L-9904-2390
Application note
RLE plane mirror application note
The RLE fibre optic laser encoder uses interferometry to
provide high resolution, high linearity position feedback. Any
RLE system comprises an RLU laser unit, RLD10 detector
head and an additional target optic, either a plane mirror or
a retroreflector, to complete the interferometer configuration.
Mirror selection and installation should be carried out carefully
to avoid degrading the metrological advantages of the
interferometer system. In the case of an X-Y stage application
mirrors can contribute to system errors via:
• Surface non-uniformity (flatness), which can be minimised
by using an optically flat target and approved mounting
techniques.
• Thermal expansion, which can be reduced by using the
correct substrate and mounting materials.
• Misalignment, which can be avoided through careful
installation.
This document discusses how these errors may be minimised
through careful mirror specification, mounting and alignment.
Mirror flatness
In multi-axis applications, such as an X-Y stage, the
interferometer’s laser beam will traverse the length of the
mirror as the stage travels along the cross axis. An uneven
surface results in a path length change between the target
optic and the interferometer, which cannot be distinguished
from actual motion.
Global flatness
Global flatness is macro distortion of a mirror. This figure is
usually specified as a maximum peak to valley figure over a
particular length. Global distortion can cause measurement
errors and beam misalignment.
Any distortion of mirror structure is very much dependant
on the method of mounting used (mounting methods are
discussed later in this document).
The table below shows the measurement error possible with
different flatness levels.
Flatness*
Maximum error (nm)
λ/4
158
λ/8
79
λ/10
63
λ/12
53
λ/20
32
Mirror flatness, which generally describes undulating
distortion, is specified as local or global (see Figure 1).
Local
flatness
Global
flatness
Figure 1: Local and global flatness
N.B. Diagram exaggerated for clarity
Local flatness
Local surface flatness distortions of a mirror can degrade the
fringe contract in the interferometer and cause measurement
errors. Local flatness is usually specified as a peak-to-valley
figure, with the error quoted as a fraction of a wavelength.
* λ = 633 nm
Some motion controllers are capable of generating a flatness
correction table, which means that it is possible to compensate
for any residual distortion after mounting. (Error mapping is
discussed laser in this document.)
Cosmetic surface quality
Local flatness can be reduced by purchasing mirrors with
a very high flatness specification over the local area. This
method is suitable when using small mirrors but notoriously
expensive when longer mirrors are required.
Surface flatness generally describes undulating distortions,
whilst cosmetic surface quality refers to discontinuities
(defects). Poor cosmetic surface quality can reduce signal
intensity and possibly cause beam mis-alignment and
measurement errors.
A local flatness of λ/4 may reduce the fringe intensity to
a level that renders interferometry impossible. Renishaw
recommends using mirrors with a local flatness of not less
than λ/10 over an area of 12 mm by 7 mm.
Surface quality is described using the military scratch and dig
specification MIL-0-13830A, e.g. a 60 - 40 specification allows
scratches of up to 60 µm in width and digs of up to 0.4 mm in
diameter.
Renishaw recommends using a mirror with a scratch and dig
specification of no more than 60 - 40. For a more detailed
description of this specification, including maximum combined
length figures, please contact a Renishaw representative or
reference MIL-0-13830A.
Thermal expansion error
Mirror substrate material can contribute to measurement
error through thermal expansion, although it will usually be
negligible when compared to the expansion of the rest of
the system. In order to minimise this error, a material with a
low coefficient of thermal expansion (CTE) should be used.
The table below shows the CTE (ppm/°C) for some common
substrates and the maximum measurement error (µm)
generated by a 25 mm thick substrate over a 1 °C change.
CTE (ppm/°C)
Maximum error
(µm)
Fused silica
0.5
0.013
Zerodur™
0.1
0.003
8
0.2
Typical glass
Angular deviation
(arc sec)
Measurement
error (ppm)
Measurement
error* (ppm)
0.5
2
0.7
1
5
1.5
2
10
3
3
15
4
4
20
6
5
24
7
* for a 300 mm long mirror
• Cosine error is caused when the mirror is not perpendicular
to the axis of motion, or the laser beam is not parallel to the
axis of motion (see Figure 4).
Interferometer
Stage travel
Mirror
Mirror misalignment
In plane mirror interferometry, the position of the motion
platform is obtained by direct reference to the mirrors, which
eliminate the influence of any mechanical inaccuracies in the
motion system slideways. If mirrors are properly aligned,
linear errors, which would normally result from mechanical
deviations in straightness, orthogonality, pitch and yaw, are
removed (assuming no Abbé errors are present).
Mirror misalignment can cause three types of error: parallel,
orthogonal and cosine.
• Parallel error is caused when the mirror is not aligned
parallel to stage travel (see Figure 2).
Stage travel
Interferometer
Figure 4: Cosine error
A measurement error, x, is produced when a mirror is
misaligned such that it has an angular deviation, ø, from the
perpendicular motion axis of length L (x = L(1 - cosine ø)).
