DF Thesis - Revision history

Friadavi: /* Appendicies */

2019-06-11T02:16:04Z

Appendicies

Friadavi: /* Kalman Fitter */

2019-06-11T02:10:10Z

Kalman Fitter

Friadavi at 23:04, 7 June 2019

2019-06-07T23:04:50Z

Friadavi at 22:22, 7 June 2019

2019-06-07T22:22:46Z

Friadavi at 22:08, 7 June 2019

2019-06-07T22:08:15Z

Foretony: /* Introduction */

2019-06-07T03:41:01Z

Introduction

Foretony: /* Abstract */

2019-06-07T03:33:02Z

Abstract

Friadavi: /* Kalman Fitter */

2019-06-06T05:37:37Z

Kalman Fitter

Friadavi: /* Conclusion */

2019-06-06T05:33:01Z

Conclusion

Friadavi: /* Analysis */

2019-06-06T05:32:19Z

Analysis

Show changes

@@ Line 568: / Line 568: @@
 With respect to the relationship between the reconstruction efficiency and the span of the search, it would seem that the Raster Based Algorithm is acting as a filter of sorts. As the span increases, both the sigma of the reconstruction and the efficiency increases. This seems to suggest that broadening the quantity of events which can be successfully reconstructed results in a worse quality of reconstruction. This, in turn, would seem to suggest that the algorithm intrinsically culls out events which are not reconstructed well enough.
-=Appendicies=
+=Appendices=
 ==Appendix A==
@@ Line 764: / Line 764: @@
 ====Linked Helices====
-First, track candidates that don't have at least five segments within their crosses are culled. Then four initial fits are performed, one for each combination of one of the region one segments being coupled with one of the region three segments. In these fits, the slopes of the segments are used to calculate the momentum and charge of the particle. Those values are then input into a swimmer which will swim from the region one cross to thex-y plane of the region two cross and then on to the x-y plane of the region three cross. If the \textchi{}\textsuperscript{2} is bad or the integrated magnetic field over the path is zero, the candidate is culled.
+First, track candidates that don't have at least five segments within their crosses are culled. Then four initial fits are performed, one for each combination of one of the region one segments being coupled with one of the region three segments. In these fits, the slopes of the segments are used to calculate the momentum and charge of the particle. Those values are then input into a swimmer which will swim from the region one cross to the x-y plane of the region two cross and then on to the x-y plane of the region three cross. If the \textchi{}\textsuperscript{2} is bad or the integrated magnetic field over the path is zero, the candidate is culled.
-The momentum and charge are reconstructed, again, from the second segment of the region 1 and 3 crosses. If the momentum is greater than 11GeV, it is set to 11GeV. A state vector is formed from combining the region 1 cross information with the momentum. A Kalman fitter is created and attempts to fit the crosses. If this fails, the candidate is culled. The \textchi{}\textsuperscript{2} of the fit between the Kalman fit and the crosses is calcualted, and the candidate is culled if the value is too large. One final check to see if the Kalman fit either failed or if the final state vector produced by it is done. If passed, the candidate is added to the list of track candidates.
+The momentum and charge are reconstructed, again, from the second segment of the region 1 and 3 crosses. If the momentum is greater than 11GeV, it is set to 11GeV. A state vector is formed from combining the region 1 cross information with the momentum. A Kalman fitter is created and attempts to fit the crosses. If this fails, the candidate is culled. The \textchi{}\textsuperscript{2} of the fit between the Kalman fit and the crosses is calculated, and the candidate is culled if the value is too large. One final check to see if the Kalman fit either failed or if the final state vector produced by it is done. If passed, the candidate is added to the list of track candidates.
 ===Crosses to Tracks Part II===
@@ Line 783: / Line 783: @@
 ===Reconstructing Tracks===
-The algorithm now begins track reconstruction, failing if the Hit Based Tracks were not saved correctly. First, all of the Hit Based track information stored in the data banks are read into an array, and all of the segment-track associations are set. The algorithm now considers each track, failing if the track has less than four segments, and creating crosses in the same fashion as the Hit Based algorithm. These tracks are now run through a Kalman fitter. The track is culled if the interaction vertex is too large. Finally, for each surviving track, the overall trajectory is calculated and associated hits and segements are set accordingly.
+The algorithm now begins track reconstruction, failing if the Hit Based Tracks were not saved correctly. First, all of the Hit Based track information stored in the data banks are read into an array, and all of the segment-track associations are set. The algorithm now considers each track, failing if the track has less than four segments, and creating crosses in the same fashion as the Hit Based algorithm. These tracks are now run through a Kalman fitter. The track is culled if the interaction vertex is too large. Finally, for each surviving track, the overall trajectory is calculated and associated hits and segments are set accordingly.
 ==Appendix C==

