# resolution

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## resolution

1. a judicial decision on some matter; verdict; judgment
2. Med
a. return from a pathological to a normal condition
b. subsidence of the symptoms of a disease, esp the disappearance of inflammation without the formation of pus
3. Music the process in harmony whereby a dissonant note or chord is followed by a consonant one
4. the ability of a television or film image to reproduce fine detail
Resolution: images of an optical double of separation 0.8" through apertures (left to right) of 30, 15, and 7.5

## resolution

The ability of a telescope or other instrument to distinguish fine detail, or a numerical measure of that ability. A spectrometer has a chromatic resolution, and an imaging device has a linear resolution or a spatial resolution. Detectors can have an energy resolution.

The spatial or angular resolution of a telescope is the smallest angle between two point objects that produces distinct images. It depends on both the wavelength at which observations are made and on the diameter, or aperture, of the telescope. This minimum angle can be given by the Rayleigh limit:

2.52 × 105 λ/d arc seconds
where λ and d are the wavelength and aperture (in meters). For an optical system the Rayleigh limit is approximately
0.13/d arc seconds
The Dawes limit, originally determined experimentally, gives the angular resolution as
0.12/d arc seconds

When the angular separation of two stars is very small, it might be thought that the use of a large enough aperture or high enough magnification would always resolve the light into two distinct images. Because of diffraction effects however, the image of each star is not a point of light but a disk (see Airy disk). If the two disks substantially overlap then increased aperture or magnification merely gives a larger blur of light, and the telescope has not sufficient resolving power to separate the images. The stars will just be resolved, however, when their Airy disks touch. This gives the Dawes limit. Two stars are at a telescope's Rayleigh limit when the center of the Airy disk of one star falls on the first dark ring of the diffraction pattern of the other. The illustration shows the images of two stars of equal magnitude separated by 0.8 seconds of arc. Viewed under perfect seeing conditions with a 7.5-cm aperture (right) they are not resolved; with 15-cm (center) they are just resolved and with 30-cm (left) they are clearly separated.

The discovery of Pluto's satellite Charon in 1978 shows that the Dawes (or Rayleigh) limit cannot be too strictly applied. Although well above the limiting angle for large telescopes, Charon had not been resolved; it was detected as an elongated photographic image. This is partly because of the difference in brightness and because Pluto is not a point source, but mainly because poor seeing prevented the larger-aperture telescopes from reaching the limiting angle. The distorting effects of the Earth's atmosphere are greatly reduced in telescopes with active or adaptive optics, and are removed in orbiting telescopes. Very high spatial resolution is thus now feasible.

In radio astronomy, where the same formulae for spatial resolution apply but where very much greater wavelengths are studied, apertures maybe 30 times greater than those used in optical telescopes can only give poor resolution. The situation has been greatly improved by the use of aperture synthesis and very long baseline interferometry (VLBI).

## Resolution

(1) A decision adopted as a result of the discussion of a question at a meeting, congress, conference, or session of a collective organ.

(2) An inscription made on a document by an official that contains the decision he has adopted.

## resolution

[‚rez·ə′lü·shən]
(control systems)
The smallest increment in distance that can be distinguished and acted upon by an automatic control system.
(electronics)
In television, the maximum number of lines that can be discerned on the screen at a distance equal to tube height; this ranges from 350 to 400 for most receivers.
(electromagnetism)
In radar, the minimum separation between two targets, in angle or range, at which they can be distinguished on a radar screen. Also known as resolving power.
(mathematics)
For a vector, the determination of vectors parallel to specified (usually perpendicular) axes such that their sum equals the given vector.
(optics)
(organic chemistry)
The process of separating a racemic mixture into the two component optical isomers.
(physics)
For a measurement of energy or momentum of a collection of particles, the difference between the highest and lowest energies at which the response of an instrument to a beam of monoenergetic particles is at least half its maximum value, divided by the energy of the particles.
The procedure of breaking up a vectorial quantity into its components.
(spectroscopy)

