Line spread function formulation proposed by W. H. Steel: a revision.
A revised formulation of the image light distribution of an incoherent line source proposed by Steel [Rev. Opt. 31, 334-340 (1952)] is presented. Analytical and numerical results based on this new representation are given. We explicitly show that a major error in Steel's final expression generates singularities, thereby preventing convenient numerical computation.
Exploring the precision of backlight optical imaging in microfluidics close to the diffraction limit
Abstract We evaluate the precision of backlight optical imaging to locate the position of a free surface close to the diffraction limit. For this purpose, we acquired and processed images of liquid films at equilibrium deposited on a capillary 10 μm in diameter. The detected contours were compared with the solution of the exact Young–Laplace equation. Deviations of about 10 nm were obtained, which constitutes the first quantitative validation of backlight optical imaging for fluid shapes a few microns in size. The local mean curvature measured in the experiments agreed remarkably with the theoretical values. We illustrate the applicability of this technique by analysing five interfacial phenomena: (i) the flow in the tip of a capillary tapering meniscus formed by flow focusing, (ii) the extensional deformation of viscous micro-jets by the action of a co-flowing gas stream, (iii) the growth of small-amplitude capillary waves on a micro-jet free surface, (iv) the flow in the tip of a capillary tapering meniscus produced by electrospray, and (v) the characterization of glass micro-nozzles.
On the Theory of the Directional Patterns of Continuous Source Distributions on a Plane Surface
This paper contains a study of the directional patterns which may be obtained by driving a plane surface with specified normal velocities. Part I is devoted to the general theory of such distributions. The directional pattern at any distance from an arbitrary continuous distribution of sources is first obtained. The approximate relation which holds at large distances is then derived, and the simpler formulae which hold when the surface distribution has several different kinds of symmetry are developed. In particular, the case is studied in which the sources are distributed along a line. An interesting relation between linear distributions and those with circular symmetry is pointed out. Part II contains the derivations of a number of directional patterns corresponding to specific source distributions. It is pointed out that although it is easy to specify a source distribution which will yield any directional pattern satisfying certain methematical conditions of convergence, such distributions are usually of infinite extent, and therefore do not correspond to distributions which are of practical interest. A method of attack is suggested for the problem of determining the distribution of specified extent which yields the directional pattern of optimum characteristics for any particular application. Part III contains 22 tables, 21 of which are tables of the directional patterns of the source distributions considered in Part II. In addition to the column giving the argument, each of the 21 tables contains three columns, the first giving the relative sound pressure, the second the square of the relative sound pressure, and the third, ten times the common logarithm of the inverse square of the relative sound pressure. Table II, which is more detailed than the others insofar as the interval is smaller, is a table of the directional pattern of a circular piston.