Image Sensor Format - Sensor Size and Diffraction

Sensor Size and Diffraction

The resolution of all optical systems is limited by diffraction. One way of considering the effect that diffraction has on cameras using different sized sensors is to consider the modulation transfer function (MTF) due to diffraction, which will contribute a factor to the overall system MTF along with the other factors, typically the MTFs of the lens, anti-aliasing filter and sensor sampling window. The spatial cut-off frequency due to diffraction through a lens aperture is

where λ is the wavelength of the light passing through the system and N is the f-number of the lens. If that aperture is circular, as are (approximately) most photographic apertures, then the MTF is given by

for and for The diffraction based factor of the system MTF will therefore scale according to and in turn according to (for the same light wavelength).

In considering the effect of sensor size, and its effect on the final image, the different magnification required to obtain the same size image for viewing must be accounted for, resulting in an additional scale factor of where is the relative crop factor, making the overall scale factor . Considering the three cases above:

For the 'same picture' conditions, same angle of view, subject distance and depth of field, then the F-numbers are in the ratio, so the scale factor for the diffraction MTF is 1, leading to the conclusion that the diffraction MTF at a given depth of field is independent of sensor size.

In both the 'same photometric exposure' and 'same lens' conditions, the F-number is not changed, and thus the spatial cutoff and resultant MTF on the sensor is unchanged, leaving the MTF in the viewed image to be scaled as the magnification, or inversely as the crop factor.