Paraxial Optics for Axis-Symmetrical Systems

  • Psang Dain LinEmail author
Part of the Springer Series in Optical Sciences book series (SSOS, volume 178)


Conventional paraxial optics, which is sometimes known as Gaussian optics or first-order optics, uses the \( 2 \times 2 \) matrices as first estimates of meridional rays in early design stages of 2-D axis-symmetrical optical systems [1, 2]. In order to extend conventional paraxial optics for 3-D systems containing prisms, we have presented the \( 6 \times 6 \) matrices obtained from the first-order Taylor series expansion to approximate skew-ray tracing equations [3]. We shall begin this chapter by modifying the \( 6 \times 6 \) matrices of [3] to be applicable only to axis symmetrical systems. The obtained matrices are used to determine the cardinal points for an optical system. The imaging equations for multi-surface system are derived next.


Optical Axis Focal Length Principal Plane Thin Lens Aspherical Surface 
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    A. Gerrard, J.M. Burch, Introduction to Matrix Methods in Optics (Wiley, New York, 1975)Google Scholar
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    A.E. Attard, Matrix optical analysis of skew rays in mixed systems of spherical and orthogonal cylindrical lenses. Appl. Opt. 23, 2706–2709 (1984)ADSCrossRefGoogle Scholar
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    P.D. Lin, C.K. Sung, Matrix-based paraxial skew ray-tracing in 3D systems with non-coplanar optical axis. OPTIK—Int. J. Light Electron Opt. 117, 329–340 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Cheng Kung UniversityTainanTaiwan R.O.C

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