Page 195 - Phase Space Optics Fundamentals and Applications

176 Chapter Five

j(x, y)
x x x m
y n y y

n y

x W(x, n) A(m, y) m

m x m m
n n J(m, n) n y

FIGURE 5.7 Same as Fig. 5.4, but for the mutual intensity and the mutual
spectrum.

5.5 Noncoherent Imaging Systems
Under noncoherent illumination, a space-invariant optical system is
2
represented by the noncoherent impulse response |q(x)| = h(x). Ex-
ceptforanormalizationfactor,theFouriertransformof h(x) isdenoted
as the optical transfer function (OTF), H( ). The modulus of the OTF,
|H( )|, is known as the modulation transfer function (MTF). Next, we
analyze the impact of focus errors on the MTF of an optical proces-
sor working under noncoherent illumination. Hence, the generalized
pupil function of the optical system is

2
W 2,0
Q( ; W 2,0 ) = T( ) exp i2 (5.27)

In Eq. (5.27), T( ) is the complex amplitude transmittance of a mask
located over the pupil aperture. We denote as W 2,0 the wavefront aber-
ration coefficient for describing focus error. 16−18 Consequently, except
for a normalization factor, the out-of-focus MTF is

|H( ,W 2,0 )|

∞

2W 2,0
= T + T ∗ − exp i2 d (5.28)
2 2 2

−∞