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Chapter 3. Wave optics
where K c represents the cutoff value of K. No spatial frequencies
above this value are transmitted by the optical system. We notice
that a/f 2 is the tangent of the semiangle subtended by the pupil
at the Gaussian image plane. The modulation transfer function
(MTF) is plotted in Figure 3.15.
3.3.7 The wave front aberration function
An image point in the paraxial approximation is formed by a spherical wave converging on an ideal point in the Gaussian image plane.
With aberrations present, the image is blurred and displaced from
its ideal position. The aberrated image is formed by a wave which
is distorted from an ideal spherical wave.
This is shown schematically in Figure 3.16. An ideal spherical
wave front S i fills the angular acceptance cone of the aperture.
A ray emanates from every point along the wave front in a direction locally perpendicular to the wave front. These rays converge
to an ideal point in the Gaussian image plane, as shown by the
broken lines in the figure. The aberrated wave front S a is locally
displaced from the ideal wave front by a distance χ, which we designate the wave front aberration function. The rays emanting from
the aberrated wave front converge to a region which is blurred and
displaced from the ideal image point in general. These rays are depicted by the solid lines in the figure.
As discussed earlier, every optical system, however complicated,
can be analyzed in terms of an equivalent system consisting of two
ideal lenses. This is shown schematically in Figure 3.17. A point
object is located in an object plane at O. The object plane coincides with the front focal plane of the first lens L 1 . A physical
aperture is located at the back focal plane of the first lens L 1 ,
which coincides with the front focal plane of the second lens L 2 .
Chapter 3. Wave optics
where K c represents the cutoff value of K. No spatial frequencies
above this value are transmitted by the optical system. We notice
that a/f 2 is the tangent of the semiangle subtended by the pupil
at the Gaussian image plane. The modulation transfer function
(MTF) is plotted in Figure 3.15.
3.3.7 The wave front aberration function
An image point in the paraxial approximation is formed by a spherical wave converging on an ideal point in the Gaussian image plane.
With aberrations present, the image is blurred and displaced from
its ideal position. The aberrated image is formed by a wave which
is distorted from an ideal spherical wave.
This is shown schematically in Figure 3.16. An ideal spherical
wave front S i fills the angular acceptance cone of the aperture.
A ray emanates from every point along the wave front in a direction locally perpendicular to the wave front. These rays converge
to an ideal point in the Gaussian image plane, as shown by the
broken lines in the figure. The aberrated wave front S a is locally
displaced from the ideal wave front by a distance χ, which we designate the wave front aberration function. The rays emanting from
the aberrated wave front converge to a region which is blurred and
displaced from the ideal image point in general. These rays are depicted by the solid lines in the figure.
As discussed earlier, every optical system, however complicated,
can be analyzed in terms of an equivalent system consisting of two
ideal lenses. This is shown schematically in Figure 3.17. A point
object is located in an object plane at O. The object plane coincides with the front focal plane of the first lens L 1 . A physical
aperture is located at the back focal plane of the first lens L 1 ,
which coincides with the front focal plane of the second lens L 2 .