Telescopes

Refractive telescopes are based on refractive optical elements, utilizing refraction of light.

Figure 2 shows the basic setups of two common types of refractive types of telescopes (refractors). The Keplerian telescope uses two positive (focusing) lenses separated by the sum of their focal lengths, producing an inverted image and a real intermediate image plane. The Galilean telescope uses a positive objective lens and a negative ocular lens; it produces an upright image and has no real intermediate image plane.

The larger input lens is called the objective; the lens near the eye is the ocular (eyepiece). For Keplerian designs, the field of view is limited by the eyepiece's field stop; inserting a field lens can increase the usable field.

Lenses introduce chromatic aberrations because their focal length depends on wavelength. Objectives are commonly corrected with achromatic doublets or apochromatic triplets (often using low‑dispersion “ED” glasses). See below for more information on optical aberrations.

Refractors for visual use may remain simple if only a small field is required; wide‑field astro‑cameras employ more elaborate multi‑element objectives. For refractors that invert the image, one may accept inversion or add erecting optics (e.g., Porro or roof‑prism systems in binoculars). For telescopes with light delivery to photographic films or image sensors, the inversion is of course not relevant.

Note that afocal refractors used as beam expanders can also be realized with prisms, including anamorphic prism pairs that magnify differently along two axes.

Reflective telescopes are based on reflective optical elements, i.e., mostly on mirrors. While focusing and defocusing functions are easily achieved with curved mirror surfaces, one requires design adaptations to cope with the inevitable change in beam direction upon reflection.

Two common solutions — the Cassegrain telescope and the Newton telescope — are shown in Figure 3. Both have a secondary mirror which is suspended by some spider structure and causes a circular central obscuration of the primary mirror. This mainly reduces image contrast (redistributing light into the diffraction rings); it only slightly degrades the Rayleigh‑limit resolution.

Reflective telescopes are not afocal by themselves; they form a focus where a camera, spectrograph slit or eyepiece can be placed.

Reflective telescopes typically work with aspheric mirrors. For example, Cassegrain reflectors are based on a parabolic primary mirror and a hyperbolic secondary mirror, which reflects light through a hole in the primary mirror.

The main advantages of reflective telescopes, compared with refractive telescopes, are the following:

• Any chromatic dispersion is avoided. That advantage has already been realized by Isaac Newton, who therefore in 1668 developed the first reflecting telescope, called the Newtonian telescope.
• One can produce relatively large telescope mirrors which still have a reasonable weight, while large lenses would become very heavy and expensive.

For those reasons, reflective telescopes have become the usual solution for astronomy.

Early reflective telescopes suffered from the problem of rapid tarnishing of the reflecting surfaces, when using speculum metal mirrors. This problem was largely solved by using metal-coated first surface mirrors based on glass or ceramic mirror substrates. Those are also harder, i.e., they preserve their shape more accurately, and some of them exhibit very small thermal expansion coefficients.

Extremely precise large telescope mirrors are nowadays usually made with glass ceramic substrate materials, optimized for a very low coefficient of thermal expansion. Note that deviations from the ideal shape should ideally be far below one optical wavelength. The wavefront accuracy can be further improved with adaptive optics, which usually correct distortions from the primary mirror not at their source, but at a more convenient location, where the beam path is more compact.

At X‑ray energies, conventional mirrors and lenses fail as X‑rays penetrate or are absorbed at normal incidence. Grazing‑incidence optics solve this by reflecting at very shallow angles (typically a degree or less).

Wolter showed that combinations of paraboloid and hyperboloid (Type I), hyperboloid and ellipsoid (Type II), or paraboloid and ellipsoid (Type III) surfaces can form true images with minimal aberration. Practical telescopes nest many thin mirror shells to increase collecting area. Modern multilayer coatings extend reflectivity to higher energies. Famous examples include Chandra (Type I), XMM‑Newton (Type I), and hard‑X‑ray missions with multilayers.

Catadioptric designs combine refractive and reflective optical elements to correct aberrations and compact the system. Well‑known examples are Schmidt–Cassegrain and Maksutov–Cassegrain telescopes. A simple dialyte uses a thin positive lens as objective and a concave mirrored element for focusing.

