## 1 Introduction  
Currently, optical diagnostic techniques are essential experimental tools employed in a large and diverse set of research and industrial applications. Based on measurements of scattering intensity and light extinction, a number of these techniques are able to determine the parameters of scattering particles, such as size, shape, and concentration [1]. Examples of applications are numerous: in meteorology, the measurement of atmospheric constituents is performed by analyzing the backscattering light signal via the LIDAR (Light Detection and Ranging) technique [2]. In oceanography, marine picoplankton is characterized from the laser light scattered by the illuminated particles [3]. The optical radiation is actively used in various bio-medical applications as a non-invasive diagnostic tool, as well as to treat a number of diseases [4]. During the past three decades, the investigation of laser light propagation in skin tissue and the human brain has been particularly extensive [4; 5; 6; 7; 8; 9; 10]. In combustion engineering, a variety of laser-based diagnostics have been developed over more than three decades in order to determine the physical properties of fuel droplets from atomizing sprays [6]. These optical measurements are of fundamental importance in the improvement of combustion efficiency and in the reduction of pollutant emissions from modern internal combustion engines and gas turbines. Another field where optical diagnostic techniques are of particular significance is free-space transmission of energy or information, namely, free-space optical communications, wireless energy transfer through the scattering and turbulent atmosphere, imaging objects through scattering atmospheric aerosol, space debris removal, etc. One of the limitations of the optical techniques is related to the radiation attenuation and scattering. Under optically thick conditions, the scattering can significantly decrease the quality of the beam and thus introduce errors in measurements. However, it is necessary not only to simulate the propagation of the radiation through the medium but also to establish techniques to measure the beam distortions introduced by that medium. Measuring laser beam distortions is one of the existing problems that has to be solved. Another problem that is also of great importance is compensating measured distortions. As is known, in a turbid medium, a part of a laser beam energy is absorbed while the rest is scattered. This scattered light makes objects look blurred and degrades beam-focusing efficiency. There are a wide variety of applications for which the solution of the problem is very important, i.e., wireless data transmission, pattern recognition, and medical noninvasive diagnosis, among others [11; 12]. The wavefront-shaping technique to focus the radiation that propagates through a strongly scattering layer was developed back in 2007 [13]. The authors used the SLM and were able to properly shape the wavefront to focus the radiation through scattering objects. Various techniques have been developed since 2007 to resolve the focusing of light through scattering media [14; 15]. Authors of [16] showed the ability to obtain clear images of objects by means of holographic techniques that reverse a scattering process. Authors of [17] use coherence and spatial gating to produce images of optical properties of a tissue up to 9-mm deep with millimeter-scale resolution via a technique known as multispectral multiple-scattering low-coherence interferometry. Imaging of fluorescent objects when the space behind a scattering medium is limited can be achieved using the technique described in [18]. SLM can be used to obtain images of objects located within or behind a scattering layer [19; 20; 21; 22]. In [23], authors demonstrated a steady-state focusing of coherent light through dynamic scattering media. In [24], authors demonstrated the use of the method of inversion of transmission matrix. They proved that the focus' peak-to-background intensity ratio can be higher compared to conventional methods.