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