Technical note discusses optical system properties quantified by the Modulation Transfer Function (MTF).
Up to this point, this discussion has considered the performance of the optical system only in terms of image location. Another factor is the resolution of a system, normally specified in terms of the finest detail that can be imaged by the system. This property is quantified by the Modulation Transfer Function (MTF). An object whose brightness (I) varies sinusoidally with a frequency of (L) lines/mm is imaged through the optical system. Referring to Figure A below, the modulation of the object (Mo) is defined as:
Mo = (Imax – Imin)/(Imax + Imin),
where Imax = maximum intensity,
min = minimum intensity.
The image can be measured using the same procedure, where modulation of the image (Mi) is defined as
Mi = (Imax – Imin)/(Imax + Imin).
Then, the modulation transfer factor is given by the ratio of the modulation of the image to that of the object:
modulation transfer factor = Mi/Mo.
The modulation transfer factor varies with the frequency of the sinusoidal grating. The frequency at which the modulation transfer factor falls below a minimum detectable level is called the limiting resolution of the system. The Modulation Transfer Function curve is a plot of the modulation transfer factors at various spatial frequencies (see Figure B). The total aberration of a lens or lens system degrades the image contrast and causes the MTF to decrease.
Determination of system resolution