Abstract:
With technical surfaces, in particular in semiconductor manufacture, it is a regular requirement to obtain the reflection coefficient of an inspected object ( 12 ). To better match the calculated model spectrum ( 16 ) to the obtained measured spectrum ( 18 ) with respect to damping when thick layers are measured, the measuring system ( 10 ) is measured with respect to its line spread I(λ). The measured line spread I(λ) is iteratively used for calculating the damping of the model spectrum ( 16 ), so that a damped model spectrum ( 20 ) is obtained.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This patent application claims priority of German Patent Application No. 10 2006 003 472.4, filed on Jan. 25, 2006, which application is incorporated herein by reference. 
       FIELD OF THE INVENTION 
       [0002]    The invention relates to a method for matching a model spectrum to a measured spectrum of an object, of a multi-layer system. 
       BACKGROUND OF THE INVENTION 
       [0003]    With technical surfaces, in particular in semiconductor manufacture, it is often necessary to determine the structural parameters of the surface. During the manufacturing process, applied line widths and line profiles of structured layers must be checked, for example, with respect to their dimensions and uniformity. The exact compliance with specifications for layer thicknesses is critical for the operativeness of the product. To check these manufacturing parameters the reflection on the sample is measured at different wavelengths. These measurements do not directly provide, however, the desired material data, such as the above-mentioned layer thickness. Rather, it is necessary to match the calculated values to measured values and to calculate a theoretical spectrum with the aid of a model using the theory of light scattering, and to compare it with the measurement. Subsequently, model parameters are changed until there is a best match between theory and measurement. 
         [0004]    Reflection spectroscopy is a well-known and widely used method for inspecting layered systems, in particular of wafers, and for determining layer thicknesses and other optical parameters. To do this, a sample, preferably comprising a plurality of layers, is irradiated with light of a predetermined wavelength. If the layers are transparent in the range of this wavelength, light penetrates the layer and is partially reflected at the interfaces between two layers including the interface between the top layer and the ambient atmosphere. By overlapping the incident and reflected light beams, an interference results which affects the intensity of the reflected light. The ratio of the intensities of incident and reflected light thus determines the so-called absolute reflectance so that the two intensities have to be measured. If the wavelength is now continuously varied in a predetermined range, the reflection spectrum is obtained, which has maxima and minima as a function of the wavelength. These are caused by interference. The position of these extrema depends on the material properties of the sample inspected. The latter therefore determines the optical behavior. These optical parameters include the refractive index or the coefficient of absorption. Further, the layer thickness affects the position of the extrema in the reflection spectrum. 
         [0005]    The basic formulae which are used to calculate the desired quantities from the comparison of the model with the measurement can be derived from Fresnel&#39;s diffraction theory. 
         [0006]    These are described, for example in “Spectroscopic Ellipsometry and Reflectometry—A users Guide” by H. G. Tompkins and W. A. McGahan. 
         [0007]    In this context, reflection refers to the ratio of the outgoing intensity and the incoming intensity. It is calculated separately for the two polarization planes, “s” referring to vertical and “p” referring to parallel. The intensity in turn is proportional to the square of the amplitude of the light wave function. 
         [0008]    Equation (1) describes the wave function on a simple surface, i.e. on an interface between two media having different, complex, where applicable, dispersions. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       r 
                       12 
                       p 
                     
                     = 
                     
                       
                         
                           
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 2 
                               
                               · 
                               cos 
                             
                              
                             
                                 
                             
                              
                             
                               φ 
                               1 
                             
                           
                           - 
                           
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 1 
                               
                               · 
                               cos 
                             
                              
                             
                                 
                             
                              
                             
                               φ 
                               2 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 2 
                               
                               · 
                               cos 
                             
                              
                             
                                 
                             
                              
                             
                               φ 
                               1 
                             
                           
                           + 
                           
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 1 
                               
                               · 
                               cos 
                             
                              
                             
                                 
                             
                              
                             
                               φ 
                               2 
                             
                           
                         
                       
                        
                       
                           
                       
                        
                       and 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       r 
                       12 
                       s 
                     
                     = 
                     
                       
                         
                           
                             
