Revisiting Diffraction with an Apodized "Iris"

Started Aug 15, 2017 | Discussions thread
Re: PSF and MTF vs. Apodization strength
1

J A C S wrote:

OpticsEngineer wrote:

Looks pretty good, matching what Zemax shows using Gaussian apodization with an apodization factor of 2. A(r) = exp(-2*r^2)

I didn't participate in the previous thread on this. But in case it was of interest to someone, we get pretty much complete suppression of the Airy rings with an apodization factor of 1 (A(r)=exp(-r^2) ) without reducing the high frequency response nearly so much.

There is something missing in that formula? Why the factor 1 and the parentheses? Without that, this is just a Gaussian?

A colleague recently raised this topic in relation to truncation of Gaussian beams by the aperture of a lens. I ran simulations showing the dependence on apodisation strength (expressed in terms of the width of the Gaussian profile at the lens).

First, here are the apodisation profiles. An ideal F/2 lens is assumed (NA 0.25).

Zemax Gaussian apodisation factor G=1 corresponds to beam NA 0.25 (intensity 1/e^2 at aperture boundary). G=2 corresponds to beam NA 0.18.

Intensity profile across lens aperture for a range of Gaussian apodisation widths

Point spread functions were calculated via a 2D FFT of the optical field across the aperture. Zero aberrations and perfect focus assumed.

PSF for a range of Gaussian apodisation widths.

Expanded PSF showing suppression of Airy disk diffraction rings as strength of Gaussian apodisation increases.

The width of the PSF varies rather slowly for modest apodisation. As noted by others, the most noticeable effect is suppression of the diffraction rings of the Airy disk. With stronger apodisation the PSF width varies inversely with the Gaussian beam width at the aperture.

PSF full width as a function of apodisation width, calculated at 10% and 50% of peak intensity.

The optical transfer function (MTF) is calculated from the Fourier transform of the point spread function.

Optical transfer function as a function of Gaussian apodisation width

Resolution as a function of apodisation width for a range of MTF contrast levels

WIth modest apodisation strength (large beam NA), MTF at low spatial frequencies is increased, resulting in an initial increase in resolution for MTF contrast 10% and 20%.

At higher spatial frequencies, the broadening of the central peak of the PSF dominates over the suppression of the outer diffraction rings.

PSF width scales with lens F-number. A diffraction-limited F/4 lens will have twice the PSF diameter and half the spatial resolution, provided apodisation width is scaled in proportion with lens NA.

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Alan Robinson

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