@@ Line 152: / Line 152: @@
 In general, the Kalman Filter Algorithm proceeds as follows. First, the initial state vector of interest and it's associated uncertainties are evolved until there is a measurement available to compare against. The algorithm then compares the predicted and and measured values and takes a weighted average of them wherein more weight is given to values with smaller uncertainties. The state vector is updated and the algorithm repeats. It is worth mentioning that the Kalman Filter is efficient in the sense that there is no need to keep track of old state vectors. There is instead a  covariance matrix which is updated every step.\autocite{miller87}
-A summary of the mathematics of the Kalman Filter is layed out in equations \ref{eq:kalman:1} through \ref{eq:kalman:16}. It is quoted from An Introduction to Kalman Filtering with Applications by Miller and Leskiw.
+A summary of the mathematics of the Kalman Filter is layed out in equations \ref{eq:kalman:1} through \ref{eq:kalman:16}. It is quoted from An Introduction to Kalman Filtering with Applications by Miller and Leskiw.\autocite{miller87}
 Let $\pmb{x}(t)$ be a state vector which satisfies the deterministic ordinary differential system

@@ Line 2: / Line 2: @@
 \qquad{}The thesis reports the results of an improved track reconstruction program that is used to determine the momentum and interaction vertex of particles scattering in experiments performed using the CLAS12 Detector at Jefferson Lab. Particles are reconstructed from the CLAS12 Drift Chamber and scintillator detector sub-systems. The improved algorithm performs a three dimensional grid search in momentum space in an attempt to minimize the distance of closest approach between the particle’s path and the transverse location of the incident electrons that scatter from nucleons in a cryogenic target. Analysis has shown that the new algorithm is capable of improving the reconstruction in the X and Y directions (orthogonal to the incident electrons) by a factor of no less than ten, while at least maintaining the quality of the reconstruction in the Z direction.
-\qquad{}An improvement in the reconstruction of the Z direction allows for statistical certainty in stating which part of the physics target an interaction occured. This is of particular importance in the polarized SIDIS dual target, a physics target with two distinct sub-targets that can be filled with ammonia and polarized in different directions. Being able to state which of the two sub-targets an event occurred in paramount to being able to distinguish the difference in interactions between the two. Analysis of the proposed algorithm shows that one can resolve the two target if they are separted by at least 4cm.
+\qquad{}An improvement in the reconstruction of the Z direction allows for statistical certainty in stating which part of the physics target an interaction occurred. This is of particular importance in the polarized SIDIS dual target, a physics target with two distinct sub-targets that can be filled with ammonia and polarized in different directions. Being able to state which of the two sub-targets an event occurred in paramount to being able to distinguish the difference in interactions between the two. Analysis of the proposed algorithm shows that one can resolve the two targets with if they are separated by at least 4cm.
 =Introduction=

