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The theory of dispersion applied to electro-optical distance measurement and angle measurement

PoG 13, J.C. de Munck, The theory of dispersion applied to electro-optical distance measurement and angle measurement

J.C. de Munck

Publications on Geodesy 13 (Vol. 3 Nr. 4). Delft, 1971. 30 pagina's.
ISBN-13: 978 90 6132 214 6. ISBN-10: 90 6132 214 6.


A general expression is derived for the group propagation time in a dispersive inhomogeneous medium. This expression is more exact than the usual concept of the group refraction index.

The above mentioned expression is applied to an extension of the theory of Moritz. Moritz gives the propagation time and the refractive angle in an inhomogeneous medium as a power series expansion. So first order- and second order corrections or errors are derived for electromagnetic distance measurement on one, two and three wavelengths and for angle measurement on two wavelengths.

For the E.D.M. the following influences are considered: the first order dry air correction for the refraction index, the first order humidity correction, and the dry air-, humidity-, and mixed curvature corrections. For the three-wavelengths method the different temperature dependence for light- and for microwaves and the inaccuracies in the dispersion formulae for the air are also considered.
For angle measurements, where the dispersion effect is extremely small, only the first order corrections for dry air and for humidity are considered.

For E.D.M. an accuracy of a few parts in 109 seems to be obtainable provided that the refractive index of air as a function of the wavelength, the temperature, the pressure and the humidity are known with sufficient accuracy, and provided that the instrumental errors are sufficiently small.
For angle measurement on two optical wavelengths it will be very difficult to obtain a sufficient instrumental accuracy because of the small phase dispersion and because of the serious influence of very local effects in angle measurements.


List of units and symbols  4
Summary  6

  1. Introduction  7
  2. The group propagation time of an amplitude-modulated signal  8
  3. The influence of an inhomogeneous medium on electromagnetic distance measurement using one carrier wave  12
  4. Electromagnetic distance measurement on two optical wavelengths  17
  5. Electromagnetic distance measurement on two optical wavelengths and one micro wavelength  19
  6. A survey of the non-instrumental inaccuracies of electromagnetic distance measurements  22
  7. The dispersion for angle measurements  26
  8. Concluding remarks  29

References  30
Tables  31
Appendixes  39

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