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Grating Monochromator Optics

TK Solver Model for the optics of a grating monochromator in a Czerny-Turner or Fastie-Ebert mounting. Assumptions: equal entrance and exit slits, equal focal lengths of collimator and focusing elements (net image magnification = 1).

Variable sheet:

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St  Input     Name    Output    Unit      Comment                                
    1         m                           order (unitless)                       
    400       lambda            nm        wavelength (mm, m, nm, A)             
              d       .00083333 mm        grating constant (cm, mm, m)          
              theta   14.386773 degrees   rotation angle of grating (radians, degrees)
    15        Phi               degrees   monochromator takeoff angle (radians, degrees)
              alpha   -.6132267 degrees   incidence angle (radians, degrees)     
              beta    29.386773 degrees   diffraction angle (radians, degrees)   
    1200      lines             lines/mm  grating ruling density (lines/mm)      
              AngDisp .00137721 nm-1      Angular dispersion (mm-1, nm-1)        
              LinDisp .03443024 mm/A      Linear Dispersion (mm/nm, mm/A)        
              RLD     2.9044237 nm/mm     Reciprocal linear dispersion (nm/mm, A/mm)
    25        f                 cm        Focal length (mm, cm, m)               
              Sg      .07261059 nm        Geometrical spectral bandpass (mm, m, nm, A) 
              S       .08138252 nm        Spectral bandpass (mm, m, nm, A)      
    .5        H                 cm        Slit height (cm, mm, m)               
    25        W                 m        Slit width (cm, mm, m)                
              Sd      .00877193 nm        diffraction limited resolution (mm, m, nm, A)
              N       45600               Total number of lines in grating (unitless) 
    38        Wg                mm        aperture (mm, cm, m)                   
              R       52333.962           Resolving power (unitless)             
              FSR     200       nm        Free spectral range (mm, m, nm, A)    
              omega   .02310268 sr        acceptance solid angle, steradians )sr)    
              Fnumber 5.8306073           F-number of monochromator   (unitless)             
              Ap      14.439173 cm2       grating area viewed from entrance slit (cm2)
              As      .00125    cm2       Slit area (cm2, mm2)                   
              PhiO    .00209687 watts    Radiant power passed by monochromator  
    .002      Blambda           W/sr/nm/c Source spectral radiance (W/sr/nm/cm2) 
    .5        Top                         Transmission factor of monochromator   
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Rule sheet.
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* d=1/lines                                                                     
* AngDisp = m/(d*cos(beta))                                                     
* LinDisp = f*AngDisp                                                           
* RLD=1/LinDisp                                                                 
* Sg=W/LinDisp                                                                  
* S = Sg+Sd                                                                     
* Sd = lambda/(m*N)                                                             
* N = Wg/d                                                                      
* R = m*N/cos(beta)                                                             
* theta=beta-Phi                                                                
* alpha=theta-Phi                                                               
* m*lambda=2*d*cos(Phi)*sin(theta)                                              
* FSR=lambda/(m+1)                                                              
* omega=Ap/f^2                                                                  
* Ap=Wg^2*cos(alpha)                                                            
* As=0.01*W*H                                                                   
* PhiO=Blambda*As*omega*Top*Sg*1e6                                              
* Fnumber=f/sqrt(4*Ap/pi())  
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T. C. O'Haver, Chem 623, 1994