The Use and Calibration of the Kern ME5000 Mekometer - SLAC ...

ME5000 Data Reductions
:. 3. Corrected Distance
The correction for refractive index is the refractive index of the standard atmosphere n, divided
by the refractive index of the actual atmosphere nt
D=D%
2.2.2. Beam curvature correction
ns = standard ref. index (1 Xl002845 15) (19)
- nt = *actua.l ref. index
‘l’he laser beam does not follow the chord between instrument and reflector, but follows a gentle arc
whose radius of curvature p is c.7-8 times larger than that of the earth R, Fig. 2.
FIGURE 2. Path curwature of the ME%00 signal
The beam curvature correction K1 is the difference between the arc and the chord,’
D3
K1 = -k2s
22.3. Second Speed Correction
D = distance
R = earth’s radius (see sec. 3.3.1.)
k = coefficient of refraction = R/p = 0.13
On a local scale refractive index and air density decrease more or less uniformly with increasing
altitude. Following its gentle arc, the laser beam passes closer to the earth surface in its midpath, thus
traversing denser air. The second speed correction K2 compensates for this higher refractive index,
03
Kz=-k(1 -WE
Application of these three atmospheric corrections to the raw distance D,, gives D,, the straight-line
slant distance between the instrument and the target,
1 The derivation of the beam curvature correction and the second speed correction is given in most standard
survey texts.
30
(20)
(21)