Adaptive optics technique to overcome the turbulence in a large-aperture collimator

A collimator with a long focal length and large aperture is a very important apparatus for testing large-aperture optical systems. But it suffers from internal air turbulence, which may limit its performance and reduce the testing accuracy. To overcome this problem, an adaptive optics system is introduced to compensate for the turbulence. This system includes a liquid crystal on silicon device as a wavefront corrector and a Shack-Hartmann wavefront sensor. After correction, we can get a plane wavefront with rms of about 0.017 lambda (lambda=0.6328 microm) emitted out of a larger than 500 mm diameter aperture. The whole system reaches diffraction-limited resolution.     

Fringing fields in a liquid crystal spatial light modulator for beam steering

Abstract

Phase modulating spatial light modulators (SLMs) can be used to alter the shape of a laser wavefront to achieve a deflection or change in the shape of a laser beam. This paper reports the results of characterization, simulation and optimization of a one-dimensional liquid crystal (LC) SLM. The device has a large ratio between LC layer thickness and pixel pitch that results in a fringing field between pixels. In effect, the applied phase patterns will be lowpass filtered and the loss of high frequency components limits, for instance, the usable steering range. A method is presented where intensity measurements in the far field are used to determine how the phase modulation at the SLM is distorted. The inhomogeneous optical anisotropy of the device was determined by modelling the liquid crystal director distribution within the electrode-pixel structure. Finite-difference time-domain (FDTD) simulations were used to calculate the light propagation through the LC. The simulated phase distortion was compared with the experimental results. A voltage compensation scheme to improve the diffraction efficiency was developed utilizing the measured and simulated results. It is demonstrated that a modification of the voltage patterns can give a better realization of high frequency components in the phase distribution and an increase in maximum steering angle by a factor two.     

Interferences in light deflection by ferroelastic domain walls

Deflection of light is studied in a crystal of glycine phosphite containing two twin walls. When the crystal is rotated in the incident laser beam, interferences are observed in both the direct beam and in the main deflected beam (A or B) for both polarizations of the incident light. The contrast is especially high, because the mutual tilt angle of the principal axes is close to 45 degrees in this twinned crystal. On this principle, fundamental-harmonic beam splitters could be built from as-grown twin crystals. Furthermore, the electrical modulation of the light deflected by ferroelectric-ferroelastic crystals can be now explained in terms of interference effects.     

Theoretical analysis of tuning coherent laser array for several applications

Theoretical analysis for the far-field diffraction of the coherent laser array (CLA) is presented. Based on the theoretical model of the propagation of CLA, the conditions and restrictions for coherent beam combination, two-dimensional steering, and dark-hollow beam generation are theoretically described in detail. With properly organized phase distributions and tilt control, the peak location of the far-field pattern of the CLA could shift two-dimensionally in a large scale of steering angle. With additional amplitude modulation, the far-field pattern could have special shapes. The simulated results agree with the theoretical analysis. It is a feasible way to realize all these applications by a CLA with well-arranged phase distributions and/or additional amplitude modulation.     

Achromatic system for a twisted alignment liquid crystal wavefront corrector

A twisted nematic liquid crystal wavefront corrector (TN-LCWFC) partially modulates the incident polarized light. A blazed grating may be preapplied on the TN-LCWFC to filter the unmodulated light for the purpose of stable adaptive correction. However, for broadband light, the dispersion of the blazed grating affects the image resolution. An achromatic method is presented to eliminate the dispersion of the blazed grating. Based on a prism model, we analyze the achromatic principle. An achromatic system with a conjugated blazed grating and an achromatic lens is given to eliminate the dispersion. An experiment was done with two transmitted blazed gratings so as to validate our method. Finally, a liquid crystal spatial light modulator was used as a conjugated grating to eliminate the dispersion of the blazed grating in an adaptive optics system. The results showed that the dispersion was partially compensated, and a resolvable image was achieved with a 600-700 nm wave band.     

用于检测激光棒的变倾角马赫-曾德尔干涉仪

为实现激光棒透射波前的测量,改善一般泰曼型或斐索型干涉仪测量小口径激光棒透射波前时的边缘衍射效应,研究了一种变倾角移相马赫-曾德尔干涉仪。通过调整移相反射镜的倾斜姿态,改变入射到马赫-曾德尔干涉光路的光束倾角,参考光束与测试光束的光程差随之变化,从而在相干光之间引入相移,实现了相移干涉测量。利用该干涉仪测量一根口径为Ф6 mm、长度为60 mm激光棒(Nd:YAG)的透射波前,测量结果的峰谷值(PV)为0.391λ,均方根值(RMS)为0.056λ;使用ZYGO激光干涉仪测量同一根激光棒,其透射波前的峰谷值(PV)为0.370λ,均方根值(RMS)为0.064λ。对比结果表明该干涉仪能实现光学元件透射波前的高精度检测,测试结果的一致性验证了该方案的可行性。该变倾角移相方法具有较高的移相精度和较大的移相范围,且该变倾角干涉系统中光束仅一次透过待测激光棒,可有效抑制多光束干涉现象,改善小口径激光棒的边缘衍射效应。     

