Conclusion

Currently the largest uncertainty lies in published models for the refractive index of air and water vapour across the near infrared. If the discrepencies between published results can be resolved (either through a better understanding of errors in previous models of air refractive index, or through new measurements) then it may not be necessary to evacuuate the DDL during PRIMA astrometric operations. The DDLs could be used for characterising the dispersion of air at near infrared wavelengths. If an alternative method is found for obtaining laboratory measurements of the refractive index of air in the K-band and at the laser metrology wavelength before construction of the DDL begins, then it may not be necessary to make the DDLs vacuum-compatible.

If an accurate model for the refractive index is obtained, then an error budget for the effects of air in the VLTI can be constructed. A metre of air path in the main delay line introduces a larger error for differential astrometry measurements than a metre of air introduced in the DDL. The error due to the uncertainty in stellar temperature and stellar spectrum is currently far too large to meet the astrometric accuracy requirements. This error scales as $\frac{1}{R^{2}}$ for stellar temperature uncertainties where $R$ is the spectral resolution of PRIMA. A small increase in the spectral resolution of PRIMA should allow accurate astrometry to take place. Alternatively, PRIMA could be operated as a Fourier-transform spectrometer in order to accurately measure the centroid wavelength of the observing bandpass for each astronomical target.