Phase space methods in optics

Phase space in optics corresponds to a visualization of the position and the angles of rays within an optical system.

Thus paraxial ray-tracing corresponds to an ABCD-like linear transformation, whereas a real ray-tracing will also reveal aberrations, as illustrated in Fig. 1: 

Fig.1: Ray-tracing of a single ray through an optical system and the corresponding trajectories in phase space.
Fig.1: Ray-tracing of a single ray through an optical system and the corresponding trajectories in phase space.

In phase space an optical system acts as transformation of the input light distribution onto the light distribution at the image plane. Therefore an analysis of these transformation properties provides a complete picture of the optical functionality. For example phase space can provide insight into aberration contributions within imaging optical systems (see Fig. 2) or for illumination systems it can give an overview of the general radiation transport and radiance redistribution (see Fig. 3).

Phase Space Distribution

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Fig. 2: Movie of phase space motion of a grid of rays. The color indicates regions of high aberrations.

Fig. 3: Ray-tracing picture (top) and Phase space transformation of a mixing rod (bottom): a) Initial distribution; b) Propagated distribution in the absence of the rod side-walls; c) Final distribution resembling the back-folding effect of the rod.
Fig. 3: Ray-tracing picture (top) and Phase space transformation of a mixing rod (bottom): a) Initial distribution; b) Propagated distribution in the absence of the rod side-walls; c) Final distribution resembling the back-folding effect of the rod.

Recent Publications

  1. Herkommer, Alois M. "Phase space optics: an alternate approach to freeform optical systems." Optical Engineering 53 (3) (2014).
  2. Rausch, D., Herkommer, A.M. "Illumination Optics in Phase Space." Fringe 2013. Springer Berlin Heidelberg, 373-376 (2014).
  3. A. M. Herkommer and D. Rausch, "Phase space transformations - a different way to understand freeform optical systems," in Renewable Energy and the Environment, OSA Technical Digest (online) (Optical Society of America, 2013), paper FT2B.5.
  4. Rausch D., Herkommer A.M. “Phase space approach to the use of integrator rods and optical arrays in illumination systems”, Advanced Optical Technologies, Vol. 1, page 69-78, (2012).
  5. Rausch D., Herkommer A.M. “Phase space approach to the use of integrator rods and optical arrays in illumination systems”, Advanced Optical Technologies, Vol. 1, page 69-78, (2012).
  6. Herkommer, A. M., Rausch D. “Phase space optics – an engineering tool for illumination design”, Proc. SPIE 8429, 84290C (2012).
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