The Primary Optical device is the first lens or mirror that light touches. The diameter of the Primary Optical Device is also (generally) the Aperture Diameter. The light-gathering power of a telescope depends on the area of the aperture, and so this “light-gathering power” goes with the square of the diameter or radius.

The physical or effective distance between the Primary Optical Device and the focal point is called the focal length, measured along the optical axis. Given a point-like object sufficiently far away that its light rays impinge the primary optical device as light rays parallel to each other and parallel to the optical axis, the optical system will focus the rays to the focal point. The plane perpendicular to the line containing the optical axis and the focal point is the focal plane. It is on this plane that all images are formed.

Optical systems can use lenses, mirrors, or a combination of both to focus light. Both methods of redirecting light rays to focus an observed object into an image may require more than just one lens or one mirror. In such systems, the total system is a compound system that has an effective focal length that can be intuitive in the case of using thin lenses or more mathematically obscure such as in the cases of using spheroidal/paraboloid/hyperboloid mirrors.

Refractor telescopes make use of lenses to focus light. When light strikes an interface between two media, the direction of the light ray changes according to Snell's Law. The $n$ that appears on either side of this law is called the “refractive index” and is modulated by material properties and usually depends strongly on the wavelength of the incident light. In this way, a prism can be constructed that separates a light ray of white light into a range of colors.

Due to this, images from refractors can suffer from a chromatic aberration, where the colors of light spread-out on the focal plane.

Refractor tubes must generally accommodate the entire focal length of the system. This, coupled with the desire for high light-gathering power makes the feat of engineering a long tube that holds a large lens at an end cumbersome.

Reflector telescopes make use of mirrors to focus light. When light strikes a mirror, the direction of the light ray changes according to the Law of Reflection ($\theta_i = \theta_f$; angle of incidence and angle of reflection are equal about a plane normal to the mirror surface).

In contrast to refractors, reflectors suffer from no chromatic aberration, but can suffer from spherical aberration if using spherical mirrors. This aberration owes to the spherical focal plane and is observed as a loss of focus radially from the focal point. Further, the coma aberration can smear focused light. Both of these are correctable with geometric modifications of the mirrors at manufacture-time.

Since mirrors can be arbitrarily thin (so long as they're still reflective on one side) the weight of reflectors can be much less than a similarly powered refractor. Further, the introduction of non-flat mirrors allows for the effective focal length to be reduced many times the actual number of mirrors, lending shorter tubes to reflector telescopes.

In either case, we can determine the so-called “plate scale”. This plate scale is a measure of what angle each linear piece of the focal plane can image. Consider a detector of linear size, $s$, placed along the focal plane (at the end of the focal length ($f$)). Treat this detector size as the far-leg of a right triangle and the other leg as the focal length. In general, the focal length will be much larger than the detector size, so you can employ a small angle approximation to find that the angle the detector “sees” is roughly $\frac{s}{f}[rad]$. To convert this measure from radians to arcseconds, make clever use of unit ratios :)

There exists a fundamental limit to the angular resolution of any telescope. This is because light diffracts around the edges of the aperture. This diffraction has the effect of smearing out the incident light into an Airy Disk.



This diffraction can cause two distinct light sources to seem to merge on the focal plane – effectively reducing the angular resolution of the system. The Rayleigh Criterion is the threshold of resolving point sources angularly. It is based on the wavelength of the incident light and the diameter of the aperture.

If the only hindrance to angular resolution is the focal length, detector size, and this fundamental diffraction limit, the system is said to be “diffraction limited”.

Many ground-based telescopes dream of being diffraction limited. Our functional angular resolution is much higher than this diffraction limit since we must also deal with a turbulent atmosphere. This turbulent atmosphere creates many interfaces on which incident star light can refract (even if only very slightly) and therefore change direction. Over the course of the exposure time of the image (the integration time), these slight deviations in direction have the effect of smearing the incident light over a region of the detector called the “seeing disk”. We can think of each beam of light hitting the detector and creating an Airy Disk, but every fraction of a second the atmosphere changes the direction of the beam of light ever-so-slightly so that it hits another part of the detector and creates another Airy Disk, and so on through the entire integration time. Adding these all together gives us our seeing disk and a stellar profile that is much broader than any single Airy Disk.

[The original Airy profile is narrow (giving a Normal std of 1.3). The sum of many slightly displaced Airy profiles is wider (giving a Normal std of 5)]

Written by Roy Prouty 20240318
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