Displacement laser interferometry with sub-nanometer uncertainty

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.