Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model
A very simple Gaussian model is used to illustrate an interesting fitting result: a linear growth of the resolution with the number <i>N</i> of detecting layers. This rule is well beyond the well-known rule proportional to <inline-formula><math xmlns="http://www.w3.org/1998...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-01-01
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| Series: | Instruments |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2410-390X/6/1/10 |
| Summary: | A very simple Gaussian model is used to illustrate an interesting fitting result: a linear growth of the resolution with the number <i>N</i> of detecting layers. This rule is well beyond the well-known rule proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula> for the resolution of the usual fits. The effect is obtained with the appropriate form of the variance for each hit (observation). The model reconstructs straight tracks with <i>N</i> parallel detecting layers, the track direction is the selected parameter to test the resolution. The results of the Gaussian model are compared with realistic simulations of silicon micro-strip detectors. These realistic simulations suggest an easy method to select the essential weights for the fit: the lucky model. Preliminary results of the lucky model show an excellent reproduction of the linear growth of the resolution, very similar to that given by realistic simulations. The maximum likelihood evaluations complete this exploration of the growth in resolution. |
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| ISSN: | 2410-390X |