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Class of topological space
A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general
Lens_space
Optical lens
A telecentric lens is a special type of optical lens (often an objective lens or a camera lens) that has its entrance or exit pupil, or both, at infinity
Telecentric_lens
Subclass of manifold
precisely the 3-dimensional lens spaces. A lens space is not determined by its fundamental group (there are non-homeomorphic lens spaces with isomorphic fundamental
Spherical_3-manifold
Light bending by mass between source and observer
A gravitational lens is matter, such as a cluster of galaxies or a point particle, in sufficient quantity and density to bend light noticeably from a distant
Gravitational_lens
Representation of mathematical space
Hauptvermutung were built based on lens-spaces: In its original formulation, lens spaces are 3-manifolds, constructed as quotient spaces of the 3-sphere: Let p
Triangulation_(topology)
Topological space
have different normalized symbols, because a few manifolds (such as lens spaces) can have more than one sort of Seifert fibration. Also an oriented fibration
Seifert_fiber_space
Large contact lens resting on the sclera, creating a tear-filled vault over the cornea
A scleral lens, also known as a scleral contact lens, is a large contact lens that rests on the sclera and creates a tear-filled vault over the cornea
Scleral_lens
Optical device which transmits and refracts light
visible light are also called "lenses", such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses. Lenses are used in various imaging
Lens
Type of knot in knot theory
that the 2-sheeted branched cover of the 3-sphere over the knot is a lens space. The names rational knot and rational link were coined by John Conway
2-bridge_knot
Concept of using the Sun as a large lens
gravitational lens or solar gravity lens (SGL) is a theoretical method of using the Sun as a large lens with a physical effect called gravitational lensing. It
Solar_gravitational_lens
Type of n-manifold in topology
which is not a ball (it is the product of the 2-sphere and a line). A lens space L ( p , q ) {\displaystyle L(p,q)} with p ≠ 0 {\displaystyle p\neq 0}
Prime_manifold
Decomposition of a compact oriented 3-manifold by dividing it into two handlebodies
to define the lens space in question. It follows from the structure of the mapping class group of the two-torus that only lens spaces have splittings
Heegaard_splitting
Image artifact in a lens system
A lens flare is a visual artifact caused by light scattering, or flaring, in a lens system. This can happen through light scattered by the imaging mechanism
Lens_flare
Polyhedron with 2 faces
Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an
Dihedron
Class of mathematical knot with special properties
knots with lens space surgeries and classified all the Berge knots. Cameron Gordon conjectured these were the only knots admitting lens space surgeries
Berge_knot
Spherically symmetric gradient-index lens
A Luneburg lens (original German Lüneburg-Linse) is a spherically symmetric gradient-index lens. A typical Luneburg lens's refractive index n decreases
Luneburg_lens
American mathematician (born 1981)
low-dimensional topology. He is a professor at Boston College. Greene solved the lens space realization problem, while he and a co-author have made advances in the
Joshua_Evan_Greene
Type of camera lens with long focal length
A telephoto lens, also known as telelens, is a specific type of a long-focus lens used in photography and cinematography, in which the physical length
Telephoto_lens
Smartphones with the highest optical zoom magnification level
phone-camera hybrids use a retractable lens design, while newer zoom-equipped phones mostly use periscope lenses. In a fixed space, greater focal lengths further
List of longest smartphone telephoto lenses
List_of_longest_smartphone_telephoto_lenses
Lens that is designed to limit the effects of chromatic and spherical aberration
An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected
Achromatic_lens
Six points which determine imaging properties of an optical system
focal plane of the lens (or a lens group within the overall lens), and a sufficiently small aperture will make the lens image-space telecentric. This is
Cardinal_point_(optics)
(pseudo-)Riemannian manifold whose geodesics are reversible
symmetric space but not a symmetric space. Every lens space is locally symmetric but not symmetric, with the exception of the real projective space L ( 2
Symmetric_space
Compact composite lens
A Fresnel lens (/ˈfreɪnɛl, -nəl/ FRAY-nel, -nəl; /ˈfrɛnɛl, -əl/ FREN-el, -əl; or /freɪˈnɛl/ fray-NEL) is a type of composite compact lens which reduces
Fresnel_lens
International Space Station has a large number of cameras, lenses, and other photography equipment on board. Some of the modular lenses that are known
List of cameras on the International Space Station
List_of_cameras_on_the_International_Space_Station
Photographic and cinematographic technique using a large depth of field
foreground to background; the space between the two sharp objects is out of focus. Because split focus diopters only cover half the lens, shots in which they are
Deep_focus
Mathematical set with some added structure
