What about the parameters of the telescope?

Abstract: Do you know the optical parameters of astronomical telescope? The aperture of the objective lens is the most important parameter of the telescope, which generally refers to the effective aperture, that is, the light passing diameter, that is, the entrance pupil diameter of the telescope. The focal length (f) is the distance from the lens (or primary mirror) to the focal point, usually in millimeters (mm). Bian Xiao will teach you how to look at the parameters of astronomical telescope. Telescope parameters Optical parameters of astronomical telescope explain how to treat the parameters of astronomical telescope.

Aperture of 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 passing light, that is, the diameter of the entrance pupil of the telescope, which is the main symbol of the telescope's condensing ability, rather than the diameter of the lens glass. Generally expressed in inches (in) or millimeters (mm), the larger the aperture, the more light collected, and the better the brightness and clarity of the image.

(Note: 1 inch = 25.4 mm)

Light-gathering ability (light-gathering ability)

This is the theoretical ability of the telescope to collect light relative to the eyes. It is proportional to the area of the aperture. First, divide the aperture of the telescope (in mm) by 7mm (the size of the pupil of young people's eyes), and then square the quotient, and the result is the light collection ability. For example, an 8-inch telescope focuses 843((203.2/7))? =843)。

Focal length (f)

Is the distance from the lens (or primary mirror) to the focus, usually in millimeters (mm). Generally speaking, the longer the focal length of a telescope, the greater the magnification and the larger the imaging 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 telescope with a focal length of 2000mm are twice that of the former and 1/2, respectively. If you don't know the focal length, but only the focalratio, you can get the focal length by calculation: the aperture (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 length ratio of f/ 10 has a focal length of 203.2x10 = 2032mm.

Relative aperture (a) and focal length ratio (1/A)

The ratio of the effective aperture D to the focal length F of a telescope is called relative aperture or relative aperture A, that is, a = d/f, which is a sign of the optical power of the telescope, so it is sometimes called A optical power. The illumination of visible objects such as comets, nebulae or galaxies is directly proportional to the square of the relative aperture (A2). The illuminance of so-called linear celestial bodies, such as meteors or artificial satellites, is directly proportional to the product (D2/f) of relative aperture A and effective aperture D, so we should pay attention to choosing the appropriate focal ratio of A or 1/A (that is, f/D) when taking celestial photography. Called the aperture number or coefficient on the camera).

Resolution angle

For a telescope, it means Dawsley Mitt. That is, the ability to separate two very close stars, in 1' (sofa arc per second). Resolution is directly related to the aperture size, that is, the larger the aperture, the better the resolution. The theoretical resolution of the telescope is 4.56 divided by the aperture of the telescope in inches. For example, the resolution of an 8-inch telescope is 0.6'(4.56/8 = 0.6). However, the resolution is also related to the atmospheric conditions and the visual acuity of the observer.

contrast

When observing low contrast objects, such as the moon and planets, we expect the highest imaging contrast. Newton's telescope and reflecting telescope both have secondary mirrors (or secondary mirrors), which block part of the light emitted by the primary mirror. Unless more than 25% of the primary mirrors are blocked, the contrast of imaging will not be greatly affected. In order to calculate the secondary blocking rate, the formula (pi)r? Calculate the area of primary mirror and secondary mirror. Then divide it. For example, the diameter of the secondary mirror of an 8-inch telescope is 2? Inches, the shielding rate is 1 1.8%;

Main area of 8 inches =(pi)r? =(pi)4？ =50.27

2? Quadratic area of inch =(π)r? =(pi) 1.375=5.94

The plugging rate of 5.94 is 50.27 1 1.8%.

Observation condition (atmospheric disturbance) is the most important factor affecting contrast and planetary details.

Airy spot brightness factor

When you look at the stars with a well-focused telescope, you won't see the magnified image. This is because the distance between the star and us is so far (so that the light emitted is parallel light and converges directly on the focal plane), so even if magnified many times, the star should look like a light spot, not a light spot or a light ball. However, if the telescope is enlarged to a multiple of 60 times the aperture size (unit: inch), it will be found that there is a halo around the star, which is not the halo of the star itself, but the circular aperture of the telescope and the physical characteristics of light. Further observation, when the star is in the middle of the telescope's field of view, there will be two phenomena in the enlarged star map: there is a bright area in the middle, called Airy spot, and there are one or a series of dim rings around it, called diffraction rings.

When you increase the size of the aperture, the Airy spot will become smaller. The brightness of Airy spot (the image brightness of a star with a point light source) is directly proportional to the fourth power of the aperture size. Theoretically, when you double the aperture of the telescope, its resolution will increase by 1 times, and its light collection capacity will increase by four times. But more importantly, you can also change the area of Airy spot to 1/4 times, thus changing the brightness of stars to 16 times.

Emergent light _

The exit pupil of a telescope refers to the diameter of the circular beam exiting from the eyepiece in mm. In order to calculate the exit pupil, the aperture (in mm) can be divided by the magnification of the eyepiece. For example, for an 8-inch (203.2 mm) telescope, the magnification of the 20-mm eyepiece is 102, so its exit pupil is 2mm(203.2/ 102=2mm). Alternatively, you can divide the focal length of the eyepiece by the focal length ratio of the telescope to get the size of the exit pupil.

magnification times

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 independent optical systems-the telescope objective and the eyepiece used.

