Calculations

  • A rangefinder uses equations involving geometry and Gaussian beam physics.
  • To calculate the distance using the transient-time principle, the equation used is:
             pic 7
                https://upload.wikimedia.org/wikipedia/commons/f/f1/20200501_Time_of_flight.svg
  • Where d is the distance between a point A and point B, c is the speed of light, and t is the time it takes for the beam to make around trip from point A to point B.
    • t = ϕ÷ωϕ÷ω
    • where ϕ is the phase delay created by the traveling light beam and ω is the angular frequency of the optical wave.
    • Thus, substituting these in the equation become:
      • D=1÷2ct=cϕ÷2ω=c(Nπ+Δϕ)÷4π𝔣=λ(N+ΔN)÷4D = 1÷2ct = cϕ÷2ω = c(Nπ+Δϕ)÷4π𝔣 = λ(N+ΔN)÷4

      • {\displaystyle D={\frac {1}{2}}ct={\frac {1}{2}}{\frac {c\phi }{\omega }}={\frac {c}{4\pi f}}(N\pi +\Delta \phi )={\frac {\lambda }{4}}(N+\Delta N)
      • {\displaystyle D={\frac {1}{2}}ct={\frac {1}{2}}{\frac {c\phi }{\omega }}={\frac {c}{4\pi f}}(N\pi +\Delta \


 

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