A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, or complete rotation, one arcminute is 1/21600 of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth circumference is very near 21600 nmi. A minute of arc is π/10800 of a radian.
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or half-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects, so parallax can be used to determine distances.
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit, defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as rad = m/m. Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.
A spotting scope is a compact lightweight portable telescope optimized for detailed observation of distant objects. They are used as tripod mounted optical enhancement devices for various outdoor activities such as birdwatching, skygazing and other naturalist activities, for hunting and target shooting to verify a marksman's shot placements, for tactical ranging and surveillance, and for any other application that requires higher magnification than ordinary binoculars.
In trigonometry, the gradian – also known as the gon, grad, or grade – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees. It is equivalent to 1/400 of a turn, 9/10 of a degree, or π/200 of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement, initiated as part of metrication and decimalisation efforts.
A reticle, or reticule also known as a graticule, is a pattern of fine lines or markings built into the eyepiece of an optical device such as a telescopic sight, spotting scope, theodolite, optical microscope or the screen of an oscilloscope, to provide measurement references during visual inspections. Today, engraved lines or embedded fibers may be replaced by a digital image superimposed on a screen or eyepiece. Both terms may be used to describe any set of patterns used for aiding visual measurements and calibrations, but in modern use reticle is most commonly used for weapon sights, while graticule is more widely used for non-weapon measuring instruments such as oscilloscope display, astronomic telescopes, microscopes and slides, surveying instruments and other similar devices.
A telescopic sight, commonly called a scope informally, is an optical sighting device based on a refracting telescope. It is equipped with some form of a referencing pattern – known as a reticle – mounted in a focally appropriate position in its optical system to provide an accurate point of aim. Telescopic sights are used with all types of systems that require magnification in addition to reliable visual aiming, as opposed to non-magnifying iron sights, reflector (reflex) sights, holographic sights or laser sights, and are most commonly found on long-barrel firearms, particularly rifles, usually via a scope mount. Similar devices are also found on other platforms such as artillery, tanks and even aircraft. The optical components may be combined with optoelectronics to add night vision or smart device features.
A milliradian is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel. Milliradians are also used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances. When using a scope with both mrad adjustment and a reticle with mrad markings, the shooter can use the reticle as a ruler to count the number of mrads a shot was off-target, which directly translates to the sight adjustment needed to hit the target with a follow-up shot. Optics with mrad markings in the reticle can also be used to make a range estimation of a known size target, or vice versa, to determine a target size if the distance is known, a practice called "milling".
Tacheometry is a system of rapid surveying, by which the horizontal and vertical positions of points on the Earth's surface relative to one another are determined using a tacheometer. It is used without a chain or tape for distance measurement and without a separate levelling instrument for relative height measurements.
A filar micrometer is a specialized eyepiece used in astronomical telescopes for astrometry measurements, in microscopes for specimen measurements, and in alignment and surveying telescopes for measuring angles and distances on nearby objects. "Filar" derives from the Latin filum ("thread"). It refers to the fine threads or wires used in the device.
Stadia marks, also called stadia lines or stadia hairs, are crosshairs on the reticle of a theodolite or other surveying instrument that allow stadiametric rangefinding.
A coincidence rangefinder or coincidence telemeter is a type of rangefinder that uses the principle of triangulation and an optical device to allow an operator to determine the distance to a visible object. There are subtypes split-image telemeter, inverted image, or double-image telemeter with different principles how two images in a single ocular are compared. Coincidence rangefinders were important elements of fire control systems for long-range naval guns and land-based coastal artillery circa 1890–1960. They were also used in rangefinder cameras.
A stereoscopic rangefinder or stereoscopic telemeter is an optical device that measures distance from the observer to a target, using the observer's capability of binocular vision. It looks similar to a coincidence rangefinder, which uses different principles and has only one eyepiece. German instruments tended to use the stereoscopic principle while British ones used coincidence.
Schmidt & Bender is a German company specialized in producing high-end telescopic sights for hunting, sports, law enforcement and military arms.
The PSO-1 is a 4×24 telescopic sight manufactured in Russia by the Novosibirsk instrument-making factory and issued with the Russian military Dragunov sniper rifle. It was introduced on 3 July 1963 together with the Dragunov sniper rifle.
A red dot sight is a common classification for a non-magnifying reflector sight that provides an illuminated red dot to the user as a point of aim. A standard design uses a red light-emitting diode (LED) at the focus of collimating optics, which generates a dot-style illuminated reticle that stays in alignment with the firearm the sight is attached to, regardless of eye position.
In trigonometry, a skinny triangle is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians. The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions or tables can be entirely dispensed with.
Length measurement, distance measurement, or range measurement (ranging) refers to the many ways in which length, distance, or range can be measured. The most commonly used approaches are the rulers, followed by transit-time methods and the interferometer methods based upon the speed of light.
In shooting sports, a shot grouping, or simply group, is the collective pattern of projectile impacts on a target from multiple consecutive shots taken in one shooting session. The tightness of the grouping is a measure of the precision of a weapon, and a measure of the shooter's consistency and skill. On the other hand, the grouping displacement is a measure of accuracy.
