Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 23

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

0 012345
ω x /π x 0

6789 0

FIGURE 2.2 MTF of uniform motion in x-direction.

The previous discussion is fairly general in the sense that it applies to imaging
systems with nonsymmetrical PSF too. However, in many practical systems, such as
the lens and the optics of a digital camera, printer, or scanner, the PSF is rotationally
invariant or circularly symmetric. In such cases,

the previous analysis can be

simpli ed. Now, we consider a circularly symmetric imaging system. The PSF of

such a system is 1-D and is given by

p

x 2 h ( r ) ¼ h þ y 2 ( 2 : 16 )

where r is the radial distance. The OTF of this system like its PSF is circularly
symmetric. To show this, consider

1 1

h ( x, y ) e j (v x x þv y y ) d x d y H (v x , v y ) ¼

1 1

1 1

p

x 2

Þ e j (v x x þv y y ) d x d y

¼ h ð þ y 2 ( 2 : 17 )

1 1

Using polar coordinates, Equation 2.17 can be rewritten as

ð 1

2 p

h ( r ) e j (v x r cos uþv y r sin u) r d r du

H (v x , v y ) ¼ ( 2 : 18 )

0 0