# Reflective Beam Expanders

Excerpt from Optical Design Fundamentals for Infrared Systems, Second Edition

Reflective beam expanders are modified Cassegrain and Gregorian mirror systems. Both the object and the image are located at infinity, which means that the input and output beams are collimated (afocal system). We shall assess how well that can be achieved with two spherical mirrors. Figure 1 shows the Cassegrain configuration. To avoid obstruction, the mirrors are used in an off–axis mode. Due to the spherical shape of the mirrors, the exiting beam is not collimated. The marginal ray converges under an angle γ relative to the optical axis. Due to the off-set of the mirrors from the optical axis, the convergence angle α of the total beam in the meridional plane shown is somewhat smaller than γ. The Gregorian beam expander is shown in Fig. 2.

Figure 1 Cassegrain beam expander.

Figure 2 Gregorian beam expander.

The angular convergence for both configurations is

where m is the magnification or expansion ratio D/d. It is important to remember that m is positive for the Cassegrain expander and negative for the Gregorian.

The relative aperture (f /#) = fB /(2yB)) = |fA|/(2yA), the separation of the mirrors t = fA + fB. For an f /2 system with m = 5, the convergence angle γ for the Cassegrain expander is @ −1.5 mrad, and for the Gregorian with m = −5, γ @ −2.3 mrad. Notice that the factor in front of the square bracket of Eq. (3.73) is equal to twice the value of the minimum angular blur spot size of a single spherical mirror due to spherical aberration.

To correct spherical aberration with two reflectors, at least one of them has to be aspheric. For both configurations, the classical Gregorian and the Cassegrain, all mirrors have to be paraboloids.

Citation:

M. Riedl, Optical Design Fundamentals for Infrared Systems, Second Edition, SPIE Press, Bellingham, WA (2001).