CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence...
Transcript of CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence...
![Page 1: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/1.jpg)
CoherenceCoherenceCoherence
This is based on
Chapter 10. Statistical Optics, Fundamentals of PhotonicsBahaa E. A. Saleh, Malvin Carl Teich
and
Lecture Note on Laser Technology and OpticsProf. Matti Kaivola
Optics and Molecular Materials, Helsinki University of Technologyhttp://omm.hut.fi/optics/l_o/2005/
and
Coherence and Fringe LocalizationT. D. Milster and N. A. Beaudry
Optical Sciences Center, University of Arizonawww.optics.arizona.edu/milster
![Page 2: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/2.jpg)
CoherenceCoherenceCoherenceCoherence is a measure of the correlation between the phases measured at
different (temporal and spatial) points on a wave
Coherence theory is a study of the correlation properties of random light which is also known as the statistical optics.
![Page 3: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/3.jpg)
Coherence theoryCoherence theoryCoherence theoryCoherence and Fringe Localization, T. D. Milster and N. A. Beaudry,
![Page 4: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/4.jpg)
Coherence as StatisticsCoherence as StatisticsCoherence as Statistics
![Page 5: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/5.jpg)
Statistical Properties of Random LightStatistical Properties of Random LightStatistical Properties of Random Light
Second order average of a function
![Page 6: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/6.jpg)
Mutual coherence functionMutual coherence functionMutual coherence function
Mutual coherence function
![Page 7: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/7.jpg)
Degree of CoherenceDegree of CoherenceDegree of Coherence
![Page 8: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/8.jpg)
CoherenceCoherenceandand
VisibilityVisibility
Young’s double pinhole interferometer (YDPI)
![Page 9: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/9.jpg)
Temporal Coherence Temporal Coherence Temporal Coherence
See the next example
( ) ( ) and ( ) ( )G gτ τ τ γ τ= Γ =
1 2r r=
The temporal autocorrelation meansthe time average at the same position
Note, we use both notations of
![Page 10: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/10.jpg)
Degree of Temporal CoherenceDegree of Temporal CoherenceDegree of Temporal Coherence
![Page 11: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/11.jpg)
Coherence Time and LengthCoherence Time and LengthCoherence Time and Length
Coherence lengthc cl cτ=
Coherence time
Coherence length
Note, it is different from ½ width, 1/e width, …
Later, we will similarly define the spectral width
![Page 12: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/12.jpg)
Temporal CoherenceTemporal CoherenceTemporal Coherence
1/c aveτ τ ν= = Δ
2/ /c cl c cτ ν λ λ= = Δ = Δ
Actually, what is the definition of Δv , why is satisfied the relation ?
![Page 13: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/13.jpg)
Coherence Time and Spectral WidthCoherence Time and Spectral WidthCoherence Time and Spectral WidthFundamentals of Photonics, Bahaa E. A. Saleh, Malvin Carl Teich
where,
![Page 14: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/14.jpg)
Coherence Time and Spectral WidthCoherence Time and Spectral WidthCoherence Time and Spectral Width
FWHM (full width at half maximum)
![Page 15: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/15.jpg)
Δt Δv = 1
Example : A wave comprising a random sequence of finite wave train.
Note, it is not a monochromatic wave
A truncated monochromatic waveIs not monochromatic, any more.
![Page 16: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/16.jpg)
Example 10.1-1. A wave comprising a random sequence of wavepackets decaying exp.
![Page 17: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/17.jpg)
Quasi-monochromatic wavesQuasiQuasi--monochromatic wavesmonochromatic waves
Now, start to investigate concretely a relation between the visibility and the coherence from a 2-wavelength light source up to a polychromatic light source.
![Page 18: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/18.jpg)
A point source with two wavelengths A point source with two wavelengths Young’s double pinhole interferometer (YDPI)
OPD = vΔtd << zo
![Page 19: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/19.jpg)
A point source with two wavelengths A point source with two wavelengths
T = 2π/ωm = nλeq /c, where 1 1 1 2
/ meq a b c n
ωλ λ λ
= − =
![Page 20: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/20.jpg)
Now, under the constraint that d << zo
A point source with two wavelengths A point source with two wavelengths
![Page 21: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/21.jpg)
Coherence length
λeq
λ
C.L. =2
1 1 12 2 2eq
cλλΔλ Δν
⎛ ⎞ ⎛ ⎞⎜ ⎟≈ = ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
and a b a bλ λ λ ν ν νΔ = − Δ = −
![Page 22: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/22.jpg)
A Polychromatic light sourceA Polychromatic light source
3 λ’s
5 λ’s
V decreased
![Page 23: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/23.jpg)
A Polychromatic light sourceA Polychromatic light source
![Page 24: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/24.jpg)
Fringe visibility
A Polychromatic light sourceA Polychromatic light source
![Page 25: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/25.jpg)
![Page 26: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/26.jpg)
0o
o
dysinc sinc lz c c
c l=
Δν ΔνΔ
ΔΔν
⎛ ⎞ ⎛ ⎞⋅ = ⋅ =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠
⇒
Coherence length
Coherence time
oz cyd v
ΔΔ
= ⋅
oz cyd v
ΔΔ
= ⋅
![Page 27: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/27.jpg)
![Page 28: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/28.jpg)
Δv
Δvm
2Δl =
![Page 29: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/29.jpg)
![Page 30: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/30.jpg)
Spatial CoherenceSpatial CoherenceSpatial Coherence
Remind!
