Two point calibration

A two-point calibration or two-point measurement is a calibration or parameter determination in which the dependence of a physical variable on another variable is determined by measuring two different values ​​of . ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle y}$ ${\displaystyle x}$

In mathematical terms, linear relationships are the determination of the function term from two points .

One example is the determination of the dependence of the electrical resistance of a material on the temperature in order to be able to manufacture a resistance thermometer for temperature measurement from it, for example. The prerequisite is that the functional relationship between temperature and resistance is known in terms of its type (here e.g. a linear function ) and that only a maximum of two unknown parameters of this function can be determined (in the example the slope and, if necessary, a zero point Shift).

Applications

Temperature-dependent resistance

The temperature-dependent resistance of an idealized metallic conductor is approximately given by the following relationship:

${\displaystyle R(T)=R_{0}+R_{c}\cdot T}$

It is the drag coefficient and the resistance at absolute zero temperature. By measuring at two temperatures and one obtains two equations with the two unknowns and . Solving the equations gives the desired values. ${\displaystyle R_{c}}$ ${\displaystyle R_{0}}$ ${\displaystyle R(T)}$ ${\displaystyle T_{1}}$ ${\displaystyle T_{2}}$ ${\displaystyle R_{0}}$ ${\displaystyle R_{c}}$

Calibration of liquid thermometers

To calibrate liquid thermometers , the two temperature fixed points ice water (0 ° C, 32 ° F) and boiling water (100 ° C, 212 ° F) were traditionally used to obtain two measuring points on the liquid column. The distance between the points corresponds to the gradient of the function that can be approximated as a linear function, the position corresponds to the zero point shift. The scale between these points is divided according to the temperature unit. For the unit degree Celsius (° C) or Kelvin this is 100 parts and for the Réaumur scale (° Ré) 80 parts.

Two-point exposure metering

The two-point measurement is an exposure measurement (mostly object measurement ) in which the exposure time is determined by measuring the lightest and darkest parts of the image ( spot measurement ).

If the difference in brightness (contrast) between the two measurements is smaller than that which can be processed by the film (digital sensor), the middle between the lightest and the darkest value is usually chosen as the exposure value for the picture. The image could also be specifically overexposed or underexposed without losing information. If the contrast exceeds the possible dynamics of the recording material, you have to decide which area (e.g. lights, mid-tones or shadows) should be reproduced correctly.

When calculating the mean aperture or shutter speed, make sure that these scales are not marked by e.g. B. allow simple averaging to be calculated. The increase by one f-stop (e.g. from 8 to 11) corresponds to halving the shutter speed. Instead of calculating the mean value, it is therefore easier to count the number of "f-stops" or "exposure levels" between the darkest and lightest values ​​and then go back half the number of steps.

The approach is similar to the zone system .