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ECE-1466 Modern Optics Course Notes Part 3

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Presentation on theme: "ECE-1466 Modern Optics Course Notes Part 3"— Presentation transcript:

1 ECE-1466 Modern Optics Course Notes Part 3
Prof. Charles A. DiMarzio Northeastern University Spring 2002 March 02002 Chuck DiMarzio, Northeastern University

2 Chuck DiMarzio, Northeastern University
Diffraction Fresnel-Kirchoff Integral Fraunhofer Approximation Some Common Examples Fourier Optics Generalized Pupil Function Optical Testing Diffraction Gratings Gaussian Beams March 02002 Chuck DiMarzio, Northeastern University

3 Fresnel-Kirchoff Integral (1)
The Basic Equation An Approximation March 02002 Chuck DiMarzio, Northeastern University

4 Fresnel-Kirchoff Integral (2)
March 02002 Chuck DiMarzio, Northeastern University

5 Paraxial Approximation
z March 02002 Chuck DiMarzio, Northeastern University

6 Circular Aperture, Uniform Field
March 02002 Chuck DiMarzio, Northeastern University

7 Square Aperture, Uniform Field
March 02002 Chuck DiMarzio, Northeastern University

8 No Aperture, Gaussian Field
March 02002 Chuck DiMarzio, Northeastern University

9 Chuck DiMarzio, Northeastern University
Fraunhoffer Examples March 02002 Chuck DiMarzio, Northeastern University

10 Single-Mode Optical Fiber
Beam too Large (lost power at edges) Beam too Small (lost power through cladding) March 02002 Chuck DiMarzio, Northeastern University

11 Resolution: Rayleigh Criterion
March 02002 Chuck DiMarzio, Northeastern University

12 Chuck DiMarzio, Northeastern University
Fourier Optics Revisit of the Fresnel-Kirchoff Integral The Fourier Transform Definition of the Spatial Frequencies Relation to Pupils Some Examples Optical Testing Gratings March 02002 Chuck DiMarzio, Northeastern University

13 Fraunhofer Diffraction (1)
March 02002 Chuck DiMarzio, Northeastern University

14 Fraunhofer Diffraction (2)
March 02002 Chuck DiMarzio, Northeastern University

15 Linear Systems Approach to Imaging
x x’ Any Optical System Exit Window Entrance Window Isoplanatic March 02002 Chuck DiMarzio, Northeastern University

16 Chuck DiMarzio, Northeastern University
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 Uobject Uimage Uobject Uimage March 02002 Chuck DiMarzio, Northeastern University

17 Concepts of Fourier Optics
Any Isoplanatic Optical System Exit Window Entrance Window Entrance Pupil Exit Pupil Scale x,y and Multiply by OTF Fourier Transform Fourier Transform March 02002 Chuck DiMarzio, Northeastern University

18 Chuck DiMarzio, Northeastern University
Kohler Illumination Illumination Source in a Pupil Plane Incoherent Source Fourier Transform Has Uniform Power Homework Exercise March 02002 Chuck DiMarzio, Northeastern University

19 Some Resolution Charts (1)
Edge Point and Lines Sinusoidal Chart Bar Charts March 02002 Chuck DiMarzio, Northeastern University

20 Some Resolution Charts (2)
Air Force ISO Bar Charts March 02002 Chuck DiMarzio, Northeastern University

21 Radial Target and Image
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Radial Target and Image Colorbar for all 20 40 60 80 100 120 140 160 180 Object Image 20 40 60 80 100 120 140 160 180 20 40 60 80 100 120 140 160 180 Point-Spread Function of System March 02002 Chuck DiMarzio, Northeastern University

22 Chuck DiMarzio, Northeastern University
Grating Equation sin(qd) 5 1 4 3 0.5 sin(qi) 2 1 -sin(qi) n=0 -0.5 -1 -2 -1 -100 100 200 -3 Reflected Orders Transmitted Orders degrees March 02002 Chuck DiMarzio, Northeastern University

23 Grating Fourier Analysis
Diffraction Pattern Sinc Slit Convolve Multiply Repetition Pattern Result Multiply Convolve Apodization Result March 02002 Chuck DiMarzio, Northeastern University

24 Chuck DiMarzio, Northeastern University
Laser Tuning Gain f Cavity Modes f qi March 02002 Chuck DiMarzio, Northeastern University

25 Acousto-Optical Modulator
Sound Source Absorber March 02002 Chuck DiMarzio, Northeastern University

26 The Spherical-Gaussian Beam
Gaussian Profile Rayleigh Range Diameter Radius of Curvature Axial Irradiance March 02002 Chuck DiMarzio, Northeastern University

27 Visualization of Gaussian Beam
w r z=0 Center of Curvature March 02002 Chuck DiMarzio, Northeastern University

28 Parameters vs. Axial Distance
-5 5 1 2 3 4 z/b, Axial Distance d/d , Beam Diameter -5 5 z/b, Axial Distance r /b, Radius of Curvature m4053 m4053 March 02002 Chuck DiMarzio, Northeastern University

29 Complex Radius of Curvature: Physical Results
March 02002 Chuck DiMarzio, Northeastern University

30 Chuck DiMarzio, Northeastern University
Making a Laser Cavity Make the Mirror Curvatures Match Those of the Beam You Want. March 02002 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 m Note: Irradiance Images rendered with g=0.5 March 02002 Chuck DiMarzio, Northeastern University

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