handbook of modern sensors

7.5 Optical Sensors 285
is proportional to its intensity. That current will flow to both outputs (A and B) of the
sensors in corresponding proportions to the resistances and, therefore, to the distances
between the point of incidence and the electrodes:
I A = I 0
R D − R x
R D
and I B = I 0
R x
R D
. (7.9)
If the resistances versus distances are linear, they can be replaced with the respective
distances on the surface:
I A = I 0
D − x
D
and
I B = I 0
c
D . (7.10)
To eliminate the dependence of the photoelectric current (and of the light intensity),
we can use a ratiometric technique; that is, we take the ratio of the currents,
which we can rewrite for a value of x:
P = I A
I B
= D x
x =
− 1, (7.11)
D
P + 1 . (7.12)
Figure 7.35 shows geometrical relationships between various distances in the measurement
system. Solving two triangles for L 0 yields
L 0 = f L B
x , (7.13)
where f is the focal distance of the receiving lens. Substituting Eq. (7.12) we obtain
the distance in terms of the current ratio:
L 0 = f L B
(P + 1) = k(P + 1), (7.14)
D
where k is called the module geometrical constant. Therefore, the distance from the
module to the object linearly affects the ratio of the PSD output currents.
A similar operating principle is implemented in an industrial optical displacement
sensor (Fig. 7.37) where a PSD is used for measurement of small displacements at operating
distances of several centimeters. Such optical sensors are highly efficient for
the on-line measurements of the height of a device (printed circuit board inspection,
liquid- and solids-level control, laser torch height control, etc.), for the measurement
of eccentricity of a rotating object, for thickness and precision displacement measurements,
for the detection of the presence or absence of an object (medicine bottle
caps), and so forth. A great advantage of an optical displacement sensor with a PSD
is that its accuracy may be much greater than the accuracy of the PSD itself [12].
The PSD elements are produced of two basic types: one and two dimensional.
Equivalent circuits of both are shown in Fig. 7.38. Because the equivalent circuit
has a distributed capacitance and resistance, the PSD time constant varies depending