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"Aperture" is just another word for opening, especially the opening in optical devices. Consider this image of a wave going through an aperture and getting diffracted: (image from Wikipedia - Diffraction) For devices with structures that have dimensions very much larger than the wavelength As you probably know: When the object structures are not ...


Suppose we apply this integral to $S$ of size much smaller than wavelength of light and much smaller than $z-z_1$. In this case the wavefront will coincide with $S$, by construction. Now consider a set of such small apertures $\{S_i\}_{i=1}^N$ on an arbitrary surface $T$. By superposition principle, the final EM field originating from $T$ will be the sum of ...


You could accomplish this with two lenses. The first, a spherical lens, would be selected to give you the large horizintal angular spread that you want. The second, a cylindrical lens, would be oriented with its axis horizontal and could be placed either before ir after the spherical lens. Adjusting the distance between the two lenses would adjust the ...


Assuming this is a CW laser operating between 400nm-700nm: $E$ (our irradiance) is taken to be the MPE (maximum permissible exposure) of a Class 2 laser: $1.8T^{-0.25} \times 10^{-3} \text{ watts/cm}^2$ Our NOHD will be: $$D_{\text{NOHD}}=\frac{\phi}{w\times\theta\frac{\pi}{180}\times1.8T^{-0.25} \times 10^{-3} \text{ W/cm}^2}$$ where $w$ is our beam width (...


No, the coherence length cannot be derived from the field equation. Or rather, the equation is an approximation, made with the assumption of infinite coherence length. A real source will have $\omega$ (and thus $k$) varying at least slightly over time. It's the characteristic period of this variation of $\omega$ that produces a finite coherence length.


This is just a way of speaking, using the analogy with a well understood case of plane wave. As long as you understand what stands behind this (i.e. the equations that you wrote), this results in no ambiguity.

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