numerical aperture ( N.A. ) ; ;

The numerical aperture should be in general close to unity.

This phenomenon results in a loss of contrast especially when using objectives with a high resolving power, typically oil immersion objectives with a high numerical aperture.

is the numerical aperture of the lens as seen from the wafer

According to this equation, minimum feature sizes can be decreased by decreasing the wavelength, and increasing the numerical aperture ( to achieve a tighter focused beam and a smaller spot size ).

The resolvable spatial size of objects viewed through a microscope is limited according to the Rayleigh criterion, the radius to the first null of the Airy disk, to a size proportional to the wavelength of the light used, and depending on the numerical aperture:

where the numerical aperture is defined as for θ being the half-angle of the cone of rays accepted by the microscope objective.

A variation of the cutback technique is the substitution method, in which measurements are made on a full length of fiber, and then on a short length of fiber having the same characteristics ( core size, numerical aperture ), with the results from the short length being subtracted to give the results for the full length.

Photons are emitted spontaneously in all directions, but a proportion of those will be emitted in a direction that falls within the numerical aperture of the fiber and are thus captured and guided by the fiber.

In telecommunications, launch numerical aperture ( LNA ) is the numerical aperture of an optical system used to couple ( launch ) power into an optical fiber.

The numerical aperture with respect to a point P depends on the half-angle θ of the maximum cone of light that can enter or exit the lens.

In optics, the numerical aperture ( NA ) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by

A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture.

This ratio is related to the image-space numerical aperture when the lens is focused at infinity.

Based on the diagram at the right, the image-space numerical aperture of the lens is:

The approximation holds when the numerical aperture is small, but it turns out that for well-corrected optical systems such as camera lenses, a more detailed analysis shows that is almost exactly equal to even at large numerical apertures.

In multimode fibers, the term equilibrium numerical aperture is sometimes used.

A court may strike down a law on the basis of an intuitive feeling that the law is inimical to the numerical majority.

The first step in using a formula is to insert the numerical values of the factors involved in their correct positions in the formula.

Part 1, deals with the classification of crystalline substances by space groups and is not a numerical data compilation.

The instrumental method, however, is about 100 times more sensitive and yields numerical results which can be accurately repeated at will over a period of time.

The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.

In mathematics, the absolute value ( or modulus ) of a real number is the numerical value of without regard to its sign.

A key problem in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.

Chan's method for estimating the mean is numerically unstable when and both are large, because the numerical error in is not scaled down in the way that it is in the case.

In the IERS numerical standards, the speed of light in a vacuum is defined as c < sub > 0 </ sub > = in a vacuum, in accordance with the SI units.

As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes ' numerical definitions and representations.

Although the absolute numerical values of astronomical and historical years only differ by one before year 1, this difference is critical when calculating astronomical events like eclipses or planetary conjunctions to determine when historical events which mention them occurred.

While the numerical difference between the decimal and binary interpretations is relatively small for the prefixes kilo and mega, it grows to over 20 % for prefix yotta, illustrated in the linear-log graph ( at right ) of difference versus storage size.

Magnifying this fault is that the numerical parts of OPS are not themselves typically equal ( league-average slugging percentages are usually 75-100 points higher than league-average on-base percentages ).

These need not be greater numerical losses-if one side is much more numerous than the other than pursuing a strategy based on attrition can work even if casualties on both sides are about equal.

where is the numerical integration step size of the trapezoidal rule used in the bilinear transform derivation.

This is supported by numerical simulations.

The classic French historiography often refers to Coalition troops three times more numerous than those of the King of France ( Philip Contamine is not of this opinion: " In front, his opponents did not have a clear numerical superiority ").

The way in which the numerical instruction value is interpreted is defined by the CPU's instruction set architecture ( ISA ).

*: This number arises so often in numerical linear algebra that it is given a name, the condition number of a matrix.

Other advantages are that one can easily find the first or last elements on the list ( most likely to be useful in the case of numerically sorted data ), or elements in a given range ( useful again in the case of numerical data, and also with alphabetically ordered data when one may be sure of only the first few letters of the sought item or items ).

In many collation algorithms, the comparison is based not on the numerical codes of the characters, but with reference to the collating sequence – a sequence in which the characters are assumed to come for the purpose of collation – as well as other ordering rules appropriate to the given application.

Using these tables, often calculated out to 16 decimal places or more for some functions, one could look up values to plug into the formulas given and achieve very good numerical estimates of some functions.

In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.

The attributes of the characters ( such as magic and fighting ability ) are given as numerical values which can be increased as the gamer progresses and gains rank and experience points through accomplishing goals or fighting enemies.

Keys may be a string of characters, or numerical digits in a given ' radix '.

Empirical thermometers are not in general necessarily in exact agreement with absolute thermometers as to their numerical scale readings, but to qualify as thermometers at all they must agree with absolute thermometers and with each other in the following way: given any two bodies isolated in their separate respective thermodynamic equilibrium states, all thermometers agree as to which of the two has the higher temperature, or that the two have equal temperatures.

Physicist Conrad Longmire has given numerical values for a typical case of the E1 pulse produced by a second generation nuclear weapon such as those used in high altitude tests of Operation Fishbowl in 1962.

The amount of optical power launched into a given fiber by a given transmitter depends on the nature of its active optical source ( LED or laser diode ) and the type of fiber, including such parameters as core diameter and numerical aperture.

The amount of optical power launched into a given fiber by a given transmitter depends on the nature of its active optical source ( LED or laser diode ) and the type of fiber, including such parameters as core diameter and numerical aperture.

Thus, Avogadro's number is a dimensionless quantity and has the numerical value of the Avogadro constant given in base units.

Aircraft were given names or numerical designations by manufacturers, like Ilya Muromets or Anatra Anasal.

The numerical Ewbank system is open-ended, starting from 1, which you can ( at least in theory ) walk up, to the four climbs located in Australia given the hardest currently confirmed grade of 34.

Blofeld is head of the global criminal organisation SPECTRE and is commonly referred to as Number 1, an official numerical position given to members of SPECTRE.

He initially planned to take the offensive against the French, in a move he hoped would lead to the capture of Paris, but was persuaded by his advisors that this was impossible given the vast numerical superiority of the enemy.

One application of SVD to rather large matrices is in numerical weather prediction, where Lanczos methods are used to estimate the most linearly quickly growing few perturbations to the central numerical weather prediction over a given initial forward time period – i. e. the singular vectors corresponding to the largest singular values of the linearized propagator for the global weather over that time interval.

In addition, the differently stained regions and sub-regions are given numerical designations from proximal to distal on the chromosome arms.

A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f ( x ) = 0, for a given function f. Such an x is called a root of the function f.

In this context, a scalar field should also be independent of the coordinate system used to describe the physical system — that is, any two observers using the same units must agree on the numerical value of a scalar field at any given point of physical space.

the logarithms of any given number a to two different bases ( here b and c ) differ only by the constant factor log < sub > c </ sub > b. This constant factor can be considered to represent the conversion factor for converting a numerical representation of the pure ( indefinite ) logarithmic quantity Log ( a ) from one arbitrary unit of measurement ( the unit ) to another ( the unit ), since