Almost from the invention of the telescope in the 17th century the advantages of mounting two of them side by side for binocular vision seems to have been explored. Most early binoculars used Galilean optics; that is, they used a convex objective and a concave eyepiece lens. The Galilean design has the advantage of presenting an erect image but has a narrow field of view and is not capable of very high magnification. This type of construction is still used in very cheap models and in opera glasses or theater glasses. The Galilean design is also used in low magnification binocular surgical and jewelers' loupes because they can be very short and produce an upright image without extra or unusual erecting optics, reducing expense and overall weight. They also have large exit pupils making centering less critical and the narrow field of view works well in those applications. These are typically mounted on an eyeglass frame or custom-fit onto eyeglasses.
Binoculars with Keplerian optics
An improved image and higher magnification is achieved in binoculars employing Keplerian optics, where the image formed by the objective lens is viewed through a positive eyepiece lens (ocular).
Since the Keplerian configuration produces an inverted image, different methods are used to turn the image right way up.
Binoculars with erecting lenses
Cross-section of relay lens assembly – system 2.
In aprismatic binoculars with Keplerian optics (which were sometimes called "twin telescopes") each tube has one or two additional lenses (relay lens) between the objective and the ocular. These lenses are used to erect the image. The binoculars with erecting lenses had a serious disadvantage: they are too long. Such binoculars were popular in the 1800s (for example, G.& S. Merz models), but became obsolete shortly after the Karl Zeiss company introduced improved prism binoculars in the 1890s.
Optical prisms added to the design are another way to turn the image right way up, usually in a Porro prism or roof-prisms design.
Porro prism binoculars
Double Porro prism design
Porro prism binoculars are named after Italian optician Ignazio Porro who patented this image erecting system in 1854, which was later refined by makers like the Carl Zeiss company in the 1890s. Binoculars of this type use a pair of Porro prisms in a Z-shaped configuration to erect the image. This results in binoculars that are wide, with objective lenses that are well separated and offset from the eyepieces, giving a better sensation of depth. Porro prism designs have the added benefit of folding the optical path so that the physical length of the binoculars is less than the focal length of the objective.
Abbe-Koenig "roof" prism design
Binoculars with Schmidt-Pechan "roof" prisms
Binoculars using roof prisms may have appeared as early as the 1870s in a design by Achille Victor Emile Daubresse. In 1897 Moritz Hensoldt began marketing roof prism binoculars. Most roof prism binoculars use either the Abbe-Koenig prism (named after Ernst Karl Abbe and
Albert Koenig and patented by Carl Zeiss in 1905) or the Schmidt-Pechan prism (invented in 1899) designs to erect the image and fold the optical path. They have objective lenses that are approximately in line with the eyepieces.
Roof-prisms designs create an instrument that is narrower and more compact than Porro prisms. There is also a difference in image brightness. Porro-prism binoculars will inherently produce a brighter image than Schmidt-Pechan roof-prism binoculars of the same magnification, objective size, and optical quality, because this roof-prism design employs silvered surfaces that reduce light transmission by 12% to 15%. Roof-prisms designs also require tighter tolerances for alignment of their optical elements (collimation). This adds to their expense since the design requires them to use fixed elements that need to be set at a high degree of collimation at the factory. Porro prisms binoculars occasionally need their prism sets to be re-aligned to bring them into collimation. The fixed alignment in roof-prism designs means the binoculars normally will not need re-collimation.
Binoculars are usually designed for specific applications. These different designs require certain optical parameters which may be listed on the prism cover plate of the binoculars. Those parameters are:
Given as the first number in a binocular description (e.g. 7x35, 8x50), magnification is the ratio of the focal length of the objective divided by the focal length of the eyepiece. This gives the magnifying power of binoculars (sometimes expressed as "diameters"). A magnification factor of 7, for example, produces an image 7 times larger than the original seen from that distance. The desirable amount of magnification depends upon the intended application, and in most binoculars is a permanent, non-adjustable feature of the device (zoom binoculars are the exception). Hand-held binoculars typically have magnifications ranging from 7x to 10x, so they will be less susceptible to the effects of shaking hands. A larger magnification leads to a smaller field of view and may require a tripod for image stability. Some specialized binoculars for astronomy or military use have magnifications ranging from 15x to 25x.
