## 7 Wide Angle Large Reflective Unobscured System (WALRUS)  
None of the three designs (RT, TMA, OR) presented up to now has a large FOV. A 20\({}^{\circ}\)\(\times\) 30\({}^{\circ}\) wide-angle unobscured design, for example, is attractive for many applications. One such system is described next. For convenience, we approach it conceptually from a three-lens optical system again, i.e., an inverse-telephoto derivative, shown in Figure 13. This is a negative-positive-positive lens combination. The aperture stop is placed between the first and the second positive lens (corresponding to the second and the third lens). The pair composed of the first two elements performs as an inverse-telephoto lens. The matching two-mirror counterpart is the classical afocal Schwarzchild objective [30]. This similarity may best be appreciated by examining the Y-\(\bar{\mathrm{Y}}\) diagram, except for the location of the optical stop. The Y-\(\bar{\mathrm{Y}}\) diagram, corresponding to the WALRUS of Figure 13, is displayed in Figure 14. The object is located at infinity, so the generalized ray is initially parallel to the \(\bar{\mathrm{Y}}\)-axis. At the divergent primary component, the generalized ray is deviated counterclockwise, until it encounters a convergent, secondary one. The secondary imaging element converts the expanding beam into a collimated beam, causing the generalized ray to travel parallel to the \(\bar{\mathrm{Y}}\)-axis. The beam expander configuration/the inverse-telephoto lens transforms the narrow beam in the object space into a wide beam in the intermediary space, between two positive imaging components. After encountering the tertiary convergent element, the generalized  
Figure 12: Offner relay system is a concentric (Mirror 1 plus Mirror 3 and Mirror 2) system. The new system now is, literally, top- and bottom-symmetric with respect to the optical axis. The curved _plane parallel_ plate CP is a weak lens in front of the complete system, and physically behind the secondary mirror. It corrects the fifth-order spherical aberration. O denotes object; I is image; P, S, and T stand for the primary, the secondary, and the tertiary mirror; and AS denotes the aperture stop, in this case, at the secondary, that is, a negative mirror. OA denotes the optical axis. Figure 13: The WALRUS design may be considered an optical layout of an inverse-telephoto derivative, having the optical stop located between the second and the third lens. O denotes object, in this case, located at infinity; I is the image location; P, S, and T stand for the primary, the secondary, and the tertiary lens; and AS denotes the aperture stop, in this case between the secondary and the tertiary lens. OA denotes the optical axis. ray is directed toward the \(\bar{\Upsilon}\)-axis, where the image is found when the generalized ray crosses the \(\bar{\Upsilon}\)-axis. This last part is similar to the Offner relay in Figure 11. The generalized ray is thus parallel to the \(Y\)-axis until it crosses the \(\bar{\Upsilon}\)-axis. A detector may be placed at the image location at Y = 0. Its size is OA-I. The aperture stop radius or half of the square aperture side is equal to OA-AS. A slow optical system additionally featuring wide FOV results in a large-volume optical system. One easy way to mitigate this disadvantage is to insert a flat mirror [31] at the optical stop (Item 34), giving us the configuration presented in Figure 15. The secondary and the fourth mirror may be united into a single piece to simplify the manufacturing process and to further reduce the overall cost. As mentioned already for the RT case, the offset angle may be as large as 45\({}^{\circ}\) or even larger, leading to a large amount of distortion [8; 32]. One simple optical solution is the addition of a thin lens with a low power, placed near the focal plane. The location of a distortion corrector, Item 32, is illustrated in Figure 16[32]. With modern artificial intelligence technology, a software solution might be implemented as well.