Estimation of the effective wavenumber for a collimated beam in an interferometer, case study for FG5/X absolute gravimeters.

The paper describes an improved method for the estimation of the effective wavenumber in optical interferometers previously published by the authors, which allows reaching accuracy better than one part per billion. The method is based on analyses of spatial intensity profiles of a laser beam and its propagation at different distances, when images are captured by a digital camera. The method has been used for the evaluation of the so-called diffraction correction for FG5 and FG5X absolute gravimeters, which represents one of the most important contributions in the uncertainty budget of these gravimeters. We show that the commonly used estimates tend to systematically underestimate the correction.

Comment on "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb".

The measured oxygen refractive index formulas are still not sufficient for precise metrological applications. Thus, a new dispersion formula for the molecular oxygen refractive index at standard conditions is derived. The agreement of the standard air refractive index obtained from indices of its components with recent dry air refractive index formulas is within a few billionths.

Femtosecond frequency comb based distance measurement in air.

Interferometric measurement of distance using a femtosecond frequency comb is demonstrated and compared with a counting interferometer displacement measurement. A numerical model of pulse propagation in air is developed and the results are compared with experimental data for short distances. The relative agreement for distance measurement in known laboratory conditions is better than 10(-7). According to the model, similar precision seems feasible even for long-distance measurement in air if conditions are sufficiently known. It is demonstrated that the relative width of the interferogram envelope even decreases with the measured length, and a fringe contrast higher than 90% could be obtained for kilometer distances in air, if optimal spectral width for that length and wavelength is used. The possibility of comb radiation delivery to the interferometer by an optical fiber is shown by model and experiment, which is important from a practical point of view.

Environmental influences on autocollimator-based angle and form metrology.

Deflectometric profilometers are indispensable tools for the precision form measurement of beam-shaping optics of synchrotrons and x-ray free electron lasers. They are used in metrology labs for x-ray optics worldwide and are crucial for providing measurement accuracy dictated by the form tolerances for modern state-of-the-art x-ray optics. Deflectometric profilometers use surface slope (angle) to assess form, and they utilize commercial autocollimators for the contactless slope measurement. In this contribution, we discuss the influences of environmental parameters, such as temperature and air pressure, including their gradients, on high-accuracy metrology with autocollimators in profilometers. They can cause substantial systematic errors in form measurement, especially in the case of large and strongly curved optical surfaces of high dynamic range. Relative angle and form measuring errors of the order of 10-4 are to be expected. We characterize environmental influences by extended theoretical and experimental investigations and derive strategies for correcting them. We also discuss the possibility to minimize the contributions of some errors by the application of sophisticated experimental arrangements and methods. This work aims at approaching fundamental limits in autocollimator-based slope and form metrology.

Comparison of 127I2-stabilized frequency-doubled Nd:YAG lasers at the Bureau International des Poids et Mesures.

A frequency comparison was carried out between iodine-stabilized Nd:YAG lasers at 532 nm from the Bureau International des Poids et Mesures, the Centre for Metrology and Accreditation, the Czech Metrology Institute, and the Bureau National de Métrologie-Institut National de Métrologie. The frequency differences between lasers, as well as the frequency reproducibility of each system,were investigated. Pressure-, modulation-, and power-induced shifts were studied. A frequency dispersion (1 sigma) of 3.5 kHz (6.2 x 10(-12) in relative terms) with an average reproducibility for each laser of the order of 0.4 kHz (7.1 x 10(-13) in relative terms) was observed over the duration of the comparison. Relative stabilities better than 1 x 10(13) at 1 s were demonstrated for the third-harmonic systems.