The following table shows the measurement errors possible as
a result of cosine misalignment on a 300 mm axis.
Angular deviation (arc sec)
Measurement error* (nm)
5
0.09
10
0.4
20
1.4
30
3.2
40
5.6
50
8.8
Mirror misalignment errors can be overcome in the following
ways:
Mirror
Figure 2: Parallel error
• Orthogonality error is caused when the mirror axes are not
truly orthogonal to each other (see Figure 3).
Stage travel
Stage travel
Interferometer
Figure 3: Orthogonality error
These misalignments mean that as an axis is traversed the
path difference between the cross-axis interferometer and
the mirror changes. This change is interpreted as stage
movement, which results in a measurement error.
A measurement error, x, is produced when a mirror of length L
is misaligned such that it has an angular deviation, ø, from the
parallel axis, or, ø±90, from the orthogonal mirror (x = L sine ø).
The following table shows the measurement errors possible as
a result of parallel or orthogonality misalignment.
• Carefully following a thorough alignment procedure, such as
the one detailed in this document.
• Using a mono-lithic L-mirror with a high orthogonality
specification, instead of two stick mirrors.
N.B. L-mirrors are expensive and vendors may be
unwilling to quote below 1 arcsec (1 arcsec can create a
measurement error of 5 µm/m).
• Approximately aligning the system and then compensating
for any error through a controller or compensation unit.
It is important to note that the accurate alignment of stick
mirrors, or the use of L-mirrors, can produce a mirror system
with a superior orthogonality to that of the stage axes.
Mirror mounting
Mounting is critical if mirror movement or distortion, which
results in measurement errors, is to be avoided. Mirrors can
be mounted directly to the stage, but it is more useful for
them to be secured via a mount that can assist in alignment.
Mounts are commercially available for stick mirrors, plate
mirrors and L-mirrors.
Renishaw stick mirror mounts
Renishaw supply three point kinematic mounts for mirrors
of up to 350 mm in length and 25 mm square cross section,
which allow fine pitch and yaw adjustment. The mounts are
constructed to minimise errors due to differential expansion
and have reliable positional locks that provide clamping to
overcome acceleration, deceleration and bump forces.
Adjustment sensitivity
Yaw sensitivity*
Pitch sensitivity
0.5 arcsec / degree of rotation
< 1 arcsec / degree of rotation
• Finely adjust the pitch of the Y-mirror to allow the laser to
reflect back into the interferometer output (set to a suitable
resolution), move the X-axis along full travel and align the
mirror yaw for minimum count difference between end limits.
4. Engage the locking mechanism on the Y-mirror.
5. Align the X-axis mirror and interferometer parallel to the Yaxis by repeating steps 1, 2, 3 and 4.
3-point levelling
stand
True square
X-mirror
* for a 350 mm long mirror
Y-mirror
For more information regarding Renishaw mirror mounts,
please contact a Renishaw representative or refer to
M-9904-2179.
Y-travel
Autocollimator
X-travel
Figure 6: Set-up terminology
Figure 5: Renishaw stick mirror mount
Typical alignment procedure
The following instructions demonstrate one method of aligning
two plane mirrors to an X-Y stage*. It is assumed that the
person performing the procedure is familiar with the test
equipment, all mechanical adjustments of the motion stages
have been completed, the RLD10 detector heads are fully
mounted and the axes are fully operational.
The pitch of the mirrors is now aligned and they are parallel
to the axes of travel. However, the mirrors are aligned to
the mechanical orthogonality of the X and Y-axes, which
may not provide you with the ultimate accuracy. The mirrors’
orthogonality can be aligned to the precision of a true square,
which can provide accuracy to better than 0.5 arcsec.
Orthogonality alignment
Suitable equipment and recommended specification:
• Optical autocollimator - should have an aperture > 75 mm
and a resolution of at least 0.1 arcsec.
Suitable equipment and recommended specification:
• Master true square - should have an orthogonality of less
than 0.5 arcsec and be traceable to a calibration standard,
e.g. Starett-Weber Corporation produce a true square that
is traceable to National Institute of Standard and Technology
(NIST).
• Electronic indicator with a resolution of at least 0.1 µm
• Levelling stand.
1. Install the Y-mirror in its mount.
1. Align the true square onto the levelling plate in the centre of
the X and Y mirrors.
• Mount the autocollimator to the system base so that its
field of view is over both the Y-mirror and true square front
surface. It is important that the centre line field of view
coincides with the mirror / true square boundary. Ensure
the collimator is stable, free from vibration and that the
equipment has had adequate time to thermally adjust to the
measuring environment before performing any adjustments.
* If a vertical axis of motion is located under the mirrors a different
method of pitch alignment may be necessary.
