Gratings, diffraction plane

Figure 2. Recording and readout of hologram gratings, (a) During recording two plane waves interfere to produce sinusoidal interference fringes with period A. (b) During readout one incident plane wave produces various diffracted plane waves.

Figure 28.5 shows schematically how a crystal acts like a diffraction grating. Two planes of lattice points are shown in which lattice points of the first plane are perpendicularly opposed to lattice points of the second plane. We assume that there... 

Figure 3.5 Various orders of diffraction tfom a plane reflection grating G R indicates the red end of the spectrum V indicates the violet end of the spectrum the central number is the order of diffraction...

The diffracted amphtude from illuminating such a grating with a unit plane wave normal to the surface is easily calculated again by resolving equation 9 into complex exponentials (as in eq. 10) where is the mUi Bessel function. 

Figure 1 Plane wave scattering from two consecutive iines of a one-dimensionai diffraction grating. The wave scatters in-phase when the path difference (the difference in iength of the two dotted sections) equais an integrai number of waveiengths.

As one may infer from the quotation, W. L. Bragg realized that a crystal can act as an x-ray grating made up of equidistant parallel planes (Bragg planes) of atoms or ions from which unmodified scattering of x-rays can occur in such fashion that the waves from different planes are in phase and reinforce each other. When this happens, the x-rays are said to undergo Bragg reflection by the crystal and a diffraction pattern results. 

This section refers to classically-ruled plane diffraction gratings where the grooves have a blazed profile as illustrated in Fig. 2a. 

Unlike the case of diffraction of light by a ruled grating, the diffraction of x-rays by a crystalline solid leads to the observation that constructive interference (i.e., reflection) occurs only at the critical Bragg angles. When reflection does occur, it is stated that the plane in question is reflecting in the nth order, or that one observes nth order diffraction for that particular crystal plane. Therefore, one will observe an x-ray scattering response for every plane defined by a unique Miller index of (h k l). 

It is readily apparent that a mask consisting of equal lines and spaces constitutes a diffraction grating and when uniformly illuminated will produce a diffraction pattern similar to that just discussed with an intensity profile depending on the grating period ( ), the wavelength (X) and the position of the image plane. This will be discussed in more detail later. 

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