I deriving a pupil function in a coherent imaging system

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Start date Apr 27, 2021
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Coherent deriving Function Imaging System

In summary, a pupil function is a mathematical representation of the aperture of a coherent imaging system that describes how light passes through the aperture and affects the formation of an image. It is important to derive a pupil function in order to analyze and optimize the system's performance. A pupil function can be derived using various methods and is affected by factors such as aperture shape and size, wavelength of light, and refractive index of the medium. The pupil function plays a crucial role in image formation and a well-designed one can result in a sharper and more accurate image.

Apr 27, 2021

silentt

Homework Statement: The aperture is opaque with 3 circular holes, each with a diameter of w. The coordinates of the center of the circular apertures are: {0, d/2}, {0, -d/2}, {d/2, 0}.
Derive the coherent transfer function.

Relevant Equations: {0, d/2}, {0, -d/2}, {d/2, 0}

Hello all. I have a question about building the coherent transfer function and specifically how I would go about deriving the pupil function for this figure. I have not come across this in my class yet and am a bit stumped.
Any help would be appreciated.

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Apr 27, 2021

Dr Transport

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the pupil would be a circular aperture and 3 2-d delta functions

Apr 28, 2021

silentt

Awesome, thanks for confirming my suspicions.

FAQ: I deriving a pupil function in a coherent imaging system

What is a pupil function in a coherent imaging system?

A pupil function is a mathematical representation of the aperture or entrance pupil of an imaging system. It describes the amplitude and phase of the light that passes through the system's aperture, and is used to analyze and optimize image formation.

How is the pupil function derived in a coherent imaging system?

The pupil function is typically derived using Fourier optics principles, which involve taking the Fourier transform of the aperture function. This results in a complex-valued function that describes the optical transfer function of the imaging system.

What factors affect the shape of the pupil function in a coherent imaging system?

The shape of the pupil function is affected by several factors, including the size and shape of the aperture, the wavelength of light, and any aberrations present in the system. Additionally, the pupil function can be manipulated by using optical elements such as lenses or apertures.

How does the pupil function impact image quality in a coherent imaging system?

The pupil function plays a crucial role in determining the quality of the final image in a coherent imaging system. It affects the resolution, contrast, and depth of field of the image, and can also be used to correct for aberrations and improve image quality.

Can the pupil function be measured experimentally in a coherent imaging system?

Yes, the pupil function can be measured experimentally using techniques such as point spread function (PSF) imaging or interferometry. These methods involve capturing images of a known object or using a reference beam to reconstruct the pupil function of the imaging system.