product space Kolmogorov space Lp-space Lens space Liouville space Locally finite space Loop space Lorentz space Mapping space Measure space Metric space Minkowski
Space_(mathematics)
Eye structure
The lens, or crystalline lens, is a transparent biconvex structure in most land vertebrate eyes. Relatively long, thin fiber cells make up the majority
Lens_(vertebrate_anatomy)
Topological invariant of manifolds that can distinguish homotopy-equivalent manifolds
of geometric topology as a distinct field. It can be used to classify lens spaces. Reidemeister torsion is closely related to Whitehead torsion; see (Milnor
Analytic_torsion
Optical device used with a camera to create images
A camera lens, photographic lens or photographic objective is an optical lens or assembly of lenses (compound lens) used in conjunction with a camera
Camera_lens
Wide-angle photographic lens with strong barrel distortion
fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image. Fisheye lenses achieve
Fisheye_lens
Instrument in space to study astronomical objects
2016. "Ultraviolet Waves". NASA Science. 10 August 2016. "Space Telescopes". "Planetary Lensing: Enter the 'Terrascope'". Centauri Dreams. August 12, 2019
Space_telescope
Camera lens with fixed focal length
In film and photography, a prime lens is a fixed focal length photographic lens (as opposed to a zoom lens), typically with a maximum aperture from f/2
Prime_lens
Camera technique
the use of camera movements that change the orientation or position of the lens with respect to the film or image sensor on cameras. Sometimes the term is
Tilt–shift_photography
Feature seen when light is gravitationally lensed by an object
optical follow-up with the Hubble Space Telescope of a gravitational lens imaged with MERLIN. The galaxy causing the lens at B1938+666 is an ancient elliptical
Einstein_ring
Aesthetic quality of blur in the out-of-focus parts of an image
the lens renders out-of-focus points of light". Differences in lens aberrations and aperture shape cause very different bokeh effects. Some lens designs
Bokeh
Topological space with only one nontrivial homotopy group
M. This is a consequence of the Cartan–Hadamard theorem. An infinite lens space L ( ∞ , q ) {\displaystyle L(\infty ,q)} given by the quotient of S ∞
Eilenberg–MacLane_space
Space Odyssey character
hardware is shown toward the end of the film, he is mostly depicted as a camera lens containing a red and yellow dot, with such units located throughout the ship
HAL_9000
Type of optical lens
optical surfaces, thicknesses, and formulations, especially as the space between lenses may be considered an "element". With additional degrees of freedom
Doublet_(lens)
Type of topological space
the Universal coefficient theorem. Complex projective space Quaternionic projective space Lens space Real projective plane See the table of Don Davis for
Real_projective_space
4-manifold. Brieskorn manifold Exotic sphere Homology sphere Homotopy sphere Lens space Spherical 3-manifold Einstein manifold Ricci-flat manifold G2 manifold
List_of_manifolds
Duality in string theory
it, which leads to Lens spaces L ( p , q ) {\displaystyle L(p,q)} . Gopakumar–Vafa duality can only be carried over to the Lens space L ( p , 1 ) {\displaystyle
Gopakumar–Vafa_duality
Concept of using Earth's atmosphere as a large lens
Gravitational lens Solar gravitational lens Gravitational microlensing Sloman, Leila (2019-08-14). "Earth Could Be a Lens for a Revolutionary Space Telescope"
Terrestrial_atmospheric_lens
Type of continuous map in topology
\mathbb {Z_{p}} \backslash S^{3}=:L_{p,q}} is the universal covering of the lens space L p , q {\displaystyle L_{p,q}} , hence Deck ( f ) ≅ Z / p Z ≅ π 1 (
Covering_space
Proposed space telescope
Outgoing Cyclopean Astronomical Lens) is a proposed space telescope that would use the Sun as a gravity lens. The gravitational lens effect was first derived
FOCAL_(spacecraft)
fibers Irreducible manifold Isotopy Jet Jordan curve theorem Lens space – A lens space is a quotient of the 3-sphere (or (2n + 1)-sphere) by a free isometric
Glossary of differential geometry and topology
Glossary_of_differential_geometry_and_topology
Earth shield to reduce sunlight
dispersing light before it reaches the Earth by putting a very large lens in space, perhaps at the L1 point between the Earth and the Sun. This plan was
Space_sunshade
Image recognition tool developed by Google
Google Lens is an image recognition technology developed by Google, designed to bring up relevant information related to objects it identifies using visual
Google_Lens
Photographic equipment
lens hood or lens shade is a device used on the front end of a lens to block the Sun or other light source(s) to prevent glare and lens flare. Lens hoods
Lens_hood
Lens system whose pupil is far in front of itself
hypercentric or pericentric lens is a lens system where the entrance pupil is located in front of the lens, in the space where an object could be located
Hypercentric_lens
Camera that typically uses a mirror and prism system
a single-lens reflex camera (SLR) is a type of camera that uses a mirror and prism system to allow photographers to view through the lens and see exactly
Single-lens_reflex_camera
First photographic portrait objective lens
The Petzval objective, or Petzval lens, is the first photographic portrait objective lens (with a 160 mm focal length) in the history of photography.