Many astronomical questions are answered not by images alone, but also require optical spectra and/or polarization measurements. Telescopes feed such instruments at a focal plane:

• Long‑slit and multi‑slit spectrographs disperse light from one or many targets across a detector. Echelle spectrographs provide high resolution by cross‑dispersing multiple orders.
• Fiber‑fed spectrographs mounted on a bench receive light from the focal plane through an optical fiber. Robotic fiber positioners enable multi‑object spectroscopy (MOS) on thousands of targets in one exposure.
• Integral‑field spectrographs (IFS/IFU) collect a spectrum at every spatial element in a small field using micro-lens arrays, image slicers or fiber bundles; the result is a 3D “data cube” (x, y, λ).
• Polarimeters (often at the same focal station) analyze the polarization state across wavelength, e.g. for studying magnetic fields and scattering.

Adaptive‑optics‑fed spectrographs can work close to the diffraction limit. Image slicers and pupil slicers reformat the light to match slits and detectors efficiently.

The used lenses and/or mirrors are responsible for various types of optical aberrations, which reduce the obtained image quality to some extent:

• Chromatic aberrations: In refractors, lenses and prisms cause chromatic aberrations, related to the dependence of the focal length of a lens on the optical wavelength. One may use achromatic lenses for minimizing such problems, or avoid lenses altogether.
• Monochromatic aberrations: There are further aberrations in the form of astigmatism, coma and geometrical image distortion. One usually restricts the field of view such that excessive aberrations of those types are avoided. Particularly if the magnification is large, a smaller field of view may be required. For achieving a larger field of view with good quality, one can replace the objective and ocular with combinations of several lenses, designed for compensating aberrations as much as possible.
• Field curvature: For some telescope designs, the image “plane” is significantly curved, so that sharp images could not be obtained over the whole image area when using a flat image sensor. Therefore, curved image sensors are used with some telescopes, where the field curvature cannot be reduced.

For visual use, the angular magnification is set by the objective and eyepiece and equals ($M_\theta = -f_\textrm{objective} / f_\textrm{ocular}$); it is negative for Keplerian designs (with image inversion). Changing oculars changes magnification. A rough practical upper limit for useful magnification is about 2× per millimeter of aperture under good seeing; beyond that, the image grows but reveals no finer detail.

Astronomers specify aperture and focal ratio ($f/\# = f / D$). For imaging, the focal ratio governs field of view and exposure time at a fixed detector pixel size. The plate scale (image scale, connecting the angular separation of objects with their linear separation in the focal plane) is 206265 arcsec / ($f$), from which the arcsec‑per‑pixel value can be calculated with the given pixel size.

The achievable image resolution of a telescope, quantified as an angular resolution on the object side, is ultimately limited by diffraction if the optical quality is excellent; the essential design parameter is the diameter ($D$) of the entrance aperture. (Although the output aperture is much smaller, diffraction is less relevant there due to the image magnification.) The diffraction‑limited angular resolution is approximately ($1.22 \lambda / D$) (in radians).

For green light in a telescope with a 1-m mirror, this leads to a resolution of ≈0.67 μrad = 0.14 arcseconds.

Larger apertures also collect more light — proportional to ($D^2$) — which is crucial for faint objects. In practice, however, Earth’s atmosphere (seeing) usually limits resolution for large ground‑based telescopes unless adaptive optics is used.

The field of view is the angular extent visible for a fixed telescope orientation. It is set by the optical design (correctors, field stop) and the detector size. High-resolution telescopes often have a rather narrow field of view, while survey telescopes achieve very wide fields at the expense of resolution.

Visual instruments (e.g., binoculars) are often labeled like 8×30 (8× magnification, 30 mm aperture). Additional specs include apparent field of view, exit pupil (aperture/magnification), and eye relief. Astronomical telescopes are usually specified by aperture and focal ratio, e.g., 200 mm f/5 (1000 mm); magnification then depends on the eyepiece.

Small terrestrial telescopes are often made in the form of hand-held binoculars, essentially consisting of two independent telescopes — one for each eye. The spatial separation of the two objectives can be increased beyond the spacing of the human eyes to achieve better 3D vision. The required modification of the beam paths can be made with prisms which may at the same time undo the image inversion, as far as that is caused by the other optics. Binoculars are typically used for purposes like ornithology, hunting, sports watching and military reconnaissance.