![Page 31: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/31.jpg)
Spatial Coherence: point sourceSpatial Coherence: point sourceSpatial Coherence: point source
![Page 32: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/32.jpg)
Spatial Coherence: two point sourceSpatial Coherence: two point sourceSpatial Coherence: two point source
lc ~ λ/θ
![Page 33: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/33.jpg)
Basic Spatial CoherenceBasic Spatial Coherence
d
![Page 34: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/34.jpg)
Basic Spatial CoherenceBasic Spatial Coherence
![Page 35: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/35.jpg)
Basic Spatial CoherenceBasic Spatial Coherence
Basic properties of spatial coherence
![Page 36: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/36.jpg)
Basic Spatial CoherenceBasic Spatial CoherenceNow, extend to a continuous source distribution (an ensemble of incoherent point sources)
ss s A
s
y dOPD yz
θ= ≡
![Page 37: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/37.jpg)
Basic Spatial CoherenceBasic Spatial Coherence
Fringe visibility
![Page 38: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/38.jpg)
Basic Spatial CoherenceBasic Spatial Coherence
Fringe visibility
van Cittert-Zernike Theorem :Degree of Spatial Coherence is Fourier Transform (or, Fraunhofer Diffraction Pattern) of the source irradiance distribution Appendix I
![Page 39: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/39.jpg)
Example: Spatial coherence length from a circular source
![Page 40: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/40.jpg)
Lc ~ λ/θ
![Page 41: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/41.jpg)
sOPDs
θs
θs
Since and ss
s
y dOPDz
= As
dz
θ =
ss
y SOPDf
⇒ =
ASf
θ⇒ =
![Page 42: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/42.jpg)
![Page 43: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/43.jpg)
Concept of Coherent areaConcept of Coherent area
![Page 44: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/44.jpg)
A = 1 mm d = 3 mm
λ = 500 nm
l
V = 0
![Page 45: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/45.jpg)
Terminology Used in Coherence TheoryTerminology Used in Coherence TheoryRemind!
Define the normalized mutual coherence function, or complex degree of coherence
![Page 46: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/46.jpg)
Terminology Used in Coherence TheoryTerminology Used in Coherence Theory
Normalized mutual coherence functionComplex degree of coherence
![Page 47: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/47.jpg)
Making Light Coherent Making Light Incoherent
Spatial Filter forSpatial Coherence
Wavelenth Filterfor Temporal Coherence
Ground Glass toDestroy Spatial Coherence
Move it toDestroy Temporal Coherence
Control of CoherenceControl of CoherenceControl of Coherence
![Page 48: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/48.jpg)
Appendix IAppendix IAppendix I
Chuck DiMarzioNortheastern University
van Cittert-Zernike Theorem for Spatial Coherence
![Page 49: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/49.jpg)
Summary of van Cittert-Zernike Theorem for Spatial Coherence
![Page 50: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/50.jpg)
Van Cittert-Zernike Theorem: 1
Chuck DiMarzio, Northeastern University
![Page 51: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/51.jpg)
Van Cittert-Zernike Theorem: 2
Chuck DiMarzio, Northeastern University
![Page 52: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/52.jpg)
Van Cittert-Zernike Theorem: 3
Chuck DiMarzio, Northeastern University
![Page 53: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/53.jpg)
Van Cittert-Zernike Theorem: 4
Chuck DiMarzio, Northeastern University
![Page 54: CoherenceCoherenceoptics.hanyang.ac.kr/~shsong/5-Coherence.pdf · 2016-08-31 · CoherenceCoherence This is based on Chapter 10. Statistical Optics, Fundamentals of Photonics Bahaa](https://reader035.fdocuments.net/reader035/viewer/2022070712/5ecebb3d45693554a363aef0/html5/thumbnails/54.jpg)
Van Cittert-Zernike Theorem: 5
Source Irradiance
Far-Field Correlation Function
Chuck DiMarzio, Northeastern University