Open-loop correction of horizontal turbulence: system design and result

Adaptive optics systems often work in a closed-loop configuration due to the hysteretic and nonlinearity properties of conventional deformable mirrors. Because of the high-precision wavefront generation and nonhysteretic properties of liquid-crystal devices, the open-loop control becomes possible. Open-loop control is a requirement for advanced adaptive optics concepts. We designed an open-loop adaptive optics system with a liquid-crystal-on-silicon wavefront corrector. This system is simple, fast, and can save much more light compared to conventional liquid-crystal-based closed-loop systems. The detailed principle, construction, and operation are discussed. The 500 m horizontal turbulence correction experiment was done using a 250 mm telescope in the laboratory. The whole system can reach a 60 Hz correction frequency. Evaluation of the correction precision was done at closed-loop configuration, which is 0.2 lambda (lambda=0.633 microm) in peak to valley. The dynamic image under open-loop correction got the same resolution compared to closed-loop correction. The whole system reached 0.68 arc sec resolution capability at open-loop correction, which is slightly larger than the system's diffraction-limited resolution of 0.65 arc sec.     

Computer simulations of effects of disk tilt and lens tilt on push-pull tracking error signal in an optical disk drive

We quantify the effects of disk tilt and objective lens tilt on the push-pull tracking error signal of an optical disk data storage system. For a grooved disk, such as a recordable compact disk that operates at a laser wavelength of lambda, it is found that disk tilt produces a tracking offset of 0.05lambda per degree of tilt, whereas objective lens tilt produces an offset of 0.012lambda per degree of tilt. The amplitude of the tracking error signal decreases by 2.5% at the disk tilt angle of 0.3 degrees and by 5% at the objective lens tilt of 0.3 degrees . We achieved these simulations with the computer program Diffract, which performs a combination of diffraction and ray-tracing calculations through the entire optical path, from the light source to the detectors.     

Reflection and transmission of strongly focused light beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally, radially and linearly polarized electromagnetic wave beams with subwavelength spot size and wavefront curvature at a dielectric interface are investigated. For a given wavefront radius, the existence of the optimal radius of beam spot corresponding to a minimal reflectance and maximal transmittance is shown. Significant lateral shift in the transmitted intensity peak is revealed for strongly focused azimuthally and radially polarized beams that are normally incident to an interface. The reflection and transmission of transverse-electric- and transverse-magnetic- polarized extremely narrow wave beams which are obliquely incident on the dielectric interface is analysed. Disappearance of the Brewster angle and total internal reflection effects for the strongly focused beams are predicted. The change in beam profile after reflection and transmission for different polarizations, incident beam spots and incidence angles are analysed.     

Measurement of two-dimensional small angle deviation with a prism interferometer

A new technique for the measurement of two-dimensional small angular deviation is presented. A compound prism, which effectively produces a combination of two right-angled prisms in orthogonal directions, and plane reference surfaces have been utilized for the measurement of the orthogonal components of the angular tilt of an incident plane wavefront. Each orthogonal component of the angular tilt is separately measured from the angular rotation of the resultant wedge fringes between two plane wavefronts generated due to splitting of the incident plane wavefront by the corresponding set of right-angled prism and plane reference surface. The technique is shown to have high sensitivity for the measurement of small angle deviation. A monolithic prism interferometer, which is practically insensitive to vibration, is also proposed. Results obtained for the measurement of a known tilt angle are presented.     

Holographic display with tilted spatial light modulator

In this paper, we analyze a holographic display system utilizing a phase-only spatial light modulator (SLM) based on liquid crystal on silicon (LCoS). An LCoS SLM works in reflection, and, in some applications, it is convenient to use with an inclined illumination. Even with a highly inclined illumination, the holographic display is capable of good-quality image generation. We show that the key to obtain high-quality reconstructions is the tilt-dependent calibration and algorithms. Typically, an LCoS SLM is illuminated with a plane wave with normal wave vector. We use inclined illumination, which requires development of new algorithms and display characterization. In this paper we introduce two algorithms. The first one is designed to process a digital hologram captured in CCD normal configuration, so it can be displayed in SLM tilted geometry, while the second one is capable of synthetic hologram generation for tilted SLM configuration. The inclined geometry asymmetrically changes the field of view of a holographic display. The presented theoretical analysis of the aliasing effect provides a formula for the field of view as a function of SLM tilt. The incidence angle affects SLM performance. Both elements of SLM calibration, i.e., pixel phase response and wavefront aberrations, strongly depend on SLM tilt angle. The effect is discussed in this paper. All of the discussions are accompanied with experimental results.     

The influence of high-frequency phase and correction distance on the phase correction effect

By studying the propagation characteristics of the wavefront phase of laser beams in adaptive optics systems, the influence of the high-frequency phase on the correction effect has been analyzed and the variations of correction effect with the position of optical deformable mirror have been analyzed quantitatively. The results show that the beam quality of the corrected beam in far field obviously degrades with an increase of high-frequency phase in a distorted wavefront, and the correction effect becomes worse and worse. In addition, the correction effect is related to the position of the deformable mirror; with an increase of the distance between the deformable mirror and the output mirror of the laser the correction effect is better. For a deformable mirror with a given unit size, when the distance of correction is more than 20?m the correction effect is perfect.     

