* The MTF is thus the ratio of the image modulation to the
target modulation. If the contrast ratio, C, is I max/I min,
then
C+1
1-M
The MTF curve is plotted as a function of the spatial
frequency, with the values normalized to zero spatial fre
quency, The MTF of an aberration free, or aperture-limited,
lens is determined solely by the relative aperture and the
wavelength of the light, the general form being shown in
figure 4, For any aperture and wavelength combination there
is a definite cut-off point at a spatial frequency given by
♦ ; 4
R =
X (f-number)
10
X (f-number)
(cycles per mm)
cycles per mm where X^ s expressed in millimicrons. Higher
frequencies cannot pass through the aperture. The MTF of
actual lenses usually lies well below the theoretical MTF
for their aperture, especially off-axis, due to the residual
imperfectly-corrected abberations. The MTF of a typical
aerial mapping lens is shown in Figure 4. In general, as a
lens is stopped down its MTF approximates more closely to
the aperture limit, and may reach it at very small apertures.
Modulation Transfer Function for Emulsions
The emulsion MTF is defined as the Fourier Transform of
the spread function. Since the latter is isotropic, no phase
effects occur.
The spread function cannot be directly observed, and the
MTF is derived indirectly, using the concept of "effective
exposure". For example, sinusoidal targets are imaged on the
emulsion at known modulation, and after exposure the developed
images are traced with a microdensitometer, using a long enough
slit to average out the random density fluctuations due to
granularity "noise". It is then assumed that the H and D curve
applies to micro images, and the image density modulation is
transformed into apparent or effective exposure modulation by
known graphical methods. The MTF is then given by the ratio of
applied modulation to apparent or effective modulation in the
image at the time of exposure. Analogous methods can be used,
based on slit or edge esposures instead of sinusoidal expos
ures, The MTF of Plus X, a typical aerial emulsion, is
18 - "Normalization"