2. Align the Y-interferometer parallel to Y-axis travel (remove
Y-interferometer cosine error):
• Move the Y-axis (with the X-axis movement locked) to
achieve the shortest separation between the Y-axis
interferometer and the mirror. Attach an alignment target
on the mirror surface so that the laser beam is on the target.
Move the axis to the further position from the RLD10 and
adjust the pitch and yaw of the RLD10 so the laser spot
does not exhibit any translation from the target. N.B. this
can be an iterative process and may require multiple near
and far field adjustment for the best alignment.
3. Align the Y-axis mirror parallel to the X-axis travel:
• Remove the target and visually align the Y-mirror so it is
parallel to the X-axis travel. (Alternatively lock the Y-axis
and position an electronic indicator on the front surface of
the mirror outside the optical aperture to prevent surface
damage. Move the X-axis along full travel and align the
mirror yaw for a zero reading at the end limits.
• Visually align the Y-mirror pitch so the mirror is perpendicular
to the X-Y plane.
• Block the front surface of the square and align the collimator
to the Y-mirror to obtain zero pitch and yaw measurements
(0.0 arcsec).
• Block the front surface of the mirror and view the pitch and
yaw of the true square. Adjust the true square until a zero
reading on the autocollimator is achieved.
Take care not to move the true square again as it is now the
reference for all remaining mirror adjustments.
2. Align the X-axis mirror parallel to the perpendicular surface
of the true square.
• Move and mount the autocollimator to the perpendicular
side of the machine, allowing its field of view to fall over the
X-axis mirror and true square. Ensure the centre line of the
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field of view coincides with the mirror / true square boundary.
• Cover the X-mirror and align the collimator to get a zero
reading (0.0 arcsec) from the front surface of the true
square. DO NOT move the true square.
• Block the true square and, viewing the X-mirror through the
collimator, adjust the yaw of the mirror for a zero reading.
Identification and ordering
Plane mirrors
Renishaw supply plane stick mirrors up to 300 mm in length
in multiples of 10, which meet the following specification
(DS/9904/1492/01A):
λ/10 over 100 mm
< 0.5 µm over 500 mm
Zerodur™
Hard oxide dielectric
L* (+ ~ 20 mm) × 25 × 25
3. If a locking function is provided on the mirror mounts*,
carefully tighten while reading the autocollimator to ensure
the mirror has not moved.
Local flatness
Global flatness
Substrate
Mirror coating
Dimensions
* some locking mechanisms may have a slight effect on the mirror
* L = optical aperture (working length)
alignment and must be considered when performing adjustments.
Upon completion of the above steps it is highly recommended
to bring the collimator back to the Y-axis mirror set-up and
perform the measurements again to verify nothing has
changed to affect the orthogonality.
Error mapping
As mentioned earlier in this document, orthogonality errors
and macro-mirror distortion can sometimes be compensated
for using the motion controller.
• Compensating for mirror distortion
A typical method involves locking one axis in place and,
using the stage interferometer and mirror, monitoring any
cross axis displacement as the axis is traversed. At the
same time, the stage motion is monitored independently
of the mirror, for way straightness deviations. If these two
readings are subtracted from each other any mechanical
variations will be isolated from the mirror deformation,
allowing the mirror’s distortion profile to be calculated.
Way straightness can be monitored down to 0.1 µm using a
calibration laser (or RLD10 with no internal optics (RLD10A3-XX)) and straightness optics (see Figure 7). If higher
precision mapping is required, a master should be used.
For a more detailed specification, please contact a Renishaw
representative.
Stick mirrors may be ordered directly from Renishaw using the
part numbering protocol shown below.
Y = modified for Renishaw mounts
N = not modified for Renishaw mounts
Part
number
RPM10 - Y X X X X
If your application demands a higher specification, please
contact a Renishaw representative.
Mirror mounts
Renishaw supply adjustable mirror mounts for stick mirrors of
up to 350 mm total length and 25 mm square cross section.
(For a more detailed specification, please contact a Renishaw
representative.)
Stick mirror mounts may be ordered directly from Renishaw
using the part number below.
S = stick mirror mount
Part
number
Laser source
Optical aperture
(mm) (< 300 mm,
multiples of 10 only)
RAM10 - S X - 0 1
Mirrors used in the Renishaw mounts must have location
features added to the base, so, if using mirrors not supplied by
Renishaw, it is advisable to contact a Renishaw representative
for further advice.
Stage
travel
Interferometer
Figure 7: Monitoring way straightness
• Compensating for mirror distortion and orthogonality
A typical method maps the system to a master on the
stage, e.g. a four-point standard such as a wafer calibrated
with fuducials. The master, in conjunction with a vision
system, can be used to obtain the constants for a crossaxis algorithm that the motion controller can then employ to
perform compensation.
Renishaw reserves the right to change specifications without notice.
© 2005 Renishaw plc. All rights reserved.
For worldwide contact details, please visit our
main website at www.renishaw.com/contact
Printed in England 0805 Part No. L-9904-2390-01