The design of refractive beam shaping optics using (geometrical) ray optics, rather than (physical) diffractive optics, has
been justified theoretically in the cases of interest and validated empirically. Measured output beam profiles have
matched to design profile with surprising accuracy. As the number of aspheric optics manufacturers increases, beam
shaping optics will become affordable, even for prototypes. For those not already familiar with the subject, this paper
provides a brief review of the theory and demonstrates how to easily calculate the coefficients of the finite polynomial
series used to produce aspheric surfaces. The numerical integration step found in the literature has been eliminated
resulting in a simplified algorithm which is easily implemented with math processors such as Mathcad®, MATLAB®, or
An optical polyspectral sensor has been developed and tested which calculates the magnitude and directional velocity of an incoming projectile to queue a reactive countermeasure. This paper describes the sensor modeling, sensitivity analysis, and experimental results of a sensor consisting of four sheets of light. Sensor application could be extended to all projectiles that present a measurable laser radar cross section to the sensor.
SC606: Laser Propagation Through Optical Systems Using ABCD Matrices
This course provides the tools to analyze the effects of optical components, tolerances, and misalignments on a laser beam propagating through optical systems. Laser beam parameters (position, direction, waist position and size, divergence, Rayleigh range, diameter, radius of curvature) are calculated with ABCD matrices and an equation processor, such as MathCad. This approach is applied, first, to simple optical configurations to illustrate the ABCD matrices, then to complex systems to demonstrate the generality and utility of this analytical method. Being a diffraction-based theory, this method is accurate for all paraxial beams, even in regimes where geometry-based tools used by optical designers are not valid. In the absence of other diffractive tools, the ABCD matrices provide and easy, accurate, and powerful method for designing or analyzing optical systems for laser beams. The course notes contain numerical examples bridging theory and application, and provide a convenient reference.