                               
                                 N 
                                 ~ 
                               
                               1 
                             
                             · 
                             cos 
                           
                            
                           
                               
                           
                            
                           
                             φ 
                             1 
                           
                         
                         - 
                         
                           
                             
                               
                                 N 
                                 ~ 
                               
                               2 
                             
                             · 
                             cos 
                           
                            
                           
                               
                           
                            
                           
                             φ 
                             2 
                           
                         
                       
                       
                         
                           
                             
                               
                                 N 
                                 ~ 
                               
                               1 
                             
                             · 
                             cos 
                           
                            
                           
                               
                           
                            
                           
                             φ 
                             1 
                           
                         
                         + 
                         
                           
                             
                               
                                 N 
                                 ~ 
                               
                               2 
                             
                             · 
                             cos 
                           
                            
                           
                               
                           
                            
                           
                             φ 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0009]    If there is a further medium, this is referred to as a simple layer or a film having the thickness d. For this model, too, the reflection R can be indicated using a closed formula for each of the polarization planes s and p (Eq. 2). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       R 
                       p 
                     
                     = 
                     
                       
                         
                           
                             r 
                             12 
                             p 
                           
                           + 
                           
                             
                               r 
                               23 
                               p 
                             
                             · 
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   
                                     - 
                                     j 
                                   
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   β 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           1 
                           + 
                           
                             
                               r 
                               12 
                               p 
                             
                             · 
                             
                               r 
                               23 
                               p 
                             
                             · 
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   
                                     - 
                                     j 
                                   
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   β 
                                 
                                 ) 
                               
                             
                           
                         
                       
                        
                       
                           
                       
                        
                       and 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       R 
                       s 
                     
                     = 
                     
                       
                         
                           r 
                           12 
                           p 
                         
                         + 
                         
                           
                             r 
                             23 
                             p 
                           
                           · 
                           
                             exp 
                              
                             
                               ( 
                               
                                 
                                   - 
                                   j 
                                 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                               ) 
                             
                           
                         
                       
                       
                         1 
                         + 
                         
                           
                             r 
                             12 
                             s 
                           
                           · 
                           
                             r 
                             23 
                             s 
                           
                           · 
                           
                             exp 
                              
                             
                               ( 
                               
                                 
                                   - 
                                   j 
                                 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0010]    It is composed of the Fresnel coefficient (equation 1) of the two interfacing layers and a complex e-function, wherein the indices 1 and 2 must be replaced by 2 and 3 for the lower interfacing layer. 
         [0011]    In 
         [0000]    
       
         
           
             
               
                 
                   β 
                   = 
                   
                     2 
                      
                     
                         
                     
                      
                     
                       π 
                        
                       
                         ( 
                         
                           d 
                           λ 
                         
                         ) 
                       
                     
                      
                     
                       
                         N 
                         ~ 
                       
                       2 
                     
                      
                     cos 
                      
                     
                         
                     
                      
                     
                       φ 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    the e-function has the complex optical thickness d·Ñ as an argument and, with its periodicity, it describes the oscillating behavior of the reflection, which results from interferences within the film. 
         [0000]        Ñ   2   =n   2   −j·k   2   (4) 
         [0012]    The values for the dispersion Ñ is also complex, as is that of the cosine function cos Φ 2 . 
         [0013]    The measurable reflection on the surface is calculated separately for vertically and horizontally polarized light from the values of the wave functions according to the equations (5). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ℜ 
                               p 
                             
                              
                             
                               : 
                             
                             = 
                             
                               
                                  
                                 
                                   R 
                                   p 
                                 
                                  
                               
                               2 
                             
                           
                           = 
                             
                            
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         R 
                                         x 
                                         p 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         R 
                                         y 
                                         p 
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 ( 
                                 
                                   R 
                                   x 
                                   p 
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               
                                 ( 
                                 
                                   R 
                                   y 
                                   p 
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   and 
                    
                   
                     
 
                   
                    
                   
                     
                       
                         ℜ 
                         s 
                       
                        
                       
                         : 
                       
                       = 
                       
                         
                            
                           
                             R 
                             s 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             R 
                             x 
                             s 
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             R 
                             y 
                             s 
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0014]    With an equal distribution of the polarizations in the incident light, the whole of the unpolarized reflection is given by the arithmetic mean according to equation (6). 
         [0000]    
       
