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Refractive Indices
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It may happen that a good agreement is found by luck, if one happens to choose a grating for which the efficiency curve is insensitive to variations in the groove profile or to the inaccuracies of the theory. It is not always possible to measure the efficiency in all desired geometries, nor is it always possible to measure the groove profile with adequate accuracy. - Dr. M. C. Hultley33.  
 
 
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Measuring diffraction efficiency and scattered light for some gratings, especially for new samples, is a very important and challenging task. Both manufacturers of spectral devices for gratings and metrology laboratories use different approaches and equipment for precision measurements of the gratings efficiency over many years. Gratings efficiencies could be also accurately calculated for a broad range of wavelengths and others parameters based on the measured border profiles and measured or calculated refractive indices data of the layers. However, parameters of the gratings layers are usually measured so as not to be intended for further precise efficiency modeling. On the other hand, the existing accurate diffraction theories and appropriate software make use of some ideal models for parameters without any consideration of measuring inaccuracy and, as a rule, are difficult to use.  
 
In actual practice, only some of the simplest models are used for calculation, such as the scalar (Fresnel-Kirchhoff) diffraction theory, along with empirical factors introduced to cover the gap between ideal and real parameters. However, application of approximate theories is rather restricted and the empirical factors mentioned above are not suitable for modeling even under a slight change in parameters. Meanwhile, existing programs based on the accurate theory lack some important parameters which sometimes considerably affect the diffracted energy. Among them are the following:  
  • A non-plane form of the incident wave front.  
  • A finite width of the light beam.  
  • Gaussian distribution of the incident flux power.  
  • A non-plane shape of the grating surface.  
  • The thickness of substrate is unknown or greater than the light coherence length.  
  • Profile changes along the grating surface.  
  • A finite number of grating periods.  
  • Periodical and random roughness of the borders with due regard for the growth models.  
  • Inter-diffusion of the coating materials.  
  • Inclusions inside of the layers.  
  • Complex functions of the border profiles, and others.  
So far the concept explaining the role of different real grating parameters for diffraction efficiency modeling has not been reflected in scientific publications. As far as we know, any systematic comparison between measured and computed data for various types of gratings has not been drawn as well. Only several attempts were made for some particular cases,1-8 including those which are presented on these pages as Efficiency Certificates. Therefore, this problem is one of the most pressing for many present-day gratings and will be very important for grating technology of the future.  
 
 
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