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The talk is devoted to the correlation properties for bipartite optical systems. In the first part we report an experimental approach to entanglement characterization in high-dimensional quantum systems using Schmidt decomposition techniques as well as physical properties of the Schmidt decomposition. A particular experiment uses spatial degrees of freedom of biphotons. We present a technique to realize projective measurements in Schmidt basis, allowing us to measure the coefficients in Schmidt decomposition and to estimate the degree of entanglement directly. Issues of modeling the spatial part of biphoton amplitude with simple double-Gaussian functions are discussed and shown to be in good agreement with experimental results. The second part of the talk relates to investigation of mode structure of the thermal light beam. We apply the developed technique [1] to quasi-thermal light and discuss close analogy between quantum and classical correlations. Usual Hanbury Brown and Twiss scheme is used for revealing intensity correlations of the quasi-thermal source (rotating ground disk). After proper preparation of the thermal light beam by means of appropriate lenses and apertures we introduce the spatial light modulator (SLM) followed by single-mode fiber in one arm of intensity interferometer followed by single-mode fiber. The other channel of the interferometer is supplied with single-mode fiber which might be scanned in the transverse direction(s). Switching by SLM between different Hermite-Gauss modes we check the angular correlation function in the fourth order in the field. The preliminary results show that there is no correlations ( ) between orthogonal modes while choosing the same modes the corresponding meaning reaches its maximal weighted value .