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- W319317412 abstract "The development and implementation of cylindrical holography is derived from the time independent homogeneous Helmholtz equation for acoustic pressure, p, in cylindrical coordinates $$({nabla ^2} + {k^2})p(r,phi ,z) = 0$$(1), where k = w/c. In solving this equation an e -iwt time dependence is assumed and the method of separation of variables is used. Furthermore, it is assumed that the source is confined to a finite cylindrical band of radius, a, and length, l, in an infinite cylindrical baffle. Also, free-space propagation exists external to a so that at any r ≥ a$$p(r,phi ,z) = sumlimits_{n = - infty }^infty {{e^{inphi }}} int_{ - infty }^infty {{A_{n{k_z}}}} {H_n}^{(1)}({k_r}r){e^{i{k_z}z}}d{k_z}]$$(2), where ({k_r} = sqrt {{k^2} - k_z^2}) and the Hankel function of the first kind represents outgoing waves. By applying a two-dimensional Fourier transform to both sides of (2) and evaluating at r 0, the hologram radius, one obtains $${P_n}({r_0},{K_z}) = frac{1}{{2pi }}{A_{n{k_z}}}H_n^{(1)}({k_r}{r_0})$$(3)." @default.
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- W319317412 date "1988-01-01" @default.
- W319317412 modified "2023-09-27" @default.
- W319317412 title "An Examination of Aperture Effects in Cylindrical Nearfield Holography" @default.
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- W319317412 doi "https://doi.org/10.1007/978-1-4613-0725-9_26" @default.
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