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Topic: Numerical aperture

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	Nikon MicroscopyU: Common Formulas in Microscopy: Numerical Aperture
		In the numerical aperture equation, n represents the refractive index of the medium between the objective front lens and the specimen, and
		The numerical aperture of a microscope objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance.
		The numerical aperture of an objective is also dependent, to a certain degree, upon the amount of correction for optical aberration.
	www.microscopyu.com /articles/formulas/formulasna.html (459 words)

	Olympus Microscopy Resource Center: Anatomy of the Microscope - Numerical Aperture and Resolution
		Numerical aperture determines the resolving power of an objective, but the total resolution of a microscope system is also dependent upon the numerical aperture of the substage condenser.
		As the numerical aperture and light cone angle of an objective increases however, the size of the Airy disk decreases as illustrated in Figure 4(b) and Figure 4(c).
		Careful positioning of the substage condenser aperture diaphragm is also critical to the control of numerical aperture and indiscriminate use of this diaphragm can lead to image degradation (as discussed in the section on substage condensers).
	www.olympusmicro.com /primer/anatomy/numaperture.html (2208 words)

	Numerical aperture (microscopy) - Wikipedia, the free encyclopedia
		Numerical aprture is most often used as a measure of the resolving power of a lens; A lens with a larger numerical aperture will be able to visualize finer detail of the specimen the a lens with a smaller numerical aperature.
		Lenses with larger numerical apertures also collect more light from the specimen and will generaly provide a brighter image.
		Numerical aperture is basically a measure of the diameter of the aperture compared to the focal length.
	en.wikipedia.org /wiki/Numerical_aperture_(microscopy) (166 words)

	Olympus Microscopy Resource Center: Anatomy of the Microscope - Numerical Aperture Light Cones: Interactive Java ...
		The light-gathering ability of a microscope objective is quantitatively expressed in terms of the numerical aperture, which is a measure of the number of highly diffracted image-forming light rays captured by the objective.
		As the angular aperture is varied with the slider, the size and shape of the illumination cone entering the objective front lens is altered.
		Theoretically, the highest angular aperture obtainable with a standard microscope objective would be 180 degrees, resulting in a value of 90 degrees for the half-angle utilized in the numerical aperture equation.
	www.olympusmicro.com /primer/java/nuaperture (611 words)

	Station Information - Numerical aperture
		The sine of the vertex angle of the largest cone of meridional rays that can enter or leave an optical system or element, multiplied by the refractive index of the medium in which the vertex of the cone is located.
		This refers to the numerical aperture with respect to the extreme exit angle of a ray emerging from a fiber in which equilibrium mode distribution has been established.
		In microscopy, the numerical aperture () of an objective is:
	www.stationinformation.com /encyclopedia/n/nu/numerical_aperture.html (278 words)

	Apertures
		In such a case, the numerical aperture of the system is determined by the numerical aperture of the illuminating beam, and the paraxial constants correctly describe the system.
		However, the extent of the meridional section of the on-axis beam is no longer determined by the entrance beam radius, which means that the numerical aperture as reported by the paraxial constants command will not be correct (actually, it is not well-established what is meant by the numerical aperture under these circumstances).
		The fractional aperture coordinates used to describe a ray are normalized to the reference surface radius rather than the entrance beam radius.
	www.sinopt.com /software1/usrguide54/evaluate/aperture.htm (1079 words)

	Definition: numerical aperture loss (Site not responding. Last check: 2007-10-21)
		numerical aperture loss: A loss of optical power that occurs at a splice or a pair of mated connectors when the numerical aperture of the "transmitting" fiber exceeds that of the "receiving" fiber, even if the cores are precisely the same diameter and are perfectly aligned.
		[FAA] Note 1: The higher numerical aperture of the transmitting fiber means that it emits a larger cone of light than the receiving fiber is capable of accepting, resulting in a coupling loss.
		[FAA] Note 2: In the opposite case of numerical aperture mismatch, where the transmitting fiber has the lower numerical aperture, no numerical aperture loss occurs, because the receiving fiber is capable of accepting light from any bound mode of the transmitting fiber.
	www.its.bldrdoc.gov /projects/devglossary/_numerical_aperture_loss.html (138 words)