@@ Line 18: / Line 18: @@
 =Theory=
-This chapter is meant to provide sufficient knowledge and background to understand the general workings of the CLAS12 drift chambers, the most critical elements of the reconstruction process, and the rasterization of the scattering electrons. With regards to the drift chambers, particular attention is paid to the geometry and physical construction as that directly effects the acceptance of the detector. The elements of the most importance discussed here are the concepts of Runge-Kutta approximations and Kalman Fitters. Both are used heavily in the reconstruction process. And finally, the discussion about rasterized beams gives background as to why this project exists to begin with.
+This chapter is meant to provide sufficient knowledge and background to understand the general workings of the CLAS12 drift chambers, the most critical elements of the reconstruction process, and the rasterization of the scattering electrons. With regards to the drift chambers, particular attention is paid to the geometry and physical construction as that directly effects the acceptance of the detector. The elements of the most importance discussed here are the concepts of Runge-Kutta approximations and Kalman Fitters. Both are used heavily in the reconstruction process. And finally, the discussion about rastered beams gives background as to why this project exists to begin with.
 ==Drift Chambers==
@@ Line 244: / Line 244: @@
 This is implemented in the Fitter as a method of refining a trajectory provided by calculations done on the raw hits. In essence, this method takes the initial state vector and steps it to each drift chamber region using the Runge-Kutta based Swimmer discussed in the previous section. At each region, the Kalman Filter is used to refine the trajectory. After finishing with the third region, the algorithm then steps back to near the starting location of the inital state vector and repeates the process up to 30 times. The algorithm will exit early if the \textchi{}\textsuperscript{2} is sufficiently small.
-==Rasterized Beam==
+==Rastered Beam==
 A rastered beam is the intentional movement of the incident electrons, ideally translating without rotation, over the surface of the target. The primary purpose of this is to distribute the energy deposited into the target more uniformly and avoid localized target heating that would result in physical changes to the target. In the case of a cryogenic target, overheating can cause localized target boiling, reducing the effective length of the target, and result in a lower luminosity of the experiment. In the case of a polarized target, overheating can impact the ability of the target to be polarized resulting in a need to recover target polarization through annealing.

@@ Line 1: / Line 1: @@
 =Abstract=
-\qquad{} The thesis reports the results of an improved track reconstruction program that is used to determine the momentum and interaction vertex of particles scattering in experiments performed using the CLAS12 Detector at Jefferson Lab. Particles are reconstructed from the CLAS12 Drift Chamber and scintillator detector sub-systems. The improved algorithm performs a three dimensional grid search in momentum space in an attempt to
+\qquad{}The thesis reports the results of an improved track reconstruction program that is used to determine the momentum and interaction vertex of particles scattering in experiments performed using the CLAS12 Detector at Jefferson Lab. Particles are reconstructed from the CLAS12 Drift Chamber and scintillator detector sub-systems. The improved algorithm performs a three dimensional grid search in momentum space in an attempt to minimize the distance of closest approach between the particle’s path and the transverse location of the incident electrons that scatter from nucleons in a cryogenic target. Analysis has shown that the new algorithm is capable of improving the reconstruction in the X and Y directions (orthogonal to the incident electrons) by a factor of no less than ten, while at least maintaining the quality of the reconstruction in the Z direction.
-\qquad{}An improvement in the reconstruction of the Z direction allows for statistical certainty in stating which part of the physics target an interaction occured. This is of particular importance in the polarized SIDIS dual target, a physics target with two distinct sub-targets that can be filled with ammonia and polarized in different directions. Being able to state which of the two sub-targets an event occurred in  paramount to being able to distinguish the difference in interactions between the two. Analysis of the proposed algorithm shows that one can resolve the two target if they are separted by at least '''2 cm'''.
+\qquad{}An improvement in the reconstruction of the Z direction allows for statistical certainty in stating which part of the physics target an interaction occured. This is of particular importance in the polarized SIDIS dual target, a physics target with two distinct sub-targets that can be filled with ammonia and polarized in different directions. Being able to state which of the two sub-targets an event occurred in paramount to being able to distinguish the difference in interactions between the two. Analysis of the proposed algorithm shows that one can resolve the two target if they are separted by at least 4cm.
 =Introduction=

