Abstract
Geometric optics is used to find the shape of the image and the irradiance cast on a spherical target by a circular beam after reflection by a far off-axis paraboloidal mirror. For moderately large f/No. the image is found to be nearly circular with its center shifted slightly from the beam axis. However, the target irradiance can be highly asymmetric unless the beam intensity falls off rapidly with radius. An expansion in powers of inverse f/No. is used to obtain closed form expressions for the image shape and the target irradiance. Numerical studies are carried out for parameters relevant to the design of a laser fusion reactor. Limits are placed on allowable tilt errors by means of a naive analysis of ray aberrations. A useful formula is derived for the perturbed target irradiance under small tilt errors, based on a new expression for the caustic. These simple formulas allow one to carry out detailed design studies without recourse to ray tracing codes.
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