Abstract
Development in industry is asking for improved resolution and higher accuracy
in mechanical measurement. Together with miniaturization the demand
for sub nanometer uncertainty on dimensional metrology is increasing rapidly.
Displacement laser interferometers are used widely as precision displacement
measuring systems. This thesis describes the error sources which should be
considered when measuring with these systems with (sub-)nanometer uncertainty,
along with possible methods to overcome these errors.
Whenconsidering interferometricdisplacementmeasurementswithnanometer
uncertainty over small distances (below 1 mm) the measurements are influenced
by periodic deviations originating frompolarizationmixing. Inmeasurements
with nanometer uncertainty over larger distances this errormay become
negligible compared to errors introduced by the refractive index changes of the
medium in which the measurement takes place.
In order to investigate the effect of periodic deviations, models were developed
and tested. A model based on Jones matrices enables the prediction
of periodic deviations originating from errors in optical alignment and polarization
errors of the components of the interferometer. In order to enable the
incorporation of polarization properties of components used in interferometers,
different measurement setups are discussed. Novel measurement setups are
introduced to measure the polarization properties of a heterodyne laser head
used in the interferometer system. Based on ellipsometry a setup is realized
to measure the polarization properties of the optical components of the laser
interferometer.
With use of measurements carried out with these setups and the model
it can be concluded that periodic deviations originating from different error
sources can not be superimposed, as interaction exists whichmay cause partial
compensation.
To examine the correctness of the predicted periodic deviations an entire
interferometer system was placed on a traceable calibration setup based on
a Fabry-P´erot interferometer. This system enables a calibration with an uncertainty
of 0,94 nm over a range of 300 µm. Prior to this measurement the
polarization properties of the separate components were measured to enable
a good prediction of periodic deviations with the model. The measurements
compared to the model revealed a standard deviation of 0,14 nm for small
periodic deviations and a standard deviation of 0,3 nm for periodic deviations
viii 0. ABSTRACT
with amplitudes of several nanometers.
As a result the Jones model combined with the setups for measurement
of the polarization properties form a practical tool for designers of interferometer
systems and optical components. This tool enables the designer to
choose the right components and alignment tolerances for a practical setup
with (sub-)nanometer uncertainty specifications.
A second traceable calibration setup based on a Fabry-P´erot cavity was
developed and built. Compared to the existing setup it has a higher sensitivity,
smaller range and improved uncertainty of 0,24 nm over a range of 1 µm, and
0,40 nm over a range of 6 µm.
To improve the uncertainty of existing laser interferometer systems a new
compensation method for heterodyne laser interferometerswas proposed. It is
based on phase quadraturemeasurement in combination with a compensation
algorithm based on Heydemann’s compensation which is used frequently in
homodyne interferometry. The system enables a compensation of periodic
deviations with an amplitude of 8 nm down to an uncertainty of 0,2 nm. From
measurements it appears that ghost reflections occurring in the optical system
of the interferometer cannot be compensated by this method.
Regarding the refractive index of air three measurement methods were
compared. The three empirical equations which can be found in literature,
an absolute refractometer based on a commercial interferometer and a newly
developed tracker system based on a Fabry-P´erot cavity. The tracker was
tested to investigate the feasibility of the method for absolute refractometry
with improved uncertainty. The developed tracker had a relative uncertainty
of 8 ·10-10. The comparison revealed some temperature effectswhich cannot be
explained yet. However the results of the comparison indicate that an absolute
refractometer based on a Fabry-P´erot cavity will improve the uncertainty of
refractive index measurement compared to existing methods.
Original language | English |
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Qualification | Doctor of Philosophy |
Awarding Institution |
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Supervisors/Advisors |
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Award date | 11 Oct 2004 |
Place of Publication | Eindhoven |
Publisher | |
Print ISBNs | 90-386-2656-8 |
DOIs | |
Publication status | Published - 2004 |