By Poon T.-C., Liu J.-P.
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Extra resources for Introduction to Modern Digital Holography: With Matlab
This is done purposely to be consistent with the engineering convention for a traveling wave. In the convention, exp[j(ω0t − k0z)] denotes a plane wave traveling in the þz-direction. 1 as long as we replace “j” by “−j” in the transform pairs. Let us return our attention to Eq. 53). The result of Eq. 53) is the Wiener– Khinchin theorem, which states that the Fourier transform of the auto-correlation of the light ﬁeld is proportional to the power spectrum of the light source, P c ðωÞ. , a ﬁeld represented by a complex quantity.
48), γðτÞ ¼ Λðτ=τ 0 Þe jω0 τ , and Eq. 61) becomes ! τ 2 2 cosðω0 τÞ : ð2:62Þ IðτÞ ¼ 2 jEðtÞj ½1 þ jγðτÞj cosðω0 τÞ ¼ 2 jEðtÞj 1 þ Λ τ0 The power spectrum, according to Eq. 55), is ! 1, taking into account that we are dealing with one-dimensional time functions. 566/Δω. Other examples of spectra are the Gaussian spectrum and the rectangular spectrum. For a Gaussian spectrum, we have ω − ω 2 ! 0 P N ðωÞ / exp − ð2:64aÞ 2σ 2 with its complex degree of coherence given by 2 2 σ τ γðτÞ / exp − e jω0 τ , 2 ð2:64bÞ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ where the FWHM of the power spectrum Δω is related to σ by σ ¼ Δω= 8 Â ln2.
72) as γAB ¼ hEÃ1A ðtÞE 1B ðtÞi hEÃ2A ðtÞE 2B ðtÞi þ : 2hE1A ðtÞj2 2 jE 2A ðtÞj2 ð2:73Þ Because both E1A(t) and E1B(t) come from the same source, their relationship must be E1B(t) ¼ E1A(t þ τ1); similarly, we will also have E2B(t) ¼ E2A(t þ τ2), where τ1 and τ2 are the time delays between the waves at point A and point B, respectively, from source 1 and source 2. 74) shows that γAB depends on the complex degree of coherence of the two source points. If the light emitted from the two point sources is quasi-monochromatic, we can use the result from Eq.
Introduction to Modern Digital Holography: With Matlab by Poon T.-C., Liu J.-P.