@@ Line 11: / Line 11: @@
 =Introduction=
-The CLAS12 is a charged and neutral particle detector constructed in Hall B of Jefferson Lab used to reconstruct nuclear physics interactions that result when GeV energy electrons interact with select targets. CLAS12's precursor, the original CLAS (CEBAF Large Acceptance Spectrometer), was built to facilitate measurements of excited states of nucleons and characterize nucleon-nucleon correlations. Contemporaneous with the 12GeV upgrade to Jefferson Lab's accelerator, CLAS was removed and CLAS12 was built in its place.\autocite{hallBMainPage}
+The CLAS12 is a charged and neutral particle detector constructed in Jefferson Lab's Hall B.  The detector is used to reconstruct nuclear physics interactions that result when GeV energy electrons interact with select targets. CLAS12's precursor, the original CLAS (CEBAF Large Acceptance Spectrometer), was built to facilitate measurements of excited states of nucleons and characterize nucleon-nucleon correlations. Contemporaneous with the 12GeV upgrade to Jefferson Lab's accelerator, CLAS was removed and CLAS12 was built in its place.\autocite{hallBMainPage}
-CLAS12 is designed to not only continue the mission of its predecessor, but to also explore even deeper physics such measuring the generalized parton distributions of nucleons and searching for exotic forms of matter. It is currently slated to perform experiments extending for more than ten years into the future and will likely continue to contribute even after that.\autocite{hallBMainPage} Figure \ref{fig:clas12-design} shows a model of the detector with labels detailing some of the sub detector's and other components. It is important to note here that CLAS12 is not a singular detector, but instead a suite of detectors which can be correlated together in order to more precisely reconstruct the interactions that occur within the physics target.
+CLAS12 is designed to not only continue the mission of its predecessor, but to also measure generalized parton distributions of nucleons and search for exotic forms of matter. It is currently slated to perform experiments for more than ten years into the future and will likely continue to contribute even after that.\autocite{hallBMainPage} Figure \ref{fig:clas12-design} shows a model of the detector with labels detailing some of the sub detector's and other components. It is important to note here that CLAS12 is not a singular detector, but instead a suite of detectors which can be correlated together in order to more precisely reconstruct the interactions that occur within the physics target.
-Alongside the construction of CLAS12, several software packages have been created to handle simulating events, reconstructing events from detector data, and visualizing the reconstructed interactions. For simulation, the CLAS Collaboration has developed a package that provides all of the necessary information to GEMC\autocite{gemc} (GEant4 Monte-Carlo), a general program designed to make interfacing with Geant4\autocite{geant4} easier. The program used for viewing events is called CED (CLAS Event Display), and is a continuation of a program originally designed for use with the CLAS. Most importantly for this document, as it is the topic of discussion, is the reconstruction software. Known as clas12-offline-software\autocite{coatjava}, it is a collection of various (mostly) java programs used to process the data collected from CLAS12 and reconstruct the observed particle mass, momentum, and location within the detector.
+Alongside the construction of CLAS12, several software packages have been created to handle simulating the detector response, reconstructing events from detector the detector response, and visualizing the reconstructed interactions. For simulation, the CLAS Collaboration has developed a package that provides all of the necessary information to GEMC\autocite{gemc} (GEant4 Monte-Carlo), a general program designed to make interfacing with Geant4\autocite{geant4} easier. The program used for viewing events is called CED (CLAS Event Display), and is a continuation of a program originally designed for use with the CLAS. Most importantly for this document, as it is the topic of discussion, is the reconstruction software. Known as clas12-offline-software\autocite{coatjava}, it is a collection of various (mostly) java programs used to process the data collected from CLAS12 and reconstruct the observed particle mass, momentum, and location within the detector.
-This thesis is two-fold in purpose. First, it is intended to provide an understanding of the current methods used to reconstruct particle trajectories from the drift chamber sub-detectors of CLAS12. This includes both a theoretical understanding of the underlying math and physics as well as the actual implementation of those ideas. The second purpose is to present an additional method of reconstruction which takes the already existing drift chamber reconstruction output and further refines it so that interactions which arise from a rasterized beam may be reconstructed more accurately.
+This thesis is two-fold in purpose. First, it is intended to provide an understanding of the current methods used to reconstruct particle trajectories from the drift chamber sub-detectors of CLAS12. This includes both a theoretical understanding of the underlying algorithms  and physics as well as the actual implementation of those ideas. The second purpose is to present an additional method of reconstruction which takes the already existing drift chamber reconstruction output and further refines it so that interactions which arise from a rastered beam may be reconstructed more accurately.
-It should be noted that, in the context of this thesis, the primary motivation behind the development of this new reconstruction algorithm is to allow for the reconstruction of SIDIS (Semi-Inclusive Deep-Inelastic Scattering) events from a particular physics target which contains two polarized target regions separated by some distance. More details will be given about the target in the Simulation and Reconstruction chapter. SIDIS events are those in which one only considers the scattering particle, an electron in this case, and the highest energy hadron produced by the interaction, if any. The core idea is that when the scattering particle interacts with a parton in the struck particle, there will be a primary product hadron accompanied by a hadron shower. The kinematics of this primary product and the scattering particle are believed to encode most of the information about the struck parton.
+It should be noted that, in the context of this thesis, the primary motivation behind the development of this new reconstruction algorithm is to allow for the reconstruction of events from a physics target that contains two polarized target regions separated by some distance. More details will be given about the target in the Simulation and Reconstruction chapter. Semi-Inclusive Deep Ineslatic Scattering (SIDIS) events are of particle interest.  SIDIS events only consider the scattered incident particle, an electron in this case, and the highest energy hadron produced by the interaction, if any. The core idea is that when the scattering particle interacts with a parton in the struck particle, there will be a primary product hadron accompanied by a hadron shower. The kinematics of this primary product and the scattering particle are believed to encode most of the information about the struck parton.
 IMG

