Fast vectorial calculation of the volumetric focused field distribution by using a three-dimensional Fourier transform.

We show that the volumetric field distribution in the focal region of a high numerical aperture focusing system can be efficiently calculated with a three-dimensional Fourier transform. In addition to focusing in a single medium, the method is able to calculate the more complex case of focusing through a planar interface between two media of mismatched refractive indices. The use of the chirp z-transform in our numerical implementation of the method allows us to perform fast calculations of the three-dimensional focused field distribution with good accuracy.

[1]  Andreas Dress,et al.  On integral representations , 1969 .

[2]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .

[3]  Brian Vohnsen,et al.  Polarization structuring for focal volume shaping in high-resolution microscopy , 2007 .

[4]  C. McCutchen.  Generalized Aperture and the Three-Dimensional Diffraction Image , 1964 .

[5]  J C Dainty,et al.  Direct calculation of a three-dimensional diffracted field. , 2011, Optics letters.

[6]  H. H. Juynboll.  Erratum to: J , 1902 .

[7]  Colin J. R. Sheppard,et al.  Axial imaging through an aberrating layer of water in confocal microscopy , 1992 .

[8]  R. Burge,et al.  Variable-radius focused optical vortex with suppressed sidelobes. , 2006, Optics letters.

[9]  Theo Lasser,et al.  Fast focus field calculations , 2008, SPIE BiOS.

[10]  P. Varga,et al.  Electromagnetic diffraction of light focused through a stratified medium. , 1997, Applied optics.

[11]  C. McCutchen,et al.  Generalized aperture and the three-dimensional diffraction image: erratum , 2002 .

[12]  Min Gu,et al.  Focusing of doughnut laser beams by a high numerical-aperture objective in free space. , 2003, Optics express.

[13]  Taco D. Visser,et al.  Comparison of different theories for focusing through a plane interface , 1997 .

[14]  Q. Zhan.  Cylindrical vector beams: from mathematical concepts to applications , 2009 .

[15]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[16]  E. Wolf,et al.  Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  Peter Török,et al.  Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation , 1995 .

[18]  Peter R T Munro,et al.  Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.