Optical Design

Activities such as astronomy, nature studies and viewing sports must often be done from a distance. For various reasons we cannot get close enough to the subjects to view them in the detail that is needed. Our eyes are general purpose tools and their resolution is limited, their magnifying properties are minimal and they are limited in how much light that they can gather. We must use optical devices such as telescopes and binoculars to increase our visual range.A telescope is an optical device which makes distant objects appear closer. It samples a small area of view, a field, and then magnifies it so that distant objects appear larger. Parallel light rays entering the telescope are focussed to a single point, called the focus or focal point. These focussed rays are then magnified with a very powerful lens, or more commonly a set of lenses, called an eyepiece, to give enlarged views of distant objects. The eyepiece acts in the reverse direction to the telescope lens, taking the focussed rays and sending them to the eye as parallel rays.

 

REFLECTOR The second method of focussing light is to reflect the rays off of the surface of a curved mirror, producing a type of telescope called a reflector. The most common reflectors in use today are called Newtonians because this design was pioneered by Isaac Newton. A mirror is made by coating the front surface of a concave piece of glass with a reflecting material. Light rays entering the telescope reflect off of the mirror and since they never pass through the glass no false colour is produced.

The surface of the mirror of a high focal ratio reflector can be shaped or figured to that of the surface of a sphere. This works for small reflectors and those with focal ratios of f9 or higher. However, with large reflectors and those with focal ratios of f8 or lower, these spherical mirrors do not bring all of the light rays to the same focal point. The rays from the mirror’s perimeter are focussed at a different point from it’s centre, resulting in an image which lacks contrast due to spherical aberration. To overcome this defect, mirror surfaces are shaped during polishing to a paraboloidal shape which focusses all of the light rays to the same point.
Since the light rays are reflected back up the optical tube by the primary mirror, they must be redirected in order to be viewed. A secondary mirror, which has a flat surface is mounted at a 45 degree angle in the centre of the tube to reflect the rays to the focal point. The secondary is usually oval in shape because this presents a circular shape when viewed from a 45 degree angle. Obstructions, such as secondary mirrors, have a limited visual effect when placed in the path of the light entering the telescope. They modify the diffraction patterns, which can cause very minute loss of contrast, and they reduce the amount of light reaching the focal point. However, they are not seen in the focussed image presented through the eyepiece. Since the eyepiece is near the front of the tube, reflectors can be mounted lower to the ground giving more convenient viewing and greater stability. Only two surfaces need to be shaped, polished and coated and these can be tested separately. This makes them less expensive to produce than other telescope designs. On the negative side, a long optical tube Newtonian on a German equatorial mount can be more susceptible to wind vibrations than shorter designs. Collimation of both mirrors is part of the regular maintenance for reflectors.

 

REFRACTORS There are three basic ways to bring light rays to a focal point. The earliest method used by telescope makers, was to bend the rays by passing them through one or more pieces of glass which had curved, polished surfaces. This method produces a type of telescope called a refractor. Refractors have several advantages over other designs. They are enclosed so that dust and moisture doesn’t enter the optical tube.

They have fixed optics so that they don’t require routine collimation, which means that the optics don’t have to be aligned by the user.They do not have a central obstruction, which reduces the amount of light entering the tube and causes an alteration of the diffraction pattern. The resulting high-contrast, fine-resolution images produced are considered ideal for planetary viewing. A problem with refractors is that since many wavelengths of light are passing through glass, the uneven bending of the rays causes false colour, around bright objects. This must be counteracted with additional lenses and special glass. Since at least four lens surfaces usually have to be very accurately shaped, polished and coated, they are more expensive to produce than other telescope designs.

 

CASSEGRAIN A third group of telescopes, called Cassegrain, are hybrids of the two previous methods. Cassegrain telescopes use a combination of both mirrors and lenses to manipulate and focus the light rays. Examples of these are the Schmidt-Cassegrain, and the Maksutov-Cassegrain.

Schmidt-Cassegrain telescopes use a thin aspherical corrector plate, which is a lens carefully matched to the primary concave mirror to correct for spherical aberration. Parallel light rays enter the telescope through the corrector plate and are then reflected by the primary mirror to a convex secondary mirror which is mounted inside the focal point and concentric with the corrector plate. The secondary mirror reflects the rays back down the tube and through a hole in the centre of the primary. The eyepiece can be placed directly behind the primary mirror or a diagonal can be used to change the angle at which the image is viewed. Focussing may be achieved by moving the primary mirror or by moving the eyepiece.

Maksutov-Cassegrain telescopes are similar to the Schmidt-Cassegrains. They also have a corrector plate to remove spherical aberration, but they use a thick, meniscus lens instead of a Schmidt lens. Light enters through the concave side of the corrector plate and the primary mirror reflects it back up the tube to the secondary which is often a mirrored spot on the convex side of the corrector plate. As with the Schmidt-Cassegrain, the light rays are reflected through a hole in the primary to reach the eyepiece This design is easier to produce than the Schmidt-Cassegrain, but the thicker corrector plate makes it heavier. The Maksutov-Cassegrain telescope was developed in the 1940’s by several different inventors of slightly varying designs. Most commercial Maksutov telescopes available have similar optical designs. The main advantage of this design is that, because the light path is folded back on itself, it provides a very portable, short physical length telescope with a long focal length.

