224
Chapter 3. Wave optics
2
,
/
/
$
Figure 3.17: Equivalent confocal system.
function χ can be regarded as a function of transverse coordinates
(x A , y A ) in the aperture plane A.
The product kχ is the phase shift associated with the aberration,
where k is the wave number given by k = 2π/λ. For a well-designed
optical system χ is a small fraction of the wavelength λ. Equivalently, the phase shift due to aberrations is much less than 2π. All
information about the aberrations is contained in the wave front
aberration function χ. This is discussed in many books [11], [16],
[67].
In the equivalent confocal system we consider the aberration to
be entirely introduced in the aperture plane as an abrupt phase
shift. This is conceptually equivalent to introducing a thin phase
plate in the aperture plane, which shifts the phase by an amount
kχ. This is depicted in Figure 3.17.
The wave front aberration χ(x A , y A ) is a scalar function defined
in a plane. Assuming a round aperture, the function χ can in
principle be expanded in a series of Zernike polynomials. Zernike
polynomials are orthonormal functions defined on the unit disk
0 ≤ ρ ≤ 1, where (ρ, φ) are polar coordinates in a plane. Here ρ is
defined as the radial ray position in the aperture plane divided by
Chapter 3. Wave optics
2
,
/
/
$
Figure 3.17: Equivalent confocal system.
function χ can be regarded as a function of transverse coordinates
(x A , y A ) in the aperture plane A.
The product kχ is the phase shift associated with the aberration,
where k is the wave number given by k = 2π/λ. For a well-designed
optical system χ is a small fraction of the wavelength λ. Equivalently, the phase shift due to aberrations is much less than 2π. All
information about the aberrations is contained in the wave front
aberration function χ. This is discussed in many books [11], [16],
[67].
In the equivalent confocal system we consider the aberration to
be entirely introduced in the aperture plane as an abrupt phase
shift. This is conceptually equivalent to introducing a thin phase
plate in the aperture plane, which shifts the phase by an amount
kχ. This is depicted in Figure 3.17.
The wave front aberration χ(x A , y A ) is a scalar function defined
in a plane. Assuming a round aperture, the function χ can in
principle be expanded in a series of Zernike polynomials. Zernike
polynomials are orthonormal functions defined on the unit disk
0 ≤ ρ ≤ 1, where (ρ, φ) are polar coordinates in a plane. Here ρ is
defined as the radial ray position in the aperture plane divided by