@@ Line 157: / Line 157: @@
 ===Kalman Fitter===
-%TODO: NEED TO INCLUDE GENERAL KALMAN FITTING AS WELL AS THE SPECIFICS FROM KFITTER.JAVA
+The Kalman Fitter is is built on the concept of a Kalman Filter. A Kalman Filter is a statistical algorithm which combines a hypothetical model with measurements to find the Best Linear Unbiased Estimate (BLUE) of an evolved system. Included in this section is a description of the Kalman Filter process, a summary of the mathetmatics of it, and a discussion of the implementation used in the Hit Based and Time Based Reconstruction algorithms.
 ==Rasterized Beam==

← Older revision		Revision as of 05:33, 6 June 2019
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	=Conclusion=		=Conclusion=
		+	The goal of this project was ultimately to be able to say with confidence from which of the two subtargets within the polarized SIDIS dual target the electrons scattered. As the distance between the two subtargets is four centimeters, it follows that to be able to state with five sigma confidence which of the two an event spawned from, the reconstuction's fit must have a sigma of at most eight millimeters. The analysis in the previous section has shown that there is a set of search parameters which allows for one to state just that with five sigma certainty for electron events. Unfortunately, the best and least efficient case of pion reconstruction can only be claimed with four sigma certainty.
		+
		+	With respect to the relationship between the reconstruction efficiency and the span of the search, it would seem that the Raster Based Algorithm is acting as a filter of sorts. As the span increases, both the sigma of the reconstruction and the efficiency increases. This seems to suggest that broadening the quantity of events which can be successfully reconstructed results in a worse quality of reconstruction. This, in turn, would seem to suggest that the algorithm intrinsically culls out events which are not reconstructed well enough.

	=Appendicies=		=Appendicies=