Imaging equations for spectroscopic systems using Lie transformations: I. Theoretical foundations

Christopher A. Palmer; Wayne R. McKinney; Benjamin S. Wheeler

doi:10.1117/12.323404

24 September 1998 Imaging equations for spectroscopic systems using Lie transformations: I. Theoretical foundations

Christopher A. Palmer, Wayne R. McKinney, Benjamin S. Wheeler

Proceedings Volume 3450, Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications; (1998) https://doi.org/10.1117/12.323404
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

The conceptual framework for the characterization of systems of gratings and mirrors is reviewed, based on the methods of Lie optics, which represents each optical element by a mapping that transforms a ray in object space into a ray in image space. The mathematical tools of Lie optics are presented, the complete transformation for a single grating is given in terms of its elementary transformations, and imaging equations are derived using this transformation that correspond with well-known expressions for aberration coefficients. Lie algebraic techniques have certain significant advantages over the more commonly used wavefront aberration theory, which will become apparent when the imaging properties of multi-element systems are considered in Part II of this work.

Citation Download Citation

Christopher A. Palmer, Wayne R. McKinney, and Benjamin S. Wheeler "Imaging equations for spectroscopic systems using Lie transformations: I. Theoretical foundations", Proc. SPIE 3450, Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, (24 September 1998); https://doi.org/10.1117/12.323404

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available