Studio delle prestazioni di un sistema a fosfori per mammografia ...

its direction is a constant function covering all the spatial frequency range. The image of a slit
is the so-called Line Spread Function.
2.2.1 Digital MTF
In a digital system, the sampling procedure usually leads to complication due to undersampling
in the MTF analysis since, as will be explained later, the system response depends on the spatial
frequency content of the images being evaluated. Undersampling in digital systems occurs
when the image is not sampled finely enough to record all spatial frequencies without aliasing.
Undersampling is almost always present to some degree in any real digital imaging device,
and not only makes the physical measurement of MTF more difficult but it also complicates the
proper understanding and interpretation of these quantitative measures. The main complications
are related to the fact that, when applying classical analysis to undersampled digital systems,
the MTF do not behave as transfer amplitude of a single sinusoid and the response of a digital
system to a delta function is not spatially invariant. There are two main elements distinguishing
the MTF of a digital system from that of an analog system: replication of FTs in frequency
space and the overlapping of FT segments from aliasing 1 when the system is undersampled.
While replication and aliasing overlap are certainly related, they are different in the effects they
have on the interpretation of MTF in undersampled digital systems. The replication of FTs
is a result of the infinite sum of sinusoids required to produce a signal comprised of a string
of infinitely sharp delta function, i.e. from multiplying the original function by the sampling
function � ¡ ÁÁÁ Ü� � . The overlap of these FT replications, on the other hand, is the result of
undersampling, by which aliasing causes sampled frequencies above the Nyquist frequency to
contaminate their counterpart frequencies below the Nyquist frequency (see Fig. 2.2).
In order to understand how these effects reflect quantitatively on the MTF, the terms con-
tributing to the system OTF must be considered. The OTF of a digital system is comprised
of a presampling component and a sampled component. The presampled OTF is the result of
image blurring from geometric considerations (for instance focal spot blurring), analog input
1aliasing is so named because a sampled sinusoid of frequency¡Ù above the Nyquist frequency Ù Æ is identical
in every regard to a sampled sinusoid of frequency ¡Ù below Ù Æ (if at the same phase); thus the higher-frequency
sinusoid takes the alias of the lower frequency.
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