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Its impulse response is defined by a sinusoidal wave (a plane wave for 2D Gabor filters) multiplied by a Gaussian function. [6] Because of the multiplication-convolution property (Convolution theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function (sinusoidal function) and the Fourier transform of the Gaussian ...
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A blazed diffraction grating reflecting only the green portion of the spectrum from a room's fluorescent lighting. For a diffraction grating, the relationship between the grating spacing (i.e., the distance between adjacent grating grooves or slits), the angle of the wave (light) incidence to the grating, and the diffracted wave from the grating is known as the grating equation.
The parameters of the filters are designed by proper choice of the grating parameters. The advantage of such filters are the few layers needed for ultra-narrow bandwidth filters (in contrast to dichroic filters), and the potential decoupling between spectral bandwidth and angular tolerance when more than 1 mode is excited.
A special form of a blazed grating is the echelle grating. It is characterized by particularly large blaze angle (>45°). Therefore, the light hits the short legs of the triangular grating lines instead of the long legs. Echelle gratings are mostly manufactured with larger line spacing but are optimized for higher diffraction orders.
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).
A grating can be defined by six parameters: Spatial frequency is the number of cycles occupying a particular distance (e.g. 10 line pairs per millimeter). The period of the grating is the inverse of the spatial frequency, measured in distance (e.g. 0.1 mm). Duty Cycle is the relative thickness of high and low lines. The duty cycle is the ratio ...
The AWGs consist of a number of input (1) and output (5) couplers, a free space propagation region (2) and (4) and the grating waveguides (3). The grating waveguides consists of many waveguides, each having a constant length increment (ΔL). Light is coupled into the device via an optical fiber (1) connected to the input port.