116 |
3.1.6 Geometrical optics |
[Ref. p. 131 |
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x
y1
1
1
x1 |
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z |
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y |
Fig. 3.1.35. Three-dimensional ray in the input plane I. |
transposition of the matrix and I the identity matrix [86Sie, 05Hod]. The matrix S contains at most 10 independent parameters [76Arn, 86Sie, 05Hod].
In Table 3.1.15 general ray-transfer matrices are given.
3.1.6.2.5 General astigmatic system
A general astigmatic system can be generated by two cylindrical lenses with their axes non-parallel and non-orthogonal, separated by a distance L: SGA = R−1 Scyl,1 R SL Scyl,2 .
3.1.6.2.6 Symplectic optical system
Symplectic optical systems in the paraxial range can be described by the formalism of the symplectic geometry [03Wal]. They can be generated by a finite number of cylindrical and spherical lenses separated by free spaces. The mathematical formulation is connected with the matrix properties given in Sect. 3.1.6.2.4. For theoretical foundation and practical calculations see [64Lun, p. 216], [83Mac, 85Sud, 86Sie, 99Gao, 05Gro1, 05Hod].
3.1.6.2.7 Misalignments
The geometric optical calculations of misalignments with matrix techniques require, generally, higher dimensional matrices [05Gro1, p. 51], for example 3 × 3-matrices [86Sie] or 4 × 4-matrices [85Wan] for two-dimensional problems or 6 × 6-matrices for three-dimensional problems [76Arn].
Landolt-B¨ornstein
New Series VIII/1A1