 

Usable Magnifications

Some telescope advertisements include phrases about the very high magnification or power that their instruments can achieve. These telescopes usually have about 60mm (2.4") diameter apertures, and claim magnifications of 600x or more. It is true that their images can be magnified that much but what they end up magnifying is all the turbulence in the air between the telescope and the subject. When you are looking at astronomical objects, you are looking through a column of air that reaches to the edge of space and that column seldom stays still. Similarly, when viewing over land you are often looking through waves of heated air radiating from the ground, houses, buildings, etc. A good rule of thumb is that the usable magnification of a telescope is about 50x per inch (2x per mm) of aperture under good conditions. Values of 3x per millimeter or higher are often quoted for ideal conditions, but these conditions are usually very rare. The final resolution that an astronomical telescope can achieve depends on the amount of light that it can capture. The bigger the aperture, the higher the resolution and therefore the better the image. However, there are times when the earths atmosphere is so unsettled that a smaller aperture will give better results because it sees fewer turbulent zones. A telescope cap with a smaller opening which acts as a mask, can prove to be a useful accessory under these conditions. Sky conditions are usually defined by two atmospheric characteristics, seeing, or the steadiness of the air, and transparency, the clarity of the air due to the amount of water vapour and particulate material present.
 

Correcting optical aberrations

When light is focussed by passing it through a lens made from ordinary glass, such as crown glass, each wavelength of light bends a different amount. This is the reason, we are able to see light separated into its spectrum when it passes through a glass prism. This different bending leads to a problem, because each wavelength focusses at a different point. The result is a focal zone rather than a focal point. When a bright object is viewed through such a lens, it is blurry and has a fringe of false colour. Technically, this is referred to as chromatic aberration. Reflectors dont suffer from this effect because their light rays dont pass through any glass. A second problem, called spherical aberration, occurs when optical surfaces of lenses or mirrors are not properly figured or shaped. As with chromatic aberration, the focal point becomes a focal zone.

The first way telescope makers tried to correct these problems was to make telescopes longer. This results in a higher focal ratio and the aberrations become less pronounced. The focal ratio is the focal length, (the distance from the primary lens or mirror to the focal point), divided by the aperture (the diameter of the primary). Small focal ratio telescopes, often referred to as fast telescopes, are more subject to chromatic aberration. Making telescopes longer is fine for small apertures, but with large apertures they quickly become unwieldy. A second approach is to add another matching lens of a glass having a different refractive index. For example, when positive, low-index, BK7 crown glass is matched with negative, high-index, F2 flint glass, the light rays are bent again so that all wavelengths focus near the same point.

The result is called an achromatic refractor and the matched lenses may either be cemented together, or air-spaced by mounting them in a cell which holds them in their correct positions. The two-element lenses used in todays achromats greatly reduce the chromatic aberration. For example, it has been brought to low levels in Sky-Watcher 1201EQ5 and 15012EQ6. In the ongoing search for the perfect telescope, lens makers produced other lens element combinations and special types of glass, in order to remove all of the false colour. These developments have resulted in semi-apochromatic (almost without colour) and apochromatic (corrected in three colours) refractors but these are very expensive compared to achromatic refractors.

 

Importance of coatings

When light enters or leaves a lens, there is a loss of some transmitted light due to reflection. By applying a surface coating of an antireflective material such as magnesium fluoride, the transmission can be greatly increased and internal flare can be reduced. When all lens surfaces have been coated they are said to be fully-coated and when the surfaces are coated with multiple layers to maximize transmission, the optics are said to be multi-coated.

Coatings also play a big part in the performance of reflectors because not all of the light is reflected; there is a small loss at each mirror surface. Todays reflectors usually have a thin coat of aluminum as the mirror and then an overcoat of silicon monoxide or silicon dioxide to protect it. Silicon dioxide produces a more durable coat than silicon monoxide but requires specialized equipment to apply it and is therefore more expensive. Protection is needed because, in most reflectors, the mirror is open to the elements and deterioration of the reflective layer reduces the resolution of the telescope. All Sky-Watcher reflectors are multi-coated with silicon dioxide for more durability.

 

Resolution

Resolution can be defined as how much detail a particular telescope can see. It is dependent upon the size of the aperture and the quality of the optical surfaces, assuming that the optical system is correctly collimated. If the diameter of the aperture is twice as big then the resolving power should be twice as good. What it really comes down to is that the more light that a telescope can gather, the more detail that it can provide. Resolution is generally stated in arc-seconds and there are sixty arc-seconds in an arc-minute and sixty arc-minutes in a degree.

The second factor that affects resolution is the quality of the lens or mirror surface. Optics which are badly figured, poorly mounted or which have surface imperfections can present many different aberrations. Well made optics where everything snaps into focus are a joy to use. When we look at the moon or a planet through a telescope, we are looking at an extended object and as we increase magnification under good conditions, we see more detail. However, when we look at a star, we are looking at a point source and no matter how much we magnify, it is so far away that all we get is a point of light.

In fact, due to diffraction, we dont even see a point of light through a telescope, we see a circle of light called an Airy disk. The arc-second diameter of this disk decreases as the aperture of the telescope increases. The Airy disk is surrounded by increasingly faint concentric rings of light and the whole grouping is called a diffraction image.

A method that is often used to measure resolution, is to split two very close stars. The ability to separate the two stars is actually the ability to separate their Airy disks. This is often called the resolving power of a telescope. A formula to estimate the distance apart that two equal brightness stars must be to separate them is 4.54 divided by the aperture in inches (or 116 divided by the aperture in mm). This is known as the Dawes limit after the amateur astronomer who derived it in the Nineteenth century. It should be remembered that it is an empirical value, found by trial and error, for approximately magnitude six stars and using an unobstructed telescope. It is frequently exceeded by well made, modern telescopes.
 

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