Design and construction of an optical test bed for LISA imaging systems and tilt-to-length coupling

The laser interferometer space antenna (LISA) is a future space-based interferometric gravitational-wave detector consisting of three spacecraft in a triangular configuration. The interferometric measurements of path length changes between satellites will be performed on optical benches in the satellites. Angular misalignments of the interfering beams couple into the length measurement and represent a significant noise source. Imaging systems will be used to reduce this tilt-to-length coupling. We designed and constructed an optical test bed to experimentally investigate tilt-to-length coupling. It consists of two separate structures, a minimal optical bench and a telescope simulator. The minimal optical bench comprises the science interferometer where the local laser is interfered with light from a remote spacecraft. In our experiment, a simulated version of this received beam is generated on the telescope simulator. The telescope simulator provides a tilting beam, a reference interferometer and an additional static beam as a phase reference. The tilting beam can either be a flat-top beam or a Gaussian beam. We avoid tilt-to-length coupling in the reference interferometer by using a small photo diode placed at an image of the beam rotation point. We show that the test bed is operational with an initial measurement of tilt-to-length coupling without imaging systems. Furthermore, we show the design of two different imaging systems whose performance will be investigated in future experiments

Displacement laser interferometry with sub-nanometer uncertainty

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

Heterodyne standing-wave interferometer with improved phase stability

This paper describes a standing-wave interferometer with two laser sources of different wavelengths, diametrically opposed and emitting towards each other. The resulting standing wave has an intensity profile which is moving with a constant velocity, and is directly detected inside the laser beam by two thin and transparent photo sensors. The first sensor is at a fixed position, serving as a phase reference for the second one which is moved along the optical axis, resulting in a frequency shift, proportional to the velocity. The phase difference between both sensors is evaluated for the purpose of interferometric length measurements

Fiber-based two-wavelength heterodyne laser interferometer

Displacement measuring interferometry is a crucial component in metrology applications. In this paper, we propose a fiber-based two-wavelength heterodyne interferometer as a compact and highly sensitive displacement sensor that can be used in inertial sensing applications. In the proposed design, two individual heterodyne interferometers are constructed using two different wavelengths, 1064 nm and 1055 nm; one of which measures the target displacement and the other monitors the common-mode noise in the fiber system. A narrow-bandwidth spectral filter separates the beam paths of the two interferometers, which are highly common and provide a high rejection ratio to the environmental noise. The preliminary test shows a sensitivity floor of 7.5pm/rtHz at 1Hz when tested in an enclosed chamber. We also investigated the effects of periodic errors due to imperfect spectral separation on the displacement measurement and propose algorithms to mitigate these effects

The AEI 10 m prototype interferometer

A 10 m prototype interferometer facility is currently being set up at the AEI in Hannover, Germany. The prototype interferometer will be housed inside a 100 m^3 ultra-high vacuum envelope. Seismically isolated optical tables inside the vacuum system will be interferometrically interconnected via a suspension platform interferometer. Advanced isolation techniques will be used, such as inverted pendulums and geometrical anti-spring filters in combination with multiple-cascaded pendulum suspensions, containing an all-silica monolithic last stage. The light source is a 35 W Nd:YAG laser, geometrically filtered by passing it through a photonic crystal fibre and a rigid pre-modecleaner cavity. Laser frequency stabilisation will be achieved with the aid of a high finesse suspended reference cavity in conjunction with a molecular iodine reference. Coating thermal noise will be reduced by the use of Khalili cavities as compound end mirrors. Data acquisition and control of the experiments is based on the AdvLIGO digital control and data system. The aim of the project is to test advanced techniques for GEO 600 as well as to conduct experiments in macroscopic quantum mechanics. Reaching standard quantum-limit sensitivity for an interferometer with 100 g mirrors and subsequently breaching this limit, features most prominently among these experiments. In this paper we present the layout and current status of the AEI 10 m Prototype Interferometer project

A novel heterodyne interferometer for scanning optical microscopy

A phase sensitive scanning optical microscope is described which can measure surface height changes of about 1 Å. The system is based on a heterodyne version of the Michelson interferometer, and has been designed to reject phase noise caused by vibration in the optics and the sample. A specially constructed objective lens is used to direct two laser beams onto the object surface. The first beam forms a tightly focused spot to probe the sample structure and the second remains collimated, acting as a large area on sample reference beam. In the simplest implementation, the objective may be fabricated by drilling a hole in a lens singlet. The configuration allows the relative areas illuminated by the two beams to be varied both arbitrarily and independently, thus guaranteeing an accurate absolute phase measurement. This is an important advantage over existing techniques, in which the range of suitable samples is restricted by the limited size of the on sample reference beam. The two beams reflected from the sample are interfered with a third frequency shifted beam, so forming two heterodyne Michelson interferometers in parallel. The light from each interferometer is detected separately, resulting in two AC signals. The phase of these signals are then compared to provide the object surface phase structure. Path length fluctuations due to microphonics are common to both interferometers and are cancelled by this comparison. Results from a bench top version of the system are presented which demonstrate the principle of the technique and a detailed study is made of the factors limiting the sensitivity of the phase measurement. The conclusions of this study have been applied to the design of a prototype microscope and this has been used to record micrographs of a number of representative samples. In addition the particular imaging characteristics of the system are discussed using a combination of geometrical optics and a transfer function approach

FPGA-based signal processing of a heterodyne interferometer

A heterodyne interferometer and a data acquiring algorithm have been developed to measure the movement of a mirror in one dimension, as well as its rotation around two axis. The interferometer uses spatially separated beams to reduce periodic optical non-linearities, furthermore the optical set-up was designed for low drift, few number of optical elements and easy adjustment. The FPGA-based signal processing is based on an undersampling technique with the aim to minimise the calculation effort. The working principles of the interferometer and the electronics are described and their remaining non-linearities are investigated. Finally, the z-position, the tip and tilt angle of a planar stage are measured with the described system as an example of use