<title>Inverse problem of heterodyne differential microscope for steplike object</title>

Abstract

The solution of inverse problem of heterodyne differential microscope based on representation of linear part of microscope response by moments of object function is realized. The parameters of step-like object was determined with superresolution.

Study of the Distribution and Modification of Writing in Proto-Chinese Language Communities: Correct Identification of Hieroglyphic Signs in the Jiaguwen Inscriptions

“…Recall that our method is based on photometry of surface profiles, in which a sampling of brightness levels in a discrete set of points is carried out, followed by conversion into digital form [12,13]. The obtained data (optical response) are digitally processed in order to determine the characteristics and parameters (including statistical ones) characterizing the properties of the investigated surface [12][13][14][15]. As a result, from the digitized distribution of the intensity of the light scattered by the surface, one can find, for example, the form of the approximating ACFs, and also determine the corresponding statistical parameters of the roughness of the profiles of the studied surface: the standard deviation and the correlation radius (see details in [9][10][11][12][13]).…”

“…The mathematical model of the groove in the optical range of wavelengths can be described by the following expression (see e.g. [14]):…”

“…In particular, if the illumination wave is plane and the projection of the modulus of the wave vector on the plane of the object q = 0, then the reflected wave is determined by one column of the scattering matrix. Then the object can be characterized by the local reflection coefficient r , which depends only on the object shape function, which is, in fact, the Fourier transform of the scattering amplitude [14]. It is this method of the signal registration that was used in this paper.…”

“…When illuminated by a focused wave, an object can also be described by a local reflection coefficient if such a registration scheme is chosen, in which only one (for example, normally reflected with a projection ' q = 0) plane wave is recorded. Then the object is described by one row of the scattering matrix, and the corresponding local reflection coefficient is determined by a similar dependence (for more details, see, for example, in [14]).…”

“…However, in the first case, to solve the inverse problem of reconstructing the groove profile, it is necessary to use complex methods of recording the real and imaginary parts of the nonlinear response. For example, register the amplitude and phase of a complex response or a correlation signal that requires the development of complex algorithms for its processing (see, for example, [14]). As a rule, this problem arises when solving various problems of super-resolution, i.e.…”