### Modulation Transfer Function

Another concept that may be new to neophyte vision people is that of modulation transfer function.

Most lenses including the human lens are not perfect optical systems. As a result when visual stimuli are passed through them they undergo a certain degree of degradation. The question is how can this degradation be evaluated? Before we can answer this question we need to define "modulation."

Recall in a square wave grating there were dark bars and light bars. We can measure the amount of light coming from each. The maximum amount of light will come from the light and the minimum from the dark bars. If the light is measured in terms of luminance (L) we can define modulation according to the following equation:

modulation = (Lmax - Lmin ) / (Lmax + Lmin)

where Lmax is the maximum luminance of the grating and Lmin is the minimum. When modulation is defined in terms of light it is frequently referred to as Michelson contrast. Indeed when one takes the ratio of the illumination from the light and dark bars one is measuring contrast.

Now, let's assume that you have a square wave grating of a specific frequency (v) and modulation (contrast) and this stimulus is passed through a lens. The modulation of the image can now be measured.

The modulation transfer function (MTF) is defined as the modulation, Mi, of the image divided by the modulation of the stimulus ( the object), Mo, as shown in the following equation.

MTF(v) = Mi / M0

A lens system may behave differently depending on the nature of the optical information that passes through it. For example, lens systems vary as a function of the spatial frequency of the stimuli that they handle. You undoubtedly noticed, above, that MTF has spatial frequency (v) as a parameter. Click on image modulation as a function of spatial frequency to see a graphical illustration of how the transfer function of a lens effects the image modulation.