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The general results presented above for Hamilton's principle can be applied to optics using the Lagrangian defined in Fermat's principle.The Euler-Lagrange equations with parameter σ =x 3 and N=2 applied to Fermat's principle result in ˙ = with k = 1, 2 and where L is the optical Lagrangian and ˙ = /.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
Principles of Optics, colloquially known as Born and Wolf, is an optics textbook written by Max Born and Emil Wolf that was initially published in 1959 by Pergamon Press. [1] After going through six editions with Pergamon Press, the book was transferred to Cambridge University Press who issued an expanded seventh edition in 1999. [ 2 ]
Hamilton's optico-mechanical analogy is a conceptual parallel between trajectories in classical mechanics and wavefronts in optics, introduced by William Rowan Hamilton around 1831. [1] It may be viewed as linking Huygens' principle of optics with Maupertuis' principle of mechanics.
So the Helmholtz principle is a more simply described special case of electromagnetic reciprocity in general, which is described by distinct accounts of the interacting electric and magnetic fields. The Helmholtz principle rests mainly on the linearity and superposability of the light field, and it has close analogues in non-electromagnetic ...
The resolution of a digital imaging device is not only limited by the optics, but also by the number of pixels, more in particular by their separation distance. As explained by the Nyquist–Shannon sampling theorem , to match the optical resolution of the given example, the pixels of each color channel should be separated by 1 micrometer, half ...
X-ray ptychography at a small-angle scattering beamline of a synchrotron. This x-ray ptychograph of a zone plate shows the luminosity data in image (a) and the phase data in image (b). Insets I, II and III from (b) are shown in (i), (j) and (k) respectively as processed in 2015; they show a clear improvement in resolution over the algorithms ...
When the hologram plate is illuminated by a laser beam identical to the reference beam which was used to record the hologram, an exact reconstruction of the original object wavefront is obtained. An imaging system (an eye or a camera) located in the reconstructed beam 'sees' exactly the same scene as it would have done when viewing the original.