Coherence chapter 8 Coherence theory is the study

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Coherence (chapter 8) • Coherence theory is the study of correlation that exist between

Coherence (chapter 8) • Coherence theory is the study of correlation that exist between different parts of a light field • Two type of coherences: • Temporal coherence: correlation between • Spatial coherence: correlation between • Temporal coherence can be measured with a Michelson interferometer • Spatial coherence can be measured with a two-slit interferometer P. Piot, PHYS 430 -530, NIU FA 2018 1

Michelson Interferometer • Case of a monochromatic plane wave • Total intensity at the

Michelson Interferometer • Case of a monochromatic plane wave • Total intensity at the detector is • Case of two wave packets? P. Piot, PHYS 430 -530, NIU FA 2018 2

Michelson interferometer II • Consider two arbitrary waveforms the total field is • The

Michelson interferometer II • Consider two arbitrary waveforms the total field is • The total intensity is then P. Piot, PHYS 430 -530, NIU FA 2018 3

Degree of coherence function • Integrate previous equation over time Use of P a

Degree of coherence function • Integrate previous equation over time Use of P a theo rseval’s rem • And introduce the fluence • The 3 rd term is • So that Degree of coherence function P. Piot, PHYS 430 -530, NIU FA 2018 4

Example of a Gaussian wavepacket • Consider a Gaussian wavepacket • Its power spectrum

Example of a Gaussian wavepacket • Consider a Gaussian wavepacket • Its power spectrum is • The degree of coherence is given by • So that P. Piot, PHYS 430 -530, NIU FA 2018 5

Coherence time and fringe visibility • P. Piot, PHYS 430 -530, NIU FA 2018

Coherence time and fringe visibility • P. Piot, PHYS 430 -530, NIU FA 2018 6

Fourier Spectroscopy • The output signal of a Michelson interferometer for a pulsed signal

Fourier Spectroscopy • The output signal of a Michelson interferometer for a pulsed signal • If we take the Fourier transform we get • So a measurement of the autocorrelation provides the spectrum of the signal. This is the essence of Fourier spectroscopy a widely used technique P. Piot, PHYS 430 -530, NIU FA 2018 7

Spatial coherence • P. Piot, PHYS 430 -530, NIU FA 2018 8

Spatial coherence • P. Piot, PHYS 430 -530, NIU FA 2018 8

Case of an extended source • The fields are • And the total field

Case of an extended source • The fields are • And the total field is found via • Total intensity is P. Piot, PHYS 430 -530, NIU FA 2018 9

Case of an extended source II • Assume the phases of emission are random:

Case of an extended source II • Assume the phases of emission are random: • The we get the time-averaged intensity • Of the form P. Piot, PHYS 430 -530, NIU FA 2018 10

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