ECE-1466 Modern Optics Course Notes Part 5

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ECE-1466Modern OpticsCourse NotesPart 5

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

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Basic Equations of Interference
Im E
Re E
3
Mach Zehnder (1)
Example
M2
BS1
Gas Cell ngt1
Source, s
M1
BS2
Straight-Line Layouts
Transit Time
s
BS1
BS2
M1
s
BS1
M2
BS2
Geometric
s
BS1
M1
BS2
s
BS1
M2
BS2
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Mach Zehnder (2)
Straight-Line Layout Transit Time
s
BS1
BS2
M1
s
BS1
M2
BS2
q
Diffuser
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Optical Testing
M1, Known Reference
Spheres 4-wave difference
Same with 2-wave bump
BS
M2, Mirror Under Test
Flats with 8-wave tilt
Same with 2-wave bump
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Fabry-Perot Interferometer (1)
I1
I4
Straight Line Model
Multiple Sources, with decreasing amplitudes
(usually) and increasing distances (and thus
phases).
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Fabry-Perot Interferometer (2)
10mm
650nm
600nm
FSR
d f
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Laser Tuning (1)

• Gain Lines
• Depend on Medium
• Often Multiple
• 10s to 100s of THz.
• Cavity Modes
• qc/2L
• q is an inteter
• L is cavity length
• Free Spectral Range
• c/2L (Mode Spacing)

Gain
f
Cavity Modes
f
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Laser Tuning (2)

• Fine Tuning
• Cavity Length
• Usually Piezoelectric
• Intracavity Modulator
• Single Mode
• Intracavity Etalon or
• Short Cavity
• Single Gain Line
• Prism or Grating

Gain
f
Cavity Modes
f
qi
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Etalon Transmission
Only Coherent Sources contribute to the fringes
Im (1/t)
Re (1/ t)
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Thin Films Three Approaches
Sum the multiple Reflections
Use Wave Equation and Boundary Conditions
Network Approach with Fresnel Coefficients
EB
EC
ED
EA
E1
E2
E3
E4
E1
E2
E3
E4
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Thin Film Matrices (2)
M4
M1
MM1M2M3M4
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High Reflection Stack (1)
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High Reflection Stack (2)
L
H
H
L
Phase0
pp
2p0
3pp
Sign of Reflectivity is inverted on going from
High to Low Index.
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Anti-Reflection Coatings
Examples
R
Uncoated Glass
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One Layer
Two Layers
Phase 0
p
Three Layers
Quarter-Wave Coating
Magnesium Flouride n1.35 is a close match, low
cost and durable.
l
Red
Violet
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Interference Magnitudes
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Quadrature Imaging Concept
Quadrature
Balanced Mixing
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Quadrature Images from Original Setup

• One-Cell Embryo

• Two-Cell Embryo

Amplitude
Phase
Amplitude
Phase

• Multi-Cell Blastocyst

Amplitude
Phase
Images by Dan Hogenboom, NU
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Quadrature Imaging Microscope Design

• Design Features
• 4 CCD Cameras - Balanced Mixing
• 10x and 20x Interchangeable Objectives
• Virtual Pinhole Focusing System

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Original Setup
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Experiment vs. Analytical Model

• Fiber Model n1.43-1.46-1.48

• Fiber in Sugar Water

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Unwrapped Phase Image of a Mouse Oocyte
Unwrapped Phase
Amplitude
Phase
10027.jpg
3993.jpg
10028.jpg
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How Could QTM Count Cells in Compact Embryo?
QTM Phase
DIC
Assumed Index Profile Before Compaction
M10026.m
M10026.m
Assumed Index Profile During Compaction
M10026.m
M10026.m
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Third Generation QTM
.