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

OPTICAL TOF RANGE MEASUREMENT 31
phase as long as the integration time of each sampling point is shorter than the
modulation period of the sampled signal, which is a reasonable claim. Only the
measured amplitude is attenuated by a factor of δ / (∆t⋅sin δ) depending on the
integration interval ∆t, with δ = π⋅∆t / T, T: modulation period. This factor, already
considered in Equation 2.18, leads to a decrease in measured amplitude to 90% of
the real amplitude, if the integration time is chosen as a fourth of the modulation
period ∆t = T/4 = 1/(4f). For ∆t = T/2 the measured amplitude is 64% of the real
amplitude.
In order to increase the SNR (signal to noise ratio) it is possible to perform a
continuous, synchronous sampling of the periodic signal and to accumulate shorttime
integrated sampling points ai belonging to the same phase to the long-time
integrated values AI (see Figure 2.9). This technique can be described as a
convolution or correlation of the input function with a square wave, the sampling
function.
A repetitively accumulated short-time integrated sampling point is given by:
+
⎪⎧
⎛ t − j ⋅N
⋅ tsamp
⎞⎪⎫
Ai
= lim ∫ ⎨s(
t − tϕ
− ( i ⋅ tsamp
) ) ⋅ ∑ rect⎜
⎟⎬dt
Tint
→∞
T
j
t
int ⎪⎩
⎜
⎟
⎝ ∆ ⎠⎪⎭
−
= s
( t − t )
ϕ
Tint
2
2
⎛ t ⎞
⊗ squ⎜
, N⋅
tsamp
⎟
⎝ ∆t
⎠
With: squ(t/a,b): square wave with pulse width a and period b.
a 0
A
a 1
0
∑
= a0,
i
s(t-t ϕ)
a 2
a 3
∆t t samp N·t samp 2·N·t samp
Figure 2.9 Repetitive accumulating sampling.
a 0
a 1
a 2
a 3
a 0
Equation 2.20
ampl.
For very high frequencies a real system can no longer perform integration with
sharp integration boundaries. The necessary electrooptical shutter mechanism has
characteristic rise/fall times and a frequency dependent efficiency as described in
offs.
t