By Virendra N. Mahajan

This e-book discusses the features of a diffraction photograph of an incoherent or a coherent item shaped through an aberrated imaging approach. Numerical leads to aberrated imaging were emphasised to maximise the sensible use of the fabric. This new, moment printing contains a variety of updates and corrections to the 1st printing. starting with an outline of the diffraction concept of photo formation, theRead more...

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**Extra info for Optical imaging and aberrations**

**Example text**

Unapodized Pupil A system with a pupil that is uniformly illuminated is said to be unapodized. For r such systems, G rp is a constant varying inversely with the distance zo of the entrance r pupil from the object. For an unapodized pupil, let A rp be equal to a constant, say, A0 . r If we redefine ri , as illustrated in Figure 1-5, as the position vector of an image point Pi r r with respect to the Gaussian image point rg = M rj when the image is observed in the r Gaussian image plane, or with respect to the corresponding point zi zg rg (where the line joining the center of the exit pupil and the Gaussian image point intersect the defocused image plane) if it is observed in a defocused image plane at a distance zi from the plane of the exit pupil, Eq.

Thus, the PSF is shift invariant in the sense that its form does not change as the object point is shifted; only its location changes by virtue of r it being centered at rg . Accordingly, Eq. (1-52) for the irradiance distribution of the image of an isoplanatic incoherent object may be written r ( Ii ( ri ; zi ) = d Sen zo2 ) r r r , (1-56a) ) 0 B (rr M ) PSF (rr < rr ; z ) d rr (1-56b) object ( = d Sen zo2 M 2 = r 0 B ( ro ) PSF ( ri < M ro ; zi ) d ro r g r 0 Ig ( rg ) PSF ( ri r i ) r < rg ; zi d rg g i g , (1-56c) where we have made use of Eq.

The conditions that the distances zi and zg be much greater than the sizes of the pupil and the image, and the condition of Eq. (145) under which these approximations are valid may be referred to as Fresnel conditions. The integral in Eq. (1-49) is called the Fresnel diffraction integral of the pupil function r r P rp ; ro and represents the diffraction pattern of the aberrated pupil in a defocused image plane. Similarly, when zi = zg , it is called the Fraunhofer diffraction integral and represents the Fraunhofer diffraction pattern of the aberrated pupil in the Gaussian image plane.