The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, even though no one realized that the "vibrations" of the wave were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system.
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps.
A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
A 3D projection is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
A total station (TS) or total station theodolite (TST) is an electronic/optical instrument used for surveying and building construction. It is an electronic transit theodolite integrated with electronic distance measurement (EDM) to measure both vertical and horizontal angles and the slope distance from the instrument to a particular point, and an on-board computer to collect data and perform triangulation calculations.
Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom.
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.
Solar irradiance is the power per unit area received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre (W/m2) in SI units.
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 without using a chain or tape, or a separate levelling instrument. Instead of the pole normally employed to mark a point, a staff similar to a level staff is used. This is marked with heights from the base or foot, and is graduated according to the form of tacheometer in use.
Angular distance or angular separation, also known as apparent distance or apparent separation, denoted , is the angle between the two sightlines, or between two point objects as viewed from an observer.
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle, and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted simply as and .
A cave survey is a map of all or part of a cave system, which may be produced to meet differing standards of accuracy depending on the cave conditions and equipment available underground. Cave surveying and cartography, i.e. the creation of an accurate, detailed map, is one of the most common technical activities undertaken within a cave and is a fundamental part of speleology. Surveys can be used to compare caves to each other by length, depth and volume, may reveal clues on speleogenesis, provide a spatial reference for other areas of scientific study and assist visitors with route-finding.
In mathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle θ describing the magnitude of the rotation about the axis. Only two numbers, not three, are needed to define the direction of a unit vector e rooted at the origin because the magnitude of e is constrained. For example, the elevation and azimuth angles of e suffice to locate it in any particular Cartesian coordinate frame.
A vector measuring current meter (VMCM) is an instrument used for obtaining measurements of horizontal velocity in the upper ocean, which exploits two orthogonal cosine response propeller sensors that directly measure the components of horizontal velocity. VMCM was developed in the late 1970s by Drs. Robert Weller and Russ Davis and commercially produced by EG&G Sealink System . The instrument has the capability of one year long deployment at depths of up to 5000 m. Both laboratory and field test results show that the VMCM is capable of making accurate measurements of horizontal velocity in the upper ocean. The VMCM is the current standard for making high quality velocity measurements in near-surface regions and it has been used for benchmarking other current meters.
8 Field Survey Squadron was a unit of the Australian Army and the Royal Australian Survey Corps, being raised in December 1971 at Popondetta, Territory of Papua New Guinea and disbanded twenty-four years later on 1 December 1995 in Port Moresby, Papua New Guinea (PNG). The squadron's initial role was to establish geodetic survey control, establish topographic survey control for mapping, compile and field complete preliminary topographic maps, and conduct other surveys and mapping including acquiring air photography. In 1980 the role changed to provide support and advice to the PNG Defence Force and PNG National Mapping Bureau on all aspects of survey and mapping and to provide liaison support for Australian based survey units on operations in the country.
