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Thomas Dehaeze
2021-05-02 20:37:00 +02:00
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content/article/fleming13_review_nanom_resol_posit_sensor.md
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@@ -4,15 +4,11 @@ author = ["Thomas Dehaeze"]
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Backlinks:
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Position Sensors]({{< relref "position_sensors" >}})
Reference
: ([Fleming 2013](#org35f9cea))
: ([Fleming 2013](#org336a947))
Author(s)
: Fleming, A. J.
@@ -37,7 +33,7 @@ Usually quoted as a percentage of the fill-scale range (FSR):
With \\(e\_m(v)\\) is the mapping error.
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{{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="Figure 1: The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}}
@@ -46,7 +42,7 @@ With \\(e\_m(v)\\) is the mapping error.
If the shape of the mapping function actually varies with time, the maximum error due to drift must be evaluated by finding the worst-case mapping error.
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{{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="Figure 2: The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}}
@@ -151,9 +147,9 @@ The empirical rule states that there is a \\(99.7\%\\) probability that a sample
This if we define the resolution as \\(\delta = 6 \sigma\\), we will referred to as the \\(6\sigma\text{-resolution}\\).
Another important parameter that must be specified when quoting resolution is the sensor bandwidth.
There is usually a trade-off between bandwidth and resolution (figure [3](#org2ee752d)).
There is usually a trade-off between bandwidth and resolution (figure [3](#orge95682f)).
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{{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}}
@@ -186,6 +182,7 @@ A convenient method for reporting this ratio is in parts-per-million (ppm):
| Encoder | Meters | | 6 nm | >100kHz | 5 ppm FSR |
## Bibliography {#bibliography}
<a id="org35f9cea"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
<a id="org336a947"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.