         
           
             
               
                 
                   ℜ 
                    
                   
                     : 
                   
                   = 
                   
                     
                       
                         ℜ 
                         p 
                       
                       + 
                       
                         ℜ 
                         S 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0015]    Snell&#39;s law also applies for the complex sine function 
         [0000]        Ñ   i+1 ·sin φ i+1   =Ñ   1 ·sin φ i ,  (7) 
         [0000]    so that for the incident angle of the i-th layer 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           sin 
                            
                           
                               
                           
                            
                           
                             φ 
                             
                               i 
                               + 
                               1 
                             
                           
                         
                         = 
                         
                           sin 
                            
                           
                               
                           
                            
                           
                             
                               φ 
                               i 
                             
                             · 
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 i 
                               
                               
                                 
                                   N 
                                   ~ 
                                 
                                 
                                   i 
                                   + 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           sin 
                            
                           
                               
                           
                            
                           
                             
                               φ 
                               
                                 i 
                                 - 
                                 1 
                               
                             
                             · 
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 
                                   i 
                                   - 
                                   1 
                                 
                               
                               
                                 
                                   N 
                                   ~ 
                                 
                                 i 
                               
                             
                             · 
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 i 
                               
                               
                                 
                                   N 
                                   ~ 
                                 
                                 
                                   i 
                                   + 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           sin 
                            
                           
                               
                           
                            
                           
                             
                               φ 
                               0 
                             
                             · 
                             
                               
                                 
                                   N 
                                   ~ 
                                 
                                 0 
                               
                               
                                 
