Merge branch 'studen-master-patch-80445' into 'master'

Update README.md

See merge request studen/simulpet!1

README.md

@@ -1,13 +1,50 @@
 
+## Resolution modeling
 
-### Combined resolution calculation
+The helper function is loaded by:
+
+```shell
+root[].L getResolution.C
+```
+
+### Individual resolution calculation
+According to literature, the resolution contribution from spatial resolution of the crystals is calculated from sum of sines, which is coded in `getResolution(ctheta0,N)` where ctheta0 is the smalles cosine theta still captured by the system geometry (assumming coverage from 1), and N is number of splits in cos theta used in numeric integration. 
+
+
+```shell
+root[] double detRes=2.;//resolution in mm
+root[] double sigmaRSquared=detRes*detRes/getResolution(ctheta0,40);
+```
+
+In the same manner, resolution contribution for timing is calculated:
+```shell
+root[] double tRes=50.;//resolution in ps
+root[] double xtRes=3e11*tRes*1e-12;//resolution in mm
+root[] double sigmaTSquared=xtRes*xtRes/getResolutionT(ctheta0,40);
+```
 
+To generate individual graphs, do
 ```shell
+TGraph gr(20);
 for (int i=0;i<gr.GetN();i++) { 
     double ctheta0=1-(i+0.5)/(gr.GetN()); 
     double ttheta0=sqrt(1-pow(ctheta0,2))/ctheta0;
-    double sigmaT=getResolutionT(ctheta0,40)/15;
-    double sigmaX=getResolution(ctheta0,40)/2;
-    gr.SetPoint(i,ttheta0,1./sigmaT+1./sigmaX);
+    gr.SetPoint(i,ttheta0,1./sqrt(getResolutionT(ctheta0,40)));
+}
+//equivalent for getResolution
+```
+
+### Combined resolution calculation
+
+```shell
+root[] double tRes=50.;//resolution in ps
+root[] double xtRes=3e11*tRes*1e-12;//resolution in mm
+root[] double xRes=2;//resolution in mm
+root [] for (int i=0;i<gr.GetN();i++) { 
+    double ctheta0=1-(i+0.5)/(gr.GetN()); 
+    double ttheta0=sqrt(1-pow(ctheta0,2))/ctheta0;
+    double sigmaT=getResolutionT(ctheta0,40)/xtRes/xtRes;
+    double sigmaX=getResolution(ctheta0,40)/xRes/xRes;
+    gr.SetPoint(i,ttheta0,sqrt(1./sigmaT+1./sigmaX));
 }
-```
+```