Update Content - 2022-03-30

content/zettels/acquisition_systems.md

@@ -1,12 +1,12 @@
 +++
 title = "Acquisition Systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 category = "equipment"
 +++
 
 Tags
-: [Analog to Digital Converters]({{<relref "analog_to_digital_converters.md#" >}})
+: [Analog to Digital Converters]({{< relref "analog_to_digital_converters.md" >}}), [Simulink Real Time Target Machines]({{< relref "simulink_real_time_target_machines.md" >}})
 
 
 ## Manufacturers {#manufacturers}
@@ -16,3 +16,9 @@ Tags
 | [Dewesoft](https://dewesoft.com/)                                                                  | Slovenia |
 | [Oros](https://www.oros.com/)                                                                      | France   |
 | [National Instruments](https://www.ni.com/fr-fr/shop/pc-based-measurement-and-control-system.html) | USA      |
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+</div>

content/zettels/materials.md

@@ -0,0 +1,19 @@
++++
+title = "Materials"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+
+## Metals {#metals}
+
+| Material        | Young's Modulus (GPA) | Thermal Expansion (\\(\mu m/m/^oC\\)) | Density | Thermal Conductivity (W/mK) |
+|-----------------|-----------------------|---------------------------------------|---------|-----------------------------|
+| Aluminum        | 68                    | 23.6                                  | 2.7     | 167                         |
+| Copper          | 110                   | 20                                    | 8.53    | 120                         |
+| Invar           | 148                   | 1.3                                   | 8       | 10.2                        |
+| Stainless Steel | 190                   | 10.8                                  | 8       | 17                          |
+| Titanium        | 108                   | 8.6                                   | 4.5     | 16.3                        |

content/zettels/optical_fibers.md

@@ -0,0 +1,31 @@
++++
+title = "Optical Fibers"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+
+## Connectors {#connectors}
+
+<a id="figure--fig:optical-fibers-sc"></a>
+
+{{< figure src="/ox-hugo/optical_fibers_sc.png" caption="<span class=\"figure-number\">Figure 1: </span>SC Connector (used for instance with Attocube)" >}}
+
+<a id="figure--fig:optical-fibers-fc"></a>
+
+{{< figure src="/ox-hugo/optical_fibers_fc.png" caption="<span class=\"figure-number\">Figure 2: </span>FC connector" >}}
+
+PC connector is used with Fabry-Perot interferometers when we wish to have some reflection at the end of the fiber.
+Otherwise, APC connectors are used.
+
+<a id="figure--fig:optical-connector-PC-APC"></a>
+
+{{< figure src="/ox-hugo/optical_connector_PC_APC.png" caption="<span class=\"figure-number\">Figure 3: </span>PC (usually black) and APC (usually green) connectors" >}}
+
+
+## Multi-mode and Single-mode fibers {#multi-mode-and-single-mode-fibers}
+
+If laser is used (fiber interferometer for instance), a single-mode fiber should be used and the wavelength of the mode should be matched with the wavelength of the laser.

content/zettels/position_sensors.md

@@ -18,6 +18,7 @@ High precision positioning sensors include:
 -   [LVDT]({{< relref "linear_variable_differential_transformers.md" >}})
 -   [Eddy Current Sensors]({{< relref "eddy_current_sensors.md" >}})
 -   [Encoders]({{< relref "encoders.md" >}})
+-   [Quadrant Photodiodes]({{< relref "quadrant_photodiodes.md" >}})
 
