Diffraction

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.

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^-4mm. The resulting formula is:

$pixelresolution={\frac {FoV}{asin\left({\frac {1}{1490*D}}\right)}}\,\!$ 

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):

          2.8      4     5.6       8      11      16      22    32    44
  50      464    325     232     163     118      81      59    41    30
 100      929    650     464     325     236     163     118    81    59
 200    1,858  1,300     929     650     473     325     236   163   118
 400    3,715  2,601   1,858   1,300     946     650     473   325   236
 800    7,430  5,201   3,715   2,601   1,891   1,300     946   650   473
1200   11,145  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