Geometric optics background

High frequency approximations in the solution of an acoustic wave equation The reader, familiar with the background of seismic exploration methods, should recall that many successful seismic interpretation algorithms are based on the simple principles of geometrical seismics, which resembles the ideas of geometrical optics. The question is how this simple but powerful approach is connected with the... 

Natural philosophy and mathematics. The first class includes discussions that fall under, or are closely linked to, physics and mathematics, specificalfy Sections 1-4. ° These discussions have a twofold background. First, they tie in with al-Mas udi s career in the sciences, particularly the mathematical sciences, which has already been highlighted in Chapter 1. Most notably, his expertise in geometry and geometrical optics comes to the fore in Section 2 of the Shukuk and in the discussion of vision in Section 4. Second, discussions of natural philosophy in the book bespeak the influence of Abu 1-Barakat s Mu tabar,... 

Fig. 5 Erosion pit inside a reducing pipe fitting, projection technique at 160 kV, profile plot with optical densities of the digitised film. The varying background caused by the geometrical set-up prevents a wall thickness calibration as in fig. 4...

It will be assumed here that the X-ray diffraction data were collected on flat films with a point focus camera. This simplifies the theoretical presentation. The TMV data analyzed in the results section were collected on cylindrical films with Guinier cameras, but positions on the cylindrical films can be mapped onto positions on a flat film by a simple geometric transformation. In general, the form of the optical density, D(r,), in a fiber diffraction pattern can be expressed in film coordinates as the sum of contributions from all reflections, I (r,iJ> ), plus a background term, B(r,) ... 

There are (n+1) unknowns in this equation where n is the number of reflections contributing at radius r on the film. The intensities, I (r,4> ), in this equation are equal to the background subtracted optical densities at the centers of the reflections. These intensities, once calculated, must be corrected for geometric factors in the same way as intensities measured by conventional procedures. 

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