chapter 11: fraunhofer diffraction. diffraction is… diffraction is… interference on the edge -a...
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- Slide 1
- Chapter 11: Fraunhofer Diffraction
- Slide 2
- Diffraction is Diffraction is interference on the edge -a consequence of the wave nature of light -an interference effect -any deviation from geometrical optics resulting from obstruction of the wavefront
- Slide 3
- on the edge of sea
- Slide 4
- on the edge of night
- Slide 5
- on the edge of dawn
- Slide 6
- in the skies
- Slide 7
- in the heavens
- Slide 8
- on the edge of the shadows
- Slide 9
- Slide 10
- With and without diffraction
- Slide 11
- The double-slit experiment interference explains the fringes - narrow slits or tiny holes -separation is the key parameter -calculate optical path difference diffraction shows how the size/shape of the slits determines the details of the fringe pattern
- Slide 12
- Josepf von Fraunhofer (1787-1826)
- Slide 13
- -far-field -plane wavefronts at aperture and obserservation -moving the screen changes size but not shape of diffraction pattern Fraunhofer diffraction Next week: Fresnel (near-field) diffraction
- Slide 14
- Diffraction from a single slit slit rectangular aperture, length >> width
- Slide 15
- Diffraction from a single slit plane waves in - consider superposition of segments of the wavefront arriving at point P - note optical path length differences
- Slide 16
- Huygens principle every point on a wavefront may be regarded as a secondary source of wavelets planar wavefront: ctct curved wavefront: In geometrical optics, this region should be dark (rectilinear propagation). Ignore the peripheral and back propagating parts! obstructed wavefront: Not any more!!
- Slide 17
- Diffraction from a single slit for each interval ds: Let r = r 0 for wave from center of slit (s=0). Then: where is the difference in path length. -negligible in amplitude factor -important in phase factor E L (field strength) constant for each ds Get total electric field at P by integrating over width of the slit
- Slide 18
- Diffraction from a single slit where b is the slit width and Irradiance: After integrating:
- Slide 19
- Recall the sinc function 1 for = 0 zeroes occur when sin = 0 i.e. when where m = 1, 2,...
- Slide 20
- Recall the sinc function maxima/minima when
- Slide 21
- Diffraction from a single slit Central maximum: image of slit angular width hence as slit narrows, central maximum spreads
- Slide 22
- Beam spreading angular spread of central maximum independent of distance
- Slide 23
- Aperture dimensions determine pattern
- Slide 24
- where
- Slide 25
- Aperture shape determines pattern
- Slide 26
- Irradiance for a circular aperture J 1 ( ) : 1 st order Bessel function where and D is the diameter Friedrich Bessel (1784 1846)
- Slide 27
- Irradiance for a circular aperture Central maximum: Airy disk circle of light; image of aperture angular radius hence as aperture closes, disk grows
- Slide 28
- How else can we obstruct a wavefront? Any obstacle that produces local amplitude/phase variations create patterns in transmitted light
- Slide 29
- Diffractive optical elements (DOEs)
- Slide 30
- Slide 31
- Phase plates change the spatial profile of the light
- Slide 32
- Demo
- Slide 33
- Resolution Sharpness of images limited by diffraction Inevitable blur restricts resolution
- Slide 34
- Resolution measured from a ground-based telescope, 1978 Pluto Charon
- Slide 35
- Resolution http://apod.nasa.gov/apod/ap060624.html measured from the Hubble Space Telescope, 2005
- Slide 36
- Rayleighs criterion for just-resolvable images where D is the diameter of the lens
- Slide 37
- Imaging system (microscope) - where D is the diameter and f is the focal length of the lens - numerical aperture D/f (typical value 1.2)
- Slide 38
- Test it yourself! visual acuity
- Slide 39
- Test it yourself!
- Slide 40
- Double-slit diffraction considering the slit width and separation
- Slide 41
- Double-slit diffraction single-slit diffraction double-slit interference
- Slide 42
- Double-slit diffraction
- Slide 43
- Slide 44
- Multiple-slit diffraction Double-slit diffraction single slit diffraction multiple beam interference single slit diffraction two beam interference
- Slide 45
- If the spatial coherence length is less than the slit separation, then the relative phase of the light transmitted through each slit will vary randomly, washing out the fine- scale fringes, and a one-slit pattern will be observed. Fraunhofer diffraction patterns Good spatial coherence Poor spatial coherence Importance of spatial coherence Max
- Slide 46
- Imagine using a beam so weak that only one photon passes through the screen at a time. In this case, the photon would seem to pass through only one slit at a time, yielding a one-slit pattern. Which pattern occurs? Possible Fraunhofer diffraction patterns Each photon passes through only one slit Each photon passes through both slits The double slit and quantum mechanics
- Slide 47
- Each individual photon goes through both slits! Dimming the incident light: The double slit and quantum mechanics
- Slide 48
- How can a particle go through both slits? Nobody knows, and its best if you try not to think about it. Richard Feynman
- Slide 49
- Exercises You are encouraged to solve all problems in the textbook (Pedrotti 3 ). The following may be covered in the werkcollege on 12 October 2011: Chapter 11: 1, 3, 4, 10, 12, 13, 22, 27
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