Enhancement factor in wavefront shaping depends on the spatial resolution of a spatial light modulator (SLM) and on the modulation type. For a given resolution, phase modulation provides better enhancement than amplitude modulation, and thus is more preferable. In order to make wavefront shaping practical, it is important to provide the highest possible refresh rate of SLM. Liquid crystal SLMs are known for their outstanding phase modulation capabilities but their speed usually does not exceed a few hundred hertz. Meanwhile, digital micromirror devices (DMDs) can reach the refresh rates of 20 kHz that meets demands of practical applications. Although the refresh rate is high, this kind of the SLM can operate only in binary amplitude mode. In this paper we consider conversion of binary amplitude modulation into phase modulation by removal of zero spatial frequency from the modulated beam with respect to the application in wavefront shaping. We demonstrate experimentally increasing enhancement factor in 1.5 times (theoretically up to 2-fold). The advantage of considered method is its simplicity as it requires only a telescopic system and a simple spatial filter. In our case, it did not require any modification of the existing setup except the addition of the removable filter. Also, the considered method is suitable for any kind of spatial light modulator and is not limited to DMD. The obvious benefit of the modulation conversion is that we can use fewer modes to achieve the same enhancement factor and thus increase the focusing speed.
Wavefront shaping technique makes it possible to overcome limitations for optical imaging in strongly scattering media. Various wavefront shaping algorithms are used in order to find an optimal incident optical field. However, in many cases such experiments appear to be very time consuming and suffer from instability of the scattering media. So, it seems reasonable to use computer simulation in this field. In this paper we use two different approaches to simulate the light focusing through scattering media. The first approach consists in numerical solution of Maxwell equations for the set of spherical particles in random positions, which represent the scattering media. The result of the solution represents the scattering matrix of the media. This matrix is used to simulate propagation of spatially modulated light in the “frozen” stochastic media. As entries of the scattering matrix appear to be random variables with Gaussian distribution, they could be set heuristically for modeling purposes. This makes possible modeling of the wavefront shaping with large number of orthogonal modes of incident light. We considered four focusing techniques: continuous sequential algorithm and focusing using useful properties of Hadamard matrix with a phase-only and binary amplitude modulation (BAM). We represent results on convergence of the algorithms and focal intensity enhancement. We examined spatial variations of intensity enhancement, while scanning the focal point in observation plane. We found, that the intensity enhancement strongly correlates with the speckle from unmodulated illumination, when the BAM is used for wavefront shaping. In the case of phase-only modulation, only weak correlations were observed.
Wavefront sensing techniques with local slopes measurement (the Shack-Hartmann sensor or the similar one based on the Talbot effect) involve a reference wave, which is supposed to be of well-known shape (plane or spherical). But sometimes the reference wave can’t be formed easily, for example, in X-ray measurements. A reference-free wavefront reconstruction based on the Talbot sensor is discussed in the paper. The spot images are formed in several sequential planes due to the Talbot effect. It allows reconstruct the wave front from two object images in nearby planes without a reference. The self-reproduction phenomenon takes place in a wide wavelength range, so field of use of the Talbot sensor can be significantly expanded. Experimental results of the reference-free reconstruction of a 2nd order aberration of optical wave have been compared with the classical approaches for the Shack-Hartmann and Talbot sensors.
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.
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.
The possibilities of wavefront curvature measuring by Talbot sensor are theoretically and experimentally investigated. A new method of wavefront aberrations measurement is proposed and demonstrated. It is based on the observation of the Talbot effect when the diffraction grating is adapted to the wavefront curvature of the analyzed wave. Herewith, the observation plane stay fixed and corresponds to the Talbot length for a plane wave. It is shown that the measurement range can be made several times wider, with the help of the adaptive Talbot sensor, by retaining the required angular sensitivity. A possibility of self-reproduction of the rectangular grating (with different periods along the axes) by the astigmatic wavefront is experimentally demonstrated. The possibility of the experimental realization of the adaptive Talbot sensor using the dynamic spatial light modulator is demonstrated.
When a diffraction grating is illuminated with the plane parallel light beam, its image is self-reproduced at the certain distance. This phenomenon is known as the Talbot effect. A smooth aberration of the incident light beam causes the appropriate deformation of the self-reproduced image, which is characterized with the field of local displacements. These displacements could be used to estimate the local slopes of the distorted wavefront and to restore its shape. In this paper we analyze the limitations of the local slope estimation from the self-reproduced image of the gratings with various amplitude transparency functions (binary with various fill factors, cosine) and discuss on the best choice of the grating profile for the wave-front sensing applications.
In this paper we present the results of experimental investigation of wave-front distortion by anisotropic TeO2 Bragg cell with off-axial geometry. The measurements have been carried out using Shack-Hartmann wave-front sensor at visible wavelength (0.63 mkm) over the frequency range from 85 to 115 MHz. We have not noticed the significant dependence of phase distortion on frequency, nevertheless, they are in significant excess of measurement errors.
