# Difference between revisions of "Diffraction"

Erik Krause (talk | contribs) m (→Resolution: clarified) |
(Fixed math bug. Original formular by Erik) |
||

Line 13: | Line 13: | ||

==Resolution== | ==Resolution== | ||

The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm. The resulting formula is: | The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm. The resulting formula is: | ||

− | + | <math> pixel resolution = \frac{FoV}{asin\left(\frac{1}{1490*D}\right)}</math> | |

+ | |||

''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in '''pixels/degree''' which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors: | ''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in '''pixels/degree''' which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors: | ||

'''2.8 4 5.6 8 11 16 22 32 44''' | '''2.8 4 5.6 8 11 16 22 32 44''' |

## Revision as of 14:44, 27 December 2010

## What it is

Diffraction in general is the bending of waves around an obstacle. In photography the light waves are bent around the edges of the aperture, causing f.e. the well known star like pattern around the sun if shot stopped down. Since diffraction affects any point of the image (not only very bright sources) it reduces general sharpness and limits effective resolution. Diffraction blurs any point to a pattern called "w:Airy disk".

## Sharpness

Diffraction is one of three factors limiting the image sharpness. Second is aberration (f.e. chromatic aberration) which is determined by lens build quality. Third is de-focus or Depth of Field.

Diffraction depends only on the physical aperture size. Hence it's effect is generally larger the smaller the used sensor is due to the larger magnification of the image. That's the reason why compact cameras can't (or shouldn't) be stopped down further than f/5.6. As a rule of thumb the limit for APS-C sized sensors is f/8 to f/11 and for full frame ones f/16 to f/22.

You can balance Depth of Field against diffraction. An approach is the sharpest aperture. See link at the bottom.

## Resolution

The maximum obtainable resolution is limited by diffraction according to the Rayleigh criterion. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama Field of View (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light *λ* = 550nm = 5.5*10^{-4}mm. The resulting formula is:

*D* is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in **pixels/degree** which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors:

2.8 4 5.6 8 11 16 22 32 4450464 325 232 163 118 81 59 41 30100929 650 464 325 236 163 118 81 592001,858 1,300 929 650 473 325 236 163 1184003,715 2,601 1,858 1,300 946 650 473 325 2368007,430 5,201 3,715 2,601 1,891 1,300 946 650 473120011,145 7,802 5,573 3,901 2,837 1,950 1,418 975 709

Some usage examples

- You want to shoot a gigapixel panorama of 175° width with a 800mm lens at f/11. You get 175*1,891 = 330,925 pixel maximum horizontal resolution.
- You will use an APS-C format sensor in portrait orientation for this panorama. A 800mm lens has a FoV of 1.1° in that case, which at f/11 gives 2080 pixels or app. 6 megapixels. Applying the 70% rule to compensate for bayer interpolation blur indicates that 12 megapixels per image are enough.

## External links

- wikipedia on Diffraction
- wikipedia on Angular resolution
- Ken Rockwell's page on Selecting the Sharpest Aperture