Coaxial three-mirror reflective optical system

The characteristic of a coaxial three-mirror reflective optical system is that the aperture center of the optical elements coincides with the optical axis, and the optical elements are generally rotationally symmetric. This type of optical system was proposed relatively early, with the Paul-Baker type three-mirror reflective optical system being a notable example. The Paul-Baker type three-mirror reflective optical system was first proposed in 1935 by French optical instrument manufacturer Maurice Paul and was independently re-proposed in 1945 by American James Baker. This three-mirror reflective optical system consists of a Cassegrain aplanatic optical system and a third mirror with a spherical surface. The Cassegrain aplanatic optical system is composed of a concave parabolic primary mirror and a convex spherical secondary mirror. The aplanatic optical system collimates and reduces the incident light beam, which is then reflected by the third mirror with a spherical surface, ultimately forming an image on the image plane.

In the Paul-Baker three-mirror reflective optical system, the aperture stop is positioned at the secondary mirror, and the secondary mirror and the tertiary mirror have the same radius of curvature. As a result, this system eliminates spherical aberration, coma, and astigmatism, but residual field curvature remains. The Paul-Baker three-mirror system can achieve an optical field of view of around 5°, bridging the gap between the Ritchey-Chrétien optical system (which can achieve a field of view of around 1°) and the Schmidt optical system (which can achieve a field of view of over 10°). The residual field curvature of the Paul-Baker three-mirror reflective optical system can be corrected by adjusting the axial spacing between the secondary mirror and the tertiary mirror. When this adjustment is made, the system is referred to as the Willstrop Mersenne-Schmidt type three-mirror reflective optical system.

Although the Paul-Baker three-mirror reflective optical system can achieve good imaging quality, the image plane is located inside the optical system, and there is significant aperture obstruction caused by the secondary mirror to the primary mirror and the image plane to the tertiary mirror. Therefore, the application of the Paul-Baker three-mirror reflective optical system is not very widespread. A typical improved application of this system is in the Large Synoptic Survey Telescope (LSST). In the LSST, the diameters of the primary mirror, secondary mirror, and tertiary mirror are 8.4 meters, 3.4 meters, and 5 meters, respectively. The optical system of the telescope, based on the Paul-Baker three-mirror reflective optical system, includes a set of corrective lenses in front of the image plane, forming a catadioptric structure and achieving an optical field of view of 3.5°.

In 1969, Rumsey proposed an ingenious coaxial three-mirror reflective optical system, as shown in Figure 4. In this optical system, the primary mirror and the tertiary mirror have almost the same axial position and radius of curvature. The central hole of the primary mirror is designed to house the secondary mirror, making the cross-sectional view of the primary and secondary mirrors appear as a single mirror body, similar to the LSST optical system. Additionally, the secondary mirror has a central aperture through which light passes after being reflected by the tertiary mirror, forming an image on the image plane located behind the secondary mirror.

In 1972, Korsch designed a coaxial three-mirror reflective optical system that integrated the features of both the Paul-Baker system and the Rumsey system. In this optical system, the light beam propagates at a gentle angle between the secondary mirror and the tertiary mirror, and all three mirrors are designed with hyperbolic surfaces, as shown in Figure 5. Since the axial positions and radii of curvature of the three mirrors in this system are not strictly constrained, the design has a higher degree of freedom compared to the Rumsey system, allowing for good imaging within a field of view angle range of 1.2°.

In addition to the aforementioned typical coaxial three-mirror reflective optical systems, there are also other configurations of coaxial three-mirror reflective optical systems without an intermediate image plane, such as the Robb three-mirror system and other Korsch three-mirror configurations. These system configurations are similar to the Paul-Baker three-mirror reflective optical system and consist of three reflective mirrors with optical powers of “positive,” “negative,” and “positive,” respectively, and do not have an intermediate image plane, making them single-imaging systems. The difference lies in the slight variations in the distribution of optical power between the primary and secondary mirrors, and the mirror surfaces are often composed of aspherical or higher-order aspherical surfaces, which allows for good imaging quality. The drawback of coaxial three-mirror reflective optical systems without an intermediate image plane is that they tend to be relatively large in size.