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ECE-1466 Modern Optics Course Notes Part 3

ECE-1466 Modern Optics Course Notes Part 3. Prof. Charles A. DiMarzio Northeastern University Spring 2002. Diffraction. Fresnel-Kirchoff Integral Fraunhofer Approximation Some Common Examples Fourier Optics Generalized Pupil Function Optical Testing Diffraction Gratings Gaussian Beams.

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ECE-1466 Modern Optics Course Notes Part 3

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  1. ECE-1466Modern OpticsCourse NotesPart 3 Prof. Charles A. DiMarzio Northeastern University Spring 2002 Chuck DiMarzio, Northeastern University

  2. Diffraction • Fresnel-Kirchoff Integral • Fraunhofer Approximation • Some Common Examples • Fourier Optics • Generalized Pupil Function • Optical Testing • Diffraction Gratings • Gaussian Beams Chuck DiMarzio, Northeastern University

  3. Fresnel-Kirchoff Integral (1) • The Basic Equation • An Approximation Chuck DiMarzio, Northeastern University

  4. Fresnel-Kirchoff Integral (2) Chuck DiMarzio, Northeastern University

  5. Paraxial Approximation x1 x z Chuck DiMarzio, Northeastern University

  6. Circular Aperture, Uniform Field Chuck DiMarzio, Northeastern University

  7. Square Aperture, Uniform Field Chuck DiMarzio, Northeastern University

  8. No Aperture, Gaussian Field Chuck DiMarzio, Northeastern University

  9. Fraunhoffer Examples Chuck DiMarzio, Northeastern University

  10. Single-Mode Optical Fiber Beam too Large (lost power at edges) Beam too Small (lost power through cladding) Chuck DiMarzio, Northeastern University

  11. Resolution: Rayleigh Criterion Chuck DiMarzio, Northeastern University

  12. Fourier Optics • Revisit of the Fresnel-Kirchoff Integral • The Fourier Transform • Definition of the Spatial Frequencies • Relation to Pupils • Some Examples • Optical Testing • Gratings Chuck DiMarzio, Northeastern University

  13. Fraunhofer Diffraction (1) Chuck DiMarzio, Northeastern University

  14. Fraunhofer Diffraction (2) Chuck DiMarzio, Northeastern University

  15. Linear Systems Approach to Imaging x’ x Any Optical System Exit Window Entrance Window Isoplanatic Chuck DiMarzio, Northeastern University

  16. Terminology • h is called the point spread function (PSF) • H is called the optical transfer function (OTF) • Magnitude is called Modulation Transfer Function (MTF) • Phase is Phase Transfer Function (PTF) • fx and fy are spatial frequencies Uimage Uobject Uimage Uobject Chuck DiMarzio, Northeastern University

  17. Concepts of Fourier Optics Any Isoplanatic Optical System Exit Window Exit Pupil Entrance Pupil Entrance Window Scale x,y and Multiply by OTF Fourier Transform Fourier Transform Chuck DiMarzio, Northeastern University

  18. Kohler Illumination • Illumination Source in a Pupil Plane • Incoherent Source • Fourier Transform Has Uniform Power • Homework Exercise Chuck DiMarzio, Northeastern University

  19. Some Resolution Charts (1) Edge Point and Lines Sinusoidal Chart Bar Charts Chuck DiMarzio, Northeastern University

  20. Some Resolution Charts (2) Air Force ISO Bar Charts Chuck DiMarzio, Northeastern University

  21. 1 0.9 20 0.8 40 0.7 60 0.6 80 20 0.5 100 40 0.4 20 120 60 0.3 40 140 80 0.2 60 160 0.1 100 80 180 0 120 20 40 60 80 100 120 140 160 180 100 140 120 160 140 180 20 40 60 80 100 120 140 160 180 160 180 20 40 60 80 100 120 140 160 180 Radial Target and Image Colorbar for all Object Image Point-Spread Function of System Chuck DiMarzio, Northeastern University

  22. Grating Equation sin(qd) 5 1 4 3 0.5 sin(qi) 2 1 0 n=0 -sin(qi) -0.5 -1 -2 -1 -100 0 100 200 -3 Reflected Orders Transmitted Orders degrees Chuck DiMarzio, Northeastern University

  23. Grating Fourier Analysis Grating Diffraction Pattern Sinc Slit Convolve Multiply Repetition Pattern Result Multiply Convolve Apodization Result Chuck DiMarzio, Northeastern University

  24. Laser Tuning Gain f Cavity Modes f qi Chuck DiMarzio, Northeastern University

  25. Acousto-Optical Modulator Sound Source Absorber Chuck DiMarzio, Northeastern University

  26. Gaussian Profile Rayleigh Range Diameter Radius of Curvature Axial Irradiance The Spherical-Gaussian Beam Chuck DiMarzio, Northeastern University

  27. Visualization of Gaussian Beam w r z=0 Center of Curvature Chuck DiMarzio, Northeastern University

  28. 5 5 4 /b, Radius of Curvature 0 3 , Beam Diameter 2 0 r d/d 1 -5 -5 0 5 0 z/b, Axial Distance -5 0 5 z/b, Axial Distance Parameters vs. Axial Distance m4053 m4053 Chuck DiMarzio, Northeastern University

  29. Complex Radius of Curvature: Physical Results Chuck DiMarzio, Northeastern University

  30. Making a Laser Cavity Make the Mirror Curvatures Match Those of the Beam You Want. Chuck DiMarzio, Northeastern University

  31. Sample Hermite Gaussian Beams 0:0 0:1 0:3 (0:1)+i(1:0) = “Donut Mode” 1:0 1:1 1:3 2:0 2:1 2:3 Most lasers prefer rectangular modes because something breaks the circular symmetry. 5:0 5:1 5:3 from matlab program 10021.m Note: Irradiance Images rendered with g=0.5 Chuck DiMarzio, Northeastern University

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