Current paper considers light focusing through strongly scattering medium using binary amplitude modulation of the incident light. The focusing was performed using a simple sequential algorithm. It consisted of the successive estimation of the influence of every pixel of the spatial light modulator on the intensity of the focal spot and making the decision on its target state. Also, noise characteristics of the imaging system camera-frame-grabber were estimated with further investigation of their influence on the focusing quality. Modulation of the incident light was performed by the liquid crystal spatial light modulator. For more efficient usage of the incident beam energy, pixels were combined in groups (so-called superpixels) and were controlled as one separate segment. We estimated the influence of the size of superpixel on the intensity enhancement in the focal spot maintaining the constant size of the illuminated area. The focusing at different distances behind the sample was performed. It was shown that the size of the focal spot at small focusing distances is determined by the properties of the imaging system lens. Starting from some certain distance, the size of the focal spot depends on the focusing distance and the size of the illuminated area of the sample. Hence, the scattering medium operates like a lens.
We introduce a definition of 2N-order polarization and apply this definition for analysis of general effects of the anisotropy of optical radiation. As an initial definition, we use a set of polarization matrices of order 2N, which are considered as statistical means of the Kronecker N-fold second-order tensors: g[1,1]= E+ ⊗E. Evidently, this set contains all paired mixed moments of polarization components, thus determining all possible polarization properties of the above-defined field. Furthermore, any unitary (non-depolarizing) transform in Jones vector space corresponds to the unitary transform of polarization matrix of higher orders, and therefore does not change polarization of any order. This notion allows us to determine a degree of polarization P[N] for higher order using invariants of unitary transforms of a corresponding polarization matrix. The concept of higher order polarization is applied to the problems of photon counting, intensity interferometry and nonlinear optics.
The present study is concerned with wavefront shaping algorithms and their performance in noisy environments. Simple sequential algorithms has quite low initial enhancement rate which makes it hard to overcome strong noise. As a result, more complex algorithms which use multiple spatial light modulator pixels were developed. It made it possible to overcome noise at the initial stage faster. One of such algorithms is the partitioning algorithm. The maximum length sequence algorithm considered in this paper is proposed as an improvement of the partitioning algorithm. Both algorithms have similar initial enhancement rates but the proposed one keeps higher rate also at later stages.
The features of the Talbot effect using the phase diffraction gratings have been considered. A phase grating, unlike an amplitude grating, gives a constant light intensity in the observation plane at a distance multiple to half of the Talbot length ZT. In this case, the subject of interest consists in so-called fractional Talbot effect with the periodic intensity distribution observed in planes shifted from the position nZT/2 (the so-called Fresnel images). Binary phase diffraction gratings with varying phase steps have been investigated. Gratings were made photographically on holographic plates PFG-01. The phase shift was obtained by modulating the emulsion refraction index of the plates. Two types of gratings were used: a square grating with a fill factor of 0.5 and a checkerwise grating (square areas with a bigger and lower refractive index alternate in a checkerboard pattern). By the example of these gratings, the possibility of obtaining in the observation plane an image of a set of equidistant spots with a size smaller than the size of the phase-shifting elements of the grating (the so-called Talbot focusing) has been shown. Clear images of spots with a sufficient signal-to-noise ratio have been obtained for a square grating. Their period was equal to the period of the grating. For a grating with a checkerwise distribution of the refractive index, the spots have been located in positions corresponding to the centres of cells. In addition, the quality of the resulting pattern strongly depended on the magnitude of a grating phase step. As a result of the work, the possibility to obtain Talbot focusing has been shown and the use of this effect to wavefront investigation with a gradient sensor has been demonstrated.
The present study considers ab initio computer simulation of the light focusing through a complex scattering medium. The focusing is performed by shaping the incident light beam in order to obtain a small focused spot on the opposite side of the scattering layer. MSTM software (Auburn University) is used to simulate the propagation of an arbitrary monochromatic Gaussian beam and obtain 2D distribution of the optical field in the selected plane of the investigated volume. Based on the set of incident and scattered fields, the pair of right and left eigen bases and corresponding singular values were calculated. The pair of right and left eigen modes together with the corresponding singular value constitute the transmittance eigen channel of the disordered media. Thus, the scattering process is described in three steps: 1) initial field decomposition in the right eigen basis; 2) scaling of decomposition coefficients for the corresponding singular values; 3) assembling of the scattered field as the composition of the weighted left eigen modes. Basis fields are represented as a linear combination of the original Gaussian beams and scattered fields. It was demonstrated that 60 independent control channels provide focusing the light into a spot with the minimal radius of approximately 0.4 μm at half maximum. The intensity enhancement in the focal plane was equal to 68 that coincided with theoretical prediction.