[Telescope parameters] The optical parameters of the astronomical telescope
describe in detail how to see the parameters of the astronomical telescope
Aperture of the objective lens (D)
The aperture of the objective lens is the most important parameter of the telescope, which generally refers to the effective aperture, that is, the diameter of the light, that is, the diameter of the entrance pupil of the telescope, which is the focus of the telescope’s light-gathering ability. The main sign, rather than the diameter size of the glass that refers to the lens. Generally expressed in inches (in) or millimeters (mm), the larger the aperture, the more light it collects, and the better the brightness and clarity of the image.
??Note: 1 in=25.4 mm??
Light gathering ability (light gathering power)
This is the theoretical ability of a telescope to collect light compared to the eye. It is directly proportional to the area of the caliber. First divide the diameter of the telescope (unit: mm) by 7mm (the size of the pupil of a young person’s eye), and then square the obtained quotient. This result is the light-gathering power. For example, the light-gathering power of an 8-inch telescope is 843 ((203.2/7)2 = 843).
Focal length (f)
is the distance from the lens (or primary mirror) to the focal point, usually in millimeters (mm). In general, the longer the focal length of a telescope, the greater its magnification and the larger the image size, but the smaller the field of view. For example, compared with a telescope with a focal length of 1000mm, the magnification and field of view of a 2000mm focal length telescope are 2 times and 1/2 of those of the former, respectively. If you don’t know the focal length, but only the focal ratio, you can get the focal length by calculating: the aperture (unit is mm) multiplied by the focal ratio is the focal length. For example, a lens with an aperture of 8 inches (203.2mm) and a focal ratio of f/10 would have a focal length of 203.2 x 10 = 2032mm.
Relative aperture (A) and focal ratio (1/A)
Telescope effective aperture D The ratio to the focal length f is called the relative aperture or relative aperture A, that is, A=D/f. This is a sign of the light power of the telescope, so it is sometimes called A light power. The imaging illuminance of celestial bodies with viewing surfaces such as comets, nebulae or galaxies is proportional to the square of the relative aperture (A2); the imaging illuminance of so-called linear celestial bodies such as meteors or artificial satellites is proportional to the product of the relative aperture A and the effective aperture D (D2/f). proportional. Therefore, when doing astrophotography, pay attention to choosing the appropriate A or focal ratio 1/A (ie f/D. It is called the aperture number or coefficient on the camera).
Resolution angle
For telescopes, this is the Dawes limit. That is, the ability to separate two closely spaced stars, measured in seconds of arc. The resolving power is directly related to the aperture size, that is, the larger the aperture, the better the resolving power. The theoretical resolving power of a telescope is 4.56 divided by the aperture of the telescope (in inches). For example, the resolving power of an 8-inch telescope is 0.6′ (4.56/8 = 0.6). However, resolving power is also related to atmospheric conditions and the visual acuity of the observer.
Contrast
When viewing low-contrast objects, such as the moon and planets, we expect the highest imaging contrast. Both Newtonian and catadioptric telescopes have a secondary mirror (or secondary mirror) that blocks a portion of the light emitted by the primary mirror. Unless more than 25 percent of the primary mirror is blocked, the contrast of the image is not greatly affected. To calculate the secondary blocking ratio, the primary and secondary mirror areas can be calculated using the formula (pi)r2. Then divide to get. For example, if the secondary mirror diameter of an 8-inch telescope is 2? inches, the blocking rate is 11.8 percent:
8-inch primary area = (pi)r2 = (pi)42 = 50.27
2? inches of secondary area = (pi)r2 = (pi)1.375 = 5.94
Blocking = 5.94 is 11.8 percent of 50.27
Observed Conditions (atmospheric disturbances) are the most important factors affecting contrast and planetary detail.
AIRY DISK BRILLIANCE FACTOR
When you look at the stars with a well-focused telescope, you don’t see a larger image. This is because the stars are so far away from us (so that the emitted light is all collimated and converged directly into a point at the focal plane), so even with a lot of magnification, the stars should appear as points of light, not as points of light Spots or spheres of light. However, if you magnify the telescope to a multiple of 60 times the aperture size (unit: inches), then if you look closely, you will find that there is a halo around the star. This is not the halo of the star itself, but is due to the circular aperture of the telescope. It is caused by the diaphragm and the physical properties of light. On closer inspection, when the star is in the center of the telescope’s field of view, the magnified star map will show two phenomena: a central bright region, called the Airy disk, and one or a series of faint rings around it, called Diffraction ring.
As you increase the size of the aperture, the Airy disk gets smaller. The brightness of the Airy disk (image brightness of a point source star) is proportional to the fourth power of the aperture size. Theoretically, when you double the aperture of a telescope, its resolving power doubles, and its light-gathering power quadruples. But more importantly, you can also 1/4 times the size of the Airy Disk, making the star 16 times as bright.
Exit Light
The exit pupil of a telescope is the diameter of the circular beam exiting the eyepiece in mm. To calculate the exit pupil, divide the aperture (in mm) by the magnification of the eyepiece. For example, an 8-inch (203.2mm) telescope with a 20mm eyepiece with a magnification of 102 would have an exit pupil of 2mm (203.2/102 = 2mm). Alternatively, you can get the exit pupil size by dividing the focal length of the eyepiece by the focal ratio of the telescope.
