Верньер шкаласы: өлшеу дәлдігін арттыру құралы

Auxiliary scale of a measurement device, used to increase precision

A vernier scale, named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human estimation error. It may be found on many types of instrument measuring linear or angular quantities, but in particular on a vernier caliper, which measures lengths (including internal and external diameters). The vernier is a subsidiary scale replacing a single measured value pointer, and has for instance ten divisions equal in distance to nine divisions on the main scale. The interpolated reading is obtained by observing which of the vernier scale graduations is coincident with a graduation on the main scale, which is easier to perceive than visual estimation between two points. Such an arrangement can go to a higher resolution by using a higher scale ratio, known as the vernier constant. A vernier may be used on circular or straight scales where a simple linear mechanism is adequate. Examples are calipers and micrometers to measure to fine tolerances, on sextants for navigation, on theodolites in surveying, and generally on scientific instruments. The Vernier principle of interpolation is also used for electronic displacement sensors such as absolute encoders to measure linear or rotational movement, as part of an electronic measuring system.

The first caliper with a secondary scale, which contributed extra precision, was invented in 1631 by French mathematician Pierre Vernier (1580–1637). Its use was described in detail in English in Navigatio Britannica (1750) by mathematician and historian John Barrow. While calipers are the most typical use of vernier scales today, they were originally developed for angle measuring instruments such as astronomical quadrants. In some languages, the vernier scale is called a nonius after Portuguese mathematician and cosmographer Pedro Nunes (Latin Petrus Nonius, 1502–1578). In English, this term was used until the end of the 18th century. Nonius now refers to an earlier instrument that Nunes developed. The name "vernier" was popularised by the French astronomer Jérôme Lalande (1732–1807) through his Traité d'astronomie (2 vols) (1764).

The use of the vernier scale is shown on a vernier caliper which measures the internal and the external diameters of an object. The vernier scale is constructed so that it is spaced at a constant fraction of the fixed main scale. So for a vernier with a constant of 0.1, each mark on the vernier is spaced 9/10 of those on the main scale. If you put the two scales together with zero points aligned, the first mark on the vernier scale is 1/10 short of the first main scale mark, the second is 2/10 short, and so on up to the ninth mark, which is misaligned by 9/10. Only when a full ten marks are counted, is there alignment, because the tenth mark is 10/10—a whole main scale unit—short, and therefore aligns with the ninth mark on the main scale. (In simple words, each , so each decrement of length 0.1 adds 10 times to make one MSD only in 9 divisions of vernier scale division). Now if you move the vernier by a small amount, say, 1/10 of its fixed main scale, the only pair of marks that come into alignment are the first pair, since these were the only ones originally misaligned by 1/10. If we move it 2/10, the second pair aligns, since these are the only ones originally misaligned by that amount. If we move it 5/10, the fifth pair aligns—and so on. For any movement, only one pair of marks aligns and that pair shows the value between the marks on the fixed scale.

Vernier scales work so well because most people are especially good at detecting which of the lines is aligned and misaligned, and that ability gets better with practice, in fact far exceeding the optical capability of the eye. This ability to detect alignment is called vernier acuity. Historically, none of the alternative technologies exploited this or any other hyperacuity, giving the vernier scale an advantage over its competitors.

Direct verniers are the most common. The indicating scale is constructed so that when its zero point coincides with the start of the data scale, its graduations are at a slightly smaller spacing than those on the data scale and so none but the last graduation coincide with any graduations on the data scale. N graduations of the indicating scale cover N − 1 graduations of the data scale. Retrograde verniers are found on some devices, including surveying instruments. A retrograde vernier is similar to the direct vernier, except its graduations are at a slightly larger spacing than on the main scale. N graduations of the indicating scale cover N + 1 graduations of the data scale. The retrograde vernier also extends backwards along the data scale. Direct and retrograde verniers are read in the same manner.

This section includes references to techniques which use the Vernier principle to make fine resolution measurements. Vernier spectroscopy is a type of cavity enhanced laser absorption spectroscopy that is especially sensitive to trace gases. The method uses a frequency comb laser combined with a high finesse optical cavity to produce an absorption spectrum in a highly parallel manner. The method is also capable of detecting trace gases in very low concentration due to the enhancement effect of the optical resonator on the effective optical path length.