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

OPTICAL TOF RANGE MEASUREMENT 43
From Equation 2.34 we can deduce that there is a predictable connection between
the measured phase and the real phase. (See also Figure 2.14 k.)
Aliasing phase error for different input signals using 4-tap DFT-detection.
In addition to these analytical considerations, it is helpful to use numerical
simulation in order to obtain the relation between measured and real phase for
periodic input signals differing from the pure sinusoidal wave. We have performed
those simulations for the input signals discussed above and also for several other
input signals. The results are shown in Figure 2.14, which shows the input signal,
the measured and real phase as well as the predictable phase error. Figure 2.14
(a), (c), (e) and (g) show that, for ∆t=T/2, even harmonics do not cause any phase
error (see above). Figure 2.14 (i), (j) and (l) confirm that the short-time integration
∆t plays an important role.
The following table lists the harmonics and their coefficients used for the simulation.
It also summarizes the resulting maximum phase error if no LUT correction is
performed.
Modulation signal even harmonics odd harmonics Error in
degrees
cos - - 0
cos 2 - - 0
cos(x) + cos(2x) 2 - 0
cos(x) + cos(4x) 4 - 0
cos(x) + cos(6x) 6 - 0
cos(x) + cos(3x) - 3 ± 19.5
cos(x) + cos(5x) - 5 ± 11.5
cos(x) + cos(7x) - 7 ± 8.2
cos(x) + cos(3x), ∆t=T/3 - 3 ± 0.3
cos(x) + cos(5x), ∆t=T/5 - 5 0
square wave - 1
/3⋅3, 1 /5⋅5, 1 square wave, ∆t=T/3 -
/7*7, …
1
/3⋅3,
± 4.2
1 /5⋅5, 1 /7⋅7, … ± 3.4
triangle - 1
/9⋅3, 1 /25⋅5, 1 /49⋅7, 1 ramp
1
/2⋅2,
/81⋅9, … ± 2.6
1 /4⋅4, 1 /6⋅6, …
1
/3⋅3, 1 /5⋅5, 1 /7⋅7, … ± 4.2
square wave with linear
combinations of above ± 5.4
falling edge
square wave with
exponential falling edge
combinations of above ± 3.5