For multimodal distributions, the D4σ width is a better choice.

D4σ is shorthand for the diameter that is 4 times σ, where σ is the standard deviation of the horizontal or vertical marginal distribution.

Mathematically, the D4σ beam width in the x-dimension for the beam profile is expressed as

When a beam is measured with a laser beam profiler, the wings of the beam profile influence the D4σ value more than the center of the profile since the wings are weighted by the square of its distance, x < sup > 2 </ sup >, from the center of the beam.

If the baseline value is large or if it is not subtracted out of the image, then the computed D4σ value will be larger than the actual value because the baseline value near the edges of the sensor are weighted in the D4σ integral by x < sup > 2 </ sup >.

Therefore, baseline subtraction is necessary for accurate D4σ measurements.

The D4σ width, unlike the FWHM and 1 / e < sup > 2 </ sup > widths, is meaningful for multimodal marginal distributions — that is, beam profiles with multiple peaks — but requires careful subtraction of the baseline for accurate results.

The D4σ beam width is the ISO standard definition and the measurement of the M² beam quality parameter requires the measurement of the D4σ widths.

Five definitions of the beam width are in common use: D4σ, 10 / 90 or 20 / 80 knife-edge, 1 / e < sup > 2 </ sup >, FWHM, and D86.

For an ideal single-mode Gaussian beam, the D4σ, D86 and 1 / e < sup > 2 </ sup > width measurements would give the same value.

Measurements of the 1 / e < sup > 2 </ sup > width only depend on three points on the marginal distribution, unlike D4σ and knife-edge widths that depend on the integral of the marginal distribution.

1 / e < sup > 2 </ sup > width measurements are noisier than D4σ width measurements.

On the other hand, the D4σ, 1 / e < sup > 2 </ sup >, and FWHM widths encompass fractions of power that are beam-shape dependent.

The other definitions provide complementary information to the D4σ.

The D4σ and knife-edge widths are sensitive to the baseline value, whereas the 1 / e < sup > 2 </ sup > and FWHM widths are not.

A ( named a, plural aes ) is the first letter and vowel in the ISO basic Latin alphabet.

The symbol ua is recommended by the International Bureau of Weights and Measures, and the international standard ISO 80000, while au is recommended by the International Astronomical Union, and is more common in Anglosphere countries.

AES is included in the ISO / IEC 18033-3 standard.

Australian English ( AusE, AuE, AusEng, en-AU < ref > is the language code for Australian English, as defined by ISO standards ( see ISO 639-1 and ISO 3166-1 alpha-2 ) and Internet standards ( see IETF language tag ).</ ref >) is a major variety of the English language and is used throughout Australia.

However, the defining recommendation indicates a change to a system similar to ISO 8601 and astronomical year numbering is likely in the future.

When AA was ported to the English Electric KDF9 computer, the character set was changed to ISO and that compiler has been recovered from an old paper tape by the Edinburgh Computer History Project and is available online, as is a high-quality scan of the original Edinburgh version of the Atlas Autocode manual.

An international standard for this process, ISO 16622 Meteorology — Sonic anemometers / thermometers — Acceptance test methods for mean wind measurements is in general circulation.

Although this document was subsequently adopted by International Organization for Standardization ( ISO ) and subsequent revisions published by ISO have been adopted by ANSI, the name ANSI C ( rather than ISO C ) is still more widely used.

The same standard was ratified by the International Organization for Standardization as ISO / IEC 9899: 1990, with only formatting changes, which is sometimes referred to as C90.

This standard has been withdrawn by ISO / IEC, but is still approved by INCITS.

The symbol for bit, as a unit of information, is either simply " bit " ( recommended by the ISO / IEC standard 80000-13 ( 2008 )) or lowercase " b " ( recommended by the IEEE 1541 Standard ( 2002 )).

British English ( or BrEn, BrE, BE, en-UK or en-GB )< ref > is the language code for British English, as defined by ISO standards ( see ISO 639-1 and ISO 3166-1 alpha-2 ) and Internet standards ( see IETF language tag ).</ ref > is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere.

The fact is due mainly to international wars, both hot and cold.

It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.

The enormous changes in world politics have, however, thrown it into confusion, so much so that it is safe to say that all international law is now in need of reexamination and clarification in light of the social conditions of the present era.

But is the result new barnsful of tested knowledge on the basis of which we can with confidence solve our domestic and international problems??

At the national and international level, then, what is the highest kind of morality for the private citizen represents an instance of political immorality.

and the question before these meetings was, here is a man of international reputation and proved earning power ; ;

The international economy of 1960 is markedly different from that of the early postwar years.

The immediate need for this kind of co-operation is underscored by the strain in this nation's international balance of payments.

If Jews are identified as a religious body in a controversy that comes before a national or international tribunal, it is obviously compatible with the goal of human dignity to protect freedom of worship.

What is required is the full implementation of Article 2 of the Treaty, which provides: `` The Parties will contribute toward the further development of peaceful and friendly international relations by strengthening their free institutions, by bringing about a better understanding of the principles upon which these institutions are founded, and by promoting conditions of stability and well-being.

It is possible that international organization will ultimately supplant the multi-state system, but its proper function for the immediate future is to reform and supplement that system in order to render pluralism more compatible with an interdependent world.

In other words, the Secretary General is to be a nonpartisan, international servant, not a political, national one.

It is the consequence of the system of ideas that constitutes the frame of our international -- and in some degree our domestic -- policy.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

The Office of Foreign and Domestic Commerce is also active in the field of international trade, assisting Rhode Island firms in developing and enlarging markets abroad.

The Peace Corps is not a diplomatic or propaganda venture but a genuine experiment in international partnership.

The United States Government shall have the right to terminate the financing of further sales under this Agreement of any commodity if it determines at any time after June 30, 1961, that such action is necessitated by the existence of an international emergency.

The international unit is equipotent with the USP unit adopted in 1952, which was defined as the amount of activity present in 20 mg of the USP reference substance.

It is not surprising that the international obligations of states were also viewed in terms of contract.

In fact, some -- Anzilotti is the principle example -- went so far as to say that all international law could be traced to the single legal norm, Pacta sunt Servanda.