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2 THEORY
The optical transfer function (OTF) of a linear system is given
by the Fourier transformation of its line spread function (LSF).
Thus, the OTF of one coordinate x, is given by
Oo
F(£)2.[ 1G)-expjizu£xlax (1)
-0
Where f is spatial frequency and L(x) is the intensity distri-
bution in the image of a line object formed by the optical system
under test. Then the MTF and the phase transfer function (PTF) are
given by += 5 3
MTF (f)z§Re” (F(£) )+ Im" (F(£)) (2)
PTF (f)=tan © Im(F(£)) (3) ®
Re(F(£))
Where Re and Im denote Real and Imaginary parts respectively.
When the line spread function is measured for discrete sampling points,
Eq(1) is calculated by discrete Fourier transformation.
N
F(fi)e E L(xy) expfi 2W£jxy ] (4)
k=| N
To ensure the obtaining of accurate MTF in our system, we must
get correct data of LSF from its direct measurement and minimize the
error caused by calculation of Fourier transformation using a suitable
algorithem.
MTF is a measure of lens performance as contrasted by transfer
capability from object to image with respect to different spatial
frequencies. Usually low frequency objects are well reconstructed
in images; high frequency objects have poor image appearance; and
the degree of high frequency degradation is different from one lens T
to another. : |
The resolving power corresponds to a spatial frequency
.Where MTF approaches zero for one specific lens. From this point
of view, one can say that resolution tests look at only one point
on an MTF curve instead of full contrast information of MTF from
the low to high frequency regions.
Furthermore, MTF has an advantage in a cascading system of
different imaging elements, e.g. a combination of lens and film,
as a product of each MTF with respect to spatial frequencies.
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3. INSTRUMENT
The principle of our method is based on a digital Fourier
transformation of the photo-electrically measured line spread functions.