Page 163 - Phase Space Optics Fundamentals and Applications

144 Chapter Four

underpolychromaticillumination.Infact,thepropergeneralizationof
the OTF-based description to this broadband illumination case allows
one to define quality criteria for imaging systems working with color
signals. 44,45 This extension presents, however, some difficulties. The
direct comparison of the incoming and the outgoing polychromatic
irradiance distributions does not allow, in general, a similar relation-
ship to the monochromatic case to be established. It can be shown,
in fact, that only when the input signal is spectrally uniform can the
frequency contents of both signals be related through a single poly-
chromatic OTF function, providing the imaging system does not suffer
from any chromatic aberrations regarding magnification. 46,47 Under
these restrictions, a single polychromatic OTF can be used for relat-
ing input and output polychromatic irradiances in spatial-frequency
space. This function is defined as

H ( ; W ( ))S( )V( ) d

20

H( ; W 20 ) = (4.89)
S( )V( ) d

where and S( ) are the spectral range and the spectral power of the
illumination, respectively. The function V( ) represents the spectral
sensitivity of the irradiance detector used to record the image. Note
also that a new wavelength-dependent defocus coefficient has been
defined, to account for the longitudinal chromatic aberration W 20 ( )
that the system may suffer from, namely,
W ( ) = W 20 + W 20 ( ) (4.90)

20
where W 20 is the defocus coefficient defined in the previous section.
This OTF cannot account, however, for the chromatic information
of the image, since only a single detector is assumed. 48 Indeed, by fol-
lowing the trichromacy of the human eye, three different chromatic
channels are usually employed to properly describe color features in
irradiance distributions, and, consequently, three different polychro-
matic OTFs are used, namely, 44,45

H ( ; W ( ))S( )x d

20

H X ( ; W 20 ) =
S( )x d

H ( ; W ( ))S( )y d
20

H Y ( ; W 20 ) = (4.91)
S( )y d

H ( ; W ( ))S( )z d

20

H Z ( ; W 20 ) =
S( )z d