Optical incoherent space frequency

The method for obtaining particle size distributions using optical incoherent space frequency analysis is detailed in [209,210] and resulted in the development of a low price, robust, on-line dry powder measuring system, the Jenoptik PSl-Z, (Particle Sizing using Incoherent light) which covered 32 size intervals in the range 1.5 pm to 2 mm. This was later expanded to 0.7 to 2500 pm [211]. For particles smaller than 50 pm a dispersion nozzle had to be fitted. 

Optical Space-Frequency Analysis fl91 Scattering from masked incoherent light Sizing Flow... 

Measured Performance. Under the conditions of space invariance and incoherence, an image can be expressed as the convolution of the object irradiance and the point-spread function, Eq. (26.15). The corresponding statement in the spatial frequency domain, Eq.(26.28), is obtained by taking the Fourier transform of Eq. (26.15). This states that the frequency spectrum of the image irradiance equals the product of the frequency spectrum of the object irradiance distribution and the transform of the point-spread function. In this manner, optical elements functioning as linear operators transform a sinusoidal input into an undistorted sinusoidal output [Eq. (26.33)]. Hence the function that performs this service is the transform of the point-spread function 3 A(x, y), known as the optical transfer function 0 u, v] (OTF). This is a spatial frequency-dependent complex function with a modulus component called the modulation tranter function M u. v] (MTF) and a phase component called the phase tranfer function 4>[ , v] (PTF). The MTF is the ratio of image-to-object modulation, while the PTF is a measure of the relative positional shift from object to image. 

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