Luke's variational principle

Optical format is a hypothetical measurement approximately 50% larger than the true diagonal size of a solid state photo sensor . The use of the optical format means that a lens used with a particular size sensor will have approximately the same angle of view as if it were to be used with an equivalent sized camera tube where the actual sensitive target is smaller than the overall size.

The optical format is approximately the diagonal length of the sensor multiplied by 3/2 The result is expressed in inches and is usually (but not always) rounded to a convenient fraction. For instance, a 6.4x4.8 mm sensor has a diagonal of 8.0 mm and therefore an optical format of 8.0*3/2 = 12 mm, which is expressed to the convenient imperial fraction of 1/2 inch. The reason why it is expressed in inches is historical: a standard four thirds inch image sensor has an image area with a diagonal measurement of approximately Template:Convert. Therefore a 1 inch sensor has approximately a 16 mm diagonal, a 1/2 inch sensor has approximately an 8 mm diagonal, etc.

For larger systems the size is usually given as the true rectangular dimensions of the imaging sensor in millimeters, such as 36 x 24 mm in the case of 35 mm film sized sensors.

Many image device sheets don't list the actual optical format, but do list the size of their pixels in terms of micrometers, a more helpful equation is to convert the pixel size, and array size, directly to optical format. The equation for this is:

$OF=\frac{p\sqrt{w^2+h^2}}{16000}$

with:

• w = width of array (in pixels)
• h = height of array (in pixels)
• p = pixel size (micrometers)

References

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