Page 164 - Phase Space Optics Fundamentals and Applications

The Radon-Wigner Transform 145

where x ,y , and z are three spectral sensitivity functions associated
with the measured chromaticity. These functions depend, obviously,
on the specific color detector actually used. In the case of a conven-
tional digital color camera, these channels can be associated with the
R, G, and B bands of the three pixel families in the detector array.
On the other hand, when a visual inspection of the final image is
considered, these sensitivity functions are the well-known spectral
tristimulus values of the human eye. 49
Equations (4.91) establish the formulas to describe completely the
response of a system from a spatial-frequency point of view. To
numerically compute the functions described there, the evaluation
of the monochromatic OTFs for a sufficient number of wavelengths
inside the illumination spectrum has to be performed. Since any of
these monochromatic transfer functions can be obtained from a same
single RWD, as stated in the previous section, these computations can
be done in a much more efficient way by use of this two-dimensional
display. Furthermore, the same imaging system (i.e., the same pupil
function) but suffering from different longitudinal chromatic aberra-
tion can be assessed as well, with no additional computation of the
RWD. This is a critical issue in the saving of computation time which
provides this technique with a great advantage compared to other
classic techniques, as cited above.
To illustrate this technique, we present the result of the computa-
tion of the polychromatic OTFs associated with a conventional one-
dimensional clear-pupil optical system (slit of width h) but suffering
from two different chromatic aberration states (systems I and II from
now on), as shown in Fig. 4.23. We assume that no other aberrations

2.0
Longitudinal chromatic aberration δW 20 (μm) coefficient: –1.0
1.0

0.0

–2.0
–3.0
–4.0
System II
–5.0 System I
400 500 600 700
Wavelength: λ (nm)

FIGURE 4.23 Longitudinal chromatic aberration coefficient associated with
the two different correction states of the system under study.