mr 
EEE CE PER 
EE A 3 Em - 
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. 
3 
3. INSTRUMENT 
The principle of our method is based on a digital Fourier 
transformation of the photo-electrically measured line spread functions.