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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

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Simplified formula for the illuminance in an optical system.

D G Burkhard, D L Shealy

|March 24, 2010

Summary

A new formula calculates illuminance in optical systems by tracing a single ray. This method, applicable to various surfaces, also determines caustic surfaces as a byproduct, aiding optical design.

Area of Science:

Optical engineering
Geometric optics

Background:

Calculating illuminance and caustic surfaces in optical systems is complex.
Existing methods may not efficiently handle multiple or aspherical surfaces.

Purpose of the Study:

To derive a general formula for illuminance at any surface in an optical system.
To present a computational procedure for determining illuminance and caustic surfaces.

Main Methods:

Derived a formula for illuminance based on wavefront principal curvatures before and after refraction.
Generalized Coddington equations for meridional and skew rays to determine curvatures.
Applied the method to an aspherical singlet for illustration.

Main Results:

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A single-ray tracing method to compute flux density at any point.

The formula relates illuminance to the ratio of wavefront curvature products.

The procedure yields illuminance and caustic surface equations simultaneously.

Conclusions:

The derived formula and procedure offer an efficient way to calculate illuminance and caustic surfaces.
Applicable to both spherical and aspherical optical surfaces.
Provides a unified approach for analyzing optical system performance.