Читать книгу Optical Engineering Science - Stephen Rolt - Страница 35

The telescope part of the Hubble Space Telescope instrument is made up of two mirrors, a primary and a secondary. Characteristics of the telescope are shown in Figure 1.20. Data is courtesy of the National Aeronautics and Space Administration.

There are four matrix elements to consider here. First, there is a mirror with a radius of −11.04 m (note sign), followed by a translation of −4.905 m (again note sign). The third matrix element is a mirror (M2) of radius − 1.359 m. Finally, we translate by +4.905 m, so that both the input and output co-ordinates are referenced with respect to the same origin. The matrices are as below:

The focal positions are:

The principal points are at:

Since object and image space are in the same media, then the two focal lengths are the same. In addition, the nodal and principal points are co-located. However, when dealing with mirrors, one must be a little cautious. Each reflection is equivalent to a medium with a refractive index of −1, so that the matrix of a reflective surface will always have a determinant of −1. Therefore, any system having an even number of reflective surfaces, as in this example, then its matrix will have a determinant of 1. As such, the two focal lengths will be the same and principal and nodal points co-located. However, where there are an odd number of reflective surfaces, assuming object and image spaces are surrounded by the same media, then f₂ = −f₁. In this instance, principal and nodal points are separated by twice the focal length.

Although, in terms of overall length, the telescope is compact, ∼5 m primary–secondary separation, the focal length, at 58 m, is long. The focal length of the instrument is fundamental in determining the ‘plate scale’ the separation of imaged objects (stars, galaxies) at the (second) focal plane as a function of their angular separation. As such, a long focal length, of the order of 60 m, may have been a requirement at the outset. At the same time, for practical reasons, a compact design may also have been desired. One may begin to glance, therefore, at the significance, at the very outset of these very basic calculations in the design of complex optical instruments.