
Proceedings Paper
Technique to transform optical deflection equations into linear difference ones for tomographyFormat | Member Price | Non-Member Price |
---|---|---|
$17.00 | $21.00 |
Paper Abstract
The random-direction partial derivatives in optical deflection equations were transformed into numerical differences in
reference frames for tomography. The nonlinear deflection equations were transformed into linear tomography ones. A
detecting ray will turn its propagating direction when it runs through a heterogeneous refractive index field. Its deflecting
angle a is the function of refractive index n by n's first order partial derivative. So, the optical deflection equation
involves nonlinear first order partial derivative. This kind of detecting ray equations can't be resolved by tomography
algorithm directly. At first, the nonlinear partial derivative should be transformed into numerical difference. Here, a
practical transforming algorithm was put forward. The diagnosed field was divided into tiny foursquare grids. Each grid
and its refractive index were approximated to a correct cone with an irregular bottom. With the approximation, the space
partial increment calculation was much simplified at any grid, in any direction and to any detecting ray. It was assumed
that the refractive index distribution should be coplanar in the area between three grid centers of the three close-adjacent
grids. With the assumption, the refractive index partial increment could be calculated with a numerical difference
function of close-adjacent grid refractive indexes. With the approximation and assumption, the partial derivative was
transformed into numerical difference. As the result, partial derivative related to any detecting ray could be transformed
into numerical difference. Nonlinear deflection equations could be transformed into linear difference ones. So, the
deflected angles can directly be applied to reconstruction as projections.
Paper Details
Date Published: 20 May 2009
PDF: 8 pages
Proc. SPIE 7283, 4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 72831Y (20 May 2009); doi: 10.1117/12.828690
Published in SPIE Proceedings Vol. 7283:
4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment
Yudong Zhang; James C. Wyant; Robert A. Smythe; Hexin Wang, Editor(s)
PDF: 8 pages
Proc. SPIE 7283, 4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 72831Y (20 May 2009); doi: 10.1117/12.828690
Show Author Affiliations
Zhimin Zhao, Nanjing Univ. of Aeronautics and Astronautics (China)
Published in SPIE Proceedings Vol. 7283:
4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment
Yudong Zhang; James C. Wyant; Robert A. Smythe; Hexin Wang, Editor(s)
© SPIE. Terms of Use
