Ray tracing the Wigner distribution function for optical simulations

Abstract. We study a simulation method that uses the Wigner distribution function to incorporate wave optical effects in an established framework based on geometrical optics, i.e., a ray tracing engine. We use the method to calculate point spread functions and show that it is accurate for paraxial systems but produces unphysical results in the presence of aberrations. The cause of these anomalies is explained using an analytical model.

[1]  Mj Martin Bastiaans,et al.  Wigner distribution function of a circular aperture , 1996 .

[2]  G. Mana,et al.  Vectorial ray-based diffraction integral. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  J. Stamnes Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves , 1986 .

[4]  Ramesh Raskar,et al.  Interactive Point Spread Function Simulation with Diffraction and Interference Effects , 2016, IMAGAPP/IVAPP.

[5]  A. Walther Radiometry and coherence , 1968 .

[6]  Ramesh Raskar,et al.  Rendering Wave Effects with Augmented Light Field , 2010, Comput. Graph. Forum.

[7]  M. Alonso,et al.  Diffraction of paraxial partially coherent fields by planar obstacles in the Wigner representation. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  D. Dragoman,et al.  Wigner distribution function applied to third-order aberrations. , 1996, Applied optics.

[9]  Mj Martin Bastiaans The Wigner distribution function applied to optical signals and systems , 1978 .

[10]  F. Bociort,et al.  Simulating multiple diffraction in imaging systems using a path integration method. , 2016, Applied optics.

[11]  A. Lohmann,et al.  Wigner distribution function display of complex 1D signals , 1982 .

[12]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[13]  Florian Bociort,et al.  A Wigner-based ray-tracing method for imaging simulations , 2015, SPIE Optical Systems Design.

[14]  S. A. Collins Lens-System Diffraction Integral Written in Terms of Matrix Optics , 1970 .

[15]  Assessment of a Wigner-distribution-function- based method to compute the polychromatic axial response given by an aberrated optical system , 2003 .

[16]  J. Keller,et al.  Geometrical theory of diffraction. , 1962, Journal of the Optical Society of America.

[17]  Alan W. Greynolds Propagation Of Generally Astigmatic Gaussian Beams Along Skew Ray Paths , 1986, Optics & Photonics.

[18]  Ramesh Raskar,et al.  Reflectance model for diffraction , 2012, TOGS.

[19]  Miguel A. Alonso,et al.  Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles , 2011 .

[20]  Ramesh Raskar,et al.  Validity of Wigner Distribution Function for ray-based imaging , 2011, 2011 IEEE International Conference on Computational Photography (ICCP).