The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system, which help in the analysis of its paraxial properties. In Geometry, Topology and related branches of mathematics a spatial point describes a specific point within a given space that consists of neither Volume In Geometric optics, the paraxial approximation is an Approximation used in ray tracing of light through an optical system (such as a lens) The analysis of an optical system using cardinal points is known as Gaussian optics, named after Carl Friedrich Gauss. Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German
The cardinal points and planes of an optical system include:
- The focal points and focal planes
- The principal planes and principal points
- The surface vertices (or vertexes)
- The nodal points
For a lens, there will be two of each of these, identified by "front" and "rear" depending on whether they are on the input or the output side of the lens, respectively. In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging
These points and planes, together with the aperture stop, and the chief and marginal rays of the system, define the locations and sizes of the entrance and exit pupils of the system, as well as its other image-forming properties, such as the focal length and magnification. In Optics, a ray is an idealized narrow Beam of light. Rays are used to model the propagation of Light through an optical system by dividing the real light In Optics, a ray is an idealized narrow Beam of light. Rays are used to model the propagation of Light through an optical system by dividing the real light In an optical system the entrance pupil is a virtual aperture that defines the area at the entrance of the system that can accept light In Optics, the exit pupil is a virtual Aperture in an optical system An image (from Latin imago) or picture is an artifact usually two-dimensional that has a similar appearance to some subject &mdashusually The focal length of an optical system is a measure of how strongly it converges (focuses or diverges (diffuses Light. Magnification is the process of enlarging something only in appearance not in physical size
More detailed and accurate analysis of an optical system's performance can be achieved by raytracing, either within the paraxial approximation or using "real rays", i. In physics ray tracing is a method for calculating the path of Waves or Particles through a system with regions of varying propagation Velocity, absorption e. rays that refract and reflect according to Snell's law and the law of reflection, without approximation. In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship Specular reflection is the perfect Mirror -like reflection of light (or sometimes other kinds of Wave) from a surface in which light from a single incoming
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Definitions
F, F' front and rear focal points,
P, P' front and rear principal points,
V, V' front and rear surface vertices.
The cardinal points lie on the optical axis of the optical system. In Optics, the term optical axis is used to define a direction along which there is some degree of Rotational symmetry. Each point is defined by the effect the optical system has on rays that pass through that point, in the paraxial approximation. In Optics, a ray is an idealized narrow Beam of light. Rays are used to model the propagation of Light through an optical system by dividing the real light Aperture effects are ignored—rays that do not pass through the aperture stop of the system are ignored in the discussion below.
Focal points and planes
- See also: Focus (optics) and Focal length
The front focal point of an optical system, by definition, has the property that any ray that passes through it will emerge from the system parallel to the optical axis. In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge. The focal length of an optical system is a measure of how strongly it converges (focuses or diverges (diffuses Light. The rear (or back) focal point of the system has the reverse property: rays that enter the system parallel to the optical axis are focused such that they pass through the rear focal point.
The front and rear (or back) focal planes are defined as the planes, perpendicular to the optic axis, which pass through the front and rear focal points. An object an infinite distance away from the optical system forms an image at the rear focal plane. An image (from Latin imago) or picture is an artifact usually two-dimensional that has a similar appearance to some subject &mdashusually For objects a finite distance away, the image is formed at a different location, but rays that leave the object parallel to one another cross at the rear focal plane.
A diaphragm or "stop" at the rear focal plane can be used to filter rays by angle, since:
- It only allows rays to pass that are emitted at an angle (relative to the optical axis) that is sufficiently small. In Optics, the term optical axis is used to define a direction along which there is some degree of Rotational symmetry. (An infinitely small aperture would only allow rays that are emitted along the optical axis to pass. )
- No matter where on the object the ray comes from, the ray will pass through the aperture as long as the angle at which it is emitted from the object is small enough.
Note that the aperture must be centered on the optical axis for this to work as indicated. Using a sufficiently small aperture in the focal plane will make the lens telecentric. A telecentric lens is a compound lens with an unusual geometric property in how it forms images
Similarly, the allowed range of angles on the output side of the lens can be filtered by putting an aperture at the front focal plane of the lens (or a lens group within the overall lens). This is important for DSLR cameras having CCD sensors. A digital single-lens reflex camera ( digital SLR or DSLR) is a Digital camera that uses an automatic mirror system and Pentaprism A charge-coupled device ( CCD) is an analog Shift register, that enables the transportation of analog signals (electric charges through successive stages (capacitors The pixels in these sensors are more sensitive to rays that hit them straight on than to those that strike at an angle. A lens that does not control the angle of incidence at the detector will produce pixel vignetting in the images. In Photography and Optics, vignetting is a reduction of an image's brightness or saturation at the Periphery compared to the image center
Principal planes and points
The two principal planes have the property that a ray emerging from the lens appears to have crossed the rear principal plane at the same distance from the axis that that ray appeared to cross the front principal plane, as viewed from the front of the lens. This means that the lens can be treated as if all of the refraction happened at the principal planes. The principal planes are crucial in defining the optical properties of the system, since it is the distance of the object and image from the front and rear principal planes that determines the magnification of the system. Magnification is the process of enlarging something only in appearance not in physical size The principal points are the points where the principal planes cross the optical axis.
