## 3 Reflective Triplet (RT)
The incoming beam forms an angle of about 22\({}^{\circ}\) with respect to the optical axis (Item 4). Item 40 is the internal baffle, which is used to block the beam, from striking the third mirror (Item 33). This baffle prevents light from scattering directly onto the focal plane. The coordinate system in the object space is defined around the beam (z-axis) axis. It is re-established in the image space. the incoming beam subtends an offset angle of about 22\({}^{\circ}\) with respect to the optical axis. We denote the beam axis with \(z\) and graphically with a broken line. An offset angle this large will, in general, create some distortion. It, however, does not appear in the left-right symmetrical Cooke triplet described here. Additional interesting insights about RT are described next. (i) An improvement in the optical speed (related to the throughput per pixel) may be achieved [18]. When we take a casual look at Figure 5, we observe that the footprint of the triplet may be approximately enveloped with a square. The optical speed (the F/#) of the design in Figure 5 may be estimated to be about 3.5. This is too slow for space surveillance or a night-vision application. One simple remedy might be to increase the dimension along the x-coordinate, defined up through the plane of the paper, denoted as a dot in Figure 5[19]. For example, if the ratio \(x\):\(y\) is increased from about 3:1 to 4:1, then the effective optical speed may be improved to about F/1 or even smaller. Such a change often brings along additional undesirable consequences. Specifically, the sizes of the front protecting window and of the third element become prohibitively large. However, if we move the optical stop to element one, then the size, and consequently, the cost, of the above three optical elements, together with the entire volume may be reduced. Unfortunately, the moving of the stop results in the introduction of some other higher-order aberrations. They, in turn, may be put under control by the addition of corrective high-order aspherical coefficients on each element. (ii) The other benefit of increasing the ratio \(x\):\(y\) in the aperture dimensions is that a huge field of view (FOV) may be achieved. Consider, for example, that the FOV of the nominal design in Figure 5 might be a square aperture with dimensions 10\({}^{\circ}\)\(\times\) 10\({}^{\circ}\). Then, a change of the square aperture into a rectangular one is possible to the degree that the FOV becomes, 2\({}^{\circ}\)\(\times\) 35\({}^{\circ}\). This is an ideal aperture configuration for a push-broom or scanning architecture [20; 21]. We may perform the scan along the \(x\)-axis, that is, along the narrow field dimension, placing an inexpensive, linear detector array at the focal plane. By reconfiguring the aperture, we thus replace an expensive 2D focal plane array with an economical alternative. This architecture may be optimized for an inexpensive, high-performance, extremely wide-angle (effectively 65\({}^{\circ}\)\(\times\) 35\({}^{\circ}\)) scanning sensor. Some would consider the 65-degree angle infinite in this configuration. (iii) At the other extreme, we have learned that diffraction-limited performance may be achieved for an RT with an F/3-optical system and a FOV of 3\({}^{\circ}\)\(\times\) 3\({}^{\circ}\) when the requirement on the image quality is very high. (iv) Additionally, in this compact configuration, obviously the management of stray light emerges as a critical issue. For example, when the optical beam in Figure 5 strikes onto the last mirror, the light will scatter directly onto the focal plane unless an inner baffle (Item 40), is placed there to block it. In practical applications, a reasonable length of the front baffle coupled with an inner baffle (Item 40) is required to accomplish this goal. (v) Finally, a flat image surface may be achieved when the sum of the powers (inverse radii of curvature) of the three mirrors approaches zero [5].