Temporary document

Idea

Let's assume that a sensor was put away from the designed position by amount of D. We will call D Misalignment vector. We assume also that our geometry file is produced with the SURVEY result, so that the misalignment vectors are generally smaller than 1 mm level. Our alignment goal is then finding the misalignment vector for each sensor.

As shown in the above picture, if a hit made by a track is reconstructed with the designed geometry input, the position is shifted depending on track's angle. But we can always measure a miss-vector, which is defined as a minimum distant vector from the hit to the track.

Then we can make the following equation,

D * delta = |delta|^2

D_x*delta_x + D_y*delta_y + D_z*delta_z = |delta|^2

The first idea to solve the equation is "fitting". In the fit we try to find the misalignment vector which minimizes

Sum of (D*delta - |delta|^2) over all tracks 

Method

In order to check the above idea, I did,

This is %README file... I have to rewrite this again...

Step 0 : Generation of PHOBOS data with a realistic detector
------

  - Generate an artificially misaligned geometry.
    This is done by editing GCDEFS file by hand.
    A tool for editing GCDEFS file will be available later.

  - PMC control file : RHDATA.align, contains all control card for PMC
    basically, turn off magnetic filed, physical event option with
    random vertex, etc.
    You have to have link RHDATA.align as RHDATA before running phatpmc.

  - run phatpmc

  - root[] .x xGenData.C("my.data.root",1,1000)
    (the 1st argument is the name of output DST file, the 2nd is Run number,
     and the 3rd is the number of events you wish to have)

Step 1 : Reconstruct event & Filling Ntuples
------
  (% at this moment there is only spectrometer tracking in the reconstruction)

  - run phat

  - root[] .x xFillNtuple.C("my.data.root","my.ntuple.root")

  - xFillNtuple.C will read my.data.root, and run the phobos Front-end tracking
    program (Mulguisin4: version for non-vertex seed finder). D0 cut, Z0 cut,
    chi2 probability cut are important paramters for tracking.
    For each track seed, a loop over hit list is done to calculate residuals,
    mis-vector, etc.. (These variables were introduced iduring the 1999 PHOBOS
    Engineering Run.) The out put file "my.ntuple.root" has a single object of
    TPhAlign class. The ntuples are handled via the object for better control
  - In the macro, you can turn on/off ntuples via align->SetSensor(344,1)
    or align->SetSensor(344,0), where 344 is the sensor number, 0/1 is switch.
    You can turn on whole sensors on a layer by
    align->TurnOnSubDetector(det,"SpectN",0); where 0 is the layer number

  % be careful about the file size! if you turn on whole sensors you will get
    few hundreds of ntuples.

  % your comments on ntuple content is welcome.

Step 2 : Histogramming
------

  - If you wish to plot "resx" for the sensor 344 (the first sensor of SpectP),
    do the following step (In principle, the same step as we did with ER)

  - run phat
    root[] TFile *f_align=new TFile("my.ntuple.root")
    root[] TPhAlign *align=(TPhAlign*)f_align->Get("Align");
    root[] TNtuple *ntuple=(TNtuple*)align->GetNtuple(344);
    root[] ntuple->Draw("resx")

  % after getting ntuple everything is the same as before.

Step 3 : Fitting & finding misalignment
------
  (This step is still progressing, but you can test)

  - run phat
    root[] .L xFitAlign.C
    root[] minuit()

  - minuit() will call Minuit package (look CERNLIB) and find the best guess of
    misalignment on sensor-by-sensor bases.
 
Step 4 : Creation of aligned PHOBOS geometry file
------
  (Not yet done)

  %Step 4 means that our alignement job is done!

// db= debug level

First fit result

The sensor PC01 (sensor id=349) was moved to x=+1mm,y=+1mm,z=+1mm from its original position.
Then I generated 1000 low-multiplicity events, and ran the alignment program.
After minuit fitting, I could reproduce the misaligment. PLEASE READ USAGE FIRST...

Click here to see in PS format