 
 ## Reviews of Relative Position Sensors {#reviews-of-relative-position-sensors}

content/zettels/quadrant_photodiodes.md

@@ -0,0 +1,148 @@
++++
+title = "Quadrant Photodiodes"
+author = ["Dehaeze Thomas"]
+draft = false
+category = "equipment"
++++
+
+Tags
+: [Position Sensors]({{< relref "position_sensors.md" >}}), [Optics]({{< relref "optics.md" >}})
+
+Some bibliography (<a href="#citeproc_bib_item_3">Manojlović 2011</a>; <a href="#citeproc_bib_item_4">Wu et al. 2015</a>; <a href="#citeproc_bib_item_2">Li et al. 2019</a>).
+
+
+## Working principle {#working-principle}
+
+<a id="figure--fig:quadrant-photodiode-schematic"></a>
+
+{{< figure src="/ox-hugo/quadrant_photodiode_schematic.png" caption="<span class=\"figure-number\">Figure 1: </span>Schematic of the Quadrant Photodiode" >}}
+
+The \\([x,y]\\) position of the beam on the quadrant photodiode can be estimated using the following equations:
+
+\begin{align}
+\sigma\_x &= \frac{(I\_B + I\_D) - (I\_A + I\_C)}{I\_A + I\_B + I\_C + I\_D} = \frac{I\_B + I\_D}{I\_A + I\_B + I\_C + I\_D} - 1 \\\\
+\sigma\_y &= \frac{(I\_A + I\_B) - (I\_C + I\_D)}{I\_A + I\_B + I\_C + I\_D} = \frac{I\_A + I\_B}{I\_A + I\_B + I\_C + I\_D} - 1
+\end{align}
+
+<a id="figure--fig:quadrant-photodiode-spot-size"></a>
+
+{{< figure src="/ox-hugo/quadrant_photodiode_relation_meas.png" caption="<span class=\"figure-number\">Figure 2: </span>Relation between the X position of the spot and the estimated measurement \\(\sigma\_x\\)" >}}
+
+This is true when the spot is near the center of the four quadrants (linear region).
+
+<a id="figure--fig:quadrant-photodiode-spot-size"></a>
+
+{{< figure src="/ox-hugo/quadrant_photodiode_spot_size.jpg" caption="<span class=\"figure-number\">Figure 3: </span>Effect of the spot size on the sensitibility and measurement range" >}}
+
+Basic requirements (taken from [here](https://www.aptechnologies.co.uk/home/support/photodiodes)):
+
+-   detector gap &lt; spot size &lt; detector size
+-   positional range &lt; spot size
+-   positional range is proportional to the spot size
+-   positional resolution is inversely proportional to the spot size
+
+Estimation of the linear region.
+
+The relation between the spot size and the quadrant photodiode sensitivity is well explained in (<a href="#citeproc_bib_item_1">Lee et al. 2010</a>).
+
+Usually, single mode laser are used such that the beam profile can well be approximated by a Gaussian distribution.
+The irradiance distribution is then:
+
+\begin{equation}
+I( r) = \frac{P}{\pi w^2} e^{-\frac{r^2}{w^2}}
+\end{equation}
+
+with:
+
+-   \\(r\\) the radius
+-   \\(P\\) the overall light source optical power
+-   \\(w\\) the light spot radius for which the irradiance drops to the \\(1/e\\) value of its central value
+
+
+## Estimation of photodiode gain {#estimation-of-photodiode-gain}
+
+It is function of:
+
+-   the spot size
+-   the gain size
+
+
+## Electrical Readout {#electrical-readout}
+
+[Transimpedance Amplifiers]({{< relref "transimpedance_amplifiers.md" >}}) amplifiers are required (schematic shown in Figure [4](#figure--fig:quadrant-transresistance-amplifier)).
+
+-   Trade-off between gain / noise / bandwidth (see [The art of electronics - third edition]({{< relref "horowitz15_art_of_elect_third_edition.md" >}}), chapter 8.11.4).
+
+The amplifier in Figure [4](#figure--fig:quadrant-transresistance-amplifier) produces a voltage:
+
+\begin{equation}
+V\_{\text{out}} = -I\_{\text{sig}} R\_f
+\end{equation}
+
+So the gain of the amplifier is simply \\(-R\_f\\) in [V/A].
