The precision of modern length interferometry and geodetic surveying far exceeds the accuracy, which is ultimately limited by the inadequacy of currently used equations for the refractive index of the atmosphere. I have critically reviewed recent research at the National Physical Laboratory, the International Bureau of Weights and Measures, and elsewhere that has led to revised formulas and data for the dispersion and density of the major components of the atmosphere. I have combined selected formulas from these sources to yield a set of equations that match recently reported measurements to within the experimental error, and that are expected to be reliable over very wide ranges of atmospheric parameters and wavelength.

Refractive index of air: new equations for the visible and near infrared

The need for dimensional micro and nano metrology is evident, and as critical dimensions are scaled down and geometrical complexity of objects is increased, the available technologies appear not sufficient. Major research and development efforts have to be undertaken in order to answer these challenges. The developments have to include new measuring principles and instrumentation, tolerancing rules and procedures as well as traceability and calibration. The current paper describes issues and challenges in dimensional micro and nano metrology by reviewing typical measurement tasks and available instrumentation. Traceability and calibration issues are discussed subsequently. Finally needs and gaps are identified based on these observations.

Dimensional micro and nano metrology

The non-linearities in a heterodyne laser interferometer system occurring from the phase measurement system of the interferometer and from non-ideal polarization effects of the optics are modeled into one analytical expression which includes the initial polarization state of the laser source, the rotational alignment of the beam splitter along with different transmission coefficients for polarization states and the rotational misalignment of the receiving polarizer. The model is verified using a Babinet Soleil Compensator allowing a common path for both polarization states and thereby reducing the influence of the refractive index of air. The verification shows an agreement of the model with measurements with a standard deviation of 0.2 nm. With the use of the model it is confirmed that the mean of two polarizer receivers can reduce the effect of non-linearity. However, depending on the accuracy of the polarizer angles, a second-order non-linearity remains. Also the effect of rotational misalignment of the beam splitter can not be reduced in this way.

Modeling and verifying non-linearities in heterodyne displacement interferometry

The theory of summation of electromagnetic line transitions is summarized in terms of the Taylor expansion of the refractive index of humid air as a function of the basic independent parameters (temperature, pressure, humidity, wavelength) in five separate infrared regions from the H to the Q band at a fixed percentage of carbon dioxide. These are least-squares fits to raw, highly resolved spectra for a set of temperatures from 10 to 25 °C, a set of pressures from 500 to 1023 hPa and a set of relative humidities from 5 to 60%. These choices reflect the prospective application to characterize ambient air at mountain altitudes of astronomical telescopes.

https://iopscience.iop.org/article/10.1088/1464-4258/9/5/008/pdf

Refractive index of humid air in the infrared: model fits

The refractive index of helium at atmospheric pressure can be determined from ab initio calculations in combination with careful pressure and temperature measurements. Therefore, helium can serve as a theory-based standard of refractive index; it might be used as a medium of known refractive index for high-accuracy interferometric length measurements or it can be used to characterize and correct errors in a gas refractometer. We have used helium to correct for pressure-induced distortions of two refractometers built by us, where both refractometers basically consist of a laser locked to the transmission maximum of a simple Fabry–Perot cavity. As a proof-of-principle of the helium-correction technique, we have used our device to measure the molar refractivity of nitrogen and we find reasonable agreement with previous measurements. When our two refractometers simultaneously measure the refractive index of a common nitrogen sample, we find that the two systems agree with each other within a few parts in 109.

/pdf/using-helium-as-a-standard-of-refractive-index-correcting-2opsszt2yo.pdf

W. Hou

Papers

Accurate measurement of the refractive index of air