of ;100–10 mm, and typically the position resolution
of such linear encoders ranges from ;10 to 0.5 mm,
coder that is fundamental to our new development.
The position encoder is based on the Fourier phasedependent on the electronic interpolation of the
quadrature signals. High-resolution optical linear
encoders detect position increments as small as 0.5–
0.01 mm by the observation of a fine grid of ;8–
0.5-mm period.
Most standard optical encoders are based on the
moire´
1
detection principle, employing an array of
four index gratings with photodiodes. Utilizing
the moire´ effect, one analyzes the shadow of the
ruler grating with photodiodes that are large com-
pared with the grating period. The four signals
allow the determination of the direction of travel
and incrementally the actual position of the fixed
encoder head relative to the moving glass scale.
Usually high-resolution optical encoders are
detector
2
~FPD! and works with a scale of 20-mm
period similar to a standard encoder. This abso-
lute encoder achieves a position resolution of better
than 0.1 mm and an interpolation accuracy of better
than 60.05 mm. The encoder system is equally
well suited for absolute linear and rotary encoders.
Compared with encoders with a similar resolution
and accuracy, this system offers relaxed mechanical
tolerances. This is highly desirable in reducing
the costs involved in the mounting of such an en-
coder. The most critical alignment of the absolute
encoder is the one of the yaw, the rotation of
the encoder head around an axis normal to the
scale ~see Fig. 1!. To reduce the susceptibility to
yaw, a novel phase detector has been conceived.
The improved detector geometry for the novel
encoder setup is covered in Section 3, accompanied
by the required signal-processing scheme. In Sec-
tion 4 we compare experimental results obtained
with the Fourier phase detector and the improved
sensor array at various levels of angular misalign-
The authors are with the Paul Scherrer Institute Zu¨rich, Baden-
erstrasse 569, CH-8048 Zu¨rich, Switzerland.
Received 21 May 1996; revised manuscript received 24 October
1996.
0003-6935y97y132912-05$10.00y0High-resolution optical positio
with large mounting tolerance
Kai Engelhardt and Peter Seitz
A high-resolution optical position e
standard moire´-based system, a sim
mented phase detector integrated cir
accuracy, the encoder presented offe
to the scale, while an interpolation a
well suited for high-resolution line
high-resolution rotary encoders.
Key words: Position encoder, rot
cific integrated circuit.
1. Introduction
The precision of today’s machine tools is based on the
direct position feedback from accurate linear and ro-
tary position encoders attached to or integrated into
each motion axis. Optical encoders usually incorpo-
rate a glass scale that carries a binary grating fabri-
cated photolithographically with high accuracy.
Standard optical encoders work with a grating pitch© 1997 Optical Society of America
2912 APPLIED OPTICS y Vol. 36, No. 13 y 1 May 1997n encoder
s
ncoder is described that consists of a scale as encountered in a
ple imaging system with stabilized magnification and a novel seg-
cuit. Compared with encoder systems of comparable resolution and
rs large mechanical tolerances in the alignment of the reading head
ccuracy of better than 0.1 mm is preserved. The system is especially
ar encoders as well as for the cost-effective fabrication of compact
© 1997 Optical Society of America
ary encoder, mechanical alignment, photosensitive-application spe-
based on the interference of at least 2 diffrac-
tion orders of the ruler grating so that periodic
intensity modulation is obtained as a function of
position. A careful mechanical alignment of the
encoder head to the scale and of the scale to the
stage is crucial for the proper operation of these
encoder systems.
In Section 2 we review the absolute position en-ment.