Given as the second number in a binocular description (e.g. 7x35, 8x50), the diameter of the objective lens determines the resolution (sharpness) and how much light can be gathered to form an image. When two different binoculars have equal magnification, equal quality, and produce a sufficiently matched exit pupil (see below), the larger objective diameter produces a "brighter" 
and sharper image. An 8×40, then, will produce a "brighter" and sharper image than an 8×25, even though both enlarge the image an identical eight times. The larger front lenses in the 8×40 also produce wider beams of light (exit pupil) that leave the eyepieces. This makes it more comfortable to view with an 8×40 than an 8×25. A 10x50 binoculars is better than an 8x40 for magnification, sharpness and luminous flux. Objective diameter is usually expressed in millimeters. It is customary to categorize binoculars by the magnification × the objective diameter; e.g. 7×50. Smaller binoculars may have a diameter of as low as 22 mm; 35 mm and 50 mm is a common diameter for field binoculars; astronomical binoculars have diameters ranging from 70 mm to 150 mm.
Field of view
The field of view of a pair of binoculars depends on its optical design and in general is inversely proportional to the magnifying power. It is usually notated in a linear value, such as how many feet (meters) in width will be seen at 1,000 yards (or 1,000 m), or in an angular value of how many degrees can be viewed.
Binoculars concentrate the light gathered by the objective into a beam whose diameter, the exit pupil, is the objective diameter divided by the magnifying power. For maximum effective light-gathering and brightest image and to maximize the sharpness, the exit pupil should at least equal the diameter of the pupil of the human eye — about 7 mm at night and about 3 mm daytime, reducing with age. If the cone of light streaming out of the binoculars is larger than the pupil it is going into, any light larger than the pupil is wasted. In daytime use the human pupil is typically dilated about 3 mm, which is about the exit pupil of a 7×21 binocular. Much larger 7×50 binoculars will produce a cone of light bigger than the pupil it is entering, and this light will, in the daytime, be wasted. An exit pupil that is too small will also present an observer with a dimmer view since only a small portion of the light gathering surface of the retina is used. For applications where equipment has to be carried (birdwatching, hunting), users opt for much smaller (lighter) binoculars with an exit pupil that matches their expected iris diameter so they will have maximum resolution and are not carrying the weight of wasted aperture.
A larger exit pupil makes it easier to put the eye where it can receive the light: anywhere in the large exit pupil cone of light will do. This ease of placement helps avoid, especially in large field of view binoculars, vignetting, which brings to an image with the borders darkened because the light from them is partially blocked, and it means that the image can be quickly found which is important when looking at birds or game animals that move rapidly, or for a seaman on the deck of a pitching boat or ship. Narrow exit pupil binoculars may also be fatiguing because the instrument must be held exactly in place in front of the eyes to provide a useful image. Finally, many people use their binoculars at dusk, in overcast conditions, and at night, when their pupils are larger. Thus the daytime exit pupil is not a universally desirable standard. For comfort, ease of use, and flexibility in applications, larger binoculars with larger exit pupils are satisfactory choices even if their capability is not fully used by day.
Eye relief is the distance from the rear eyepiece lens to the exit pupil or eye point. It is the distance the observer must position his or her eye behind the eyepiece in order to see an unvignetted image. The longer the focal length of the eyepiece, the greater the potential eye relief. Binoculars may have eye relief ranging from a few millimeters to 2.5 centimeters or more. Eye relief can be particularly important for eyeglass wearers. The eye of an eyeglass wearer is typically further from the eye piece which necessitates a longer eye relief in order to avoid vignetting and, in the extreme cases, to conserve the entire field of view. Binoculars with short eye relief can also be hard to use in instances where it is difficult to hold them steady.
Close focus distance
Close focus distance is the closest point that the binocular can focus on. This distance varies from about 0.5 m to 30 m, depending upon the design of the binoculars. If the close focus distance is short respect to the magnification, the binocular can be used also to see particulars not visible to the naked eye.
Binocular eyepieces usually consist of three or more lens elements in two or more groups. The lens furthest from the viewer's eye is called the field lens and that closest to the eye the eye lens. The most common configuration is that invented in 1849 by Carl Kellner. In this arrangement, the eye lens is a plano-concave/ double convex achromatic doublet (the flat part of the former facing the eye) and the field lens is a double-convex singlet. A reversed Kellner eyepiece was developed in 1975 and in it the field lens is a double concave/ double convex achromatic doublet and the eye lens is a double convex singlet. The reverse Kellner provides 50% more eye relief and works better with small focal ratios as well as having a slightly wider field.
Wide field binoculars typically utilize some kind of Erfle configuration, patented in 1921. These have five or six elements in three groups. The groups may be two achromatic doublets with a double convex singlet between them or may all be achromatic doublets. These eyepieces tend not to perform as well as Kellner eyepieces at high power because they suffer from astigmatism and ghost images. However they have large eye lenses, excellent eye relief, and are comfortable to use at lower powers.