If a Bessel beam J1(pi*x)/(pi*x) diffracted by a circular aperture, how will be the final 'PSF'?
The far field intensity (equivalently the intensity profile at the focus of a lens) will be the Fourier transform of the truncated Bessel. It is easy enough to write the integral, but I very much doubt that there is a simple closed form solution. However, the profile can be evaluated numerically.
When a Bessel beam, specifically the J1(pi*x)/(pi*x) Bessel function, is diffracted by a circular aperture, the resulting point spread function (PSF) will be modified due to diffraction effects.
The Bessel beam has an intensity distribution characterized by concentric rings with a central bright spot. However, when the Bessel beam passes through a circular aperture, it experiences diffraction, which causes the beam to spread out and interfere with itself, leading to a modification of the PSF.
The resulting PSF will exhibit a central peak, similar to the original Bessel beam, but it will also contain secondary peaks and a diffraction pattern surrounding the central peak. The specifics of the PSF will depend on the size and geometry of the circular aperture, as well as the wavelength of the light being used.
The diffraction pattern resulting from the interaction of the Bessel beam with the circular aperture can be described using mathematical models, such as the Fresnel diffraction or the angular spectrum representation. These models take into account the properties of the Bessel beam, the circular aperture, and diffraction phenomena to predict the resulting PSF.
To obtain a precise description of the final PSF, it is necessary to perform numerical simulations or analytical calculations using diffraction theory and specific parameters of the Bessel beam and the circular aperture.
If you require a more detailed analysis or have specific parameters in mind, please feel free to provide additional information or reach out to me at [email protected]. I will be glad to assist you further in understanding the characteristics of the PSF resulting from the diffraction of a Bessel beam by a circular aperture.
Thank you so much for the answers.
I want to find the expression of the final PSF for the second diffraction by circular aperture.
The primary beam is perfectly collimated produced by lazer.
This beam is diffracted by a circular aperture (radii d1) and gives the following PSF: 2*J1(pi*x)/(pi*x). Where J1 is the bessel function of first order.
Then this bessel beam will be diffracted again by a circular aperture(radii d2).
I need to find the final PSF at the CCD camera.
J2, ikinci dereceden bessel fonksiyonu ve yarıçapı d2 olur. Bessel fonksiyonunun dairesel alanda sahip olduğu yer J1, birinci dereceden bessel fonksiyonunun 2 katıdır. (4*J2(pi*x)/pi*x).sahip olduğu alan birinci bessel fonksiyonunun 2 katı ve yarım daire olur.
You can use Lighpipes package for Python which is a numerical beam propagation toolbox. You can inititate the field distribution of the laser, propagate it to the first aperture, then second aperture, then CCD.
For the PSF, I suppose you could initiate the field as a point source and propagate that through the system.
Here is an example of diffraction on an aperture at the documenation website: https://opticspy.github.io/lightpipes/DiffractionRoundHole.html
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