	Dorlands Medical Dictionary
		angle of aperture, angular aperture, the angle formed at a luminous point between the most divergent rays that are capable of passing through the objective of a microscope; called also a.
		external aperture of canaliculus of cochlea, external aperture of cochlear aqueduct, apertura externa canaliculi cochleae.
		median aperture of fourth ventricle, apertura mediana ventriculi quarti.
	www.mercksource.com /pp/us/cns/cns_hl_dorlands.jspzQzpgzEzzSzppdocszSzuszSzcommonzSzdorlandszSzdorlandzSzdmd_a_51zPzhtm (1722 words)

	Encyclopedia: Numerical aperture (microscopy) (Site not responding. Last check: 2007-10-21)
		In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units; it does not change if one alters ones system of units of measurement, for example from English units to metric units.
		The angular aperture of a lens is the apparent angle of the lens aperture as seen from the focal point: where is the focal length is the diameter of the aperture See also f-number numerical aperture Categories: Optics
		A 35mm lens set to f/11, as indicated by the white dot above the f-stop scale on the aperture ring In photography the f-number (focal ratio) expresses the diameter of the diaphragm aperture in terms of the effective focal length of the lens.
	www.nationmaster.com /encyclopedia/Numerical-aperture-(microscopy) (527 words)

	Olympus Microscopy Resource Center: Anatomy of the Microscope - Numerical Aperture and Image Resolution
		This tutorial explores the effects of objective numerical aperture on the resolution of the central bright disks present in the diffraction pattern, commonly known as Airy disks.
		As the slider is moved from left to right, the objective numerical aperture increases and the complex Airy pattern in the view port shrinks, demonstrating a progressively increased resolution of image detail.
		As the slider is moved to higher numerical aperture values (0.50-0.80), the structural outline of the image becomes sharper and higher-order diffraction rings begin to emerge.
	www.olympusmicro.com /primer/java/imageformation/airyna (711 words)

	Numerical aperture
		Note: In multimode fibers, the term equilibrium numerical aperture is sometimes used.
		In microscopy, the numerical aperture ( $A_N$ ) of an objective is:
		where $I$ is the index of refraction of the medium in which the lens is working (1.0 for air, up to 1.56 for oils), and $a$ is the angular aperture of the lens.
	www.ebroadcast.com.au /lookup/encyclopedia/nu/Numerical_aperture.html (292 words)

	Brain Research Institute
		The numerical aperture number is directly related to the cone of light from the specimen at its vertex which is brought into the lens.
		The bigger a cone of light that can be brought into the lens, the higher its numerical aperture is. Therefore the higher the numerical aperture of a lens, the better the resolution of a specimen will be which can be obtained with that lens.
		The second advantage of using a higher numerical aperture is that since more orders of diffraction from the object are brought into the lens, more light generally is brought into a higher numerical aperture lens producing brighter images.
	www.bri.ucla.edu /bri_research/microscopy_numap_reso.asp (887 words)

	Glossary Terms: A (Site not responding. Last check: 2007-10-21)
		In microscopy, a device for measuring simultaneously, the numerical and angular apertures of an objective or condenser.
		In optics an aperture is an opening that restricts the size of the light beam that enters or leaves a lens or lens system and is often controlled by an iris aperture diaphram.
		Aperture size is measured variously according to the field of use of the lens, often by its simple diameter as is that of the telescope.
	resolution.umn.edu /glossary/a.html (2550 words)

	World Intellectual Property Organization (Site not responding. Last check: 2007-10-21)
		The source output aperture of the present invention in a 18preferred embodiment is at least 0.5 na (numerical aperture).
		numerical aperture focus configuration which is typically designed to fill the full 2 9acceptance cone of the mating optical illumination fiber.
		probe and active numerical aperture control apparatus and method of use which 2 provides a unique ferrule or connector for optical fiber connection which uniquely indicates to 2 2the aforesaid apparatus source whether the optical fiber is designed, best suited, or desired for 2 3illumination or laser transmission light or both.
	www.wipo.int /ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=05/16118.050224&ELEMENT_SET=DECL (10021 words)

