Renishaw RCU10, Installation And User Manual, Page: 184 / 202

Reference G-9
G.2 Air refraction compensation
The equations below define how to calculate the refactive index of air and hence the
current laser wavelength. The equations are defined using the T
90
temperature scale and
have been taken from the following reference.
 Tables of Physical and Chemical Constants - 16
th
Edition
 G.W.C.Kaye & T.H. Laby, Longman (sections 2.5.7 and 3.4.2)
The wavelength of the laser in air (

air
) is related to its wavelength in a vacuum (

vac
) by
the equation

vac
= n x

air
where n is the refractive index of the air.
For standard air (dry air at 15 °C and 101325 Pa, containing 450 ppm by volume of CO
2
)
the refractive index n
s
is given by the dispersion equation from Birch (1994).
( n
s
– 1 ) x 10
8
= 8 342.54 + 2 406 147 (130 -

2
)
-1
+ 15 998 (38.9 -

2
)
-1
where

= 1000 /

vac
(

vac
is expressed in nm)
For dry air at a temperature of t °C and a pressure of p Pa, the refractivity ( n
tp
– 1) is given
by
n
tp
– 1 = p ( n
s
– 1 ) [ 1 + p ( 60.1 – 0.972 t ) x 10
-10
] / [ 96 095.43 ( 1 + 0.003 661 t ) ]
The refractivity of water vapour is less than that of air, so if the air is moist, its refractive
index will be smaller than the value calculated for dry air. In the visible region
(405-644 nm) the relationship is
n
tpf
– n
tp
= – f x R ( 3.7345 – 0.0401

2
) x 10
-12
where n
tpf
is the refractive index of air containing water vapour at relative humidity R
% and where f is the saturated (i.e. 100% RH) water vapour pressure in Pascal.
The saturated water vapour pressure f Pa, in air at temperature of T Kelvin, is given by the
equation from Wagner and Pruss (1993).
ln( f / f
c
) = ( a
1

+ a
2

1.5
+ a
3

3
+ a
4

3.5
+ a
5

4
+ a
6

7.5
) T
c
/ T
where

= 1 - T / T
c
a
1
= -7.859 517 83 a
4
= 22.680 7411
T
c
= 647.096 a
2
= 1.844 082 59 a
5
= -15.961 8719
f
c
= 22 064 000 Pa a
3
= -11.786 6497 a
6
= 1.801 225 02
For example at 34 °C the saturated water vapour pressure is 5325 Pa.