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

wave object � �� � , oscillating with spatial frequencies �� and �� and amplitude � around a
constant value �:
� �� � �� ¡ � � � � �� ���
� (2.11)
A highly useful parameter in evaluating the performances of a system is the contrast or modu-
lation Å, defined by:
Å � �Ñ�Ü �Ñ�Ò
�Ñ�Ü �Ñ�Ò
� ��� (2.12)
The image of the object trough the system can be calculated, in the linear space invariant system
approximation, as:
� Ü� Ý �
� �
� �£
� �£
�£
� �
� Ü �� Ý � ¡ � �� � ���� (2.13)
� �
� �
ÈË� Ü �� Ý � � � � � �� ��� ����
ÈË� Ü �� Ý � ����
ÈË� Ü �� Ý � � � � � � � Ü �� � Ý � � � � �Ü ��Ý ���� �£
where £ is the gain of the system. After a change in the integration variables � � Ü � and
� � Ý �, the same expression is:
� Ü� Ý ��£� � � � �Ü ��Ü
� �
ÈË� �� � � � � � �� ��� ���� �£ (2.14)
The integral is the Fourier transform of the PSF and is usually referred to as OTF (Optical
Transfer Function). The OTF is thus defined as the Fourier transform of the output of a system
which has a delta function as its input. The OTF is two-dimensional for a two-dimensional
image, but for simplicity of nomenclature only the one-dimensional case will be considered
here. With a last change of variables �Ü � �� and �Ý � ��, the image � Ü� Ý can be written as:
� � �ÜÜ �ÝÝ
� Ü� Ý ��£ÇÌ� �Ü��Ý �
�£ (2.15)
It appears that the image of a sinusoid is still a sinusoid and, as it could be expected from the
system linearity, with the same spatial frequency of the object; but the amplitude depends both
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