The magnification of the telescope can be obtained by dividing the focal length (unit: mm) of the objective lens of the telescope by the focal length (unit: mm) of the eyepiece. For example, the focal length of the telescope with model C8 is 2032mm, and if it is equipped with 30mm eyepiece, the magnification is 68x(2032/30=68). If it is replaced with 10mm eyepiece, the magnification is 203x(2032/ 10=203). Because the eyepiece is replaceable, the telescope can have different magnifications as needed.

In practical use, the telescope has up and down magnification. This is determined by the laws of optics and the characteristics of eyes. In an ideal state, the maximum magnification of a telescope is about 60 times its aperture (in inches). If the magnification exceeds this upper limit, the image will tend to become dim and the contrast will decrease. For example, a telescope with a diameter of 60mm (2.4 inches) has a maximum magnification of 142x. When the magnification continues to increase, the clarity and detail expression of the image will decrease. Higher magnification is usually used to observe the moon, planets and Gemini. Those manufacturers who claim that the magnification of 60mm telescope can reach 375 or even 750 are actually misleading consumers. At night, the lower limit of telescope magnification is 3 to 4 times its aperture. The lower limit of daytime is 8 to 10 times the caliber. If the magnification is lower than this lower limit, a black spot will appear in the center of the field of view of the catadioptric telescope or Newton telescope due to the projection of the secondary mirror or oblique mirror.

Limit quantity or penetration capacity

On a clear moonless night, observing the magnitude of the darkest star near the zenith with a telescope is called the limit magnitude (mb). The limit magnitude is not only related to the effective aperture of the telescope, the relative aperture, the absorption coefficient of the objective lens, the atmospheric absorption system, the brightness of the sky background and many other objective factors, but also related to the visual sensitivity of the observer. The empirical expressions given by different authors are slightly different. The simple estimation formula is mb=6.9+5lgD, where d is in cm. For photographic observation, the limit magnitude is also related to exposure time and film characteristics. There is a commonly used empirical formula: mb=4+5lgD+2. 15lgt, where t is the limit exposure time, regardless of the reciprocity law of negative film and the influence of urban lighting. A simple way to check the limit magnitude of a telescope is to estimate or calculate it by using the standard magnitude of the star selected at the center of the Pleiades or the standard magnitude of the Polaris (NPS).

Diffraction limit (Rayleigh standard)

Near the focal point, the residual wave aberration of the diffraction-limited telescope is much smaller than the incident light wavelength 1/4. Such a telescope is suitable for astronomical telescopes. The wave aberration of a single optical element must be less than 1/4 wavelength near the focus of the combined optical system. When the wavefront aberration decreases (1/8 or110 wavelength), the optical quality will be greatly improved.

Near focus

This refers to the closest distance you can see clearly with a telescope in a near-earth observation mission.

Angle of view (ω)

The angle of the sky area where the telescope can directly image well in the observer's eyes is called the field of view or field of view angle (ω). The field of view of a telescope is usually determined at the time of design. Refractive telescope is limited by image quality, which limits the field of view. Reflective telescopes or refractive reflective telescopes are often limited by the size of the secondary mirror. However, for astrophotography, the field of view may also be limited by the pixel size of the receiver. The field of view of a telescope is inversely proportional to the magnification. The larger the magnification, the smaller the field of view.

When the field of view value is unknown, it can be measured by itself. Aim the telescope at a star near the celestial equator and adjust the instrument to make the star image pass through the center of the field of view. When the instrument is stationary (the rotating clock is not turned on), record the time interval when the star passes through the field of view, which is set to t seconds, the declination of the star is δ, and the field of view angle is ω= 15tcosδ.

Optical aberration

Aberration is all the factors that cause image imperfection. There are several aberrations in telescope design, and there is no perfect optical system. Optical design engineers must be able to balance and control all kinds of aberrations in order to obtain the required design results. The following are some aberrations that exist in different telescopes:

Chromatic aberration: It often appears on the objective lens of a refractive telescope because the lens can't focus light with different wavelengths (colors) on one point. The result is a halo around bright objects. This phenomenon tends to be aggravated when the sensitivity and aperture increase.

Spherical aberration: When light passes through a lens (or emerges from a mirror) at different aperture angles, it cannot be focused on the same point on the axis. This will make the image of the star look like a fuzzy point, not a sharp point.

Coma: It is mainly related to the parabolic reflecting telescope, which affects the imaging of off-axis points, especially at the edge of the field of view. The image of this star looks like a V-shaped pattern. For high-quality instruments, the smaller the focal ratio, the more obvious the coma at the edge, but there will be no coma at the center of the field of view.

Astigmatism: This aberration lengthens the image from a horizontal position to a vertical position on both sides of the best focus. This is usually caused by inferior products or assembly errors.

Field curvature: It means that the curved surface formed by the precise focusing of light is not a plane, but a curved surface. The center of the image plane may be clear and accurately focused, but the edges are out of focus, and vice versa.