Fourier transform of the intensity distribution at a
single fixed spatial frequency that is matched to the2. Optical Position Encoder with a Fourier Phase
Detector
The position encoder system
2
shown schematically in
Fig. 2 is composed of an absolute measuring encoder
subsystem with coarse resolution and an incremental
high-resolution encoder system. To simplify assem-
bly and alignment, the encoder system is designed as
a single integrated system with a single light source,
a single scale with two tracks running in parallel, a
single imaging optics, and a single chip for detection
that contains the FPD and a line sensor. The en-
coder works with both transmissive and reflective
scales. The absolute measuring subsystem employs
a pseudo-randomly coded binary sequence with the
step width matched to one period of the scale of the
incremental subsystem. The binary code is sensed
with the line sensor whereas in the incremental sub-
system a periodic grating is projected onto the FPD.
By a proper combination of both position readouts the
final absolute high-resolution position result is ob-
tained. The encoder system was developed at the
Paul Scherrer Institute, Zurich, Switzerland, and is
now offered commercially.
3
The incremental subsystemworks with a relatively
coarse scale period of p 5 20 mm, a telecentric imag-
ing system with a low numerical aperture, and the
FPD. The FPD is composed of four sinusoidally
shaped photodiodes that are staggered by a quarter of
the sine period. The FPD optically carries out a
Fig. 1. Cartesian coordinate system connected to a linear scale
and angular misalignments of an encoder head against the scale.
Fig. 2. Schematic diagram of the high-resolution, absolute optical
position encoder system. CNC, computer numerical control.spatial frequency of the scale grating to obtain a good
signal modulation. As a main advantage, quadra-
ture signals are generated that show low harmonic
distortions, regardless of the shape of the impinging
intensity distribution traveling across the detector.
The FPD allows high-precision and high-resolution
measurements by using a rather coarse scale.
The telecentric imaging system projects the scale
with a constant magnificationm954, onto the phase
detector, even if the scale is out of focus. Although
encoder systems that are based on an interferometric
phase detection provide the largest tolerances Dz in
the distance z from head to scale, the tolerance al-
lowed by the absolute encoder is largely improved
owing to the telecentric imaging compared with stan-
dard shadow moire´ systems. The tolerance, Dz 5
680 mm, for a 3-dB reduction in signal modulation is
in a range that can be mechanically guaranteed with
no difficulty.
In addition, the system is quite insensitive against
pitch and roll because a small scale area of ;0.5-mm
diameter is observed by the phase detector. In the
presence of pitch a, image contrast and hence signal
modulation are affected owing to the variation of de-
focus in x along the scale and the slight mismatch of
the imaged grating period, p
D
95m9pcos a,tothe
detector period, p
D
5 m9p. Roll g causes the grating
image to be locally defocused along the y direction.
The grating period remains unaffected because mag-
nification is stabilized by the telecentric setup. The
variation in image contrast in the y direction intro-
duces harmonic distortions of the quadrature signal
and thus gives rise to interpolation errors. As men-
tioned above, because of the small field of view of the
phase detection, the sensitivity to pitch and roll is
small, and the system works satisfactory if both an-
gular misalignments are kept within 650 mrad, a
range that is as high as an order of magnitude larger
than that of competing systems.
An angular misalignment in the yaw b with stan-
dard moire´-based encoders causes a decrease in sig-
nal modulation, the first zero occurring at angle b5
2 arcsin ~py2y
det
! with grating period p and height
y
det
of a detector element. As an example, consider
a typical standard encoder with a scale period of 20
mm and detector elements of height y
det
5 1 mm. It
will have zero signal modulation at b520 mrad, and,
at b53.4 mrad, modulation is decreased by 3 dB.
In the case of the FPD, the yaw b primarily intro-
duces phase distortions between the four photosig-
nals because each photosite is centered at a different
height y to obtain a compact phase detector array.
The normally circular Lissajous figure of the quadra-
ture signal is deformed to an elliptical shape and
interpolation errors occur. If yaw is kept within the
range of 61.8 mrad, the interpolation error will be
less than 0.1 mm. Although this tolerance is not
worse than that of competing systems, the yaw rep-
resents themost critical mechanical alignment of this
type of position encoder.
1 May 1997 y Vol. 36, No. 13 y APPLIED OPTICS 2913