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Photomultiplier Signal-to-Noise Ratio


Variable sheet:
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St Input     Name    Output    Unit      Comment                                
   300       lambda            nm        wavelength of light (cm, , m, nm)    
             freq    9.9933E14 Hz        frequency (Hz)                         
             E       6.622E-19 Joule     energy (Joule, erg, eV, kcal/mole)     
             v       33333.333 cm-1      wavenumber (cm-1)                      
   20        T                 C         Temperature (K, C)                     
   4         g                           gain per stage                         
L            V       819.76032 volts     total voltage applied                  
             Vd      91.08448  volts     voltage per dynode (volts, KV)         
   9         k                           number of dynodes                      
             m       262144              multiplication factor                  
             rt      100.01079 sec-1     cathode thermionic emission rate (sec- 
   1         eta                         collection efficiency                  
   .2        Klam                        Quantum efficiency                     
             Rlam    .04838649 amps/watt radiant cathode responsivity (amps/wat 
             Flux    151.01902 sec-1     Photon flux on cathode (sec-1)         
   1E-16     Phi               watts     Radiant flux on cathode (watts, mwatts 
             rcp     30.203803 sec-1     rate at which electrons emitted from c 
             ic      4.839E-18 amps      cathode photocurrent (amps, mA, A, nA 
             ia      1.2684E-9 mA        anode photocurrent  (amps, mA, A, nA, 
             ict     1.602E-17 amps      cathode thermionic current (amps, mA,  
   4.2E-12   iat               amps      anode thermionic current (amps, mA, A 
             Es      .01268423 volts     signal voltage (volts, mvolts)         
   1E10      RL                ohms      load (or feedback) resistance (ohms, K 
             sigmai  2.665E-13 amps      signal shot noise current (amps, mA,  
             alpha   .33333333           secondary emission factor              
             sigmat  4.849E-13 amps      thermionic shot noise current (amps, m 
   0         excess            amps      excess noise current (amps, mA, A, nA 
             sigmad  4.849E-13 amps      total dark noise current (amps, mA, A 
             sigma   5.534E-13 amps      total shot noise current (amps, mA, A 
             sigmav  .00553352 volts     total shot noise voltage (volts, mvolt 
             sigmaJ  8.9927E-6 volts     Johnson noise voltage (volts, mvolts)  
   .0001     flicfac                     flicker factor                         
             sigmaf  1.2684E-6 volts     flicker noise voltage (volts, mvolts)  
             sigman  5.5335293 mvolts    total noise voltage (volts, mvolts)    
L            SNR     2.2922493           signal-to-noise ratio                  
   1         t                 sec       integration time (sec)                 
             tau     .5        sec       RC time constant (sec)                 
             resptim 2.5       sec       RC response time (sec)                 
             deltaf  .5        Hz        noise bandwidth, Hz                    
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Rule sheet.
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sigmaf=flicfac*Es* lambda = 1/v                                                                  
* E = (6.6261E-34)*freq                                                         
* freq = (2.998E10)/lambda                                                      
* m=g^k                                                                         
* Vd=V/k                                                                        
* g=0.17*Vd^.7    " this is partly empirical                                    
* rcp=Klam*Flux                                                                 
* Rlam=(Klam*1.602e-19)/E                                                       
* ia=eta*m*Rlam*Phi                                                             
* ic=rcp*1.602e-19                                                              
* Flux=Phi/E                                                                    
* ict=rt*1.602e-19                                                              
* iat=m*eta*ict                                                                 
* Es=RL*ia                                                                      
* sigmai=sqrt(2*1.602e-19*(1+alpha)*m*ia*deltaf)                                
* alpha=1/(g-1)                                                                 
* sigmat=sqrt(2*1.602e-19*(1+alpha)*m*iat*deltaf)                               
* sigmad=sqrt(sigmat^2+excess^2)                                                
* sigma=sqrt(sigmad^2+sigmai^2)                                                 
* sigmaJ=sqrt(4*1.38e-23*T*RL*deltaf)                                           
* sigman=sqrt((RL*sigma)^2+sigmaJ^2+sigmaf^2)                                   
* sigmav=RL*sigma                                                               
* SNR=Es/sigman                                                                 
* deltaf=1/(2*t)                                                                
* deltaf=1/(4*tau)                                                              
* resptime=5*tau                                                                
* sigmaf=flicfac*Es                                                             
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T. C. O'Haver, Chem 623, 1994