Slit diffraction

Fig. 3. X-ray diffractogram of Class-F bituminous coal fly ash. Analytical conditions diffraction data were collected using a Philips X-ray powder diffractometer (45 kV/30-40 mA CuKa theta-compensating variable divergence slit diffracted-beam graphite monochromator scintillation detector) automated with an MDI/Radix Databox. The scan parameters were typically 0.02° step size for 1 s count times over a range of 5-60° 2-theta. All data were analysed and displayed using a data reduction and display code (JADE) from Materials Data Inc., livermore, CA.

Now let us assume that a monochromatic source of flux is placed in the plane of the entrance slit so that there is no constant phase relationship between the fields at any two given points in the slit. This, in itself, is a contradiction, because a perfect source monochromaticity implies both spatial and temporal coherence. By definition of coherence, a constant phase relationship would result. To eliminate the possibility of such a relationship, we must require the source spectrum to have finite breadth. Let us modify the assumption accordingly but specify the source spectrum breadth narrow enough so that its spatial extent when dispersed is negligible compared with the breadth of the slits, diffraction pattern, and so on. Whenever time integrals are required to obtain observable signals from superimposed fields, we evaluate them over time periods that are long compared with the reciprocal of the frequency difference between the fields. We shall call the assumed source a quasi-monochromatic source. 

In optics and spectroscopy, resolution is often limited by diffraction. To a good approximation, the spread function may appear as a single-slit diffraction pattern (Section II). If equal-intensity objects (spectral lines) are placed close to one another so that the first zero of one sine-squared diffraction pattern is superimposed on the peak of the adjacent pattern, they are said to be separated by the Rayleigh distance (Strong, 1958). This separation gives rise to a 19% dip between the peaks of the superimposed patterns. 

Figure 10. Two-slit diffraction experiment of the Aharonov-Bohm effect. Electrons are produced by a source at X, pass through the slits of a mask at Y1 and Y2, interact with the A field at locations I and II over lengths h and l2, respectively, and their diffraction pattern is detected at III. The solenoid magnet is between the slits and is directed out of the page. The different orientations of the external A field at the places of interaction I and II of the two paths 1 and 2 are indicated by arrows following the right-hand rule.

I ig. 2.1 shows a modernized version of the famous double-slit diffraction experiment first carried out by Thomas Young in 1801. Light from a monochromatic (single wavelength) source is passed through two narrow slits and projected onto a screen. Each slit by itself would allow just a narrow band of light to illuminate the screen. But with both slits open, a beautiful interference pattern of alternating... 

Figure 2.7 Multiple-slit diffraction pattern for electrons, obtained by Claus Jonsson. Selected as the most beautiful experiment in the history of physics" by Physics World in 2002. (From Z. Phys. 161, 468, (1961). Used by permission of Dr. Claus Jonsson, Tubingen.)...

Figure 4. The intensity variation of an N-layer ciystal (often referred to as an N-slit diffraction pattern). (A) The intensity, plotted as F]2/fo, is shown over a broad Q range for N = 32. (B) The first-order diffraction peak is shown in detail for N = 4, 8, 16, 32. In these units, the peak intensity varies as N2. (C) The same functional form, plotted on a logarithmic scale, shows both the bulk Bragg peak near Q = 2.1 and the continuously modulated intensity found between the bulk Bragg peaks.

Note that one of the characteristics of single-slit diffraction is that the narrower the slit width the wider is the spread of the diffraction pattern. Note also that... 

Two-slit diffraction is shown in Figure 1.4. A grating of many paraleU slits acts as a dispersive element. 

Not all orders of a given wavelength appear equally strong in the focal plane, however. The single-slit diffraction pattern corresponding to the width a of each slit forms an envelope in the focal plane that determines the positions of the orders of significant intensity. The intensity pattern in the focal plane, as derived in standard texts for Fraunhofer diffraction by multiple slits, is... 

Figure 6.15 Light intensity distribution after single slit diffraction.

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