The measured distance is proportional to the refractive index of the air that depends on several quantities as shown in Table [1](#table--tab:index-air) (Taken from (<ahref="#citeproc_bib_item_5">Thurner et al. 2015</a>)).
Dependence of Refractive Index \(n\) of Air from Temperature \(T\), pressure \(p\), Humidity \(h\), and CO2 content \(x_c\). Taken around \(T = 20^oC\), \(p=101kPa\), \(h = 50\%\), \(x_c = 400 ppm\) and \(\lambda = 1530nm\)
</div>
| Physical Value | Refractive Index Sensitivity | Value |
In order to limit the measurement uncertainty due to variation of air parameters, an Environmental Unit can be used that typically measures the temperature, pressure and humidity and compensation for the variation of refractive index in real time.
Figure [1](#figure--fig:position-sensor-interferometer-precision) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from (<ahref="#citeproc_bib_item_3">Jang and Kim 2017</a>)).
{{<figuresrc="/ox-hugo/position_sensor_interferometer_precision.png"caption="<span class=\"figure-number\">Figure 1: </span>Expected precision of interferometer as a function of measured distance">}}
{{<figuresrc="/ox-hugo/interferometers_air_turbulence.png"caption="<span class=\"figure-number\">Figure 2: </span>Effect of air turbulences on measurement stability">}}
<divclass="csl-entry"><aid="citeproc_bib_item_1"></a>Bobroff, N. 1993. “Recent Advances in Displacement Measuring Interferometry.” <i>Measurement Science and Technology</i> 4 (9): 907–26. doi:<ahref="https://doi.org/10.1088/0957-0233/4/9/001">10.1088/0957-0233/4/9/001</a>.</div>
<divclass="csl-entry"><aid="citeproc_bib_item_2"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” doi:<ahref="https://doi.org/10.13140/rg.2.2.21044.35205">10.13140/rg.2.2.21044.35205</a>.</div>
<divclass="csl-entry"><aid="citeproc_bib_item_3"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” <i>International Journal of Precision Engineering and Manufacturing</i> 18 (12): 1881–90. doi:<ahref="https://doi.org/10.1007/s12541-017-0217-y">10.1007/s12541-017-0217-y</a>.</div>
<divclass="csl-entry"><aid="citeproc_bib_item_4"></a>Loughridge, Russell, and Daniel Y. Abramovitch. 2013. “A Tutorial on Laser Interferometry for Precision Measurements.” In <i>2013 American Control Conference</i>, nil. doi:<ahref="https://doi.org/10.1109/acc.2013.6580402">10.1109/acc.2013.6580402</a>.</div>
<divclass="csl-entry"><aid="citeproc_bib_item_5"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” <i>Applied Optics</i> 54 (10). Optical Society of America: 3051–63.</div>
