Page contents

Carrier wavelengths of selected EDM Air temperature and air pressure Humidity of air Normal atmosphere and distance measurement value to be corrected Formulae Leica TS30, correction of erroneous settings In the library

The refractivity of air for specified atmospheric conditions in the visual and near infrared spectrum is computed, optionally including an . A distance measurement value may be corrected.

≡ START First steps Deutsch

The methods of electronic distance measurement (EDM) are the most important modern geodetic methods of distance measurement. They are predominantly applied for tacheometry (total stations) and for laser scanners. In any case, the propagation velocity of the carrier wave is required. The longer the distance to be measured and the higher the accuracy requirement for the distance measurement value, the more accurate this value must be known or determined. It more or less depends on the following quantities:

• carrier wavelength of the EDM λ
• air temperature t
• air pressure p
• air humidity

From these quantites the refractivity of air and consequently the propagation velocity in the range of validity of their values can be computed. This task is performed by the computation tool .

≡ START First steps Deutsch Carrier wavelengths of selected EDM

Today we practically apply only EDM, which use light waves in the red or near infrared (NIR) spectral range.

Spectral range: red, visible		Spectral range: near infrared (NIR)
EDM/tacheometre/total station	nm	EDM/tacheometre/total station	nm
Kern Mekometer ME5000	633	Leica TC 2003	850
Leica TC 400 / TC 800	658	Leica TC 110	850
Leica TS30 / TM30 / TS02	658	Leica TDA / TMA 5005	850
Trimble S8	660	Trimble 3300	860
Leica TPS 110 / 1100 / 1200	670	ZEISS Rec Elta	860
(prismless+LongRange)		ZEISS ELTA4	869
Leica TPS 110 / 1100 / 1200	780	Trimble S6	870
(on prisms)		ZEISS ELTA3	910

≡ START First steps Deutsch Air temperature and air pressure

At the instant of measurement the temperature of the dry air and the air pressure along the signal path of the EDM must be known or determined. The air temperature is most critical here, because it is required relatively accurate and it is hardly constant over longer distance paths. Moreover, the air temperature changes in time. Best results would be obtained from measurements of air temperature and air pressure at equispaced points distributed over the signal path and the derivation of representative averages of these values. Unfortunately, this approach is too laborious as compared to the benefit, such that it is usually omitted. For short distances only the atmospheric measurement values at the instrument are used.

A temperature error of 1 Kelvin or a pressure error or 3 hPa produce a distance error of about 1 ppm = 1 mm/km.

≡ START First steps Deutsch Humidity of air

The humidity of air is only relevant for measurements of highest accuracy or in cases of wet or hot weather. Optionally, one of the following specifications is possible:

Measure of humidity	Symbol	Unit
partial pressure of the water vapour	e	hPa (hectopascal)
relative humidity of air	h	% (percent)
wet bulb temperature	θ	°C (Celsius)

If this information is not available, the relative humidity of air should be kept at the default value of 60%. This value causes a distance error of at most 2 ppm = 2 mm/km (reference: Leica Geosystems).

≡ START First steps Deutsch Normal atmosphere and distance measurement value to be corrected

Frequently there is an uncorrected distance measurement value to be corrected. This value refers

• either to some mean atmospheric conditions, the normal atmosphere , which is often defined by the manufacturer of the EDM, to avoid corrections in case of low accuracy requirements,
• or to some erroneous atmospheric conditions, because the correct conditions were unknown at the instance of measurement time or could not be taken into account or in case of a misapprehension.

For the correction it is required that the group refractivity of this atmosphere is known. Either the manufacture of the EDM specifies the group refractivity of the normal atmosphere or values of temperature, pressure and humidity of air, for which the uncorrected distance measurement value would be valid, are known. In the second case the group refractivity can be computed in a first run of .

≡ START First steps Deutsch Formulae

We use the formulae recommended by Buck (1981) and Rüeger (2002, p. 87) :

Ngr=	287.6155	+	4.88660  λ2	+	0.06800  λ4	e=	h 100	·10x
Nph=	287.6155	+	1.62887  λ2	+	0.01360  λ4	x=	7.5·t 237.3+t	+0.7857
NL =	273.15 1013.25	·	Ngr·p 273.15+t	−	11.27·e 273.15+t	ew=	6.112·exp	17.502·θ 240.97+θ
ppm=	(No-NL)	/	(1+NL·10-6)			e=	ew− p·(t-θ)·0.00066·(1+0.00115·θ)
D=	D´·(1+ppm·10-6)

Symbols:

Ngr, Nph	group refractivity and phase refractivity of the standard atmosphere t = 0°C, p = 1013.25 hPa, e = 0 hPa, CO2-Gehalt 0,0375%
λ	carrier wavelenght in µm	t	dry bulb air temperature in °C
p	air pressure in hPa	e	partial vapour pressure in hPa
h	air humidity in %	x	auxiliary variable
NL	group refractivity of the real atmosphere	ppm	distance measurement correction in ppm
No	group refractivity of the normal atmosphere	θ	wet bulb temperature
D´,D	uncorrected and corrected distance measurement value, resp.	ew	saturation vapour pressure related to wet­bulb temperature in hPa

≡ START First steps Deutsch Leica TS30, correction of erroneous settings

Using a total station TS30 (manufacturer: Leica Geosystems, coaxial visible red laser, λ = 658 nm = 0,658 µm ) a distance measurement was performed with the erroneous settings

t = 12°C, p = 1013.25 hPa, h = 60 %

The result was D´=175.989 . Actually, at the instance of measurement time along the signal path the following conditions were met:

t = 23°C, p = 990.7 hPa, h = 20 %

The corrected distance is required.

Firstly, the group refractivity N_o of the atmosphere, to which the distance measurement value D´ applies (normal atmosphere), must be computed.

and Compute

The result is 286.34. Secondly, the group refractivity of the real atmosphere N_L is computed. At the same time the distance measurement value is corrected.

and Compute

The correction result amouts to +16.7 ppm , this corresponds to +2.9 mm . The corrected distance is then 175.9919 m . Finally, we want to know about the influence of errors in the atmospheric parameters on the correction. Let us assume the following errors:

Δt = 2°C, Δp = 10 hPa, Δh = 20 %

and Compute

By we obtain for the maximum error of the correction result an amount of 4.8 ppm , this corresponds to 0.84 mm.

Determine the fraction of this error purely due to the error in the air humidity.

Did you know? The refractivity N relates to the refractive index n by N=(n-1)·10⁶.

≡ START First steps Deutsch