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# 物理代写|光学代考Optics代写|PHYS202 Transverse spatial coherence of light

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## 物理代写|光学代考Optics代写|Transverse spatial coherence of light

Based on the Van Cittert-Zernike theorem, derive an expression for the normalized transverse spatial coherence function $\gamma(\Delta x, \Delta y)$ of the optical field with wavelength $\lambda_0$ at the distance $z$ from spatially extended incoherent light source $\mathrm{S}$ having a rectangular shape with sides $a$ and $b$. The source has a uniform distribution of radiation intensity $I(x, y)=I_0$ over the surface. From the obtained expression for $\gamma(\Delta x, \Delta y)$, derive the formulae for determining the dimensions of the domain of transverse spatial coherence of the field, i.e., the optical field transverse coherence lengths $\rho_{c x}$ and $\rho_{c y}$ along the axes $x$ and $y$, respectively.

A quasi-monochromatic beam of light with mean wavelength $\lambda_0 \approx 628 \mathrm{~nm}$ is produced by an extended spatially incoherent source $S$ having the shape of a round disc with diameter $D=4 \mathrm{~mm}$. Determine the maximal spacing $\Delta \rho_c$ between the points $\mathrm{P}_1$ and $\mathrm{P}_2$ in the plane $(x, y)$ in which the beam of light excites partially mutually coherent oscillations. The plane $(x, y)$ is perpendicular to the direction of the beam propagation and is located at distance $z=1 \mathrm{~m}$ from the source S.

## 物理代写|光学代考Optics代写|Longitudinal spatial coherence of light

For a quasi-monochromatic optical field with sufficiently narrow frequency spectrum and relatively wide angular spectrum, the longitudinal coherence length of the field (along the direction of propagation) is mainly determined by the width of the angular spectrum $2 \theta$ rather than by the width of the frequency spectrum $\Delta \omega$, as for a quasi-collimated light beam. Determine the temporal coherence length $l_c$ and the longitudinal coherence length $L_c$ of such a field with mean wavelength $\lambda_0 \approx 0.65 \mu \mathrm{m}$ and spectral width $\Delta \lambda \approx 0.001 \mu \mathrm{m}$ at distance $z=80 \mathrm{~mm}$ from a round spatially incoherent light source with diameter $D=20 \mathrm{~mm}$.

The coherence of an optical field in the longitudinal direction, i.e., in the direction of the light propagation,is equally dependent on the parameters of the frequency and the angular spectra of the field. This may lead to a reduction of the longitudinal coherence length of the field $L_c$ as compared to the temporal coherence length $l_c$, determined by the frequency spectrum width $\Delta \lambda$, and as compared to the spatial coherence length $\rho_{c z}$, determined by the width of the angular spectrum $2 \theta$ of the field. Plot the longitudinal coherence length $L_c(z)$ of the field versus the distance $z$ from an extended spatially incoherent light source $S$ having a round shape with diameter $D=5 \mathrm{~mm}$. The source radiates the light with mean wavelength $\lambda_0 \approx 0.55 \mu \mathrm{m}$ and frequency spectral width $\Delta \lambda \approx 0.02 \mu \mathrm{m}$. Determine the temporal length $l_c$ and the longitudinal coherence length $L_c$ at distance $z=$ $9.3 \mathrm{~mm}$ from the light source.

# 光学代写

## 物理代写|光学代考Optics代写|Longitudinal spatial coherence of light

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