The prisms in binoculars serve primarily to correct the inverted and laterally reversed image that would otherwise result from the objective and eyepiece alone. A secondary effect is that they fold the light path, so that the binocular is shorter than it would otherwise be, making it easier to handle. As stated above, binoculars are often classified according to their prism type. For modern binoculars without angled eyepieces, there are two basic types: the Porro prism and the roof prism.
Figure 2.3. Image inversion and lateral reversal in Porro prisms.
The Porro prism assembly consists of two isosceles right-angled prisms mounted with their hypotenuses facing each other but with their long axes exactly perpendicular. This latter point is crucial; if they are not exactly at right angles, image rotation (usually referred to as "lean" when it applies to binoculars) will occur. The angle of lean is twice the angle of misalignment and opposite in direction (i.e., a clockwise misalignment of 0.5 degrees will result in an anticlockwise lean of 1.0 degree. The light path in Porro prisms is shown in Figure 2.3. There are four reflections, so the result is a right-handed image. The mutually perpendicular orientation of the prism hypotenuses results in one prism erecting the image and the other reverting it.
It is possible, especially when they are used with objectives of low focal ratio, for Porro prisms to reflect rays that are not parallel to the optical axis in such a manner that they are internally reflected off the hypotenuse of the prism (Figure 2.4a). The ray then emerges from the prism, having been reflected a third time, and contributes only optical "noise" to the image, thus reducing contrast. This extra reflection can be eliminated by putting a groove across the center of the hypotenuse (Figure 2.4b). Grooved prisms are a feature of better-quality Porro prism binoculars.
A development of the Porro prism is the Abbé Erecting System, also known as a Porro Type-2 prism (Figures 2.5 and 2.6). Its lateral offset is 77 percent that of an equivalent Porro prism assembly1, and for this reason it is most frequently
encountered in larger binoculars. For medium-aperture binoculars, it is more common in older instruments, particularly military binoculars from the early and mid-20th Century. Abbé Erecting Systems are usually identifiable by the cylindrical prism housing, although the reverse is not true; i.e. this feature is not diagnostic of the presence of the Abbé system.
An important consideration is the glass used for the prism. Normal borosilicate crown (BK7—the BK is from the German Borkron) glass has a lower refractive index than the barium crown (BaK4—the BaK is from the German Baritleichtkron)
glass that is used in better binoculars. A higher refractive index results in a smaller critical angle, 39.6 degrees in BaK4 as compared to 41.2 degrees in BK7), so there is less light likely to be lost because of nontotal internal reflection in the prisms (Figure 2.7). The difference is more noticeable in wide angle binoculars with objective lenses that have a focal ratio of f/5 or less. The nontotal internal reflection of the peripheral rays of light come from the objective results in vignetting of the image. This effect can easily be seen by holding the binocular up to a light sky or other light surface and examining the exit pupil. The exit pupil of a binocular with BaK4 prisms will be perfectly round, while that of a binocular with BK7 prisms will have tell-tale blue-gray segments around it (Figure 2.8). (Note: Figure 2.8b was taken from a slight angle in order to show the nature of the vignette segments. Viewed from directly behind the exit pupil, there is a square central region with vignette segments on four sides.)
The roof prism is shown in Figure 2.9. It is a combination of a Semi Penta prism (45-degree deviation prism) (Figure 2.10) and a Schmidt roof prism
\ reflected /
\ Light is totally internally reflected
Figure 2.7. BK7 and BaK4 glass. At angles close to the critical angle of BaK4 glass, some light will be lost due to transmission in BK7 glass.
Figure 2.10. Semi penta prism (45 degree deviation prism).
(Figure 2.11). The combination is a compact inversion and reversion prism that results in an almost "straight through" light path. The consequence is a very compact binocular. There is, of course, a limit to the aperture of the roof prism binoculars that is imposed by the "straight through" light path because, the centers of the objectives cannot be separated by more than the observer's interpupillary distance (iPD).
Although the roof prism configuration is physically smaller and thus uses less material in its construction, it tends to be significantly more expensive than a Porro prism binocular of equivalent optical quality. This is because the prism system, particularly the roof itself, must be made to a much higher tolerance (2 arcsec for the roof) than is acceptable for Porro prisms (10arcmin), that is, 300 times as precise! Any thickness or irregularity in the ridge of the roof will result in visible flares, particularly from bright high-contrast objects (i.e. many astronomical targets). Additionally, a result of the wave nature of light is that interference can occur when a bundle (a.k.a. pencil) of rays is separated and recombined, as happens with a roof prism. The consequence is a reduction in contrast. This can be ameliorated by the application of a "phase coating" to the faces of the roof. Binoculars with phase coatings usually have "PC" as part of their designation (see Appendix F).
As you will see from Figure 2-9, the light in a roof prism undergoes six reflections (as compared to four in a Porro prism binocular). This results in a "right-handed" image. The same is true of the Abbe-König roof prisms found in the best roof-prism binoculars. A consequence of the extra reflection and the extra lens (as compared to Porro prisms) is more light loss. In order to achieve a similar quality of image, better anti-reflective coatings need to be used.
The demand for better quality of the optical elements and their coatings in roof-prism binoculars means that they will inevitably be more expensive than Porro prism binoculars of equivalent optical quality. They do, however, offer three distinct advantages:
• They are more compact. This makes them slightly easier to pack and carry; some people (I am one) find the smaller size easier and more comfortable to hold because of the different ergonomics.
• They are usually slightly lighter. This makes them easier to carry and generally less tiring to hold.
• They are easier to waterproof because of the internal focusing. Although one does not normally do astronomy in the rain (the possible exception being the nocturnal equivalent of a "monkeys' wedding"), nitrogen-filled waterproof binoculars are immune to internal condensation in damp/dewy conditions and will not suffer from possible water penetration when used for other purposes such as bird watching or racing.
It is a matter of personal judgment whether these advantages warrant the extra expense. I find that, on account of their relative lightness and compactness, I observe with my 10x42 roof prisms far more than I do with my 10x50 Porro prisms.
An increasing number of astronomical binoculars have 45- or 90-degree eyepieces. There are a wide variety of prism combinations that will achieve this, such as a Porro Type-2 with a Semi Penta prism for 45 degrees or with a Penta prism for 90 degrees. Another 45-degree system uses a Schmidt roof with a rhomboid.
Binoviewers use a combination of a beam splitter and a pair of rhomboidal prisms (Figures 2.12 and 2.13). The beam splitter divides the light into two mutually perpendicular optical paths. A rhomboidal prism merely displaces the axis of the light path without either inverting or reverting it. In some binoviewers pairs of mirrors perform the same function. Cylindrical light tubes may be used to ensure that the optical path length is identical on both sides. Interpupillary distance is adjusted by hinging the device along the axis of the light path from the objective lens or primary mirror.
The system of image stabilization that has been most successful for astronomical purposes is that developed by Canon Inc. It employs what Canon calls a vari-angle prism (Figure 2.14), which consists of two circular glass plates that are joined at their edges by a bellows of a specially developed flexible film. The intervening space is filled with a silicon-based oil of very high refractive index. Microelectronic circuitry senses vibration and actuates the vari-angle prisms so as to compensate for the change in orientation of the binoculars.
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