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Light sheet fluorescence microscopy or selective plane imaging microscopy (SPIM) uses illumination that is done perpendicularly to the direction of observation, by using a thin sheet of (laser) light. Under certain conditions, this illumination principle can be combined with fluorescence correlation spectroscopy, to allow spatially resolved ...
In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. [1] The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an upper envelope and a lower envelope. The envelope function may be a ...
The Morlet wavelet filtering process involves transforming the sensor's output signal into the frequency domain. By convolving the signal with the Morlet wavelet, which is a complex sinusoidal wave with a Gaussian envelope, the technique allows for the extraction of relevant frequency components from the signal.
Comparison of Gaussian (red) and Lorentzian (blue) standardized line shapes. The HWHM (w/2) is 1. Plot of the centered Voigt profile for four cases. Each case has a full width at half-maximum of very nearly 3.6. The black and red profiles are the limiting cases of the Gaussian (γ =0) and the Lorentzian (σ =0) profiles respectively.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
3d plot of a Gaussian function with a two-dimensional domain. Base form: (,) = In two dimensions, the power to which e is raised in the Gaussian function is any negative-definite quadratic form. Consequently, the level sets of the Gaussian will always be ellipses.
A hyperbolic secant (sech) envelope soliton for water waves: The blue line is the carrier signal, while the red line is the envelope soliton. Dispersion and nonlinearity can interact to produce permanent and localized wave forms. Consider a pulse of light traveling in glass.
Frequency histogram (Preston plot): x-axis: logarithm of abundance bins (historically log 2 as a rough approximation to the natural logarithm) y-axis: number of species at given abundance. Rank-abundance diagram (Whittaker plot): x-axis: species list, ranked in order of descending abundance (i.e. from common to rare)