index previous model next model

Dispersive IR Spectrometer

TK Solver Model for a dispersive grating IR spectrometer with a blackbody source and a thermal detector.

Variable sheet:

St Input     Name    Output    Unit      Comment                                
             freq    2.998E13  Hz        frequency (Hz)                         
             E       1.987E-20 Joule     energy (Joule, erg, eV, kcal/mole)     
             v       1000      cm-1      wavenumber (cm-1)                      
   10        lambda            m        wavelength of light (nm, A, m, cm)    
   1         m                           order (unitless)                       
             d       .01       mm        grating constant (cm, mm, m)          
             theta   2.9671739 degrees   rotation angle of grating (radians, de 
   15        Phi               degrees   monochromator takeoff angle (radians,  
             alpha   -12.03283 degrees   incidence angle (radians, degrees)     
             beta    17.967174 degrees   diffraction angle (radians, degrees)   
   100       lines             lines/mm  grating ruling density (lines/mm)      
             AngDisp .00010513 nm-1      Angular dispersion (mm-1, nm-1)        
             LinDisp .00525633 mm/      Linear Dispersion (mm/nm, mm/A)        
             RLD     19.024668 nm/mm     Reciprocal linear dispersion (nm/mm, A 
   .5        Fm                m         Focal length on monochromator (mm, cm, 
             Sg      .01902467 m        Geometrical spectral bandpass (mm, m, 
             S       .01922467 m        Spectral bandpass (mm, m, nm, A)      
             Snu     1.9224668 cm-1      Spectral bandpass (cm-1)               
   1         H                 cm        Slit height (cm, mm, m)               
   1         W                 mm        Slit width (cm, mm, m)                
             Sd      .2        nm        diffraction limited resolution (mm, m 
             N       5000                Total number of lines in grating (unit 
   50        Wg                mm        aperture (mm, cm, m)                   
             FSR     .5        m        Free spectral range (mm, m, nm, A)    
             omega   .00978028 sr        acceptance solid angle, steradians     
             Fnumber 8.961263            F-number of monochromator              
             Ap      24.450708 cm2       grating area viewed from entrance slit 
             As      .1        cm2       Slit area (cm2, mm2)                   
             PhiO    2.3938E-7 watts     Radiant power passed by monochromator  
             Blambda .00002573 W/sr/nm/c Source spectral radiance (W/sr/nm/cm2) 
   .5        Top                         Transmission factor of monochromator   
   .5        emisiv                      emissivity of blackbody                
   1200      Tb                K         Temperature of blackbody (K, C)        
   1E9       Dstar             cm-rootHz Detectivity of detector (cm-rootHz/W)  
   1         DeltaF            Hz        electrical bandpass of detector electr 
   5         Ad                mm2       area of detector                       
             SNR     1070.537            signal-to-noise ratio for detector lim 
             B       1.871113  W/sr/cm2  Total radiance over all wavelengths    
             peak    2.4141667 m        Peak wavelength  (nm, A, m, cm)       
             flux    1.205E13  Hz        Photon flux, Hz, on detector           
             exponen 1.1983333           exponent of e in Planck's equation     
             LambdaT 12000000  nm K      product of lambda and T, nm K          
             D       4.47214E9           detectivity (W-1)                                                  
             nm      10000     nm        wavelength in nm                       
             shot    1097737.6           Signal-to-photon-noise ratio                    
   .1        klam                        Quantum efficienty of photon detector 

Rule sheet:
* d=1/lines                                                                     
* AngDisp = m/(d*cos(beta))                                                     
* LinDisp = Fm*AngDisp                                                          
* RLD=1/LinDisp                                                                 
* Sg=W/LinDisp                                                                  
* S = Sg+Sd                                                                     
* Snu=.1*S/(lambda*lambda)                                                      
* Sd = lambda/(m*N)                                                             
* N = Wg/d                                                                      
* theta=beta-Phi                                                                
* alpha=theta-Phi                                                               
* m*lambda=2*d*cos(Phi)*sin(theta)                                              
* FSR=lambda/(m+1)                                                              
* omega=Ap/Fm^2                                                                 
* Ap=Wg^2*cos(alpha)                                                            
* As=0.01*W*H                                                                   
* PhiO=Blambda*As*omega*Top*Sg*1e6                                              
* Fnumber=Fm/sqrt(4*Ap/pi())                                                    
* lambda = 1/v                                                                  
* Blambda = emisiv*1.19111E16*nm^-5/(exp(1.438e7/(nm*Tb))-1)                    
* E = (6.6261E-34)*freq                                                         
* freq = (2.998E10)/lambda                                                      
* B=emisiv*1.8047e-12*Tb^4                                                      
* peak=2.897e6/Tb                                                               
* nm=lambda*1e7                                                                 
* exponent=1.438e7/(nm*Tb)                                                      
* LambdaT=nm*Tb                                                                 
* Dstar=D*sqrt(Ad*DeltaF)                                                       
* SNR=PhiO*D                                                                    
* flux=PhiO/E                                                                   
* shot=klam*flux/sqrt(klam*flux) 
Download the Dispersive IR model.

[RETURN] to Chem 623 home page.

T. C. O'Haver, Chem 623, 1994