Introduction

The variation of refractive index with wavelength in the ducts, tunnels and laboratory, and the dependence of the measured astrometric phase on the colour of the correlated flux.

This section will be replaced by text from Richard Mathar

This document gives an order-of-magnitude calculation for the impact of air in the VLTI on differential astrometry. Both the main delay line and differential delay line are assumed to be filled with air. Some error terms are larger per metre air path offset of the DDL than per metre air path offset of the main delay line (notably errors from the uncertainty in the environmental conditions in the VLTI, and uncertainty in empirical/theoretical models for the dispersion in air and water vapour in the near infrared). Other error terms are larger per metre air path offset of the main delay line than per metre air path offset of the DDL (notably errors due to the uncertainty in the stellar wavelength/temperatures).

Errors resulting from the uncertainty in the environmental conditions in the VLTI are found to be negligible, while the errors due to the uncertainty in the stellar temperatures are found to be too large to allow accurate astrometric measurement unless the spectral resolution of PRIMA is enhanced, or a novel method is found for determining the centroid of the correlated flux from each star. There is some disagreement between published models for dispersion in air and water vapour, and until this is resolved it will not be possible to run the DDL without evacuating it. The DDLs could be used for characterising the dispersion of air at near infrared wavelengths. If an alternative method can be found for obtaining laboratory measurements of the refractive index of air and water vapour in the K-band and at the laser metrology wavelength, then it may not be necessary to make the DDLs vacuum-compatible.

The PRIMA facility is intended to measure differential OPD to an accuracy of $5\mbox{nm}$ in order to allow astrometric detection of the motion of stars due to orbiting planets [15,16]. The light from astronomical sources will be passed along air-filled ducts and tunnels in the VLTI, and the primary OPD correction will be performed in an air-filled delay line. In order to calculate the performance of the VLTI it will be necessary to know the refractive index of air in the VLTI in the observing bandpass and at the wavelength of the metrology lasers. Recent studies of the refractive index of air at near infrared wavelengths show notable disagreement, particularly concerning the influence of airbourne water vapour [12,17,18,19,20,21], and it will be important to resolve this issue before the PRIMA facility is operated. The most established model of refractive index [17] has water vapour corrections based on experiments at wavelengths shorter than $0.64\mbox{ $\mu$ m}$ [22]. Extrapolating these curves to K-band (beyond the near infrared water absorption bands) is scientifically dubious.

If the DDLs can be evacuuated, it may be possible to investigate the refractive index of air and water vapour at near infrared wavelengths using internal calibration light sources at the VLTI. It may be difficult to obtain dispersion measurements of sufficient accuracy using the DDL because of the small stroke length of the DDL.