I’m simulating a laser imaging system (diffraction limited) and would like to measure the focused spot size on the image plane.
The commercial software I’m using now takes measurement of beam spot by gaussian fitting and obtains its FWHM as the spot size.
However, in Zemax the spot size is evaluated by the Airy disk (do I understand it right?), which uses the Bessel fitting.
How can I convert the Airy disk size to the industrial measurement method FWHM ? Or is there any more realistic beam size measurement method in Zemax?
If I did not describe my question clearly, please comment and let me know. I really appreciate that.
Thank you.
Oliver
Best answer by David.Nguyen
Hi Oliver,
There’s an engineer solution to this problem, which will probably tickle the physicists and mathematicians out here, but here it is anyway.
If you look at the Wikipedia article for the Airy Disk, you’ll find an approximation using a Gaussian profile. In that section, they mention that the Gaussian RMS width should be chosen as:
whereas the Airy radius is given by:
so, there’s a factor 0.84 / 1.22 = 0.6885 between the Gaussian RMS width and the Airy radius. Additionally, the Gaussian profile definition in that section is a little bit different than the traditional normal distribution in the FWHM Wikipedia article. In fact, the standard deviation in the FWHM article is half the value of w_0 in the Airy Disk article:
In the FWHM article, they give you an approximation of the FWHM knowing the standard deviation:
So all together, assuming my maths are correct, the FWHM, knowing the Airy radius can be approximated by:
Remember, this is only an approximation, and you’d have to do the maths if you want to figure out the exact relation between the two. But I thought perhaps this approach is sufficient for you.
However, please note that the Airy radius calculation in OpticStudio is not a fit, it is a direct calculation. This is an excerpt from the Help File:
The Airy disk radius is 1.22 times the wavelength (primary wavelength is used if polychromatic) multiplied by the F/# of the system
If you want to compare your FWHM measurement against OpticStudio more accurately, assuming your system is indeed diffraction limited, you could try to fit a Gaussian to the FFT PSF or Huygens PSF, and then compute the FWHM from the width of that Gaussian.
There’s an engineer solution to this problem, which will probably tickle the physicists and mathematicians out here, but here it is anyway.
If you look at the Wikipedia article for the Airy Disk, you’ll find an approximation using a Gaussian profile. In that section, they mention that the Gaussian RMS width should be chosen as:
whereas the Airy radius is given by:
so, there’s a factor 0.84 / 1.22 = 0.6885 between the Gaussian RMS width and the Airy radius. Additionally, the Gaussian profile definition in that section is a little bit different than the traditional normal distribution in the FWHM Wikipedia article. In fact, the standard deviation in the FWHM article is half the value of w_0 in the Airy Disk article:
In the FWHM article, they give you an approximation of the FWHM knowing the standard deviation:
So all together, assuming my maths are correct, the FWHM, knowing the Airy radius can be approximated by:
Remember, this is only an approximation, and you’d have to do the maths if you want to figure out the exact relation between the two. But I thought perhaps this approach is sufficient for you.
However, please note that the Airy radius calculation in OpticStudio is not a fit, it is a direct calculation. This is an excerpt from the Help File:
The Airy disk radius is 1.22 times the wavelength (primary wavelength is used if polychromatic) multiplied by the F/# of the system
If you want to compare your FWHM measurement against OpticStudio more accurately, assuming your system is indeed diffraction limited, you could try to fit a Gaussian to the FFT PSF or Huygens PSF, and then compute the FWHM from the width of that Gaussian.
There’s an engineer solution to this problem, which will probably tickle the physicists and mathematicians out here, but here it is anyway.
If you look at the Wikipedia article for the Airy Disk, you’ll find an approximation using a Gaussian profile. In that section, they mention that the Gaussian RMS width should be chosen as:
whereas the Airy radius is given by:
so, there’s a factor 0.84 / 1.22 = 0.6885 between the Gaussian RMS width and the Airy radius. Additionally, the Gaussian profile definition in that section is a little bit different than the traditional normal distribution in the FWHM Wikipedia article. In fact, the standard deviation in the FWHM article is half the value of w_0 in the Airy Disk article:
In the FWHM article, they give you an approximation of the FWHM knowing the standard deviation:
So all together, assuming my maths are correct, the FWHM, knowing the Airy radius can be approximated by:
Remember, this is only an approximation, and you’d have to do the maths if you want to figure out the exact relation between the two. But I thought perhaps this approach is sufficient for you.
However, please note that the Airy radius calculation in OpticStudio is not a fit, it is a direct calculation. This is an excerpt from the Help File:
The Airy disk radius is 1.22 times the wavelength (primary wavelength is used if polychromatic) multiplied by the F/# of the system
If you want to compare your FWHM measurement against OpticStudio more accurately, assuming your system is indeed diffraction limited, you could try to fit a Gaussian to the FFT PSF or Huygens PSF, and then compute the FWHM from the width of that Gaussian.
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