Gesture-Based Interaction with Time-of-Flight Cameras

CHAPTER 2. TIME-OF-FLIGHT CAMERAS
.I(t)
.A
.B
.
.φ
.I0
.t
. received
signal s(t)
. emitted
signal e(t)
Figure 2.2: Measurement principle of TOF cameras based on an intensity-modulated active
illumination unit. The phase difference between the emitted signal e(t) and the received
signal s(t) is denoted by φ, the amplitude of the received signal corresponds to A, the offset
(or DC component) of received signal is given by B, and I0 represents the ambient light
present in the scene.
signal can be reconstructed as follows
Phase φ = atan
Amplitude A =
( )
A0 − A2
A1 − A3
√ (A0 − A2) 2 + (A1 − A3) 2
Offset B = A0 + A1 + A2 + A3
4
2
✞ ☎
✝2.2
✆
✞ ☎
✝2.3
✆
✞ ☎
✝2.4
✆
This concept is illustrated in Figure 2.3. Note that the sampling is done in synchrony
with the modulation frequency of the illumination unit, i.e. the first sample is taken
at the beginning of a new period.
Given the phase shift φ and the modulation frequency fmod we can compute the
distance of the object. To this end, we consider the time delay between the emitted
and received signal which corresponds to φ
ω with ω = 2πfmod. During this time de-
φ c
lay, the light travels a distance of ω , where c denotes the speed of light. Because the
light has to travel from the camera to the object and back to the sensor, the distance
of the object is given by
16
R =
φ c
2 ω .
✞ ☎
✝2.5
✆