I deriving a pupil function in a coherent imaging system

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The discussion focuses on deriving the pupil function for a coherent imaging system, specifically involving a circular aperture and three 2-D delta functions. The original poster seeks guidance on building the coherent transfer function and expresses confusion about the process. Participants confirm the approach and provide reassurance about the correctness of the pupil function concept. The conversation emphasizes the importance of understanding the relationship between the pupil function and the coherent transfer function in imaging systems. Overall, the thread highlights the need for clarity in deriving these functions in optical systems.
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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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the pupil would be a circular aperture and 3 2-d delta functions
 
Awesome, thanks for confirming my suspicions.
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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