Resolving power of the telescope
Because of the circular aperture of the telescope, point light sources are diffracted, resulting in an Airy disk on the image plane.
Source Airy disk: Geek3, CC BY-SA 3.0, via Wikimedia Commons
Source light distribution: Sakurambo 桜ん坊, Public domain, via Wikimedia Commons
The resolving power of a telescope is its ability to resolve two closely spaced objects - such as nebulae or planetary features (or two such Airy disks) - that are separated by an angular distance of ‘α’. This condition is met when the maximum of one spot lies at least on the minimum of the other spot.
Source picture: Geek3, CC BY-SA 3.0, via Wikimedia Commons
Source chart: Mpfiz, Public domain, via Wikimedia Commons (added)
This means that the minimum resolution corresponds to the radius of the Airy disk, which, according to the Rayleigh criterion, is calculated as follows based on the wavelength of the light and the aperture of the telescope (https://en.wikipedia.org/wiki/Angular_resolution#Explanation):
α – resolving power in ["]
λ – wavelength in [mm]
D – telescope aperture in [mm]
In this case Lambda is the wavelength of the light. Depending on the used filters, the appropriate wavelength can be used here for photography.
When viewing with an eyepiece, a distinction is made between photopic (day vision) and scotopic vision (night vision). During the day, the eye is most sensitive at a wavelength of 555 nm, at night it is 507 nm. (https://en.wikipedia.org/wiki/Luminous_efficiency_function)
Telescope aperture
The aperture of a telescope is the primary factor determining how much light it can gather. A larger aperture offers the following advantages:
- The formula for resolving power shown above reveals a linear relationship between the telescope’s aperture and its resolving power. If the aperture doubles, the resolving power is halved. The resolving power is therefore improved by a factor of 2.
Or to put it another way: If the Rayleigh criterion formula, which considers the radius, is extended to the diameter of a diffraction spot, it becomes clear that as the telescope aperture increases, the diameters of the Airy disk decrease, thereby revealing detailed information about objects.
- Faint objects such as galaxies and nebulae appear brighter when the focal length remains constant (because more light is projected onto the sensor).
Since the telescope aperture is a circular area, increasing the aperture has a quadratic effect. If the aperture is doubled, the light-gathering power quadruples. - But: the larger the aperture, the more sensitive the telescope is to air turbulence (seeing)
Telescope focal length
The telescope focal length (usually denoted by 'f') determines the magnification (visual in conjunction with an eyepiece) or the angle of view (when using a camera). An area of sky is projected onto the chip. The higher the focal length, the larger the objects appear. However, this also reduces the section that can be seen, which makes it more difficult to find objects and prevents the observation of large-area objects.
schematic illustration to visualize the focal length
With long focal lengths, aberrations are less significant because the light does not have to be refracted as much on the way from the telescope entrance to the focal point.
To get an impression of what commercially available telescopes with their different focal lengths can normally capture for a section of the sky, an illustrative image is shown below.
The following assumptions apply:
- The same camera chip is always used (APS-C format, 22.2x14.8 mm)
- No accessories like reducers or barlow lenses are used
- The following telescopes are compared:
- Telephoto lens with 280 mm focal length
- Refractor with 480 mm focal length
- Newtonian telescope with 1000 mm focal length
- Schmidt-Cassegrain-Telescope (SC) with 2000 mm focal length
Source: Rho Ophiuchi Komplex, Giuseppe Donatiello, CC0, via Wikimedia Commons (subsequently processed with rectangles for the field of view widths)
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