	Optical disk and optical disk system with numerical aperture of objective lens related to protective layer thickness of ...
		The thickness of the light-transmitting cover falls within the range of 0.05 mm to 0.6 mm, the numerical aperture (NA) of the objective lens is set to fall within the range of 0.55 to 1.10, and the wavelength of the light beam is selected to be between 100 nm to 780 nm.
		Since the numerical aperture NA of the objective lens has a value that is larger than the conventional NA, which ranges from 0.50 to 0.53, the minimum diameter of the convergent rays is decreased and the recording density is increased accordingly.
		The relationship between numerical aperture NA and thicknesses t for a constant coma W.sub.31 equivalent to the coma W.sub.31 when the NA of the objective lens is 0.5 and the thickness t of the light-transmitting substrate (light-transmitting cover) is 1.2 mm is shown in Table 1.
	www.freepatentsonline.com /5910932.html (5009 words)

	Olympus FluoView Resource Center: Total Internal Reflection Fluorescence Microscopy
		The numerical aperture of the Olympus APO 100x/NA 1.65 apochromatic objective lens (Olympus America Inc., Melville, NY) greatly exceeds that of the previously highest numerical aperture objective lens, i.e., the Plan APO 100x/NA 1.4 (Olympus America Inc.).
		The excitation light must pass through the portion of the lens' numerical aperture cone that is greater than 1.38.
		The high numerical aperture of the objective, convenient IX70 configuration, and relative economy of solid-state lasers bring TIRFM into the mainstream of microscopy imaging techniques.
	www.olympusfluoview.com /applications/tirfmintro.html (1285 words)

	Melles Griot Optics Guide - Numerical Aperture and Magnification (Site not responding. Last check: 2007-10-21)
		However, because of the relationship between magnification and numerical aperture, there can be a theoretical limit beyond which increasing the diameter has no effect on light-collection efficiency or image brightness.
		Since the numerical aperture of a ray is given by f/2s, once a focal length and magnification have been selected, the value of NA sets the value of f.
		Thus, if one is dealing with a system in which the numerical aperture is constrained on either the object or image side, increasing the lens diameter beyond this value will increase system size and cost but will not improve performance (i.e., throughput or image brightness).
	www.mellesgriot.com /products/optics/fo_2_3.htm (247 words)

	Glossary Terms: N (Site not responding. Last check: 2007-10-21)
		For a microscope, (the half angle of the cone of light accepted by the objective lens) x (refractive index of the medium between the specimen and the lens).
		It is the sine of one-half the angular aperture times the refractive index of the medium (1.0 for air, 1.515 for Cargille immersion oil, etc.) between objective and specimen.
		The numerical aperture is a measure of the light gathering capacity of the lens system and determines its resolving power and depth of field.
	resolution.umn.edu /glossary/n.html (700 words)

	Numeric aperture, objective lenses and condenser lenses on a microscope
		Numeric aperture, objective lenses and condenser lenses on a microscope
		Numerical Aperture (N.A.): This is a number that expresses the ability of a lens to resolve fine detail in an object being observed.
		It is derived by a mathematical formula (n sine u) and is related to the angular aperture of the lens and the index of refraction of the medium found between the lens and the specimen.
	www.microscope-microscope.org /advanced/numerical-aperture.htm (1056 words)

	Microscope Optics
		The numerical aperture, or N.A., of an objective results from the sine of half of the entrance angle of the light cone (shown as u' in the figure below) multiplied by n, the refractive index of the medium between the cover slip and the objective.
		Numerical aperture generally increases with magnification and/or degree of optical correction.
		Resolution is proportional to the Numerical Aperture of the lens and the Numerical Aperture of the condenser.
	web.uvic.ca /ail/techniques/scope_basics.html (1643 words)

