MODULATION TRANSFER FUNCTION (MTF)
Let us assume an ideal lens and a photographic scene which is composed of many different coarse and fine structures, e. g. a distribution of broad and fine line elements of intensity variations. ln this situation, the hypothetical, ideal lens will produce an image which reproduces the object faithfully. More precisely, this means that the spatial variation of density in the image is an exact representation of the intensity modulation in the object, regardless of the width of the lines.
We have been discussing an ideal situation, which, for physical reasons, cannot be realized. ln reality, coarse lines can be reproduced more easily than fine lines, and coarse lines can be reproduced with a higher modulation (contrast) than fine lines. We refer to this spatial variation (coarse and fine) by the number of line pairs per millimeter, either at the subject, or the image.
Modulation Transfer function (MTF) compares the remaining modulation in the image plane with the original object. The result is expressed in percent, as a function of spatial frequency (lp/mm), see figure on the right.
lt is apparent that the modulation transfer decreases when the spatial frequency increases. At some point, as the spatial frequency increases, the modulation will be zero. The modulation transfer function of the lens should be high over the entire region of spatial frequencies which is to be considered. The upper Limit, of spatial frequency, for a particular application is dependent upon the particular constellation of factors such as film/CCD formal size, film/CCD type, lens aperture, and desired performance.
A single MTF graph, done in the customary fashion, is representative of a small image area which could be anywhere within the image, but typically is done on axis, and at intervals up to the image diagonal. To evaluate the performance of a lens over its entire image circle, one would have to examine a large number of MTF graphs.
Consequently, we often use another method of graphic representation for MTF. This method shows the modulation transfer as a function of image height, for a few meaningful spatial frequencies. Because it is relatively easy to evaluate the overall image performance of a lens, when viewing this type of graph, Schneider-Kreuznach uses this method of representation in it's data sheets.
Of course, it couldn't be quite as simple as that; a further characteristic of the imaging process is the fact that a beam of rays emerging from a lens, exhibits differing properties, dependent on its incidence angles. What this means, in a very practical way, is that object patterns with different orientations for example perpendicular to each other, will reproduce differently.
Therefore, it is necessary to select more than one orientation of the test pattern used in evaluation, to be sure of an accurate evaluation of the lens. Under normal circumstances, it will be sufficient to select two mutually perpendicular Orientations of line elements, as illustrated in the figure on the right.
There will therefore be two different sets of MTF data representing radial and tangential orientation of test patterns. ln our diagrams, the MTF for the tangential orientation will be shown in dashed lines.
lt is possible to use a lens in a variety of ways, and this can affect the performance of the lens, as represented by the MTF data. ln particular the image magnification, and aperture at which the lens is used, have a large effect on the performance of a lens.
For a particular optical system, there is always a theoretical limit to performance. This limit also depends on the field angle which is important for wide angle systems. Generally there will be a decrease in MTF values with the cosine of the field angle (for the radial orientation) and with the third power of cosine of the field angle for tangential orientation.
The figure on the left gives an example of a diffraction limited (perfect) optical system for 20 lp/mm at f-22, as a function of field angle.
