Download presentation

Presentation is loading. Please wait.

Published byTrevon Gridley Modified over 3 years ago

1
PC20312 Wave Optics Section 4: Diffraction

2
Huygens-Fresnel Principle I Image from Wikipedia Augustin-Jean Fresnel 1788-1827 “Every unobstructed point of a wavefront… serves as a source of spherical secondary wavelets … The amplitude of the optical field at any point beyond is the superposition of all these wavelets...” Fresnel combined ideas of Huygens’ wavelets & interference Postulated in 1818: Hecht, p444

3
Huygens-Fresnel Principle II Gustav R. Kirchhoff 1824-1887 Fresnel’s postulate (1818) predates Maxwell’s equations (1861) Formally derived from the scalar wave equation by Kirchoff in 1882 Worked with Schuster for year at the University of Heidelberg Image from Wikipedia

4
Huygens-Fresnel Principle III Total area, A P dA 1 dA 3 dA 2 Optical field at P depends on the superposition of contributions from each elemental area dA of the total area A

5
Huygens-Fresnel Principle IV Divide an aperture into elemental areas each of which is a source of a spherical wavelet Image from Wikipedia http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm

6
The Huygens-Fresnel Integral Source, S Observation point, P Q Spherical wavefront s r s0s0 R

7
Fraunhofer diffraction Joseph von Fraunhofer 1787-1826 The case of small, linear phase variation, i.e.: r R + r, r << R r x,y Satisfied when s,r >> d Hence, “Far-field diffraction” Image from Wikipedia y x aperture d

8
Far-field diffraction S s0s0 s 0 >> d wavefront plane at aperture s s 0 P d D R >>d const. set K( ) 1 D >> d R

9
Analysis of Fraunhofer diffraction Source, S Observation point, P(X,Y) Q( x,y ) s r R s0s0 Z Aperture, A( x,y )

10
Single slit diffraction y x a/2 -a/2 Image from Wikipedia

11
Rectangular aperture y x a/2 -a/2 b/2 -b/2 Image from Wikipedia

12
Circular aperture I y x a u Image from Wikipedia Airy disc Airy rings The Airy Pattern

13
Circular aperture II kaθ D =3.83 I=0.0175 I(0)

14
The diffraction limit f f Image from Google Images If there was no diffraction: parallel rays focused to a point images would be perfectly sharp BUT, diffraction from instrumental apertures : produce rays at a range of angles which are focused at different points image is thus smeared out. Even for a perfect optical system, diffraction limits resolution.

15
Radius of the Airy disc f DD Radius, R A = f D = 1.22f /d Fraunhofer diffraction patterns also formed in focal plane of a lens ¶ ¶ e.g. see ‘Modern Optics’ by R Guenther Appendix 10-A

16
Two finite slits E 2 (X) E 1 (X) E 1 (X) E 2 (X) d R x X a a Image courtesy of A Pedlar

17
Point spread function Images courtesy of A Pedlar & from Wikipedia

18
The diffraction grating David Rittenhouse 1732-1796 Rittenhouse 1785: fine threads between screws – 100 threads/inch Fraunhofer 1821: thin wires Henry Augustus Rowland: curved gratings spectrocopy Henry Joseph Grayson 1899: developed precise ‘ruling engine’ 120,000 lines/inch Henry Augustus Rowland 1848-1901 A periodic structure designed to diffract light Images from Wikipedia

19
Grating structure Ruled grating Blazed grating – enhances diffraction in one direction Gratings: central to modern spectrometers reflection or transmission amplitude or phase Phase grating

20
Analysis of diffraction from gratings d d 1 2 Path length difference for incident rays:Path length difference for diffracted rays: d 1 2

21
Modern gratings Reflection gratings Transmission gratings CDs / DVDs Images from Wikipedia

22
Gratings in nature Nacre Peacock feathers Butterfly wings Images from Wikipedia

23
Grating based spectrometers The Czerny-Turner monochromator. A – input light B – entrance slit C – collimating mirror D – diffraction grating E – focusing mirror F – exit slit G – output light Image from Wikipedia

24
General diffraction (again) Source, S Observation point, P Q Spherical wavefront s r s0s0 R

25
Half-period zones s S P r m+1 rmrm rmrm S P

26
Area of the m th zone S dd s sdsd s sin P s sin d S s P rmrm s+R

27
Zone plates

28
Arago’s spot François Jean Dominique Arago (1783-1856) Siméon Denis Poisson (1781 -1840) http://demo.physics.uiuc.edu/LectDemo/scripts/demo_descript.idc?DemoID=749 Merde !

29
Fresnel diffraction from straight edges y x Q( x,y ) S s P r s0s0 R

Similar presentations

Presentation is loading. Please wait....

OK

Fraunhofer Diffraction

Fraunhofer Diffraction

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on euro currency market Ppt on concrete mix design Ppt online open channel Download ppt on rectification of errors Ppt on unity in diversity quotes Ppt on chromosomes and genes middle school Ppt on role of water resources management Ppt on iron and steel industry in india Team based pay ppt online Ppt on hindu religion facts