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

126 CHAPTER 5
As one would expect, for the sine wave the measured amplitude does not depend
on the actual phase (no aliasing). The calculated amplitude has a constant value of
0.32, 64% of the real amplitude 0.5. For the square wave, however, the measured
amplitude indeed depends on the actual phase. It varies with a standard deviation
of 0.04, which is a relative amplitude error of ± 8%. Therefore, if we measure the
amplitude of the square wave input signal in order to determine the demodulation
contrast of the pixels, we have to take into account the actual phase between the
optical input signal and the sampling signal of the demodulation pixel.
Now, what does that mean for our measurements? If we look at the optical input
signals, we see that the light source has a low-pass characteristic. For frequencies
higher than about 5 MHz, the optical signal gradually looks like a sine wave
(concerns the 630 nm LEDs that are also used for the range camera realizations).
The delay between the optical modulation signal of the LEDs and the control
voltages for the photogates (signal demodulation) is about 6 ns (measured). This
corresponds to the following phases at the different modulation frequencies:
1 kHz 6 ns = 0.00216°
10 kHz 6 ns = 0.0216°
100 kHz 6 ns = 0.216°
1 MHz 6 ns = 2.16°
10 MHz 6 ns = 21.6°
20 MHz 6 ns = 43.2°
We see that for frequencies less than 10 MHz the delay of 6 ns does not have a
significant influence on the phase. One can see from Figure 5.13 that, as long as
the phase is 0° or any multiple of π/2, the calculated amplitude of a 4-tap sampled
square wave is correct. Therefore, we can use the algorithm
A = 1/2⋅√ [(A0-A2) 2 +(A1-A3) 2 ] to calculate the amplitude and hence the demodulation
contrast without taking into account the actual signal phase. For frequencies lower
than 10 MHz the phase of the optical input signals is about 0°, so we do not make
any error in calculating the amplitude of the square wave. For 10 MHz and 20 MHz,
the input signal is nearly a sinusoidal wave, where the measured amplitude does
not depend on the phase. We measure the amplitude with a systematic error of
64% in that case. Strictly speaking, for an isolated determination of the pixels’
demodulation performance at high frequencies one would have to correct the
measured amplitude by a factor of 1 / 0.64 = 1.56. This is because, due to a