+
+The feedback resistor creates a Johnson noise that corresponds to a current noise:
+
+\begin{equation}
+i\_{n} = \sqrt{4kT/R\_f} \quad [A/\sqrt{Hz}]
+\end{equation}
+
+This is usually larger than the amplifier input current noise.
+
+<a id="figure--fig:quadrant-transresistance-amplifier"></a>
+
+{{< figure src="/ox-hugo/quadrant_transresistance_amplifier.png" caption="<span class=\"figure-number\">Figure 4: </span>Transimpedance Amplifier; Current in, Voltage out" >}}
+
+
+## Angle Measurement {#angle-measurement}
+
+
+### Working Principle {#working-principle}
+
+Combined with a lens, a quadrant photodiode can become an angular sensor is well located at the focal plane of the lens (see Figure [5](#figure--fig:quandrant-diode-angle-schematic)).
+
+The relation between the position \\([y,z]\\) of the quadrant photodiode and the angle of the incident light \\([R\_y, R\_z]\\) is:
+
+\begin{align}
+y &=  f \cdot R\_z\\\\
+z &= -f \cdot R\_y
+\end{align}
+
+<a id="figure--fig:quandrant-diode-angle-schematic"></a>
+
+{{< figure src="/ox-hugo/quandrant_diode_angle_schematic.png" caption="<span class=\"figure-number\">Figure 5: </span>Optical schematic of combination of a quandrant photodiode with a lens" >}}
+
+
+### Sensitivity of beam translation {#sensitivity-of-beam-translation}
+
+The sensitivity to translation of the beam depends on how well the quadrant photodiode is located at the focal plane of the lens.
+If we note \\(\Delta x\\) the distance between the focal plane and the quadrant plane, the sensitivity to a \\(\Delta z\\) motion of the beam is:
+
+\begin{equation}
+z = \Delta x \cdot \Delta z
+\end{equation}
+
+Therefore, the ratio \\(f/\Delta x\\) gives the ratio of the sensitivity to beam angle to the sensitivity of beam translation.
+
+<div class="exampl">
+
+Take a lens with focal of \\(f = 500\\,mm\\) and say the quadrant photodiode is positioned at the focal plane with an accuracy of \\(\Delta x = 1\\,mm\\):
+
+\begin{equation}
+\frac{f}{\Delta x} = 500
+\end{equation}
+
+This means that \\(1\\,mm\\) of vertical motion of the beam will give the same output than \\(500\\,mrad\\) of rotation of the beam.
+
+</div>
+
+<div class="exampl">
+
+Say be want to determine with which precision the quadrant photodiode should be positioned.
+We now that the maximum translation of the beam is \\(\Delta z = 1\\,mm\\) and this should have less effect than a beam rotation of \\(R\_y = 10\\,\mu rad\\), then the quadrant photodiode should be position with an accuracy \\(\Delta x\\) of:
+
+\begin{equation}
+\Delta x = f \frac{R\_y}{\Delta z} = 1\\,mm, \quad \text{with } f = 0.1\\,m
+\end{equation}
+
+</div>

content/zettels/simulink_real_time_target_machines.md

@@ -6,7 +6,7 @@ category = "equipment"
 +++
 
 Tags
-:
+: [Acquisition Systems]({{< relref "acquisition_systems.md" >}}), [Acquisition Systems]({{< relref "acquisition_systems.md" >}})
 
 
 ## Manufacturers {#manufacturers}

content/zettels/transimpedance_amplifiers.md

@@ -13,7 +13,7 @@ Tags
 
 A transimpedance amplifier is a "current to voltage converter" and is also named a current controlled voltage source.
 
-It is generally used to interface a sensor which outputs a current proportional to the measurement parameter (photodiode for instance).
+It is generally used to interface a sensor which outputs a current proportional to the measurement parameter ([Quadrant Photodiodes]({{< relref "quadrant_photodiodes.md" >}}) for instance).
 
 
 ## Manufacturers {#manufacturers}