ECE1466 Modern Optics Course Notes Part 3

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ECE-1466Modern OpticsCourse NotesPart 3

• Prof. Charles A. DiMarzio
• Northeastern University
• Spring 2002

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Diffraction

• Fresnel-Kirchoff Integral
• Fraunhofer Approximation
• Some Common Examples
• Fourier Optics
• Generalized Pupil Function
• Optical Testing
• Diffraction Gratings
• Gaussian Beams

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Fresnel-Kirchoff Integral (1)

• The Basic Equation
• An Approximation

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Fresnel-Kirchoff Integral (2)
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Paraxial Approximation
x1
x
z
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Circular Aperture, Uniform Field
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Square Aperture, Uniform Field
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No Aperture, Gaussian Field
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Fraunhoffer Examples
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Single-Mode Optical Fiber
Beam too Large (lost power at edges)
Beam too Small (lost power through cladding)
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Resolution Rayleigh Criterion
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Fourier Optics

• Revisit of the Fresnel-Kirchoff Integral
• The Fourier Transform
• Definition of the Spatial Frequencies
• Relation to Pupils
• Some Examples
• Optical Testing
• Gratings

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Fraunhofer Diffraction (1)
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Fraunhofer Diffraction (2)
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Linear Systems Approach to Imaging
x
x
Any Optical System
Exit Window
Entrance Window
Isoplanatic
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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
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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
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Kohler Illumination

• Illumination Source in a Pupil Plane
• Incoherent Source
• Fourier Transform Has Uniform Power
• Homework Exercise

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Some Resolution Charts (1)
Edge
Point and Lines
Sinusoidal Chart
Bar Charts
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Some Resolution Charts (2)
Air Force
ISO
Bar Charts
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Radial Target and Image
Colorbar for all
Object
Image
Point-Spread Function of System
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Grating Equation
sin(qd)
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1
4
3
0.5
sin(qi)
2
1
0
n0
-sin(qi)
-0.5
-1
-2
-1
-100
0
100
200
-3
Reflected Orders
Transmitted Orders
degrees
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Grating Fourier Analysis
Grating
Diffraction Pattern
Sinc
Slit
Convolve
Multiply
Repetition Pattern
Result
Multiply
Convolve
Apodization
Result
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Laser Tuning
Gain
f
Cavity Modes
f
qi
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Acousto-Optical Modulator
Sound Source
Absorber
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The Spherical-Gaussian Beam

• Gaussian Profile
• Rayleigh Range

• Diameter
• Radius of Curvature
• Axial Irradiance

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Visualization of Gaussian Beam
w
r
z0
Center of Curvature
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Parameters vs. Axial Distance
m4053
m4053
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Complex Radius of Curvature Physical Results
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Making a Laser Cavity
Make the Mirror Curvatures Match Those of the
Beam You Want.
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Sample Hermite Gaussian Beams
00
01
03
(01)i(10) Donut Mode
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11
13
20
21
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Most lasers prefer rectangular modes because
something breaks the circular symmetry.
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51
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from matlab program 10021.m
Note Irradiance Images rendered with g0.5