## resolution

i. The expression of the fineness of detail that can be recorded by a lens or an emulsion.
ii. The capability of an optical or radar system to distinguish between two objects closely adjacent and display them as separate images. The resolution can be in terms of range or azimuth. The size of the object is not the determining factor but their lateral and/or azimuthal separation. See radar resolution.
iii. A measurement of the smallest detail that can be distinguished by a sensor system under specific conditions.
iv. The measure of the ability of a lens photographic system to distinguish detail under certain specific conditions. The measure of this ability is normally expressed in lines per millimeter or angular resolution. It equates to the shortest distance between two points that allows distinct identification of both points.
v. For raster applications, the resolution is the number of pixels per unit distance or size of a pixel.

## resolution

(hardware)
the maximum number of pixels that can be displayed on a monitor, expressed as (number of horizontal pixels) x (number of vertical pixels), i.e., 1024x768. The ratio of horizontal to vertical resolution is usually 4:3, the same as that of conventional television sets.

## resolution

(logic)
A mechanical method for proving statements of first order logic, introduced by J. A. Robinson in 1965. Resolution is applied to two clauses in a sentence. It eliminates, by unification, a literal that occurs "positive" in one and "negative" in the other to produce a new clause, the resolvent.

For example, given the sentence:

(man(X) => mortal(X)) AND man(socrates).

The literal "man(X)" is "negative". The literal "man(socrates)" could be considered to be on the right hand side of the degenerate implication

True => man(socrates)

and is therefore "positive". The two literals can be unified by the binding X = socrates.

The truth table for the implication function is

A | B | A => B --+---+------- F | F | T F | T | T T | F | F T | T | T

(The implication only fails if its premise is true but its conclusion is false). From this we can see that

A => B == (NOT A) OR B

Which is why the left hand side of the implication is said to be negative and the right positive. The sentence above could thus be written

((NOT man(socrates)) OR mortal(socrates)) AND man(socrates)

Distributing the AND over the OR gives

((NOT man(socrates)) AND man(socrates)) OR mortal(socrates) AND man(socrates)

And since (NOT A) AND A == False, and False OR A == A we can simplify to just

mortal(socrates) AND man(socrates)

So we have proved the new literal, mortal(socrates).

Resolution with backtracking is the basic control mechanism of Prolog.

(networking)

## resolution

(1) See resolve and name resolution.

(2) The number of bits used to record the value of a sample in a digitized signal. See sampling.

(3) The degree of sharpness of a displayed or printed image. Resolution is defined as a matrix of "pixels" per inch.

Screen Pixels Per Inch
A screen resolution of 1920x1200 means 1,920 pixels horizontally across each of 1,200 lines, which run vertically from top to bottom. Very often, a third number is added to the specification to designate colors; for example, 1920x1200x64K indicates a setting of 64,000 colors. However, the third number may also be the refresh rate; for example, 1280x1024x60 means 1280x1024 pixels at 60Hz (refreshed 60 times per second). For a detailed list of all the resolutions used in monitors and TVs, see screen resolution. See also how to select a PC monitor.

Printed Dots Per Inch
For printers and scanners, resolution is expressed as the number of dots per linear inch. 300 dpi means 300x300, or 90,000 dots per square inch. Laser printers and plotters have resolutions from 300 to 1,200 dpi and more, whereas most display screens provide less than 100 dpi. That means jagged lines on screen may smooth out when they print. Scanners have both an optical (physical) resolution and an interpolated resolution, which is computed (see scanner). See lines of resolution and aspect ratio.

Common Screen Resolutions These are some of the resolutions commonly found on monitors. The higher the resolution, the more information (pixels) can be displayed on screen at one time. For a complete list, see screen resolution.

Common Screen Resolutions These are some of the resolutions commonly found on monitors. The higher the resolution, the more information (pixels) can be displayed on screen at one time. For a complete list, see screen resolution.
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