air
is by utilization of a wavelength tracker. Also known as a
refractometer, a wavelength tracker measures the relative
change in the refractive index of air. Because it is a relative
measure only, initial environmental conditions must be known
and computed to establish an initial wavelength scale factor.
The wavelength tracker is a purely optical device that is
highly accurate, but is only used in very high-end applications
due to its high cost.
Mechanical
Vibration and Air Turbulence Mechanical
vibration or air turbulence can cause perturbations in the
positioning feedback system that will limit overall system
performance. Mechanical vibration errors can be minimized
through proper design of the machine base vibration isolation
system. Thermal gradients across the beam path are created
due to turbulence in the air so careful design of the machine
micro-environment is critical to sub-nanometer performance.
A simple and effective means of minimizing these effects
is to "shield" the beam by placing a tube around
the system or simply by minimizing the flow of air.
Mechanical
Errors For
truly cutting edge performance, an XY system must utilize
a high-performance positioning system made up of air bearings
mounted to a granite base. Air bearing stages, with their
superior geometrical characteristics, are highly recommended
for all laser interferometer based systems, while the granite
provides an extremely flat reference surface as well as
good thermal stability. Without outstanding linear stages
as the basis of operation, Abbe effects will drastically
undermine the accuracy of the laser measurement system.
Abbe errors are linear displacement errors that are caused
by an angular deviation in the axis of motion. A properly
designed system will place the center of the measurement
mirror as close to the work piece as possible. By tracking
the motion of the actual part under test, as opposed to
the stage itself, the effect of any pitch / yaw deviations
is vastly reduced. When combined with a linear stage system
that is inherently geometrically accurate, Abbe errors are
nearly eliminated.
Dead-Path
Error A less
obvious source of error occurs as a result of both the environment
and mechanical placement of the optics. This error is known
as dead-path error and is caused by portions of the beam
that are effectively uncompensated (Figure 5). While the
moveable reflector translates throughout the measurement
path, environmental compensation electronics compute and
correct for the change in the index of refraction of air.
The dead path is a distance that the laser beam travels
where it undergoes no relative motion. Since the environmental
compensation scheme only corrects for relative motion, this
distance remains uncorrected. If uncorrected, the dead-path
error effectively moves the zero point (X0) of
the system as the environmental conditions change. There
are several means of addressing this, but the |
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Figure
5: Illustration of dead-path in an interferometer system. |
most straightforward ones are
to compensate for the error or eliminate it. Software compensation
for the dead path error requires an additional calculation
to be performed that not only accounts for temperature, pressure
and humidity, but for the dead-path distances as well. Mechanical
compensation entails separating the interferometer's retroreflector
from the beam-splitter by a distance equal to the dead-path
error. As a result, both the measurement beam and reference
beam have equal dead-paths that cancel each other out. This
approach requires careful alignment of the optics and assumes
that the environmental conditions are identical for both dead-paths.
Elimination of the dead-path
requires that the linear interferometer optics be placed
as close to the zero point of the moveable reflector as
possible. As a rule of thumb, when the optics are placed
within 50 mm of each other, the error due to dead-path is
negligible.
Alignment
Errors Assuming
that the mechanical sub-system is sound, and environmental
correction is properly implemented, the final pieces to
the puzzle are the optics themselves and their alignment.
All optics have inherent inaccuracies in the form of optical
non-linearity. This error cannot be controlled by the user,
and is a function of the quality of the optics. All interferometer
optics will have some amount of nonlinearity, so this error
cannot be completely eliminated but is minimized by the
use of high quality optics, such as the ones provided by
Aerotech.
An optical error that can be controlled
by the user is a misalignment that is commonly known as
cosine error. Cosine error occurs when the laser beam path
and the axis of stage motion are not completely parallel.
The relationship is best modeled as a triangle where the
laser beam represents one leg of the triangle, and the actual
motion is the hypotenuse (Figure 6). This error can be minimized
through careful alignment of the optics to the stage.
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Figure
6: Illustration of cosine error. |
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