Title                  :ETHA
Keywords               :EELS,STEM,COLLECTION EFFICIENCY,CONVERGENT BEAM
Computer               :DEC LSI-11/73
Operating System       :RSX-11M-PLUS
Programming Language   :DEC-FORTRAN IV
Hardware Requirements  :None
Author(s)              :Dr. Pierre TREBBIA
Correspondence Address :Laboratoire de Physique des Solides
                       :Bat. 510, F91405 ORSAY CEDEX FRANCE
Abstract: When EELS spectra are recorded with a convergent beam (STEM case), 
one has to compute an effective collection angle BETA* which should be used in 
computing the interaction cross sections, instead of the actual collection 
angle BETA. This is the job of program ETHA.
    A complete description of the algorithm is given in "Unbiased 
Method for Signal Estimation in Electron Energy Loss Spectroscopy...", 
P. TREBBIA, Ultramicroscopy (1988).
Title                  :ETHA
Keywords               :EELS,STEM,COLLECTION EFFICIENCY,CONVERGENT BEAM
Computer               :DEC LSI-11/73
Operating System       :RSX-11M-PLUS
Programming Language   :DEC-FORTRAN IV
Hardware Requirements  :None
Author(s)              :Dr. Pierre TREBBIA
Correspondence Address :Laboratoire de Physique des Solides
                       :Bat. 510, F91405 ORSAY CEDEX FRANCE
Description : see comments line in the source code text
References : see comments line in the source code text
Compilation procedure : compile the program ETHA 
Linking procedure : Link the resulting object file.
Test data : ETHA.DAT is the output that ETHA should give 
            if the appropriate parameters are entered.
General comments : If the compiler is not a DEC-FORTRAN IV compiler, do check 
                   the source code : for example, the ! sign in a line means 
                   that the remaining text is comments, or the LOG function is 
                   implicitely changed to DLOG if the variable is double 
                   precision.
Title                  :ETHA
Keywords               :EELS,STEM,COLLECTION EFFICIENCY,CONVERGENT BEAM
Computer               :DEC LSI-11/73
Operating System       :RSX-11M-PLUS
Programming Language   :DEC-FORTRAN IV
Hardware Requirements  :None
Author(s)              :Dr. Pierre TREBBIA
Correspondence Address :Laboratoire de Physique des Solides
                       :Bat. 510, F91405 ORSAY CEDEX FRANCE

