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Non-contact Position Sensing Using Optical Detectors Non-contact Position Sensing Using Optical Detectors
To understand optical position sensing instruments, it's important to
understand the sensors they make use of.These form the heart of the
systems, and fall into two basic categories: segmented and continuous.
Segmented Position Sensing Detectors
Also known as quadrant and bi-cell detectors, these devices have two
or four distinct photosensitive elements separated by a minuscule gap.
A light spot illuminating just one element only produces photocur-
rent in that element.When the spot is translated across the surface of
the detector, the energy becomes distributed between adjacent ele-
ments.The ratio between the photocurrent outputs from these ele-
ments determines the relative position of the spot on the surface.
It's important to note that the detector only provides position
information over a linear distance of the spot diameter. Elsewhere, it is
known to be in a specific segment, but not exactly where. Because of
this, when working with lasers, defocusing may be required in order to
obtain maximum range.
With a segmented device, another spatial consideration is key:The
response to movement of a circular spot is non-linear.This is because
the ratio of the spot's movement to the percentage of its area that
shifts between adjacent segments is nonlinear.
For these reasons, segmented detectors are best used as nulling
and centering devices. And for such applications, their performance is
unparalleled. In fact, a repeatability of 0.1�m has been routinely
demonstrated.This high resolution stems from the almost perfect
response uniformity between elements. Also, with light-level sensitivi-
ties approaching one picowatt, segmented devices will work with far
dimmer sources than will continuous position sensing detectors.
Continuous Position Sensing Detectors
When position sensing applications require measurement over a
wide spatial range, continuous detectors are the right choice.
The primary difference between segmented detectors and continu-
ous ones is that the latter are single photodiode.There is no gap or
dead region between cells.
Continuous position sensing detectors derive position by dividing
photo-generated electrons within their substrate, not by profiling
intensity distribution on the surface as segmented detectors do.
Therefore, a 2-axis continuous sensor acts as a pair of light-controlled
variable resistors that measure the X and Y position of an incident
light spot.
Compared to segmented detectors, the primary advantage of con-
tinuous position sensors is their wide dynamic range:They measure
the position of a light spot right out to their edge. It's also important
to note that these sensors determine the centroid of a light spot.This
gives them the advantage of being indifferent to a spot's shape or
intensity distribution.
Quadrant Detector
A
B
D
C
X Position = (A+D) - (B+C)
A+B+C+D
Y Position = (A+B) - (D+C)
A+B+C+D
Conversion Formulas
The position of a light spot with respect to
center on a quadrant detector is found using:
X=((A+D) - (B+C)) / (A+B+C+D)
Y=((A+B) - (C+D)) / (A+B+C+D)
where A,B,C and D are the photocurrent
produced in each segment.The difference signal is
divided by the sum in order to cancel out the
effects of light level variation.
For continuous position sensors the formulae are
also simple. For a one-dimensional device.
2x/L=(X
2
-X
1
) / (X
1
+X
2
)
Where X
2
and X
1
are the photocurrent signals
from each contact, and x is the position along the
axis.
Similarly, position is calculated for dual-axis
tetra-lateral or duo-lateral devices using:
2x/L=(X
2
-X
1
) / (X
1
+X
2
)
2y/L=(Y
2
-Y
1
) / (Y
1
+Y
2
)
The formulae are just slightly more complex for
pin-cushion types:
2x/L=((X
2
+Y
1
) - (X
1
+Y
2
)) / (X
1
+X
2
+Y
1
+Y
2
)
2y/L=((X
2
+Y
2
) - (X
1
+Y
1
)) / (X
1
+X
2
+Y
1
+Y
2
)
High-performance electronic circuits that
perform these simple arithmetic functions are
incorporated into UDT Instruments position
sensing instruments such as the Models 531 and
431, and into the 301 Series Differential
Amplifiers.
Quadrant detector electrical connections and formulas. For nulling or centering applications, the spatial resolution of a
continuous device is inferior to that of a comparable segmented
device.This stems from the lower signal-to-noise ratio of continuous
devices. So continuous position sensors work best for measuring a
light spot's movement over a wide range.
Continuous position sensors are available in one- and two-dimen-
sional configurations, and come in four typesduo-lateral, tetra-later-
al, pin-cushion and transparent duo-lateral.
