good morning
I'm a holo-beginner and physics teacher in high school
My setup is a HeNe laser 2mw with a spatial filter
theory sais that with a nx (10x, 20x 40x) microscope objective I need a given pinhole for spatial fintering.
for example 10x ->25 micron 40x -> 10 micron
my question is if I use a 40x and 25 micron pinhole what happen?
thanks
Best regards
Christian
pinhole dimesion
Re: pinhole dimesion
Depends on beam diameter and divergence. Most likely a small clean bright spot in middle surrounded by concentric alternating bright and dark rings.
Re: pinhole dimesion
The reason you use a pinhole is because at the focus of the objective lens you have an Airy pattern, due to diffraction caused by the limited aperture of the lens. The Airy pattern is a central bright zone surrounded by rings of dark and light (below). If there are any deviations of the input beam away from a pure Gaussian profile, for example due to dust in the beam profile, these deviations are encoded in the higher order rings; effectively the Airy pattern is the FT of the input beam profile.
It can be shown (1) that the Airy pattern is given by the Bessel function of the first order:
F(u) = (πa²/4)[2J(1)(πua)/πua]
where u is the amplitude
a is the input beam diameter
J(1) is the Bessel function of the first order.
The radii of the dark rings of the Airy pattern is given by the zeroes of the Bessel function. If you want to cut out the higher order rings of the Airy pattern - where deviations from Gaussian are encoded - then you place an annulus whose inner radius is the radius of the central disc (the first zero of the Bessel function) - you spatially filter out the higher frequencies. This radius is given by:
r(Airy) = 1.22fλ/D
where f is the focal length of the objective
λ is the wavelength of the laser
D is the diameter of the objective.
Unfortuinately, if you actually calculate the desired radius, you won't find a commercial pinhole of the calulated size, so, a rule of thumb is the one you stated - 10x ->25 micron.
So, in answer to your question, if you place an annulus - a pinhole - that's larger than the first radius of the Airy pattern, you allow through the higher order rings of the Airy, and so you do not block devaitions from Gauusian.
(1) "Fourier Optics An Introduction" - E. G. Steward
- AiryDisk.jpg (100.15 KiB) Viewed 650 times