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# Holography(2)

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### Holography(2)

1. 1. Chapter 17 Holography •• Basic Holographic Technique Basic Holographic Technique •• Light Sources Light Sources •• Recording Materials Recording Materials •• Holographic Non-Destructive Holographic Non-Destructive Testing Testing –Real-Time –Real-Time –Double-Exposure –Double-Exposure –Time-Average –Time-AverageOptics 505 - James C. Wyant Chapter 17 Page 1 of 28 Basic Hologram Setup Recording Medium Object Reference Beam Laser IlluminationOptics 505 - James C. Wyant Chapter 17 Page 2 of 28 Optics 505 - James C. Wyant Page 1
2. 2. Hologram Optics 505 - James C. Wyant Chapter 17 Page 3 of 28Hologram Seen Through Microscope Optics 505 - James C. Wyant Chapter 17 Page 4 of 28 Optics 505 - James C. Wyant Page 2
3. 3. Reconstructed ImageOptics 505 - James C. Wyant Chapter 17 Page 5 of 28 Two Reconstructed ImagesOptics 505 - James C. Wyant Chapter 17 Page 6 of 28 Optics 505 - James C. Wyant Page 3
4. 4. Basic TheoryObject Reference O( x, y ) = O( x, y ) eiα o ( x,y) R(x, y) = R( x, y ) eiα R ( x,y) Exposing Intensity Amplitude Transmission I = (O + R)(O + R)* T A = To − β I = Io + IR + OR* + O*R Primary Image 2 TA R = RTo − β [ o + IR ) + IRO + O* R ] R(I Conjugate Image T A R* = R*To − β [ * (Io + I R ) + (OR* )2 + IRO* ] R Optics 505 - James C. Wyant Chapter 17 Page 7 of 28 Separation of Orders rays coming θo from object θo θR Ref Hologram Spectrum of Object ref ref* spatial k sin θR − k sin θ R frequency 2k sin θo Optics 505 - James C. Wyant Chapter 17 Page 8 of 28 Optics 505 - James C. Wyant Page 4
5. 5. Spatial Frequency Spectrum ofHologram Transmission Function TA = To − β [(OO* + RR* ) + OR* + O* R] OO* + RR* O* R OR* 2ksin θo 4k sin θo 2ksin θo k sinθR k sinθR For separation of orders sinθRmin= 3sin θo Optics 505 - James C. Wyant Chapter 17 Page 9 of 28 Light Sources Need coherence length of laser • Pulsed Lasers – Ruby 699.3 nm – Frequency Doubled Yag 530 nm • CW Lasers – HeNe 633 nm – Argon 477, 488, 496, 502, 515 nm – Krypton 476, 521, 568, 647 nm – R6G Dye 570-650 nm Optics 505 - James C. Wyant Chapter 17 Page 10 of 28 Optics 505 - James C. Wyant Page 5
6. 6. Recording Materials • Photographic Film – Most common • Photoresist – Thin phase hologram • Dichromated Gelatin – High efficiency volume hologram • Thermoplastic Device – Convenient for holographic interferometry Optics 505 - James C. Wyant Chapter 17 Page 11 of 28Thermoplastic Recording Device +10 KV + + ++ + + + + + + + + + + + + + + + + Thermoplastic Photoconductor Transparent - - - - - - - - conductor Glass Film structure of a photoconductor-thermoplastic layer system. Corona charging device is shown. Optics 505 - James C. Wyant Chapter 17 Page 12 of 28 Optics 505 - James C. Wyant Page 6
7. 7. Recording-Erasure Cycle of Thermoplastic Hologram Step 1 +++++++++++++++ First charging Thermoplastic Photoconductor Step 2 Step 3 Exposure Second charging Light Light +++++ +++++ +++++++++++++++ +++++++++++++++ Step 4 Step 5 Development Erasure Optics 505 - James C. Wyant Chapter 17 Page 13 of 28Holographic Non-Destructive Testing •• Real-Time Real-Time •• Double-Exposure Double-Exposure •• Time-Average Time-Average Optics 505 - James C. Wyant Chapter 17 Page 14 of 28 Optics 505 - James C. Wyant Page 7
8. 8. Hologram Formation Laser Object Hologram Optics 505 - James C. Wyant Chapter 17 Page 15 of 28 Real-Time Holographic Interferometry• Make hologram of arbitrarily shaped rough scattering surface• Process hologram• Replace hologram in original position and illuminate with reference and object wavefronts• If object is deformed interference fringes will be produced telling how surface is deformed• Between adjacent fringes optical path between source and viewer changed by one wavelength• While we are not obtaining surface shape, we are measuring shape change even though object surface rough compared to wavelength of light Optics 505 - James C. Wyant Chapter 17 Page 16 of 28 Optics 505 - James C. Wyant Page 8
9. 9. Double-Exposure Holographic Interferometry • Same as real-time holography except two exposures are made before processing • Advantage - no critical replacement of hologram after processing • Disadvantage - continuous comparison of surface displacement relative to initial state cannot be made Optics 505 - James C. Wyant Chapter 17 Page 17 of 28Typical Holographic Non-Destructive Interferograms Debonded region of honeycomb Fringes on aluminum construction panel. cube due to uniform thermal expansion. Optics 505 - James C. Wyant Chapter 17 Page 18 of 28 Optics 505 - James C. Wyant Page 9
10. 10. Double Exposure Interferograms Air Flow Past Cone Candle Optics 505 - James C. Wyant Chapter 17 Page 19 of 28Interferograms of Temperature Field of Light Bulb Optics 505 - James C. Wyant Chapter 17 Page 20 of 28 Optics 505 - James C. Wyant Page 10
11. 11. Holographic Tire Testing Arrows show weak areas Optics 505 - James C. Wyant Chapter 17 Page 21 of 28 Time-Average Holographic Interferometry• Make hologram of vibrating object• Maximum vibration amplitude should be limited to tens of wavelengths• Illumination of hologram yields image on which is superimposed interference fringes• Fringes are contour lines of equal vibration amplitude Optics 505 - James C. Wyant Chapter 17 Page 22 of 28 Optics 505 - James C. Wyant Page 11
12. 12. Vibrating Membrane D( x,t) = D( x)cos ωtPhase of scattered light Objectδ (x,t) = -2(2 π / λ )D(x)cosω t O(x,t) = O(x)eiδ (x,t ) Holographic Exposure proportional to T 1 ( I = T ò O 2 + R 2 + OR* + O*R dt ) 0 Optics 505 - James C. Wyant Chapter 17 Page 23 of 28 Fringe Intensity Function Transmission function term of interest 2π ò eiδ ( x,t )d (ω t ) = Jo[λ ] 1 2 π 2 D( x ) 2π 0 Intensity of observation point proportional to 2 Jo 2π 2D(x) λ {[ ]} Optics 505 - James C. Wyant Chapter 17 Page 24 of 28 Optics 505 - James C. Wyant Page 12
13. 13. Plot of Zero Order Bessel Function 2p 2 JoA 2 D HxLE l 2p 2 D HxL l Optics 505 - James C. Wyant Chapter 17 Page 25 of 28 Time-Average Holographic Interferograms Vibrating Plate Optics 505 - James C. Wyant Chapter 17 Page 26 of 28 Optics 505 - James C. Wyant Page 13
14. 14. Interference Patterns for Different Vibration Modes Mode 1 Mode 2 Mode 1 and Mode 2 Optics 505 - James C. Wyant Chapter 17 Page 27 of 28 Vibrating Guitar Optics 505 - James C. Wyant Chapter 17 Page 28 of 28 Optics 505 - James C. Wyant Page 14