The duo-lateral type has electrodes on both its front and rear sur-
faces. From the equivalent circuit it can be seen that each position sig-
nal is divided into just two parts...but by two separate resistive layers.
This approach produces minimal position sensing error and very high
resolution.
Tetra-lateral types have four electrodes on the front surface of the
photodiode. As such, the total induced photocurrent is divided into 4
parts by the same resistive layer. Compared with the duo-lateral type,
tetra-lateral devices are more non-linear for positions further from
their mechanical centers. However, the tetra-lateral devices produce
less dark current and have a faster response time. And they are some-
what easier to operate since minimal, or even zero, bias voltage is
required.
Pin-cushion devices are basically an improved tetra-lateral, with
reduced signal non-linearity at the edges.This is achieved by increasing
the photodiode's surface sensitivity and modifying its electrodes.The
pin-cushion device offers all the advantages of the tetra-lateral type.
namely, low dark current, fast response, and minimal bias-voltage
requirements.
Transparent duo-lateral detectors are essentially the same in prin-
ciple as duo-lateral. However, they are constructed by depositing
amorphous silicon on a transparent substrate.Thus, an incident beam
can pass right through the detector after experiencing a small amount
of attenuation and diffusion.
Calculating Position Resolution
Definition:
Resolution is defined as the minimum displacement that can be
resolved by a position sensor in a given electro-optical system.
Consider a single-axis, lateral-effect position sensor which pro-
duces current x
1
and x
2
. Position is given by:
However, there is uncertainty in the values of x
1
and n
2
.
Therefore, the measured position is:
Non-contact Position Sensing Using Optical Detectors
Lateral Effect Detector
X Position = A - C
A + C
Y Position = B - D
B + D
A
B
D
C
5 4 3 2 1 0 1 2 3 4 5
0
1
2
3
1
2
3
Lateral-effect detector electrical connections and formulas.
Linear transfer function of lateral-effect diodes.
x
1
- x
2
x
1
+ x
2
L
2
)
(
P =
(x
1
� n
1
)-(x
2
� n
2
)
(x
1
� n
1
)+(x
2
� n
2
)
L
2
]
[
P
meas
= Non-contact Position Sensing Using Optical Detectors
Maximum error occurs when both noise signals are negative and
approximately equal in value.The maximum measured position is:
Since the signal-to-noise ratio is:
We can solve for n and substitute into Equation , to obtain a
maximum error value in terms of the signal-to-noise ratio which we
can readily estimate and control.Thus:
is the worst case erroneous measurement.
The Modulus of Error is:
If S/N>>I then:
For a typical 10 mm x 10 mm tetra-lateral type photodiode, one
can expect a noise equivalent current of about 40 nA, and a maximum
signal current of about 200 �A. As such, in spatial terms, the noise
equals 1 micron.
Resolution of a position sensor should not be confused with accu-
racy or linearity.The resolution is independent of these properties
which are intrinsic to the type of detector and not to the signal-to-
noise ratio of the system.
It is interesting to note that this formula for resolution equally
applies to a bi-cell when one considers L as the spot diameter.
x
1
- x
2
x
1
+ x
2+2n
L
2
]
[
P
meas(max)
=
1
x
1
+ x
2
2n
S/N =
1
x
1
+ x
2
-
L
2
)
[
P
meas(max)
=
(
x
1
- x
2
x
1
+ x
2
S/N
]
L
2
)
=
(
x
1
- x
2
x
1
+ x
2
S/N
S/N -1
1
S/N +1
L
2
)
(
P =
L
S N
P = 2 Sensing Displacements of Specular or Diffuse Surfaces
Up to this point we have discussed how to resolve the posi-
tion of a light spot on the surface of a detector. Now let us
define how this relates to resolving the position of a test
object or light source.
Measuring Linear Displacement
For all cases �� < o < 9��:
Measuring Rotation About A Fixed Point
In this case, we know that:
So the detector's position resolution is related to angular
resolution in the object plane by:
Similarly, the photodetector must have an active length of:
Error may occur if linear displacement and rotation occur at
the same time, since the position sensor cannot distinguish
between the object's linear and angular movements. However,
the error may be corrected by employing a photodetector to
measure the combined effect, and an autocollimator to meas-
ure rotation alone.
Remote Angle Sensing
One of the primary uses of position sensing detector is for
measuring angles, usually of mirrors but sometimes of relatively
diffuse surfaces. UDT Instruments manufactures a number of
electronic auto