Petzval_lens
Lens with a variable focal length
opposed to a fixed-focal-length (FFL) lens (prime lens). A true zoom lens or optical zoom lens is a type of parfocal lens, one that maintains focus when its
Zoom_lens
Operation in algebraic topology
type of the configuration space of two points in a lens space depends non-trivially on the simple homotopy type of the lens space. Toda bracket Massey, William
Massey_product
Hole or opening through which light travels
telecentricity. If the aperture stop of a lens is located at the front focal plane of the lens, then it becomes image-space telecentricity, i.e., the lateral
Aperture
Operation used to modify three-dimensional topological spaces
coefficient is b / a {\displaystyle b/a} , then the surgered 3-manifold is the lens space L ( b , a ) {\displaystyle L(b,a)} . In particular if the surgery coefficient
Dehn_surgery
constraints can include realistic lens element center and edge thicknesses, minimum and maximum air-spaces between lenses, maximum constraints on entrance
Optical_lens_design
Compound lens consisting of three single lenses
A triplet lens is a compound lens consisting of three single lenses. The triplet design is the simplest to give the required number of degrees of freedom
Triplet_lens
In imaging optics, a field lens is a positive-powered lens or group of lenses that comes after the objective lens and before the image plane or the eyepiece
Field_lens
Single-lens reflex camera with a digital image sensor and recording mechanism
digital single-lens reflex camera (digital SLR or DSLR) is a digital camera that combines the optics and mechanisms of a single-lens reflex camera with
Digital single-lens reflex camera
Digital_single-lens_reflex_camera
Ray tracing technique
for the compound optical system. For the example of free space of length d followed by a lens of focal length f: L S = [ 1 0 − 1 f 1 ] [ 1 d 0 1 ] = [
Ray_transfer_matrix_analysis
Interface between a camera body and lens
A lens mount is an interface – mechanical and often also electrical – between a photographic camera body and a lens. It is a feature of camera systems
Lens_mount
Measure of how strongly an optical system converges or diverges light
light; it has units of length, and for an idealized thin lens is equal to the distance between the lens and its focal points. A positive focal length indicates
Focal_length
Blue supergiant star in the constellation Leo
Distant Star Ever Seen". Space.com. Retrieved 2 April 2018. Sanders, Robert (2 April 2018). "Hubble peers through cosmic lens to capture most distant star
Icarus_(star)
Airspaced achromatic doublet lens design
dialyte lens (sometimes called a dialyt) is a compound lens design that corrects optical aberrations where the lens elements are widely air-spaced. The design
Dialyte_lens
Type of lens to improve visual perception
A corrective lens is a transmissive optical device that is worn on the eye to improve visual perception. The most common use is to treat refractive errors:
Corrective_lens
Lens implanted in the eye to treat cataracts and/or myopia or hyperopia
An intraocular lens (IOL) is a lens implanted in the eye usually as part of a treatment for cataracts or for correcting other vision problems such as near-sightedness
Intraocular_lens
Concept in mathematics
configuration spaces: such an example was found only in 2005 by Riccardo Longoni and Paolo Salvatore. Their example are two three-dimensional lens spaces, and
Configuration space (mathematics)
Configuration_space_(mathematics)
1968 film by Stanley Kubrick
2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick, who co-wrote the screenplay with Arthur C. Clarke
2001:_A_Space_Odyssey
Gravitational deflection of light
In astronomy, weak gravitational lensing is a technique to map the mass distribution of astronomical objects. As predicted by general relativity, the
Weak_gravitational_lensing
Clear gel within the eyeball, between the lens and retina
body (from Latin vitreus 'glassy') is the clear gel that fills the space between the lens and the retina of the eye (the vitreous chamber) in humans and other
Vitreous_body
Type of lens used in binoculars and astronomic telescopes
flattener lens is a type of lens used in modern binocular designs and in astronomic telescopes to improve edge sharpness. Field flattener lenses counteract
Field_flattener_lens
Extinct genus of trilobites
dragonflies and bees, but with (~100) ommatidia with lenses spaced further apart. There are no lens structures on the top of the eye, so their vision only
Schmidtiellus
intense spot, much smaller than the free space wavelength and the diffraction limit. A simple example of a plasmonic lens is a series of concentric rings on
Plasmonic_lens
Lens or mirror in optical instruments
shrinks. When space is needed, special long working distance objectives can be used. Some microscopes use an oil-immersion or water-immersion lens, which can
Objective_(optics)
2025 Australian film
a mix of Invader Zim and Adventure Time, with "a really queer lens on it." Lesbian Space Princess had four sold-out preview screenings at the Adelaide