In sight correction technologies, it is of extreme importance to know what outcome of the planned operation could be. Conventionally, cornea shape is measured, or even refraction distribution in the eye, that are used for calculations of the to-be-ablated cornea layers. Unfortunately, different obstacles could arise, involving errors in these calculations. We propose another approach of measuring the to-be-inserted aberrations that would compensate for existing aberrations to get maximal sight acuity. The approach is based on measurements of wave front aberrations at the exit of an eye and iterative procedure of phase conjugation of the wave front, entering the eye. As a result of the procedure, an optimized point spread function is achieved. Shack-Hartmann sensors are used for wave front measurements, and spatial modulators -- for wave front control. Local slopes of wave front being measured, Wiener-type filtering helps to reconstruct the wave front itself. The results are reported of single-pass and double-pass modeling with experimental setup and computer simulation.
A modified double-pass wave model is proposed being a wave diffraction model of the secondary coherent field formed due to double pass of light in the human eye system. The modification takes into account: cornea contribution into total eye refraction, coherent nature of light reflection from the retina, and non-additive character of the cornea and lens aberrations. Irreversibility and anisoplanatism of the optical eye system follow from this study concurrently with the fact that the coherent point-spread function of double pass is not the autocorrelation of single-pass point- spread function. We used Hartmann-Shack wave front sensor and found it to be a promising technique for eye aberrations study: refraction map of the whole eye aperture can be reconstructed from a single-pulse information, presenting essential advantage as compared with point-by-point measurements. TV image of spot pairs can be got with CCD camera, its lens being replaced with lenslet array. Image processing consists in distance calculation between corresponding spot pairs. We use two-pulse exposure for this purpose: one--for producing a reference set of spots, the second one--for getting the spots produced by a distorted wave front. The sensitivity of this technique is estimated to be of the order of several percents.
KEYWORDS: Critical dimension metrology, Phase shift keying, Compact discs, Modulation, Signal processing, Signal detection, Optical signal processing, Transparency, Signal analyzers, Binary data
Structural correlation analysis is carried out for 1D signals, represented as phase images. For LFM signals, mapped into generalized phase plane with coordinates x equals S, y equals S"/S, sensitivity of correlation analysis to staggering of deviation frequency is invariant to impulse duration and increase with increase of carrier frequency and decrease of initial deviation. Phase representation of LFM signals essentially improves the sensitivity of coherent optical processing in comparison with binary raster representation.
In the present paper the theory and experimental study of the changing of polarization of Gauss light beam scattered by a thin slab of identical spherical particles is presented. Theory study of the scattered process is based on the following suppositions: there is a single scattered event; the scattered source is a point like; polarization changings in scattered event were described by conforming amplitude scattering Mie matrix. It is shown that there exists a good agreement between theoretical and experimental results.
During ill-posed inverse problem solution authors discussed consecutive technology of account known a priori information. In the present paper they realized this technology as the unique filtration procedures of singular components or CK-components. Sample correlation and distortion operator are used for singular codebook calculation. Correlation and level of noise are used for regularization. The application of this technique for more complex stochastic objects will be subject in future investigations.
In this paper, we investigate the problem of optimal (feature) selection for texture recognition for the case, when statistical properties of the image general population are satisfactorally represented by the a prior classified training set of small size (i.e. the number of images in the training set is much smaller then the number of pixels on the image). We examine criteria, defined by the trace norm of the certain self-conjugate operator, constructed in the special manner from the elements of the training set. Karhunen-Loeve expansion, Hoteling criteria, and some of their modifications are considered for recognition of computer generated regular textures, distorted with white noise. Comparative analysis of criteria efficiency is presented for several possible kinds of classification of the training set.
For superresolving image restoration it is suggested to use unsymmetrical matrix representation of image system's pulse response function in Karhunen-Loeve basis. Basic functions of such representation are defined by Karhunen-Loeve decomposition of object and image ensembles. Finite dimensional projection of initial and distorted images on their Karhunen-Loeve bases decreases the order of inverse problem matrix, minimizes noise and ensures stable superresolved restoration of large dimension images under high noise level, when application of traditional superresolving procedures is impossible.
In the paper it is considered the problem of eigenmode conversion in optical waveguides with inhomogeneous boundaries of dielectric layers. Random boundary profile is treated as fluctuations of refraction index in boundary layer. The intensity of depolarized scattered light is expressed through dispersion and correlation radius of dielectric layer boundaries. Both longitudinal and transversal correlations of boundary profile are taken into account, therefore obtained results are true for a case of arbitrary variations of electromagnetic field in space of fluctuation size.
KEYWORDS: Computing systems, Digital holography, Electronic filtering, Holography, Optical filters, Signal processing, Data processing, Image processing, Analog electronics, Optoelectronics
In this research we have generalized the experience of the optical data processing laboratory on investigation, elaboration, and design of the multifunctional hybrid optical-electronic systems, which may be used for analysis and recognition of images, textures, and wide-band time signals.
Harnessing phased acoustic arrays for extending the operating range of optical deflectors is well known and investigated by a number of researchers. Usually, it was supposed, that acoustic waves are excited in contra-phase, or with phase difference linear dependent on wave frequency. These modes of excitation are easily achieved in deflectors of simple design, but they do not provide strict consistency between acoustic wave front and Bragg angle when scanning the optical beam. To investigate possibilities of multielement deflector with individual control of channels in phased acoustic array we examined light diffraction on a sequence of ultrasonic waves in isotropic medium.
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