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

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

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

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

Paraxial Approximation z March 02002 Chuck DiMarzio, Northeastern University

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

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

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

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

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

Resolution: Rayleigh Criterion March 02002 Chuck DiMarzio, Northeastern University

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 March 02002 Chuck DiMarzio, Northeastern University