

2- For temporal coherence you are right you can use Michelson or numerically you can use what Vladimir said.

Hello Parviz,

To measure the coherence length of a laser, yes as you point out you can use Michelson interferometry. It is also possible to do 'self-heterodyne Linewidth Measurement' to measure the laser linewidth related to the coherence length. 

For the spatial coherence, it has to do with the wavefront, and there are some wave-front analysis sensors in the market, they give directly the wave-front fluctuation (in RMS normalized to the wavelength) but they are very expensive. (10-20 k$). However it is possible to measure the M² of the beam which is usually used as a beam-quality indicator and quantify the degree of variation of the beam from an ideal Gaussian one. So for a high quality beam the M² is close to 1, thus the beam behave like an ideal one and contains no (or very weak) aberrations in his wavefront.

Now to measure this factor, if your beam is quasi-Gaussian you need to measure the Beam Parameter Product of your beam (BPP= theta*waist,where theta is the beam divergence angle (half-angle) ). the M-squared is the ratio of your BPP and the one on an ideal Gaussian beam given by: lambda/Pi. 

NB: There is an excellent paper about this by A. Sieagman: How to measure beam quality.

https://www.researchgate.net/publication/228910798_How_to_%28maybe%29_measure_laser_beam_quality

Article How to (Maybe) Measure Laser Beam Quality

Dear Mohamed

Thank you for your comments. To my knowledge, For spatial coherence, M2 factor does not show the spatial phase-front fluctuation. In fact, it is an average parameter.

Hello Parviz,

Yes the M-squared is not a direct measurement of the phase front fluctuations, what it tells you is: how far is your beam from an ideal Gaussian one whith perfect spherical wavefront, thus any aberrations in the wavefront will have an impact on the M-squared because the beam is getting farther from an ideal one. And how it propagates is directly related to its wavefront.

I’m also used to measure the wavefront fluctuations using wevefront sensors and what I see is that the higher the fluctuations the bigger is the M-squared. So I think that the simplest way to have a fairly good assessment of the beam spatial quality is the M-factor, although it is not a substitute for direct wavefront fluctuations measurement.

Hi Prof. Parviz,

This is what I think.

> Number of lasing modes is in direct relation with the spatial coherence and it can be determined by measuring the beam quality M2 of the laser output. In 1D the M2 is equal to number of modes N, and in 2D it is necessary to calculate Mx2 and My2 separately before finding the total number of modes N  = M4 = Mx2 * My2. 

And one way to control the number of lasing modes is to use variable pinhole aperture positioned in laser cavity. 

> and another way can be speckle contrast analysis of the laser output; using a polarization maintaining optical diffuser placed outside of the cavity and detecting the speckle pattern with a CCD camera. the relation between the speckle contrast C and the number of lasing modes N is assumed to be C=N(-1/2) 

for more details please refer to the following refs: 

1- https://www.osapublishing.org/ol/abstract.cfm?uri=ol-38-19-3858

2- https://www.osapublishing.org/oe/abstract.cfm?uri=oe-23-10-12989

Hello All !

Can I measure intensity of individual beams passing through different path in a cyclic shearing interferometer ?

I ask because, if my  understanding is right,as I try to measure the intensity of one beam ,I block the other.

@ Mostafa Agour According to your formula, spatial coherence length increases with measurement plane, how is it possible? I hope that formula is not correct which can not include visibility, spectral width. Would you like to give some references for your formula?

Can we measure the spatial Coherence through Michelson Interferometer?