Lesbian_Space_Princess
{\displaystyle \mathbb {KP} ^{\infty ,m}} and stunted lens spaces have also been used. James, I. M. (1959), "Spaces associated with Stiefel manifolds", Proceedings
Stunted_projective_space
Series of Soviet 35mm half-frame cameras
distance, since the space behind the lens is limited and insufficient for the rangefinder coupling which protrudes beyond the rear of the lens at infinity. Chaika
Chaika_(camera)
Type of optical telescope
refractor or dioptric telescope) is a type of optical telescope that uses a lens as its objective to form an image. The refracting telescope design was originally
Refracting_telescope
Photography genre and techniques of extreme close-up pictures
Working distance refers to the space between the front of the lens and the subject. This depends on the focal length of the lens and the magnification achieved
Macro_photography
Galaxy cluster in the Ursa Maor constellation
Camera 3 of the Hubble Space Telescope to image the cluster, which demonstrates the effects of gravitational lensing. The lens of SDSS J1152+3313 is not
SDSS_J1152+3313
Optical device for recording images
offering unique capabilities. Single-lens reflex (SLR) cameras provide real-time, exact imaging through the lens. Large-format and medium-format cameras
Camera
types Biconcave lens Biconvex lens Convex-concave lens Plano concave lens Plano convex lens Meniscus lens Designs Wollaston landscape lens There are many
List_of_lens_designs
Canon SLR EF mount prime lens
seven super-telephoto lenses made by Canon. These lenses have an EF mount that work with the EOS line of cameras. These lenses are widely used by sports
Canon_EF_400mm_lens
Mapping class group Orbifolds Examples Exotic sphere Homology sphere Lens space I-bundle topology glossary List of topology topics List of general topology
List of geometric topology topics
List_of_geometric_topology_topics
Camera lens
70–200mm lenses are a group of telephoto zoom full-frame lenses made by Canon. The lenses have an RF mount to work with the R line of cameras. The lens comes
Canon_RF_70–200mm_lens
Space of the eye
exudates—can occur in the potential space in which it creates between the vitreous and the lens, called the retrolenticular space. Som, Peter M.; Curtin, Hugh
Hyaloid_fossa
German optics company
2005. Zeiss later produced lenses for the space industry and, more recently, has again produced high-quality 35 mm camera-lenses. The eastern Zeiss Jena
Zeiss_(company)
-τροπος turning Lens or Vesica shape (the latter taking its name from the shape of the lentil seed); see also mandorla, almond-shaped Lens space Lune, from
Glossary of shapes with metaphorical names
Glossary_of_shapes_with_metaphorical_names
Connects homology and cohomology groups for oriented closed manifolds
elementary homotopy and diffeomorphism classification of 3-dimensional lens spaces. An immediate result from Poincaré duality is that any closed odd-dimensional
Poincaré_duality
Gravitationally lensed image of a quasar
the lensing galaxy is sometimes referred to as QSO 2237+0305 G. Another lensed quasar, HE 0435−1223 in Eridanus, and its surroundings Hubble Space Telescope
Einstein_Cross
Failure of a lens to focus all colors on the same point
fringing, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the
Chromatic_aberration
Microwave antenna
plate lens - a lens made of closely spaced metal plates parallel to the plane of the electric or E field. This is a fast lens. H-plane metal plate lens -
Lens_antenna
systems as a Normal lens or a Telephoto lens. Lens Controller. A lens controller is a device used to control a motorized (ZFI) lens. Lens controllers may
Glossary_of_machine_vision
Model of optics describing light as geometric rays
further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With concave lenses, incoming parallel
Geometrical_optics
Astronomical phenomenon due to the gravitational lens effect
of light by the lens can be resolved with a high resolution telescope such as the Hubble Space Telescope. With microlensing, the lens mass is too low
Gravitational_microlensing
Swiss mathematician
three-dimensional lens spaces and computed their homology, thereby establishing a necessary condition in order for two lens spaces to be homeomorphic
Georges_de_Rham
century led to an array of lens designs intended for photography. The problems of photographic lens design, creating a lens for a task that would cover
History of photographic lens design
History_of_photographic_lens_design
Type of lens
wide-angle lens is a lens covering a large angle of view. Conversely, its focal length is substantially smaller than that of a normal lens for a given
Wide-angle_lens
Gravitationally lensed galaxy
The Cosmic Horseshoe is the nickname given to a gravitationally lensed system of two galaxies in the constellation Leo. The foreground galaxy lies directly
Cosmic_Horseshoe
Mathematical space
Hyperbolic 3-manifold I-bundles Knot and link complements Lens space Seifert fiber spaces, Circle bundles Spherical 3-manifold Surface bundles over the
3-manifold
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