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Spatial & Temporal Coherence
Optical Engineering Prof. Elias N. Glytsis
School of Electrical & Computer Engineering National Technical University of Athens
08/03/2018
Spatial and Temporal Coherence
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
2 Prof. Elias N. Glytsis, School of ECE, NTUA
Coherence is a measure of the correlation between the phases measured at different (temporal and spatial) points on a wave. Temporal Coherence is a measure of the correlation of light wave’s phase at different points along the direction of propagation – it tells us how monochromatic a source is. Spatial Coherence is a measure of the correlation of a light wave’s phase at different points transverse to the direction of propagation - it tells us how uniform the phase of a wavefront is.
Temporal Coherence Time, τc Temporal Coherence Length, ℓc = c τc
Spatial Coherence Length, xc
xc
Spatial and Temporal Coherence
3 Prof. Elias N. Glytsis, School of ECE, NTUA
Spatial and Temporal
Coherence
Temporal Coherence;
Spatial Incoherence
Spatial Coherence;
Temporal Incoherence
Spatial and Temporal
Incoherence
Spatial and Temporal Coherence
4 Prof. Elias N. Glytsis, School of ECE, NTUA
Temporal Coherence
Temporal Coherence Time, τc Temporal Coherence Length, ℓc = 2d = c τc 5 Prof. Elias N. Glytsis, School of ECE, NTUA
Spatial Coherence
Spatial Coherence Area, Ac= πd2
6 Prof. Elias N. Glytsis, School of ECE, NTUA
Temporal Coherence
Temporal Coherence Function (Autocorrelation)
Degree of Temporal Coherence
Coherence Time and Coherence Length
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
7 Prof. Elias N. Glytsis, School of ECE, NTUA
Temporal Coherence
Power Spectral Density
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
8 Prof. Elias N. Glytsis, School of ECE, NTUA
Temporal Coherence
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
9 Prof. Elias N. Glytsis, School of ECE, NTUA
Temporal Coherence
Power Spectral Density
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
10 Prof. Elias N. Glytsis, School of ECE, NTUA
Young’s Experiment to Demonstrate Spatial Coherence
11 Prof. Elias N. Glytsis, School of ECE, NTUA
Spatial Coherence Mutual Coherence Function
Mutual Degree of Coherence
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
12 Prof. Elias N. Glytsis, School of ECE, NTUA
Spatial Coherence Function
Spatial Coherence Area, Ac
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007
13 Prof. Elias N. Glytsis, School of ECE, NTUA
Spatial Coherence
2 2
2cD
dλ
πΑ =
The van Cittert-Zernike Theorem states that the spatial coherence area Ac is given by:
where d is the diameter of the light source and D is the distance away.
Basically, wave-fronts smooth out as they propagate away from the source.
14 Prof. Elias N. Glytsis, School of ECE, NTUA
Spatial and Spectral Filtering to Produce Coherence Radiation
http://zeiss-campus.magnet.fsu.edu/tutorials/coherence/indexflash.html
15 Prof. Elias N. Glytsis, School of ECE, NTUA