                                   N 
                                   ~ 
                                 
                                 
                                   i 
                                   + 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    applies. The medium surrounding the layered system is usually air. With a real Φ 0 , sin Φ 0  is also real, since for Φ 0 , only n 0  is taken into account, and not k 0 . Φ 1  can take on a complex value, however, when Ñ 0  or Ñ 1  are complex. With sin Φ 0  known, sin Φ i+1  can be calculated for all layers. cos Φ i , which is required for calculating the optical parameters, with (sin Φ i ) 2 +(cos Φ i ) 2 =1, results in: 
         [0000]      cos Φ i =√{square root over (1−(sin Φ i ) 2 )}  (9) 
         [0016]    The matching of a theoretically calculated curve to a measured curve with the aid of a model of variable parameters will be referred to as a fit in the following. To do this, the model parameters are varied in such a way that there is a best match between the theoretical curve and the measured curve. 
         [0017]    The standard method for a fit is the so-called gradient method, since it enables the exact result to be found quickly, wherein the procedure to be followed is described, for example, in DE 102 27 376 A1. The calculation is carried out at intermediate points, wherein a number of the intermediate points in the model spectrum are chosen to be as good as possible, corresponding to the number of intermediate points in the measured spectrum. 
         [0018]    If the reflection spectrum of a thick layer is calculated with the aid of a model based on the above mentioned equations, the result is a strongly oscillating model spectrum. If the reflection spectrum of a thick layer is recorded with a spectral photometer, however, the resulting measured spectrum is damped when compared to the model spectrum. The reason for this, inter alia, is that in the use of light with high intensities and using objectives having high magnifications, the stability of the illumination and its insufficient adjustment means lead to a bad result with high resolutions. In DE 101 33 992 A1 it is therefore suggested that an illumination means be used having a light source and an illumination optics which allows for automatic post-adjustment. 
         [0019]    Imaging errors in the optical channel, which are caused, for example, by the entrance slit or the imaging grid, before the light is incident on the detector, cannot be compensated for, however. These cause a damping of the measured curve in the measured spectrum, which is the stronger, the thicker the layers of the measured object. For example, the strongly oscillating spectrum is already markedly damped with a spectral photometer when recording the reflection of a layer having a thickness of 5 μm. When layers having an even greater thickness are measured, the visible damping is further increased, until the oscillation of the spectrum completely disappears between 25 μm and 50 μm. For calculating the associated model spectrum for layer thicknesses of these dimensions, usually an FFT technique is used, since it is quite useful for determining the layer thickness. The damping effect described is, however, hardly reflected in this method, so that the determination of the layer thickness is hardly affected by the damping. The user of the method obtains two very diverse looking spectra for the measured spectrum and the model spectrum, even though the model spectrum is the best fit of the measured spectrum. Usually, however, the user evaluates the quality and the success of an analysis by visual means and interprets these differences as a defect or failure of the algorithms, insofar as he is not familiar with the technical reasons for the damping, which is usually not the case. The mean square error (MSE), a second quality criterion for the analysis, is very large and seems to signal an error or a bad result. 
       SUMMARY OF THE INVENTION 
       [0020]    It is therefore an object of the present invention to match a model spectrum of an object, in particular a multi-layer system, with thick layers, to a systematically damped measured spectrum. 
         [0021]    According to the present invention, this object is achieved by a method for matching a model spectrum to a measured spectrum. According to the present invention, a method for matching a model spectrum to a measured spectrum of an object, in particular a multi-layer system, is suggested. Herein, a measured spectrum of an object is first detected using a measuring system, in particular a spectrometer. An associated model spectrum is calculated with the aid of a suitable model, wherein the calculation is carried out with a plurality of wavelengths and a number of intermediate points. To match the model spectrum to the measured spectrum, first the measuring system is measured with respect to its line spread. To do this, monochromatic light, in particular, can be radiated into the measuring system. The line spread introduced by the measuring system is then measured on the detector, so that an intensity development of the widened line is obtained as a function of the wavelength. To match the model spectrum to the measured spectrum, which is damped with the measurement of thick layers, in particular, the measured line spread is iteratively used for the calculation of the damping of the model spectrum so that matching can be carried out in this manner. 
         [0022]    According to the invention, the matching is iteratively carried out in several steps. A local mean value is preferably calculated for all intermediate points of the spectrum, wherein the calculation can be carried out, for example, by dividing the sum of the values of a number of next neighboring intermediate points, weighted with a normalized flat Gaussian curve, by the sum of the weights used with the Gaussian curve for all intermediate points. Each intermediate point has therefore a local mean value associated with it, which is then varied by a damping in a plurality of iterative steps. 
         [0023]    The iterative process then begins by setting one weighting factor LS for diffraction and one weighting factor LD for the light attenuation to 1. For a first damped model spectrum, the damping of the amplitude is calculated by multiplying the model spectrum with a current value of LS and by compensating the lost height of the amplitude by adding the local mean value, multiplied by the current value of LD, wherein LS and LD are initially 1, basically however always equal to or smaller than 1 and greater than 0. The thus obtained damped model spectrum is then convoluted with the initially measured line spread. If the line spread is already known and stored for the system used, it can also be read from the present memory. After the convoluting step, the values for LS and LD are newly set and the iterative process for determining a new damped model spectrum is repeated until the difference between the old and new values for LS or LD normalized to the new values for LS or LD, respectively, is smaller than a predetermined percentage, in particular smaller than 1%. 
         [0024]    To set the new value for LD, according to a preferred embodiment of the invention, first the ratio between the mean value of all intermediate points of the measured spectrum and the mean value of all intermediate points of the model spectrum is formed and multiplied with the old value for LD. To determine the new value for LS, first the ratio between the value of the mean change of two neighboring intermediate points of the measured spectrum and the value of the mean change of two neighboring intermediate points of the model spectrum is formed and multiplied with the old value for LS. 
         [0025]    The calculation of the new damped model spectrum  20  is then iteratively continued until the percentage change from the old to the new values for LS and LD falls short of a predetermined value, such as about 1%. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0026]    Further advantages and advantageous embodiments of the invention are the subject matter of the subsequent figures and their descriptions, in which an illustration to scale has been omitted for clarity. In the figures: 
           [0027]      FIG. 1  shows the schematic structure of the measuring system according to the present invention; and 
           [0028]      FIG. 2  schematically shows the sequence of the method according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0029]      FIG. 1  schematically shows the structure of the measuring system according to the present invention with the spectra obtained thereby. A measuring or inspection system  10 , such as a spectral photometer, is provided with the aid of which a measured spectrum  18  can be recorded from an object  12 . The measuring or inspection system can be structured such as described, for example, in DE 101 33 992. Object  12  can be a multilayer system, in particular. The data of the measured spectrum  18  are also made available to a computer unit  14 , which can also be integrated into measuring system  10 . A model spectrum  16  associated with object  12  and corresponding to measured spectrum  18  is calculated with the aid of a suitable model by computer unit  14 . 
         [0030]    In the calculation of model spectra of thick layers, preferably an FFT technique is used, in which any damping, if present, is hardly effective. The determination of the layer thickness is therefore only little influenced by the damping, so that the model spectrum of a thick layer of object  12  oscillates strongly. Measured spectrum  18  of a thick layer recorded with the aid of spectral photometer  10 , however, is damped in comparison. The user of the spectral photometer therefore obtains a measured spectrum  18  and a model spectrum  16  which look very different, even though calculated model spectrum  16  is the best fit of measured spectrum  18 . 
         [0031]    To avoid this effect, a method is stored in computer unit  14 , with the aid of which a damped model spectrum  20  can be calculated from model spectrum  16 , wherein a systematic damping of the measured spectrum is taken into account without affecting the quality of the parameters calculated with the model spectrum. When a thick layer is detected, this method can be started additionally by the user, such as by selection, or automatically by the system, when a thick layer is detected. 
         [0032]    The basic sequence of the method, which can be stored in computer unit  14 , for example, as a software, is schematically illustrated in  FIG. 2 . Before the desired match can be carried out the present measuring or inspection system  10  is measured in a measuring step  22 . For this purpose, monochromatic light or the light of one or more sharp lines, such as of a sodium or mercury vapor lamp is used as a light source and the line spread caused by the system is measured by the detector. The result is an intensity curve I(λ) of the spread line versus the wavelength λ, which can have the form of a Gaussian curve, for example. This intensity curve can also be stored in a storage area of computer unit  14  as a result of measuring the system and, being system-specific, can be reused for damping other model spectra. 
         [0033]    For damping the current model spectrum  16 , the local mean values  R i    are calculated for all intermediate points of model spectrum  16  in an averaging step  24 . To do this, it can be provided, for example, that for all intermediate points from the model spectrum, the sum of the values of a number of next neighboring intermediate points, weighted with a normalized flat Gaussian curve is used. This value is divided by the sum of the used weights of the Gaussian curve, so that: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         
                           R 
                           _ 
                         
