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The Talbot effect is a diffraction effect first observed in 1836 by Henry Fox Talbot. [1] When a plane wave is incident upon a periodic diffraction grating, the image of the grating is repeated at regular distances away from the grating plane. The regular distance is called the Talbot length, and the repeated images are called self images or ...
For a better understanding of the process, it is necessary to understand interference and diffraction. Interference occurs when one or more wavefronts are superimposed. Diffraction occurs when a wavefront encounters an object. The process of producing a holographic reconstruction is explained below purely in terms of interference and diffraction.
The interference signal of a pixel has maximum modulation when the optical path length of light impinging on the pixel is exactly the same for the reference and the object beams. As before, the z-value for the point on the surface imaged by this pixel corresponds to the z-value of the positioning stage when the modulation of the correlogram is ...
In 1818, Fresnel [5] showed that Huygens's principle, together with his own principle of interference, could explain both the rectilinear propagation of light and also diffraction effects. To obtain agreement with experimental results, he had to include additional arbitrary assumptions about the phase and amplitude of the secondary waves, and ...
Diffraction is the same physical effect as interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed. [1]: 433 Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
This equation, Bragg's law, describes the condition on θ for constructive interference. [12] A map of the intensities of the scattered waves as a function of their angle is called a diffraction pattern. Strong intensities known as Bragg peaks are obtained in the diffraction pattern when the scattering angles satisfy Bragg condition.
which is the generalized diffraction grating equation. Here, θ m is the angle of incidence, φ m is the angle of diffraction, λ is the wavelength, and m = 0, 1, 2... is the order of diffraction. Under certain conditions, d m ≪ λ, which can be readily obtained experimentally, the phase term becomes [7] [10]
Because diffraction is the result of addition of all waves (of given wavelength) along all unobstructed paths, the usual procedure is to consider the contribution of an infinitesimally small neighborhood around a certain path (this contribution is usually called a wavelet) and then integrate over all paths (= add all wavelets) from the source to the detector (or given point on a screen).