Diffraction limit on resolution on camera lens

In summary, spy planes fly at high altitudes to avoid interception and have cameras that can discern features as small as 5.48 cm. To achieve this resolution, the minimum aperture of the camera lens must be 0.241m, taking into account a factor of 1.22 for circular apertures. The computation for this factor involves complicated mathematical integrals. However, it can be found in optics textbooks such as "Optics" by Blaker & Rosenblum.
  • #1
lovelylm1980
18
0
Spy planes fly at extremely high altitudes (24.0 km) to avoid interception. Their cameras are reportedly able to discern features as small as 5.48 cm. What must be the minimum aperture of the camera lens to afford this resolution? (Use lambda = 550 nm.)

This problem is unfamiliar to me, I'm not sure if the eqtion I used is correct

a= lambda*length/d= (550e-9m)*(24e+3m)/5.48e-2m= 0.241m
 
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  • #2
Go to your text and look up "Rayleigh Criterion."
YOu have the general idea already, but for circular aperatures, there is a factor of 1.22 that is multiplied to the wavelength.

By the way, anyone, where does this 1.22 come from?
 
  • #3
got it thanks:smile:
 
  • #4
The given expression is the radius of the first dark ring in the Fraunhofer diffraction pattern for circular aperture.

The computation involves summing intensity contributions from each point of the aperture accounting for path length differences.

In Optics by Rossi 6 pages are committed to doing this computation for a rectangular aperture. For a circular aperture he simply presents the results and comments
The theory of Fraunhofer diffraction by a circular aperture requires more elaborate mathematical computations then that of the Fraunhofer diffraction by a rectangular aperture
 
  • #5
Integral said:
In Optics by Rossi 6 pages are committed to doing this computation for a rectangular aperture. For a circular aperture he simply presents the results and comments

So the math involve in producing this factor of 1.22 is absurdly difficult?
 
  • #6
Chi Meson said:
So the math involve in producing this factor of 1.22 is absurdly difficult?

I do not think it is absurdly difficult, it requires setting up and evaluating an involved integral. Rossi must have felt that going through the process for the simpler case, of a rectangular aperture, was more productive then doing the same math only more difficult integrals.

I am sure that if you searched through enough optics texts you will find it worked out some where.

I have the tools to figure it out in Rossi, but frankly it would take more time then I have to commit to it now.
 
  • #7
I found it in my Blaker & Rosenblum textbook "Optics." It comes from the Fraunhoffer diffraction integral after it is crammed through a 2-dimensional Fourier transform. TO me, it looks nasty. There was a day I could blunder my way through it, but ... the sun went down.
 
  • #8
Chi Meson said:
I found it in my Blaker & Rosenblum textbook "Optics." It comes from the Fraunhoffer diffraction integral after it is crammed through a 2-dimensional Fourier transform. TO me, it looks nasty. There was a day I could blunder my way through it, but ... the sun went down.

My thoughts exactly. We have some common ground!
 

1. What is the diffraction limit on resolution on a camera lens?

The diffraction limit on resolution on a camera lens refers to the maximum level of detail that can be captured by the lens. It is determined by the size of the lens aperture and the wavelength of light being used. When the aperture is too small, diffraction occurs, causing a loss of sharpness and detail in the image.

2. How does the diffraction limit affect the quality of photographs?

The diffraction limit can have a significant impact on the quality of photographs. When the limit is reached, the image becomes less sharp and detailed, resulting in a decrease in overall image quality. This is especially noticeable in images with fine details or small subjects.

3. Can the diffraction limit be overcome?

The diffraction limit is a physical limitation and cannot be completely overcome. However, certain techniques such as using larger apertures and reducing the wavelength of light (e.g. using UV filters) can help minimize its effects and improve the overall sharpness of the image.

4. How does the diffraction limit differ between different camera lenses?

The diffraction limit can vary between different camera lenses, depending on their design and maximum aperture. Generally, lenses with larger apertures and higher quality glass will have a higher resolving power and a higher diffraction limit than smaller, cheaper lenses.

5. Can post-processing software help overcome the diffraction limit?

While post-processing software can help improve the overall quality of an image, it cannot fully overcome the effects of the diffraction limit. In some cases, sharpening tools in editing software can actually highlight the diffraction effects, making the image appear even less sharp. It is best to try to minimize the effects of diffraction during the actual photo capture process rather than relying on post-processing.

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