Group Refractive Index Of Air Research Articles

Comparative analysis of the accuracy requirements of the equipment for determining the mean integral refractive index of air using different realizations of the gradient method

The speed of propagation of electromagnetic waves in the Earth’s atmosphere differs from the speed of their propagation in a vacuum, which is one of the main factors that have a significant impact on the accuracy of long distance measurement. This influence is taken into account in long distance measurement with the correction for the mean integral group refractive index of air, which depends on such meteorological parameters as temperature, atmospheric pressure and relative air humidity. The purpose of this work is to compare the accuracy requirements for equipment designed to measure temperature, pressure, and relative humidity required to determine the above correction by the gradient method using the Euler-Maclaurin quadrature formula (hereafter, the Euler-Maclaurin method) and the formula based on Hermite interpolation polynomials (hereafter, the Hermite method). The requirements for the uncertainty of measurements carried out with the sensors of meteorological parameters, allowing to find the mean integral group refractive index of air, providing length measurements of the baselines of up to 5 km with an expanded uncertainty of not more than 1 mm, are established. Keywords: atmosphere; mean integral group refractive index of air; laser long distance measurement

Determination of calculation parameters for difference approximation of group refractive index of air based on two-point central method

BackgroundThe accurate knowledge of the refractive index of air is very important for environmental compensation in length measurements.MethodsIn this study, we apply difference approximation methods to facilitate the calculation of the group refractive index of air (GRA) over all calculable wavelengths. Our approach involves the determination of a suitable combination of the step size Δλ and numbers of significant digits of calculations of the phase refractive index of air (PRA) by balancing the two main errors (round-off and truncation errors) over the entire calculable wavelength range.ResultsBased on our calculations, we find that the GRA computation over the range of all calculable wavelengths (301.5-1698.5 nm) can be easily approximated by the two-point central difference method with Δλ = 1.5 nm and 12-digit PRA accuracy.ConclusionThe approximation accuracy is less than 5 × 10-9. Our approach can be used by non-expert users to obtain the GRA with sufficient accuracy.

SURVEY OF SELECTED PROCEDURES FOR THE INDIRECT DETERMINATION OF THE GROUP REFRACTIVE INDEX OF AIR

The main aim of the research was to evaluate numeric procedures of the indirect determination of the group refractive index of air and to choose the suitable ones for requirements of ordinary and high accuracy distance measurement in geodesy and length metrology. For this purpose, 10 existing computation methods were derived from various authors’ original publications and all were analysed for wide intervals of wavelengths and atmospheric parameters. The determination of the phase and the group refractive indices are essential parts in the evaluation of the first velocity corrections of laser interferometers and electronic distance meters. The validity of modern procedures was tested with respect to updated CIPM-2007 equations of the density of air. The refraction model of Leica AT401 laser tracker was analysed.

Frequency comb calibrated frequency-sweeping interferometry for absolute group refractive index measurement of air.

The absolute group refractive index of air at 194061.02GHz is measured in real time using frequency-sweeping interferometry calibrated by an optical frequency comb. The group refractive index of air is calculated from the calibration peaks of the laser frequency variation and the interference signal of the two beams passing through the inner and outer regions of a vacuum cell when the frequency of a tunable external cavity diode laser is scanned. We continuously measure the refractive index of air for 2h, which shows that the difference between measured results and Ciddor's equation is less than 9.6×10-8, and the standard deviation of that difference is 5.9×10-8. The relative uncertainty of the measured refractive index of air is estimated to be 8.6×10-8. The data update rate is 0.2Hz, making it applicable under conditions in which air refractive index fluctuates fast.

Selection of numerical differentiation method for calculation of group refractive index of air over all calculable wavelengths

In this study, we attempt the selection of a difference approximation method to facilitate calculation of the group refractive index of air (GRA) over all calculable wavelengths. Based on calculation and error analysis, we test the performance of the three-point forward, three-point backward, and four-point central difference methods. We find that the GRA computation over the range of all calculable wavelengths (320–1680nm) can be easily approximated by the four-point central difference method with a step size of 10nm and an approximation accuracy of less than 30×10−9.

Group refractive index calculation by difference approximation for length measurement

In this study, the possibility of employing a difference approximation to facilitate calculation of the group refractive index of air (GRA) was investigated. The forward, backward, and central difference methods were used to numerically approximate the first-order derivatives of the phase refractive index based on the Edlè-empirical equations. To confirm the validity of the calculations, the calculated results were compared with the theoretical analysis results and the values in a related paper. It was found that the GRA computation could be easily approximated by the two-point central difference method with a step size of 10 nm.

Absolute group refractive index measurement of air by dispersive interferometry using frequency comb.

The absolute group refractive index of air at 1563 nm is measured by dispersive interferometry, and a combined uncertainty of 1.2 × 10(-8) is achieved. The group refractive index of air is calculated from the dispersive interferograms of the two beams passing through the inner and outer regions of a vacuum cell by fast-Fourier-transform. Experimental results show that the discrepancies between our method and modified Edlén equation are less than 3.43 × 10(-8) and 4.4 × 10(-8) for short-term and long-term experiments, respectively. The interferogram update rate is 15 ms, which makes it suitable for application of real-time monitoring. Furthermore, it is promising to improve the measurement uncertainty to 3.0 × 10(-9) by changing the material of the vacuum cell and measuring its length more accurately through optical interferometry.

Direct measurement of the group refractive index of air with interferometry between adjacent femtosecond pulses.

The group refractive index of air in laboratory conditions is measured directly between adjacent femtosecond laser pulses by a new interferometry technique. Measurement of the repetition rate of the mode-locked pulse train that gives the maximum amplitude of the interference-signal envelope enables us to determine the group refractive index of air within a standard deviation of 2 x 10(-7). This simple method without vacuum reference is attractive for measuring the group refractive index needed for precise distance measurements in open fields.

High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser

A high-accuracy optical distance meter with a mode-locked femtosecond laser is proposed for distance measurements in a 310-m-long optical tunnel. We measured the phase shift of the optical beat component between longitudinal modes of a mode-locked laser. A high resolution of 50 microm at 240-m distance was obtained without cyclic error correction. The group refractive index of air is automatically extracted to an accuracy of 6 parts per million (ppm) by two-color measurement with the pulses of fundamental and second-harmonic wavelengths. Finally, an absolute mechanical distance of 240 m was obtained to within 8-ppm accuracy by use of a series of beat frequencies with the advantage of a wide range of intermode frequency, together with the results of the two-color measurement.

Group-phase refractive index method for improving the accuracy in two-color interferometric length measurements

A group-phase refractive index method was developed for improving the accuracy of a conventional two-color method used in an interferometer for length measurements. This method uses two closer wavelengths to reduce the errors caused by air turbulence and the chromatic aberration. We describe the new method and demonstrate preliminarily its effectiveness by measuring the group refractive index of air using a vacuum cell. We then compared the results with those calculated using the Edlén equation. The mean difference between the measured and calculated values was 2.15×10−6 with a standard deviation of 2.0×10−6 for the vacuum cell with a length of 184.5 mm.

Measurement of the group refractive index of air by two-wavelength interferometry

The group refractive index of air at 3.44 μm is directly measured with an accuracy of 2 × 10 -7 using two-wavelength simultaneous interferometry with a 3.51- and 3.37-μm simultaneous operation He-Xe laser.

The Group Refractive Index of Air

The Group Refractive Index of Air