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content/zettels/interferometers.md
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title = "Interferometers"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
category = "equipment"
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Tags
: [Position Sensors]({{<relref "position_sensors.md#" >}})
: [Position Sensors]({{< relref "position_sensors.md" >}})
## Manufacturers {#manufacturers}
@@ -25,12 +25,12 @@ Tags
## Reviews {#reviews}
([Ducourtieux 2018](#org538e4dc), [2018](#org538e4dc); [Bobroff 1993](#org9f4652e), [1993](#org9f4652e); [Thurner et al. 2015](#orgdcf4929), [2015](#orgdcf4929); [Loughridge and Abramovitch 2013](#orgd91ce9e))
(<a href="#citeproc_bib_item_2">Ducourtieux 2018</a>, <a href="#citeproc_bib_item_2">2018</a>; <a href="#citeproc_bib_item_1">Bobroff 1993</a>, <a href="#citeproc_bib_item_1">1993</a>; <a href="#citeproc_bib_item_5">Thurner et al. 2015</a>, <a href="#citeproc_bib_item_5">2015</a>; <a href="#citeproc_bib_item_4">Loughridge and Abramovitch 2013</a>)
## Effect of Refractive Index - Environmental Units {#effect-of-refractive-index-environmental-units}
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 ([Thurner et al. 2015](#orgdcf4929))).
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 (<a href="#citeproc_bib_item_5">Thurner et al. 2015</a>)).
<a id="table--tab:index-air"></a>
<div class="table-caption">
@@ -56,25 +56,25 @@ Typical characteristics of commercial environmental units are shown in Table [2]
Characteristics of Environmental Units
</div>
| | Temperature (\\(\pm\ ^oC\\)) | Pressure (\\(\pm\ hPa\\)) | Humidity \\(\pm\\% RH\\) | Wavelength Accuracy (\\(\pm\ \text{ppm}\\)) |
|-----------|------------------------------|---------------------------|--------------------------|---------------------------------------------|
| Attocube | 0.1 | 1 | 2 | 0.5 |
| Renishaw | 0.2 | 1 | 6 | 1 |
| Picoscale | 0.2 | 2 | 2 | 1 |
| | Temperature (\\(\pm\ ^oC\\)) | Pressure (\\(\pm\ hPa\\)) | Humidity \\(\pm\\\% RH\\) | Wavelength Accuracy (\\(\pm\ \text{ppm}\\)) |
|-----------|------------------------------|---------------------------|---------------------------|---------------------------------------------|
| Attocube | 0.1 | 1 | 2 | 0.5 |
| Renishaw | 0.2 | 1 | 6 | 1 |
| Picoscale | 0.2 | 2 | 2 | 1 |
## Interferometer Precision {#interferometer-precision}
Figure [1](#org24527f3) shows the expected precision as a function of the measured distance due to change of refractive index of the air (taken from ([Jang and Kim 2017](#org0cf5512))).
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 (<a href="#citeproc_bib_item_3">Jang and Kim 2017</a>)).
<a id="org24527f3"></a>
<a id="figure--fig:position-sensor-interferometer-precision"></a>
{{< figure src="/ox-hugo/position_sensor_interferometer_precision.png" caption="Figure 1: Expected precision of interferometer as a function of measured distance" >}}
{{< figure src="/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" >}}
## Sources of uncertainty {#sources-of-uncertainty}
Sources of error in laser interferometry are well described in ([Ducourtieux 2018](#org538e4dc)).
Sources of error in laser interferometry are well described in (<a href="#citeproc_bib_item_2">Ducourtieux 2018</a>).
It includes:
@@ -82,25 +82,22 @@ It includes:
- Variation of refractive index of air, which is dependent of:
- Temperature: \\(K\_T \approx 1 ppmK^{-1}\\)
- Pressure: \\(K\_P \approx 0.27 ppm hPa^{-1}\\)
- Humidity: \\(K\_{HR} \approx 0.01 ppm \% RH^{-1}\\)
- Humidity: \\(K\_{HR} \approx 0.01 ppm \\% RH^{-1}\\)
- These errors can partially be compensated using an environmental unit.
- Air turbulence (Figure [2](#org1d0f37d))
- Air turbulence (Figure [2](#figure--fig:interferometers-air-turbulence))
- Non linearity
<a id="org1d0f37d"></a>
{{< figure src="/ox-hugo/interferometers_air_turbulence.png" caption="Figure 2: Effect of air turbulences on measurement stability" >}}
<a id="figure--fig:interferometers-air-turbulence"></a>
{{< figure src="/ox-hugo/interferometers_air_turbulence.png" caption="<span class=\"figure-number\">Figure 2: </span>Effect of air turbulences on measurement stability" >}}
## Bibliography {#bibliography}
<a id="org9f4652e"></a>Bobroff, N. 1993. “Recent Advances in Displacement Measuring Interferometry.” _Measurement Science and Technology_ 4 (9):907–26. <https://doi.org/10.1088/0957-0233/4/9/001>.
<a id="org538e4dc"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” <https://doi.org/10.13140/rg.2.2.21044.35205>.
<a id="org0cf5512"></a>Jang, Yoon-Soo, and Seung-Woo Kim. 2017. “Compensation of the Refractive Index of Air in Laser Interferometer for Distance Measurement: A Review.” _International Journal of Precision Engineering and Manufacturing_ 18 (12):1881–90. <https://doi.org/10.1007/s12541-017-0217-y>.
<a id="orgd91ce9e"></a>Loughridge, Russell, and Daniel Y. Abramovitch. 2013. “A Tutorial on Laser Interferometry for Precision Measurements.” In _2013 American Control Conference_, nil. <https://doi.org/10.1109/acc.2013.6580402>.
<a id="orgdcf4929"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="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:<a href="https://doi.org/10.1088/0957-0233/4/9/001">10.1088/0957-0233/4/9/001</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Ducourtieux, Sebastien. 2018. “Toward High Precision Position Control Using Laser Interferometry: Main Sources of Error.” doi:<a href="https://doi.org/10.13140/rg.2.2.21044.35205">10.13140/rg.2.2.21044.35205</a>.</div>
<div class="csl-entry"><a id="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:<a href="https://doi.org/10.1007/s12541-017-0217-y">10.1007/s12541-017-0217-y</a>.</div>
<div class="csl-entry"><a id="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:<a href="https://doi.org/10.1109/acc.2013.6580402">10.1109/acc.2013.6580402</a>.</div>
<div class="csl-entry"><a id="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>
</div>