Re: laser beam quality factor M2

AES wrote:

But, how would you define "Strehl ratio" unambiguously in general? It'a a ratio, right? Ratio of peak (or on-axis?) intensity of the real beam to the peak on-axis intensity of . . . what?

That is, for any given real beam, what's the ideal reference against which its Strehl ratio is evaluated: What aperture shape? What aperture size? Uniform intensity and uniphase across the aperture? Or just the intensity distribution the beam already has, but with all phase perturbations removed?

That's what's missing for me in talking about "Strehl ratio".

I don't know about other people, but I normally understand it to be similar but not identical to the last one you list.

The definition I usually use for the Strehl ratio evaluated at an axial position z from the exit pupil plane is:


      | integral{ E(u,v) exp(ikBz0)/B du dv}  |2
S =   | ------------------------------------- |
      | integral{ |E(u,v)| exp(ikBz0)/B du dv}|

where u and v are the usual direction cosines, B is sqrt(1-u**2-v**2), and both are evaluated over the exit pupil in appropriately normalized coordinates, so that the quantity inside the square root is always positive. The sign of the exponent depends on whether you're a physicist or an electrical engineer, but it's intended to be the complex conjugate of a converging spherical wave centred on (0, 0, z0). The factors of 1/B in the integrands are the inverse of the obliquity factor in the Rayleigh-Sommerfeld diffraction integral, and are needed to make the amplitudes come out right when going from a surface to another surface.

This of course only works for single-frequency fields.

Cheers,

Phil Hobbs
.

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