210
Chapter 3. Wave optics
Constructive interference occurs when the path difference between
neighboring rays is an integral number of wavelengths. This can
be seen in the figure, where the surfaces of constant phase form
concentric spheres centered on each object point. All object points
are assumed to radiate coherently with respect to each other.
3.3.5 Optical transformation for a general
imaging system with coherent illumination
In the preceding analysis, we obtained the optical transformation
for a simple system in two specific configurations, each employing
of a single lens with focal length f . This was done for the formation
of an image, and separately, formation of a diffraction pattern. We
assumed perfectly coherent illumination, where a constant phase
relationship exists between all points of the object, and the illumination is monochromatic. The basic optical elements are a drift
length, a thin lens, and a pupil. In principle, these can be applied
in any order, and to any degree of complexity, to build up an arbitrary optical system. Given these mathematical tools, we are now
in a position to consider a general imaging system, consisting of
an arbitrary configuration of optical elements. In this section and
the next, we closely follow the analysis of Goodman [36].
We require only that an image be formed. Here the object is represented by a complex amplitude u O (r O ), and the image is represented by a complex amplitude u I (r I ). The relevant qantity of
physical interest is |u I (r I )|
2 , which is the intensity measured in
the image plane z I . We seek an optical transformation which expresses u I in terms of u O . Such a transformation would contain
all of the physically relevant information about the quality of the
Chapter 3. Wave optics
Constructive interference occurs when the path difference between
neighboring rays is an integral number of wavelengths. This can
be seen in the figure, where the surfaces of constant phase form
concentric spheres centered on each object point. All object points
are assumed to radiate coherently with respect to each other.
3.3.5 Optical transformation for a general
imaging system with coherent illumination
In the preceding analysis, we obtained the optical transformation
for a simple system in two specific configurations, each employing
of a single lens with focal length f . This was done for the formation
of an image, and separately, formation of a diffraction pattern. We
assumed perfectly coherent illumination, where a constant phase
relationship exists between all points of the object, and the illumination is monochromatic. The basic optical elements are a drift
length, a thin lens, and a pupil. In principle, these can be applied
in any order, and to any degree of complexity, to build up an arbitrary optical system. Given these mathematical tools, we are now
in a position to consider a general imaging system, consisting of
an arbitrary configuration of optical elements. In this section and
the next, we closely follow the analysis of Goodman [36].
We require only that an image be formed. Here the object is represented by a complex amplitude u O (r O ), and the image is represented by a complex amplitude u I (r I ). The relevant qantity of
physical interest is |u I (r I )|
2 , which is the intensity measured in
the image plane z I . We seek an optical transformation which expresses u I in terms of u O . Such a transformation would contain
all of the physically relevant information about the quality of the