3D Time-of-flight distance measurement with custom - Universität ...

OPTICAL TOF RANGE MEASUREMENT 29
A 0
P opt
f=20 MHz, T=50 ns
∆t
A 1 A 2 A 3 A 0
Figure 2.7 Optical sinusoidally modulated input signal, sampled with 4 sampling
points per modulation period. The signal frequency of 20MHz defines
the unambiguous distance range of 7.5 m.
These general equations are simplified for our application, where we use a
sinusoidal wave (only base frequency, no harmonics) as the modulation signal and
synchronously sample this wave with four equally spaced sampling points of
duration ∆t. The optical input signal is illustrated in Figure 2.7. We can thus rewrite
the above equations to:
Phase ϕ, amplitude A and offset B of a sinusoidal signal obtained by the four
sampling points A0..A3:
A3
− A1
ϕ = atan
A0
− A
Equation 2.17
2
( A − A )
2
δ 3 1 + ( A0
− A2
)
A = ⋅
Equation 2.18
∆t
⋅ sin δ
2
2
A0
+ A1
+ A2
+ A3
B = Equation 2.19
4 ⋅ ∆t
Using DFT, the finite number N of sampling points only allows the determination of
a finite number of N/2-1 discrete frequency components. For this case (N=4), the
system is only sensitive to one discrete frequency. Since this frequency selectivity
is a well-known property of lock-in amplifiers, we also call the demodulation pixels
lock-in pixels.
B
A
t