The expression used to calculate the minimum focusable (difraction limited) spot size is:
Size=(1,22*lambda/sin(theta))
considering that already from a LASER source some imperfections reduces the focusability, then this expression is expanded as
Size=(1,22*lambda/sin(theta))*M2
is there any approximate equation to compute the effect of Strehl Ratio into spot size?
(actually measuring Strehl may be easier than accurately determining M2)
I actually took, two approaches:
for a homogeneous illumination leading to an Airy disk at best focus, I assume the Strehl Ratio reduces the peak intensity of the central Airy disk, and that this energy goes to the secondary Airy rings. So this does not affect spot size (or not by much). so Factor = 1
for a Gaussian illumination (more common) leading to a Gaussian profile at best focus, I assume the Strehl Ratio reduces the peak intensity, and that this energy goes widen the size of the Gaussian profile.
Since the volume remains constant (total energy), and this total energy equals
E=pi*R0^2*I/2
so Factor = 1/Strehl^0,5 (in order to keep E constant)
Size=(1,22*lambda/sin(theta))*M2/Strehl^(1/2)
Are my assumptions correct?
May I then take as approximate equation
Factor = 1/Strehl^0,25
for general beams (somewhere in between Gaussian and Flap-Top)
so that the overall equation for spot size resembles
Size=(1,22*lambda/sin(theta))*M2/Strehl^0.25
Size=(1,22*lambda/sin(theta))*M2/Strehl^(1/4)
may this work?
it shall be noted anyway that for this equation to work the Strehl shall be determined for an ideal source (M2=1), otherwise we may be punishing spot size twice (directly by M2, and indirectly by Strehl since M2 will make Strehl be lower)
is there an expression to estimate Strehl reduction solely affected by M2?
Shall I further reduce the impact of Strehl, to avoid double accounting?
so that the overall equation for spot size resembles
Size=(1,22*lambda/sin(theta))*M2/Strehl^0.1875
Size=(1,22*lambda/sin(theta))*M2/Strehl^(3/16)
Thx
sam
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