Resolution of a circular aperture

In summary, the conversation discusses the Raleigh Criterion, which involves equations to determine the minimum angular resolution and separation distance for a circular aperture. The equations are given and explained with the help of a visual representation. The person seeking help expresses gratitude for the clarification.
  • #1
usfz28
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Just want to say hi. Iam new to the forum but here is my question. Today we were talking about resolution of a circular aperture and the instructor told us to make sure we know this he gave us some equations, but i see no examples of it in the book. could someone help me out? The equatuons he gave me were. theta(min)in rad.=1.22(lamda)/D and tan (theta(min)/2)=(d/2)/L
and theta(min)=2inverse(tan) (d/2)/(L). I didnt really understand what he was saying but he was talking about breaking it up into two right triangles. Thanks for any help you can give me or any examples!
 
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  • #2
Raleigh Criterion

These equations represent the "Raleigh Criterion" for the minimum angular resolution possible due to diffraction from a circular aperture:
[itex]\sin\theta_{min} = 1.22 \lambda/D[/itex] where D is the aperture diameter. (When the angle--in radians--is small, [itex]\sin\theta_{min} = \theta_{min}[/itex].)

To find the minimum separation distance that can be resolved, use some trig: [itex]\tan(\theta_{min}/2) = (d/2)/L[/itex], where d is the separation distance and L is the distance to the aperture. To understand the geometry involved, imagine this. Call the two points you are trying to resolve A and B. (The distance between them is d.) Now draw a line from the aperture (at X) to the midpoint (at M) between A and B. The right triangle A-M-X is what we are talking about. A-M = d/2; M-X = L; the angle at corner X is [itex]\theta_{min}/2[/itex]. (The two right triangles your professor spoke of would be A-M-X and B-M-X.)
 
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  • #3
Hey thanks for clearing it up! Big help!
 

What is the resolution of a circular aperture?

The resolution of a circular aperture is the smallest distance between two points that can be distinguished by a lens or optical system.

How is the resolution of a circular aperture calculated?

The resolution of a circular aperture is calculated using the Rayleigh criterion, which states that the resolution is equal to the wavelength of light divided by the numerical aperture of the lens.

What factors affect the resolution of a circular aperture?

The resolution of a circular aperture is affected by several factors, including the size of the aperture, the quality of the lens, and the wavelength of light being used.

What is the relationship between aperture size and resolution?

The resolution of a circular aperture is directly proportional to the size of the aperture. A larger aperture allows more light to enter the lens, resulting in a higher resolution.

Can the resolution of a circular aperture be improved?

Yes, the resolution of a circular aperture can be improved by using a lens with a larger numerical aperture, using a shorter wavelength of light, or using advanced imaging techniques such as adaptive optics.

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