1 September 1993 Mathematical modeling of the solid angle function, part I: approximation in homogeneous medium
Author Affiliations +
Optical Engineering, 32(9), (1993). doi:10.1117/12.145056
Abstract
The calculation of the solid angle subtended by a given surface is required in a wide variety of applications, ranging from optics to particles transport. Integration via a Monte Carlo process is prohibitive from the computational point of view even with state-of-the-art variance reduction techniques. Exact computation of the solid angle from the distance z between the emission and the detection plane and the lateral distance ρ to the detector center requires the two-dimensional integration of a density function. We develop an approximation strategy whose form optimizes the precision requirements and the computational speed. One way to achieve this simplification is to approximate the trigonometric function in the full description of the solid angle by a series of line segments. The approximation obtained gives results that are precise to at least 1 part in 1000 and that are as fast as known algorithms.
Patrick Olivier, Daniel Gagnon, "Mathematical modeling of the solid angle function, part I: approximation in homogeneous medium," Optical Engineering 32(9), (1 September 1993). http://dx.doi.org/10.1117/12.145056
JOURNAL ARTICLE
5 PAGES


SHARE
KEYWORDS
Solids

Mathematical modeling

Sensors

Monte Carlo methods

Atmospheric particles

Cameras

Error analysis

RELATED CONTENT

SWAD: transient conductivity and pulse-height spectrum
Proceedings of SPIE (March 09 2017)
Fiber optic sensors for machine health monitoring
Proceedings of SPIE (February 02 2001)
Research on distortion for multimedia transmission
Proceedings of SPIE (September 25 2003)
Set up of a biological monitoring module realized in LTCC...
Proceedings of SPIE (January 22 2007)
Decenter and defocus for testing aspheric surfaces
Proceedings of SPIE (December 15 1992)

Back to Top