If the medium surrounding the optical system has a refractive index of 1 (e. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium g. , air or vacuum), then the distance from the principal planes to their corresponding focal points is just the focal length of the system. This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. The focal length of an optical system is a measure of how strongly it converges (focuses or diverges (diffuses Light. In the more general case, the distance to the foci is the focal length multiplied by the index of refraction of the medium.
For a thin lens in air, the principal planes both lie at the location of the lens. In Optics, a thin lens is a lens with a thickness (distance along the Optical axis between the two surfaces of the lens that is negligible compared The point where they cross the optical axis is sometimes misleadingly called the optical centre of the lens. Note, however, that for a real lens the principal planes do not necessarily pass through the centre of the lens, and in general may not lie inside the lens at all.
Surface vertices
The surface vertices are the points where each surface crosses the optical axis. They are important primarily because they are the physically measurable parameters for the position of the optical elements, and so the positions of the other cardinal points must be known with respect to the vertices to describe the physical system.
In anatomy, the surface vertices of the eye's lens are called the anterior and posterior poles of the lens[1]. Anatomy (from the Greek anatomia, from ana separate apart from and temnein, to cut up cut open is a branch of Biology that is the consideration The lens is a transparent biconvex structure in the Eye that along with the Cornea, helps to Refract Light to be focused
Nodal points
The front and rear nodal points have the property that a ray aimed at one of them will be refracted by the lens such that it appears to have come from the other, and with the same angle with respect to the optical axis. The nodal points therefore do for angles what the principal planes do for transverse distance. If the medium on both sides of the optical system is the same (e. g. , air), then the front and rear nodal points coincide with the front and rear principal planes, respectively.
The nodal points are widely misunderstood in photography, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the iris diaphragm of the lens is located there, and that this is the correct pivot point for panoramic photography, so as to avoid parallax error. Photography (fә'tɒgrәfi or fә'tɑːgrәfi (from Greek φωτο and γραφία is the process and Art of recording pictures by means of capturing In Optics, a diaphragm is a thin opaque structure with an opening ( Aperture) at its centre Panoramic photography is a format of Photography that aims to create images with exceptionally wide fields of view, but has also come to refer to any photograph that Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between These claims are all false, and generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. The correct pivot point for panoramic photography can be shown to be the centre of the system's entrance pupil. In an optical system the entrance pupil is a virtual aperture that defines the area at the entrance of the system that can accept light [1][2][3]
See also
Notes and references
- ^ Kerr, Douglas A. A film plane is the area inside any Camera where the individual frame of film or digital sensor is positioned during exposure Radius of curvature has specific meaning and Sign convention in Optical design. The vergence (typical symbol L) of a light bundle in Optics is the reciprocal of the distance between the point of focus and a reference plane (2005). The Proper Pivot Point for Panoramic Photography (PDF). The Pumpkin. Retrieved on 2006-03-05. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 363 - Roman Emperor Julian moves from Antioch with an army of 90000 to attack the Sassanid Empire, in a
- ^ van Walree, Paul. Misconceptions in photographic optics. Retrieved on 2007-01-01. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC Item #6.
- ^ Littlefield, Rik (2006-02-06). Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 46 BC - Julius Caesar defeats the combined army of Pompeian followers and Numidians under Metellus Scipio "Theory of the “No-Parallax” Point in Panorama Photography" (pdf). ver. 1. 0. Retrieved on 2007-01-14. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1129 - Formal approval of the Order of the Templar at the Council of Troyes.
- Greivenkamp, John E. (2004). Field Guide to Geometrical Optics, SPIE Field Guides vol. FG01, SPIE. ISBN 0-8194-5294-7.
- Hecht, Eugene (1987). Optics, 2nd ed. , Addison Wesley. ISBN 0-201-11609-X.
- Lambda Research Corporation (2001). OSLO Optics Reference (PDF), Version 6. 1. Retrieved on 2006-03-05. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 363 - Roman Emperor Julian moves from Antioch with an army of 90000 to attack the Sassanid Empire, in a Pages 74–76 define the cardinal points.
External links
- Learn to use TEM
- The Grid — Alain Hamblenne's method for a precise location of the entrance pupil on a DSLR camera
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