                         i 
                       
                       = 
                       
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               
                                 - 
                                 n 
                               
                             
                             
                               + 
                               n 
                             
                           
                            
                           
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   
                                     - 
                                     
                                       1 
                                       2 
                                     
                                   
                                    
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             j 
                                             · 
                                             Δ 
                                           
                                            
                                           
                                               
                                           
                                            
                                           λ 
                                         
                                         4 
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             · 
                             
                               R 
                               
                                 i 
                                 + 
                                 j 
                               
                             
                           
                         
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               
                                 - 
                                 n 
                               
                             
                             
                               + 
                               n 
                             
                           
                            
                           
                             exp 
                              
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     1 
                                     2 
                                   
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           j 
                                           · 
                                           Δ 
                                         
                                          
                                         
                                             
                                         
                                          
                                         λ 
                                       
                                       4 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     , 
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0034]    Wherein σ=4 and 
         [0000]    i is the index of the intermediate point, 
       R i+j  is the value of the spectrum at intermediate point (i+j), if any, 
       [0035]    Δλ is the size of the interval, i.e. the distance between intermediate points,
 
n is the number of neighboring intermediate points involved, and
 
         R i    is the local mean value of the spectrum at intermediate point i. 
       [0036]    If at the edge of the model spectrum not all desired neighboring intermediate points are available, only those available are summed and divided by the corresponding sum of Gaussian weights. The result is a local mean value  R i    at each intermediate point. To prepare the iterative process for damping model spectrum  16 , a weighting factor LS for light diffraction and a weighting factor LD for light attenuation is set to 1 at the end of step  24 . 
         [0037]    For the further procedure, a mean value M for the spectrum and A for the value of the mean change of the value between neighboring intermediate points is defined. 
         [0000]    
       
         
           
             
               
