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Unformatted text preview: FRAUNHOFER DIFFRACTION The diffraction from slits of a range of widths is depicted in Fig. 1. D«x a>x Fig. 1 Intensity distribution behind an aperture of width a = A (left), a very small aper ture (center), and a large aperture (right). The Fraunhofer diffraction by a single slit is shown in Fig. 2. s Fig. 2 (a) Franhofer diffraction by a slit. (b) Diffraction pattern at inﬁnity but focused to nearby plane. Fraunhofer Diffraction — Fourier Transform The Fraunhofer diffraction pattern (in amplitude as opposed to intensity) of an aperture is the Fourier transform of the amplitude transmittance function of that aper ture. The Fraunhofer (farﬁeld) diffraction intensity pattern for a single slit is given by 1 = 10 [LWMST‘U] 2 sinO A 7T0, This is shown in Fig. 3. Plot of amplitude
and intensity I I l  I Amplitude :
/ l I
l I I I 2 I I I I
I
I
I 0} I
I
I
I
I
I \
I
I
l Fig. 3 Fraunhofer diffraction pattern for a single slit. The effect of increasing the number of slits is shown in Fig. 4. (a)
D
i o_________._____________
T l A/D sin a
l .......... N ﬁrm. (b)
L ' . 0 _b. _H »:.+_~.:z I “““““ ﬁn; ........ __ (c)
I . 0 M. .... .. 3"" . ~ —  5 ~ 9 — How—uh—
I
I  h 5",; .... N ' .  a 3‘". I ‘s  ._ A , '. . . i o X/d 2nd 3M1 4M1 sin 9 Fig. 4 Fraunhofer diffraction patterns for one, two, three, and four slits. FRAUNHOFER DIFFRACTION PATTERNS (a) Fraunhofer diffraction pattern of a single slit.
(b), (c), (d), (e) Interference patterns of 2, 3, 4, and 5 slits respectively.
The slit systems are indicated on the left. ...
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Tech.
 Spring '08
 Gaylord

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