Magnification
Magnification is one of the least important parameters of a telescope. The magnification of a telescope is actually the ratio of the focal lengths of two separate optical systems??the telescope objective and the eyepiece used.
Divide the focal length (unit: mm) of the telescope objective lens by the focal length (unit: mm) of the eyepiece to obtain the magnification of the telescope. For example, the focal length of a model C8 telescope is 2032mm, if it is equipped with a 30mm eyepiece, the magnification will be 68x (2032/30 = 68), and if you use a 10mm eyepiece, the magnification will become 203x (2032/10 = 203 ). Since the eyepieces are replaceable, the telescope can have different magnifications as needed.
In practice, telescopes have upper and lower magnification limits. This is determined by the laws of optics and the properties of the eye. Ideally, the maximum magnification available to a telescope is about 60 times its aperture size (in inches). If the magnification exceeds this upper limit, the image tends to become dim, with reduced contrast, etc. For example, a telescope with an aperture of 60mm (2.4 inches aperture) has a maximum magnification of 142x. As the magnification continues to increase, the sharpness and detail of the image decreases. Higher magnifications are often used for moon, planet and binary star observations. Those manufacturers who claim that the magnification of 60mm telescopes can reach 375 or even 750 are actually misleading consumers. The lower limit of telescope magnification at night is 3 to 4 times its aperture. The lower limit during the day is 8 to 10 times the caliber. If the magnification is below this lower limit, a black spot will appear in the center of the field of view of a catadioptric or Newtonian telescope due to the projection of the secondary or oblique mirrors.
Limiting magnitude or penetration ability
On a clear, moonless night, the magnitude of the faintest star near the zenith observed with a telescope is called The limit magnitude (mb) is not only related to various objective factors such as the effective aperture of the telescope, the relative aperture, the absorption coefficient of the objective lens, the atmospheric absorption system and the brightness of the sky background, but also the visual sensitivity of the observer. The empirical expressions given by different authors are slightly different. A simpler estimation formula is mb=6.9+5lgD, where D is in cm. For photographic observation, the limit magnitude is also related to the exposure time and the characteristics of the film. There is a commonly used empirical formula: mb=4+5lgD+2.15lgt, where t is the limit exposure time, regardless of the failure of the reciprocity law of the film, nor the influence of city lights. A convenient way to check the limit magnitude of a telescope is to use the standard magnitude of the selected target star at the center of the Subaru cluster, or to estimate or calculate with the standard magnitude (photographic magnitude, pseudo-visual magnitude) of the North Star (NPS).
Diffraction-Limited (Rayleigh Criterion)
Near the focal point, the residual wave aberration of a diffraction-limited telescope is much less than 1/4 Incident light wavelength. Such telescopes are suitable for astronomical telescopes. Near the focal point of the combined optical system, the wave aberration of the individual optical components must be less than 1/4 wavelength. When the wavefront aberration value is reduced (1/8 or 1/10 wavelength), the optical quality is greatly improved.
Near Focus
This is the closest you can see with a telescope on a near-terrestrial mission.
Field of View (??)
The angle of the sky area that can be well imaged by the telescope, directly in the observer’s eye, called the field of view or field of view (??). The field of view of a telescope is often determined at design time. The refracting telescope is limited by the image quality and the field of view is limited, and the reflecting telescope or catadioptric telescope is often limited by the size of the secondary mirror. But for astrophotography, the field of view may also be constrained by the size of the receiver’s pixel size. The field of view of a telescope is inversely proportional to the magnification, the greater the magnification, the smaller the field of view.
When the value of the field of view is unknown, you can measure it yourself. Aim the telescope at a certain star near the celestial equator, adjust the instrument so that the star image passes through the center of the field of view. The instrument does not move (do not turn on the rotator clock), record the time interval of the star passing through the field of view, set it as t seconds, the declination of the star is ??, then the field of view angle is ??=15tcos??
Optical Aberrations
Aberrations are all factors that contribute to imperfect images. There are several aberrations in telescope design, and there is no so-called perfect optical system. Optical design engineers must be able to balance various aberrations to achieve the desired design results. Here are some of the aberrations that exist in different telescopes:
Chromatic aberration: Often seen in the objective lens of a refracting telescope, it is caused by the inability of the lens to focus light of different wavelengths (colors) into a single point. The result is a halo around bright objects. This phenomenon tends to be exacerbated when sensitivity and aperture increase.
Spherical aberration: Prevents light rays passing through a lens (or emitted from a mirror) at different aperture angles from focusing on the same point on the axis. It makes the image of the star appear not as a sharp point, but as a blurred blob of light.
Coma: It is mainly related to the parabolic reflecting telescope, which affects the imaging of off-axis points, and is often more obvious at the edge of the field of view. The image of the stars looks like a V-shaped pattern. For high-quality instruments, the smaller the focal ratio, the more pronounced the coma at the edges, but not the center of the field of view.
Astigmatism: This aberration stretches the image from horizontal to vertical on both sides of the best focus point. This is often the result of poor production or assembly errors.
Field curvature: It means that the surface formed by the precise focusing of light is not a plane, but a curved surface. The center of the image plane may be sharp and in focus, but the edges are out of focus, or vice versa.