There are also compact monoculars for viewing with one eye, which can be made with lower cost and weight.

Larger telescopes, e.g. for applications in geodesy, are often made as monoculars and are mounted on a flexible system, which may be motorized for accurately looking in certain directions.

Small telescopes are mounted on rifles for precise targeting and are then called riflescopes. Similar telescopes are also used for other types of weapons.

Rather large telescopes — most often with a Cassegrain architecture — have been developed for astronomical observations. The largest realized ones have open apertures with diameters around 10 m. The diffraction limit for the angular resolution is then normally no longer reachable due to image distortions in the atmosphere — even when telescopes are placed on high mountains. Therefore, adaptive optics are increasingly used for correcting such distortions. The measurement of the distortions to be corrected can be made on the same telescope, either using light from stars or from artificial laser guide stars.

Several even larger telescopes are currently planned, with apertures above 20 m and partly even well above 30 meters.

Astronomical observations often require substantial time to acquire enough light energy for a proper exposure of a photographic film or an image sensor. It is thus a common routine to accurately move the telescope such that the effects of the rotation of Earth are compensated.

High performance is required also from the used image sensors, which are mostly of CCD type. Rather large sensor designs, possibly including multiple CCD chips, are used in various telescopes. For highest sensitivity, they are often operated at low temperatures. Further, one may take additional measurements under dark conditions and apply noise subtraction algorithms.

Some large observatories (e.g. the European Southern Observatory in Chile with its Very Large Telescope) work with a combination of several telescopes, combining signals from them with interferometry for substantial further increases of angular resolution.

Another option for avoiding the problem of atmospheric distortions is to place a telescope outside the atmosphere of Earth — typically in an orbit around Earth. The most famous example is the Hubble Space Telescope (HST), which has been launched in 1990 and has delivered astronomical images of enormous scientific value during several decades. Although its entrance aperture of 2.4 meters is small compared with that of terrestrial telescopes, the freedom of atmospheric distortions allows for very high image quality. Light in the visible, ultraviolet and near infrared region can be utilized. Other space telescopes have later been deployed, for example the Herschel telescope in 2009, which however operates in the far infrared. The planned James Webb Space Telescope is expected to cover the wavelength range from 0.6 μm to 28.5 μm with a primary mirror of 6.5 m diameter.

Instead of imaging, one may analyze the light coming from a star or a galaxy, for example, with a highly sensitive spectrometer. In other cases, the polarization properties of light are carefully studied, using polarimeters.

There are also solar telescopes, which are made specifically for imaging details of the Sun. Here, one is definitely not short of brightness; to the contrary, the system must be able to handle substantial optical powers. Because of the comparatively small observation distance, the angular resolution usually does not need to be as high as for the observation of distant stars. The telescope designs are accordingly quite different from those of other astronomical telescopes.

Modern photonics technology goes far beyond improving classical optics; it uses many modern devices and technologies such as adaptive optics, optical fibers and waveguide devices including photonic integrated circuits and frequency combs. In such areas, the term astrophotonics has become common.

Beyond visual observation and astronomical imaging, telescopes are critical components in free-space optical communications (FSO) and LIDAR systems. In these applications, the telescope often acts as a “photon bucket”, where the primary goal is to collect as much back-scattered or transmitted light as possible and focus it onto a photodetector.

• Receiver optics: For LIDAR and FSO, the field of view (FOV) is often matched to the divergence of the transmitter or the specific scene requirements. Large apertures are desired to maximize the signal-to-noise ratio, but the optical quality (wavefront error) need not always match the diffraction limit required for high-resolution imaging, depending on the detector size (e.g., “flux collectors” vs. imaging telescopes).
• Transmitter optics: Telescopes are also used in reverse to transmit laser beams. Here, they function as beam expanders to reduce the beam divergence, allowing the signal to travel longer distances with less intensity loss. In this mode, the telescope must handle high optical power densities, requiring appropriate optical coatings and substrates with high damage thresholds.