A design for an unobscured, large-aperture but otherwise compact laser-beam expander relies solely on spherical reflecting and refracting surfaces, yet provides a reasonably well corrected wavefront suitable for most applications. This design results from a tradeoff among compactness, cost, and performance.
The classical approach to the design of such a laser-beam expander typically involves the use of off-axis, aspherical mirrors and/or large lenses, which are expensive to fabricate. Spherical-surface mirrors and small spherical-surface lenses can be fabricated at substantially lower cost, but a beam-expander design based on such spherical-surface optics involves a tradeoff between compactness and performance.
The approach taken to arrive at the present design starts from an understanding that the design of a laser-beam expander need not afford all the performance characteristics of the classical telescope designs from which most beam-expander designs are derived. One consideration is that a laser-beam expander is not required to perform well over a wide field-of-view. A second consideration is that a laser-beam expander is required to perform well at only one wavelength. A third consideration is that limitations of fabrication capabilities make it impossible to achieve the maximum theoretical performance of a classical design in real hardware and that, in practice, a beam expander fabricated from a suboptimum design that calls for a small number of spherical (only) surfaces can be made to perform as well if not better, while costing much less.
The foregoing reasoning led to the present design (see figure), which calls for a minimum number of surfaces, all spherical, the largest being mirrors rather than lenses. The first optical element encountered by the incoming laser beam is a precorrector lens, which is so named because the radii of its spherical surfaces are chosen to introduce spherical aberration equal and opposite to that from the mirrors that follow. The lens is centered in the beam and tilted to introduce the correct amount of aberration to compensate for (precorrect) the off-axis aberrations caused by using the spherical mirrors at non-normal angles of incidence. The precise required thickness of the lens, radii of curvature of its surfaces, and angle at which it is tilted, depend on the index of refraction of the lens material, the wavelength of operation, and the mirror configuration.
The second optical element encountered by the laser beam is the smaller of two spherical mirrors. This mirror is tilted to redirect the now expanding beam so that, once collected and collimated by the larger spherical mirror, the beam passes the smaller spherical mirror without being obscured. The third and final optical element encountered by the laser beam is the larger spherical mirror, which is concave and is tilted to redirect the now collimated and expanded outgoing beam parallel to the incoming (unexpanded) beam. As is often found in optical systems of similar function, the placement and tilt of the mirrors can be described as being off-axis segments of a pair of larger mirrors sharing a common optical axis. The key distinction is that the "off-axis segments" in the design presented here are of spherical mirrors, so are themselves spherical, and hence easier (= relatively inexpensive) to fabricate.
The resulting wavefront performance is exceptionally well-corrected, with a nominal residual error so low as to be negligible in comparison with the effects of fabrication and assembly effects. The only aspect of performance that might be considered adverse is that the beam expansion is slightly anamorphic: the cross section of the output beam is elliptical, the minor axis being between 0.90 and 0.95 times as long as the major axis. If necessary, the anamorphism could be corrected by use of a more complex precorrector lens, still at an overall cost much less than that of a classical beam expander.
This work was done by Jeffrey Oseas of Caltech for NASA's Jet Propulsion Laboratory.