        PROGRAM ETHA
c
c       LAST VERSION : 28-JUL-1987 09:21:14
c
c       purpose
c       -------
c       This program computes etha(alpha,beta), that is the collection
c       efficiency associated to the following geometry :
c
c       alpha = half angle of illumination  (0 -> pi/2)
c       beta  = half angle of collection    (0 -> pi/2)
c                                           (pi/2 = 1570.795 mrad)
c
c           A constant angular distribution of incident electrons is assumed
c       for any incident angle (-alpha,alpha). These electrons impige the
c       target and a single energy loss event occurs, with a characteristic
c       angle theta-e (relativistic). The angular distribution of the
c       electrons after the target is analytically derived.
c           This program integrates this distribution from theta=0 up to
c       theta=beta with an adjustable angular step.
c           This program also computes beta* which is the theoretical
c       collection angle which would give the same value of etha(alpha,beta)
c       with a parallel incident beam.
c
c       subroutines and function subprograms required
c       ---------------------------------------------
c       none
c
c       comments
c       --------
c
c       The following parameters are asked as input :
c        accelerating voltage (kV), energy loss range (eV) for the study,
c        energy loss step (eV) in this range, alpha (mrad), beta (mrad).
c       The program returns for each energy loss step :
c        alpha (mrad), beta (mrad), theta-e (relativistic) (mrad),
c        energy loss (eV), etha (%), beta * (mrad)
c
c       author :
c       --------
c       Pierre TREBBIA
c       US 41 : "Microscopie Electronique Analytique Quantitative"
c       Laboratoire de Physique des Solides, Bat. 510
c       Universite Paris-Sud, F91405 ORSAY Cedex
c       Phone : (33-1) 69 41 53 68
c
        real*8 pi,zx,zi,z1,z2,z3,z4,z5,z6,z7,x0,x1,x2,x3,x4,x5,x6,x7,x8
        real*8 x9,x10,theta,dtheta,eta,etha2,beta
        logical pr
        pi=3.14159
        pr=.true.               ! enable record of data
c
c       Results storage ?
c       -----------------
c
        type 2
2       format(' Do you want a report ? [default : Y] ? ',$)
        read(5,1010,end=800) rep
        if ((rep.eq.'n').or.(rep.eq.'N')) pr=.false.
        if(pr) then
         open(4,name='ETHA.DAT',status='new')
         type *,' ** Your report is in the file ETHA.DAT **'
        endif
c
c       Ask for input values
c       --------------------
c
5       write(5,10)
10      format(' Accelerating voltage (kV) = ',$)
        read (5,*,end=800) z1
        z1=z1*1000.     ! eV
        write(5,15)
15      format(' from energy loss (ev)= ',$)
        read(5,*,end=800) z2
        write(5,20)
20      format(' to energy loss (ev)= ',$)
        read(5,*,end=800) z3
        write(5,25)
25      format(' with a step (ev)= ',$)
        read(5,*,end=800) z4
        write(5,30)
30      format(' 1/2 illumination angle (mrad)= ',$)
        read(5,*,end=800) z5
        z5=z5*0.001     ! rad
        write(5,35)
35      format(' 1/2 collection angle (mrad)= ',$)
        read(5,*,end=800) z6
        z6=z6*0.001     ! rad
        z7=500.         ! number of integration steps to be modified at will
        if(pr) then
         write(4,50) z1/1000.,z2,z3,z4,z5*1000.,z6*1000.
50       format(//,' Accelerating voltage (kV)= ',f6.1,/,
     &   ' from energy loss (ev)= ',f6.1,/,
     &   ' to energy loss (ev)= ',f6.1,/,
     &   ' with a step (ev)= ',f6.1,/,
     &   ' 1/2 illumination angle (mrad)= ',f8.3,/,
     &   ' 1/2 collection angle (mrad)= ',f8.3)
        endif
        write(5,60)
        if(pr) write(4,60)
60      format( 6x,'ALPHA',6x,'BETA',7x,'THETA-E',
     &  7x,'ENERGY',6x,'ETHA',6x,'BETA * ')
c
c       main loop on energy loss
c
        do  300  zx=z2,z3,z4                    ! zx = current energy loss
         eta=0.
         x0=zx*(z1+511060.)/(z1*(z1+1022120.))  ! x0 = relativistic theta-e
         x1=pi/(2.*x0)
         x2=x0*x0+z5*z5
         x3=z5/x0*z5/x0
         x4=0.1*sqrt(x2)
         dtheta=(z6-x4)/z7
c
c        calculation of the analytical expression
c
         do 100 zi=1.,z7,1.
          theta=x4+dtheta*zi
          x5=theta*theta
          x6=4.*x5*x0*x0
          x7=x2-x5
          x8=sqrt(x7*x7+x6)
          x9=(x8+x7)/(2.*x0*x0)
          x10=2.*theta*dtheta*log(x9)
          eta=eta+x10
100      continue
         eta=eta+x2/100.*log(1.+x3)     ! addition of the central contribution
         x4=z5*z5*log(1.+x1*x1)         ! normalisation
         eta=eta/x4
c
c        correction by geometrical factor (beta/alpha)**2
c
         if (z6.lt.z5) then
          x5=z5/z6
          eta=eta*x5*x5
         endif
150      etha2=eta*100.
c
c        calculation of beta *
c
         x6=(1.+x1*x1)**eta
         x7=x0*sqrt(x6-1.)
         beta=x7*1000.
c
c        results output
c
         write(5,200) z5*1000.,z6*1000.,x0*1000.,zx,etha2,beta
         if(pr) write(4,200) z5*1000.,z6*1000.,x0*1000.,zx,etha2,beta
200      format(3x,f7.1,4x,f7.1,7x,f7.4,5x,f7.1,4x,f7.1,4x,f7.2)
300      continue
c
c       Run again
c       ---------
        type *,' Start again. Input new data. Enter CTRL Z for exit'
        go to 5
c
c       Program exit
c       ------------
c
800     if(pr) then
         close(5)
         open(5,status='new')
         write(5,805)
805      format(10x,'Do you want your report to be printed ? ',
     &   '[default : N] ',$)
         read(5,1010,end=1000) pri
         if((pri.eq.'y').or.(pri.eq.'Y')) then
          close(4,dispose='print')
          type *,'Don''t forget your report !'
         endif
        endif
1000    stop
1010    format(a1)
        end


                     DEMONSTRATION OF PROGRAM ETHA

Accelerating voltage (kV)=  100.0
from energy loss (ev)=  500.0
to energy loss (ev)=  700.0
with a step (ev)=   10.0
1/2 illumination angle (mrad)=   15.000
1/2 collection angle (mrad)=   25.000
     ALPHA      BETA       THETA-E       ENERGY      ETHA      BETA *
     15.0       25.0        2.7228       500.0       33.4      22.60
     15.0       25.0        2.7772       510.0       33.2      22.61
     15.0       25.0        2.8317       520.0       33.0      22.61
     15.0       25.0        2.8862       530.0       32.8      22.61
     15.0       25.0        2.9406       540.0       32.6      22.61
     15.0       25.0        2.9951       550.0       32.4      22.61
     15.0       25.0        3.0495       560.0       32.2      22.62
     15.0       25.0        3.1040       570.0       32.0      22.62
     15.0       25.0        3.1584       580.0       31.9      22.62
     15.0       25.0        3.2129       590.0       31.7      22.62
     15.0       25.0        3.2674       600.0       31.5      22.62
     15.0       25.0        3.3218       610.0       31.3      22.63
     15.0       25.0        3.3763       620.0       31.2      22.63
     15.0       25.0        3.4307       630.0       31.0      22.63
     15.0       25.0        3.4852       640.0       30.8      22.63
     15.0       25.0        3.5396       650.0       30.6      22.63
     15.0       25.0        3.5941       660.0       30.5      22.64
     15.0       25.0        3.6485       670.0       30.3      22.64
     15.0       25.0        3.7030       680.0       30.1      22.64
     15.0       25.0        3.7575       690.0       30.0      22.64
     15.0       25.0        3.8119       700.0       29.8      22.65