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Optical Modeling Software - Mathematical Description

Optical modeling software SHAPE makes it possible to control and redistribute the light flux from the source for light distribution required to illuminate a given area. As in geometric optics, which involves light rays forming images of objects, optical design methods for an optical system formed by lighting fixtures are implemented via ray methods as applied to the optics intended for obtaining required output photometric characteristics of luminaire.

Optical design methods in the program provide:

  • Calculation of intensity in a ray tube corresponding to a point source. The resulting intensity is considered to be a superposition of intensities produced by these point sources.
  • Reverse ray tracing from where a ray arises from a point on the receiving surface toward the optical system until it crosses a light source according to reflection laws.
    Tracing rays leads can define the brightness of the output pupil of the optical system and, in correspondence with Mangen law, the desired characteristic of intensity.
  • Elementary maps in which, as in the reverse ray tracing, intensity calculations are carried out according to the luminance and area of flashed area, but the ray path is calculated for direct propagation.

Modern computer technologies create powerful tools of photometric analysis to estimate optical systems of lighting fixtures. Optical modeling software SHAPE is one of them.

Optical design methods use the ray-tracing method to describe the interaction of light and reflecting surfaces, which is characterized by directional reflectance distribution function of the ideal specular surface.

Mathematical methods forming the basis for the SHAPE program are stated in the book written by one of the developers – Kusch O.K. «Computer-aided optical design of illuminating and irradiating devices». References to this book can be found in IES Lighting Handbook, 9th edition, chapter 7 «Luminaries», devoted to optical design methods.

Download the book  "Computer-Aided Optical Design of Illuminating and Irradiating Devices" (Kusch O.K.)