                 
                   M 
                    
                   
                     : 
                   
                    
                   
                     = 
                     
                       
                         
                           1 
                           N 
                         
                          
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                            
                           
                             
                               R 
                               i 
                             
                              
                             
                                 
                             
                              
                             and 
                              
                             
                                 
                             
                              
                             A 
                              
                             
                               : 
                             
                           
                         
                       
                       = 
                       
                         
                           1 
                           
                             N 
                             - 
                             1 
                           
                         
                          
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                            
                           
                              
                             
                               
                                 R 
                                 
                                   i 
                                   + 
                                   1 
                                 
                               
                               - 
                               
                                 R 
                                 i 
                               
                             
                              
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0038]    The corresponding values for the measured spectrum M measured spectrum  and A measured spectrum  are then calculated from the values for the intermediate points of measured spectrum  18  in step  26 . 
         [0039]    In damping step  28 , the amplitude of the oscillation of model spectrum  16  is damped without the spectrum substantially losing in height. To do this, the spectrum is multiplied with value LS which is 1 at the first iteration and then smaller than 1, but always larger than 0. The lost height is then compensated for by adding a corresponding portion of the previously calculated local mean value  R i   . To simulate a light loss, this is not completely carried out, however, but the compensation is reduced by the value of factor LD. LD is also equal to 1 in the first iteration, then smaller than 1, but always larger than 0. Put as an equation, the damped value for R i , for intermediate point i, is therefore: 
         [0000]        R   i   =LS·R   i   +LD ·(1− LS )·   R     i .  (12) 
         [0040]    In step  30 , the damped model spectrum  20  is convoluted with the measured line spread I(λ), which now provides a damped model spectrum  20  which takes the system damping into account. 
         [0041]    To determine whether or not a further iteration step is necessary for matching the damped model spectrum  20  to the measured spectrum  18 , values M model spectrum  and A model spectrum  for model spectrum  16  are now calculated using equations (11) with the current values for LS and LD in step  32 . Subsequent to this, the values for LS and LD are newly calculated. They are obtained from the old values for LS and LD, multiplied with the ratios for M and A from the measured spectrum and the model spectrum, which yields: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       LD 
                       neu 
                     
                     = 
                     
                       
                         
                           LD 
                           alt 
                         
                         · 
                         
                           
                             M 
                             
                               measured 
                                
                               
                                   
                               
                                
                               spectrum 
                             
                           
                           
                             M 
                             
                               model 
                                
                               
                                   
                               
                                
                               spectrum 
                             
                           
                         
                       
                        
                       
                           
                       
                        
                       and 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       LS 
                       neu 
                     
                     = 
                     
                       
                         LS 
                         alt 
                       
                       · 
                       
                         
                           A 
                           
                             measured 
                              
                             
                                 
                             
                              
                             spectrum 
                           
                         
                         
                           A 
                           
                             model 
                              
                             
                                 
                             
                              
                             spectrum 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0042]    In step  34 , it must be checked whether changes in the values LD and LS are sufficiently small with respect to the previous iteration so that the iteration can be interrupted. To do this, differences Diff1 and Diff2 are formed: 
         [0000]    
       
         
           
             
               Diff 
                
               
                   
               
                
               1 
             
             = 
             
               
                  
                 
                   
                     
                       LD 
                       old 
                     
                     - 
                     
                       LD 
                       new 
                     
                   
                   
                     LD 
                     new 
                   
                 
                  
               
                
               
                   
               
                
               and 
             
           
         
       
       
         
           
             
               
                 Diff 
                  
                 
                     
                 
                  
                 2 
               
               = 
               
                  
                 
                   
                     
                       LS 
                       old 
                     
                     - 
                     
                       LS 
                       new 
                     
                   
                   
                     LS 
                     new 
                   
                 
                  
               
             
              
             
                 
             
           
         
       
     
         [0000]    and it is checked whether or not Diff1 and Diff2 fall short of a predetermined percentage, such as about 1%. If this is the case, the procedure is ended with step  36  and the damped model spectrum sought after has been found. 
         [0043]    If not, the procedure is continued with the new values of LS and LD in step  28  and the iterative loop continued until the damped model spectrum  20  sought after has been found.