	High-NA Fibers Enable High-Power Lasers - May, 2004 (Site not responding. Last check: 2007-10-21)
		Although the average index of the outer cladding -- calculated from the geometric air-to-glass ratio -- is much smaller than the index of the inner cladding, the numerical aperture of the inner cladding is not correspondingly large.
		Despite the low average index of the outer cladding, the numerical aperture of the inner cladding was disappointingly low.
		To verify their predictions, the researchers measured the numerical aperture of a number of fibers with stretched outer-cladding structures like those in Figures 3 and 4.
	www.photonics.com /spectra/tech/XQ/ASP/techid.1627/QX/read.htm (1059 words)

	Numerical Aperture (Site not responding. Last check: 2007-10-21)
		One of the properties of a fibre which we need to know is called the Numerical Aperture.
		A numerical aperture of 0 means that the fibre gathers no light (corresponding to
		A numerical aperture of 1 means that the fibre gathers all the light that falls onto it (corresponding to
	floti.bell.ac.uk /MATHSPHYSICS/6numeric.htm (62 words)

	Using the Microscope: Basic Tutorial: Part 6: Numerical Aperture, etc. Page 1.
		The Numerical Aperture (N.A.) of the objective in use.
		The ability of the objective to accept diffracted rays of a given angle is however strongly dependent on the refractive indices of the media between the objective and the specimen -- usually some combination of air, water, glass and oil.
		At this point the concept of Numerical Aperture becomes useful, and is dealt with in the next section.
	www.micrographia.com /tutoria/micbasic/micbpt06/micb0600.htm (927 words)

	Olympus FluoView Resource Center: Airy Pattern Basics - Interactive Java Tutorial
		The three-dimensional diffraction pattern formed by a circular aperture near the focal point in a well-corrected microscope is symmetrically periodic along the axis of the microscope as well as radially around the axis.
		Adjacent to the wavelength slider is the Numerical Aperture slider, which is used to modulate the numerical aperture of a virtual objective through which the Airy patterns are generated.
		The Airy pattern radius is governed by the wavelength of illumination and the combined numerical apertures of both the objective and condenser.
	www.olympusfluoview.com /java/airydiskbasics (692 words)

	Melles Griot Optics Guide - Spot On (Site not responding. Last check: 2007-10-21)
		In addition to the fixed numerical aperture, they both have a fixed entrance pupil (image) size.
		Suppose it is necessary, using a singlet lens from the Melles Griot catalog, to couple the output of an incandescent bulb with a filament 1 mm in diameter into an optical fiber as shown in the figure below.
		Assume that the fiber has a core diameter of 100 mm and a numerical aperture of 0.25, and that the design requires that the total distance from the source to the fiber be 110 mm.
	www.mellesgriot.com /products/optics/fo_6_2.htm (370 words)

	Numerical Aperture :: Numerical Aperture for Fiber Optics (Site not responding. Last check: 2007-10-21)
		This angle, beyond which light cannot be carried in a fiber, is called the CRITICAL ANGLE and may be calculated from the two indices of refraction.
		To calculate the Critical Angle, first determine the N.A. (Numerical Aperture).The N.A. of any glass combination may be calculated as follows: (where N1= the index of refraction of the core glass), and N2=(the index of refraction of the cladding glass):
		The Numerical Aperture is an important parameter of any optical fiber, but one which is frequently misunderstood and overemphasized.
	www.fiberoptix.com /technical/numerical-aperature.html (633 words)

	Intro/Background:
		The IEEE standard 802.3z requires that the beam divergence of an optical source be less than the angle of numerical aperture of the fiber in order to ensure signal propagation down the optical fiber.
		The worst possible beam divergence angle given by the unconnectorized 4080-321 VCSEL is 20 degrees at full width-half maximum.
		Since the numerical aperture angle was calculated at half width, the corresponding divergence angle from the VCSEL is 10 degrees.
	www.ece.gatech.edu /academic/courses/ece4006/fall2002/group6/FILES/appendixb.htm (131 words)

	Differential polarization imaging. V. Numerical aperture effects and the contribution of preferential scattering and ...
		Numerical aperture effects and the contribution of preferential scattering and absorption to the circular dichroism images -- Finzi et al.
		Numerical aperture effects and the contribution of preferential scattering and absorption to the circular dichroism images
		on the numerical aperture of the lens used.
	www.biophysj.org /cgi/content/abstract/59/6/1183 (231 words)

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