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chapt3/3.4_DSSD_FB_correlation_I_DSSD1.html

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<h1 id="3.4-DSSD-front-back-correlation-(I)---dssd1">3.4 DSSD front-back correlation (I) - dssd1<a class="anchor-link" href="#3.4-DSSD-front-back-correlation-(I)---dssd1">&#182;</a></h1>
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<h1 id="3.4-DSSD-front-back-correlation-(I)---dssd1">3.4 DSSD front-back correlation (I) - dssd1<a class="anchor-link" href="#3.4-DSSD-front-back-correlation-(I)---dssd1">&#182;</a></h1><h2 id="Purpose:">Purpose:<a class="anchor-link" href="#Purpose:">&#182;</a></h2><ul>
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<li>Based on the x-y correlation, normalize the amplitude of a specific strip using the amplitude of a given strip as a reference.</li>
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</ul>
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<h3 id="Principle">Principle<a class="anchor-link" href="#Principle">&#182;</a></h3><p>A double-sided silicon strip detector (DSSD) is used in nuclear physics to pinpoint the position and energy of incident particles. With orthogonal strip arrays on its front (x-strips) and back (y-strips), it detects charge carriers generated by a particle’s energy deposition. These carriers induce equal but opposite charges on the x- and y-strips, and amplifiers of opposite polarity produce positive signals of equal amplitude, reflecting the deposited energy.</p>
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<p>For a particle hitting the intersection of front strip $x_i$ and back strip $y_j$, depositing energy $E$, the calibrated energy signals from both sides should match:
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$$ E = E_{xi} = E_{yj}, $$
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where $E_{xi}$ and $E_{yj}$ are the energies measured by strips $x_i$ and $y_j$.</p>
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<ul>
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<li><p>A double-sided silicon strip detector (DSSD) is used in nuclear physics to pinpoint the position and energy of incident particles. With orthogonal strip arrays on its front (x-strips) and back (y-strips), it detects charge carriers generated by a particle’s energy deposition. These carriers induce equal but opposite charges on the x- and y-strips, and amplifiers of opposite polarity produce positive signals of equal amplitude, reflecting the deposited energy.</p>
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</li>
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<li><p>For a particle hitting the intersection of front strip $x_i$ and back strip $y_j$, depositing energy $E$, the calibrated energy signals from both sides should match:</p>
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</li>
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</ul>
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$$ E = E_{xi} = E_{yj}, $$<p>where $E_{xi}$ and $E_{yj}$ are the energies measured by strips $x_i$ and $y_j$.</p>
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<img src="fig/dssd-fb.png" alt="" width="600" />
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<h3 id="Energy-Calibration-and-Correlation">Energy Calibration and Correlation<a class="anchor-link" href="#Energy-Calibration-and-Correlation">&#182;</a></h3><p>The raw signal amplitudes (channel numbers) from strips $x_i$ and $y_j$, denoted $a_{xi}$ and $a_{yj}$, relate to the deposited energy via linear calibration:
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$$ E_{xi} = g_{xi} a_{xi} + o_{xi}, \tag{1} $$
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$$ E_{yj} = g_{yj} a_{yj} + o_{yj}, \tag{2} $$
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where $g_{xi}, g_{yj}$ are gain factors and $o_{xi}, o_{yj}$ are offsets. Since the deposited energy is the same ($E = E_{xi} = E_{yj}$), equating (1) and (2) gives a linear relationship between amplitudes:
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$$ a_{xi} = k_{yj} a_{yj} + b_{yj}, \tag{3} $$
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where:
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$$ k_{yj} = \frac{g_{yj}}{g_{xi}}, \quad b_{yj} = \frac{o_{yj} - o_{xi}}{g_{xi}}. $$
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Here, $k_{yj}$ and $b_{yj}$ are normalization coefficients that scale the amplitude $a_{yj}$ (from the &quot;calibrated&quot; strip $y_j$) to match $a_{xi}$ (from the &quot;reference&quot; strip $x_i$). A 2D plot of $a_{xi}$ vs. $a_{yj}$ shows a linear trend, and a linear fit yields $k_{yj}$ and $b_{yj}$. This calibration ensures consistent energy measurements across strips, crucial for accurate position and energy reconstruction.</p>
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<h3 id="Energy-Calibration-and-Correlation">Energy Calibration and Correlation<a class="anchor-link" href="#Energy-Calibration-and-Correlation">&#182;</a></h3><p>The raw signal amplitudes (channel numbers) from strips $x_i$ and $y_j$, denoted $a_{xi}$ and $a_{yj}$, relate to the deposited energy via linear calibration:</p>
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$$ E_{xi} = g_{xi} a_{xi} + o_{xi}, \tag{1} $$$$ E_{yj} = g_{yj} a_{yj} + o_{yj}, \tag{2} $$<p>where $g_{xi}, g_{yj}$ are gain factors and $o_{xi}, o_{yj}$ are offsets. Since the deposited energy is the same ($E = E_{xi} = E_{yj}$), equating (1) and (2) gives a linear relationship between amplitudes:</p>
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$$ a_{xi} = k_{yj} a_{yj} + b_{yj}, \tag{3} $$<p>where:
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$$ k_{yj} = \frac{g_{yj}}{g_{xi}}, \quad b_{yj} = \frac{o_{yj} - o_{xi}}{g_{xi}}. $$</p>
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<p>Here, $k_{yj}$ and $b_{yj}$ are normalization coefficients that scale the amplitude $a_{yj}$ (from the &quot;calibrated&quot; strip $y_j$) to match $a_{xi}$ (from the &quot;reference&quot; strip $x_i$). A 2D plot of $a_{xi}$ vs. $a_{yj}$ shows a linear trend, and a linear fit yields $k_{yj}$ and $b_{yj}$. This calibration ensures consistent energy measurements across strips, crucial for accurate position and energy reconstruction.</p>
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<h3 id="Multi-Particle-Position-Determination">Multi-Particle Position Determination<a class="anchor-link" href="#Multi-Particle-Position-Determination">&#182;</a></h3><p>When two particles strike the DSSD simultaneously at positions $(x_1, y_1)$ and $(x_2, y_2)$ with distinct energies $e_1 = e_{x1} = e_{y1}$ and $e_2 = e_{x2} = e_{y2}$ ($e_1 \neq e_2$), signals are recorded from x-strips $x_1, x_2$ and y-strips $y_1, y_2$. This leads to ambiguity, as possible pairings are:</p>
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<ul>
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<li>$(x_1, y_1)$ and $(x_2, y_2)$ (correct),</li>

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