Wide angle conoscopic interference patterns in uniaxial crystals

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two crossed polarizers contains information that is inherent to the crystalline sample under study. The formation of fringe patterns is analyzed from distinct approaches and with different degrees of approximation considering cones of light of large numerical aperture. We obtain analytic explicit formulas of the phase shift on the screen and compare them with the exact numerical solution. The results obtained are valid for arbitrary orientation of the optical axis and are not restricted either to low birefringence or to small angles of incidence. Moreover, they enable the extraction of the main features related to the characterization of uniaxial crystal slabs, such as the optical axis tilt angle and the principal refractive indices.     

Full-field phase modulation characterization of liquid-crystal spatial light modulator using digital holography

A direct quantitative phase measurement method to characterize intrinsic phase modulation from an entire active area of transmissive twisted-nematic liquid-crystal spatial light modulator (TN-LCSLM) is presented using digital holography (DH). The change in birefringence of liquid crystal material with respect to addressed gray scale produces phase modulation of wavefront transmitted through TN-LCSLM. Existing methods for phase modulation characterization of LCSLM mainly provides point measurement on its total active region. In this paper, the DH method is evolved to extract quantitative phase information of an entire active area from a single digital hologram formed using the complex wavefront transmitted through TN-LCSLM.     

有结构扩展目标整体倾斜信息提取有效性实验

根据互相关因子算法和绝对差分算法的基本原理,利用Matlab实现了倾斜信息提取。在此基础上,考察了两种算法的精确性问题,发现绝对差分算法的拟合精度高于互相关算法,其数量级可达到0.0001像素;结合哈特曼波前传感器的测量结果,采用比对的方法,对有结构扩展目标两种算法提取倾斜信息的有效性进行了验证,可以得到,不同倾斜范围时两种算法提取的信息高度吻合,且处理后与哈特曼波前传感器走势一致;经自适应校正后,得到了很好的长曝光像。实验结果表明,这两种算法均可有效地提取出自适应光学所需要的光束波前整体倾斜信息。     

Static and dynamic two-wave mixing in GaAs

We studied the two-wave mixing anisotropic diffraction process in GaAs for demodulation of static and dynamic phase encoded signals. The static results quantitatively agreed with a previous theoretical model for cubic crystals. This model has been described explicitly for all beam polarizations and crystal rotation angles with respect to the plane of incidence. Dynamic phase modulation, in which the signal beam was phase modulated at frequency f(s) and the reference beam at f(r) = f(s) + Df, produced a signal at Df that was proportional to the difference between the static beam intensities with and without two-wave mixing under all conditions of polarization and crystal orientation studied. A significant dynamic output signal was produced even when only a shift in polarization but no energy transfer occurred as a result of the anisotropic two-wave mixing process. Therefore not only is the two-wave mixing gain important when the photorefractive effect is used for dynamic phase demodulation, but so are the polarization shifts occurring from the mixing process.     

Stressed liquid-crystal optical phased array for fast tip-tilt wavefront correction

A liquid-crystal optical phased-array technology that uses stressed liquid crystals provides a new type of tip-tilt wavefront corrector. It demonstrates a very fast time response (10 kHz) and high beam-steering efficiency (approximately 91%). The new technology presented here will allow for a nonmechanical, high-speed correction with simple device construction.     

Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation

The diffraction properties of thick vector holograms were analyzed with the use of a simple coupled-wave theory. Two eigenpolarizations in the holograms were determined based on the dielectric perturbation, and diffraction efficiencies for the polarizations were calculated by applying the Kogelnik method. The results were compared with those simulated by the finite-difference time-domain method. As a result, it was demonstrated that the diffraction efficiencies calculated by the two methods are in good agreement for any incident polarization when the modulation depth of the anisotropic phase retardation is substantially smaller than the mean retardation. In addition, we confirmed that coupled-wave analysis provides reasonable accuracy for relatively large modulation in the case of Bragg incidence with eigenpolarization.     

Modulation depth of Michelson interferometer with Gaussian beam

Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.     

Electric field control of a two-dimensional higher order diffraction optical beam splitter based on a cubic K0.99Li0.01Ta0.63Nb0.37O3 single crystal

An electric field controlled two-dimensional higher order diffraction optical beam splitter has been realized based on a photorefractive higher order diffraction grating. In experiments, the splitter was produced by wave coupling (632.8 nm, 532.0 nm) at a small incident angle with a potassium lithium tantalate niobate single crystal. In the process of splitting, the incident beam of different wavelengths (632.8 nm, 532.0 nm) could be split into multi-output beams by the splitter. The influence of an externally applied electric field was studied and results show that the intensity of higher order diffraction could be controlled by the electric field. The polarization properties of higher order diffraction were discussed. An electric field controlled five–three optical beam splitter was investigated theoretically.