Telescopes are almost universally needed in conjunction with detectors to limit the solid angle under study, map the detector size or resolution to angular scales of interest, and concentrate radiation on the detector. Among these, imaging systems share processes and limitations imposed by radiation properties and optical design.

First, some useful terms:

All imaging systems suffer diffraction effects due to the wave nature
of radiation. The simplest example is to consider a slit aperture
(which by symmetry can be analyzed one-dimensionally). The
familiar result is a central maximum surrounded by a symmetric set of
diffracted peaks; the book's derivation starts from Huygens wavelets,
which give a very useful way of seeing how diffraction acts in a
particular situation.
For the astronomically more usual case of a circular aperture, the
derivation is more complex, but we still see a central maximum
(the *Airy disk*) surrounded by concentric diffracted rings.
A common definition of the resolution attainable with a given optical
system is the Rayleigh criterion, reached when two point sources
have separation equal to the radius of the first diffraction minimum.
This is close to
λ/*D*
(the Rayleigh criterion gives a factor 1.22)
for aperture diameter *D*; a rule
of thumb is that for visible light, a 100-mm aperture resolves 1 arcsecond.
It is common at a variety of wavelengths to take
λ/*D* as a measure
of the diffraction limit. For example, a 43-m telescope has a diffraction
limit in arcminutes numerically close to the observing wavelength in cm.

The diffraction pattern of an arbitrary aperture is closely related to its two-dimensional Fourier transform (being its power spectrum). The rings result from the sharp edges of the slit or aperture. Sometimes one wishes to minimize these rings at the expense of the width of the central peak, to detect faint companion stars or look for planets. In this case, one apodizes the aperture by placing a filter at some pupil plane (where the aperture is imaged) that gently rolls to zero transmission at the edges, so there will be little or no light outside the (broader) central pattern. You can't beat the diffraction limit, but there is scope for reshaping the details of its shape.

Fabrication: grinding, polishing, spin casting.

Testing: Foucault test, null test versions.

Optical elements are often coated, either for optimal
reflectivity or to reduce reflections at air:glass boundaries.
At the interface between substances with *n _{1},n_{2}*,
minimal reflection
is achieved by use of interference if an appropriately thin coating
of a substance with

Design of telescopes may rely on analytic or ray tracing approaches. Ray tracing is particularly amenable to programming, requiring only the Snell and reflection laws plus descriptions of the optical components.

Mirrors require support, possible across the entire back surface because they don't have to be transparent. Thermal effects are important in thick mirrors, so glasses with low thermal expansion coefficients (first Pyrex, later Cer-Vit and Zerodur) are chosen. Even so, a measure of active support improves even conventional telescope performance, and is crucial for the new generation of thin-mirror and segmented-mirror designs.

Last changes: 9/2009 © 2000-2009