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Image formats

The resolving power of lenses is not infinitely scalable. Hence large image sensors are theoretically capable of greater optical resolution than small sensors. Larger sensors also have larger pixels, which means that they collect more light and give a better signal-to-noise ratio than small sensors.
     The resolution limiting factor is diffraction.  A larger format permits a longer focal length of the lens for a given field of view; and the physical aperture size, for a given illuminating power, is a function of the focal length. When correctly stated, an aperture value should be written as " f/n " (focal length divided by a number). If we consider a 50mm lens operated at say f/16, the diameter of the aperture is 50/16 = 3.125mm. If we use a small format digital camera, we might need to use a lens with a focal length of about 10mm to get the same view as would be obtained with a 50mm (normal perspective) lens on the 35mm (36 x 24mm) format. The 10mm lens operated at f/16 however will have an aperture diameter of 10/16 = 0.625mm. This places it at a disadvantage compared to the larger format camera, because light spreads out (diffracts) when it interacts with structures of comparable size to its wavelength. Diffraction is the reason why lenses do not give progressively more resolution as the aperture size is reduced, they give instead a peak in resolution at intermediate apertures, and lose resolution progressively as the aperture becomes smaller. The point is that, for a given field of view (and assuming that the number of pixels is not the limiting factor), a small format camera with its short focal-length lens will start to suffer from loss of resolution due to diffraction at a wider relative aperture than a large format camera with its long focal-length lens, i.e., while both cameras might be operating at the same relative aperture, say f/16, the small format camera will have a physical aperture of (say) 0.6mm, while the large format camera will have a physical aperture of 3.1mm. In fact, the diffraction problem is sufficiently pronounced with small-format compact cameras that most are not provided with the facility to use apertures smaller than f/8, whereas 35mm format, and near-35mm format digital cameras can be used at apertures as small as f/22 or even f/32 with suitable lenses.
     Shown below is a list of some of the commonly used formats.  The Four Thirds and larger formats are generally suitable for high-quality imaging applications.  High resolution lenses are needed in order to realise the capabilities of the full-frame 35mm format.  Crop-frame dSLR sensors are generally referred to as "APS-C", but this is not a format definition because the dimensions vary between manufacturers and sometimes vary between models from the same manufacturer.  

Format
(or chip size) 
Dimensions
/ mm
Format diagonal
(image circle diameter)
Normal perspective
focal length
= width of format ×√2
f
multiplier*
2¼" square
(medium format)
57.15 × 57.15 80.82mm 80.8mm (80mm) 0.54
35mm film full frame 36 × 24 43.27mm 50.9mm (50mm) 1
APS 25.1 × 16.7 30.15mm 35.5mm (35mm) 1.4
35mm film, cine 24 × 18 30mm 33.9mm (35mm) 1.4
Canon EOS D30,
D60, 10D ("APS-C")
22.7 × 15.1 27.26mm 32.1mm 1.6
Four Thirds 17.3 × 13 21.63mm 24.5mm 2
1" 12.8 × 9.6 16mm 18mm 2.7
CX (Nikon 1) 13.2 × 8.8 15.86mm 18.6mm 2.7
2/3" 8.8 × 6.6 11mm 12.4mm 3.9
1/1.7" 7.6 × 5.7 9.5mm 10.7mm 4.6
1/1.8" 7.18 × 5.32 8.94mm 10.2mm (10mm) 4.8
1/2" 6.4 × 4.8 8mm 9.1mm 5.4
1/2.7" 5.3 × 4.0 6.64mm 7.5mm 6.5
1/3" 4.8 × 3.6 6mm 6.8mm 7.2
1/3.2" 4.5 × 3.4 5.7mm 6.4mm 7.6
1/3.6" 4 × 3 5mm 5.7mm 8.7
1/4" 3.2 × 2.4 4mm 4.5mm 9.6
* focal length multiplier = 43.267 / (format diagonal)

c4040ccd 1/1.8" Bayer mosaic CCD sensor.
Illustration shows a 4M pixel device as used in the Olympus C-4040.
Format (imaging area) dimensions: 7.18 × 5.32 mm.
Focal length multiplier (for 35mm format equivalent lens) is 4.84

Focal length multiplier
The focal length multiplier or 'crop factor' is defined as:
c = diagonal of the 35mm format / diagonal of the actual format.

by Pythagoras:
35mm format diagonal = √( 36+ 24) = 43.2666 mm
Hence, for example, the EOS APS-C sensor with a diagonal of 27.26mm has a crop factor of:
c = 43.267 / 27.26 = 1.587
This means that a 20mm lens used on the camera gives an angle of coverage which is the same as that of a 20 × 1.587 = 31.7mm lens on the 35mm format.  Hence, for this particular format size, a 20mm lens is said to have a 35mm equivalent focal length of 32mm.



See also Wikipedia: image sensor format

D W Knight
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