Static and dynamic properties of incommensurate smectic-AIC liquid crystals

We study the elasticity, topological defects, and hydrodynamics of the recently discovered incommensurate smectic (AIC) phase, characterized by two collinear mass density waves of incommensurate spatial frequency. The low-energy long-wavelength excitations of the system can be described by a displacement field u(x) and a ��phason�� field w(x) associated, respectively, with collective and relative motion of the two constituent density waves. We formulate the elastic free energy in terms of these two variables and find that when w=0, its functional dependence on u is identical to that of a conventional smectic liquid crystal, while when u=0, its functional dependence on w is the same as that for the angle variable in a slightly anisotropic XY model. An arbitrariness in the definition of u and w allows a choice that eliminates all relevant couplings between them in the long-wavelength elastic energy. The topological defects of the system are dislocations with nonzero u and w components. We introduce a two-dimensional Burgers lattice for these dislocations, and compute the interaction between them. This has two parts: one arising from the u field that is short ranged and identical to the interaction between dislocations in an ordinary smectic liquid crystal, and one arising from the w field that is long ranged and identical to the logarithmic interaction between vortices in an XY model. The hydrodynamic modes of the AIC include first- and second-sound modes whose direction-dependent velocities are identical to those in ordinary smectics. The sound attenuations have a different direction dependence, however. The breakdown of hydrodynamics found in conventional smectic liquid crystals, with three of the five viscosities diverging as 1/? at small frequencies ?, occurs in these systems as well and is identical in all its details. In addition, there is a diffusive phason mode, not found in ordinary smectic liquid crystals, that leads to anomalously slow mechanical response analogous to that predicted in quasicrystals, but on a far more experimentally accessible time scale.

Optimum weighting function in bispectral analysis in speckle interferometry - Binary star parity detection

In order to describe the atmospheric turbulence which limits the resolution of long-exposure images obtained using ground-based large telescopes, a simplified model of a speckle pattern, reducing the complexity of calculating field-correlations of very high order, is presented. Focal plane correlations are used instead of correlations in the spatial frequency domain. General tripple correlations for a point source and for a binary are calculated and it is shown that they are not a strong function of the binary separation. For binary separations close to the diffraction limit of the telescope, the genuine triple correlation technique ensures a better SNR than the near-axis Knox-Thompson technique. The simplifications allow a complete analysis of the noise properties at all levels of light.

Diffraction-limited imaging on the 200-inch telescope

We have used the technique of non-redundant masking at the Palomar 200-inch telescope and radio VLBI imaging software to make optical aperture synthesis maps of two binary stars, β Corona Borealis and σ Herculis. The dynamic range of the map of β CrB, a binary star with a separation of 230 milliarcseconds is 50:1. For σ Her, we find a separation of 70 milliarcseconds and the dynamic range of our image is 30:1. These demonstrate the potential of the non-redundant masking technique for diffraction-limited imaging of astronomical objects with high dynamic range.

We find that the optimal integration time for measuring the closure phase is longer than that for measuring the fringe amplitude. There is not a close relationship between amplitude errors and phase errors, as is found in radio interferometry. Amplitude self calibration is less effective at optical wavelengths than at radio wavelengths. Primary beam sensitivity correction made in radio aperture synthesis is not necessary in optical aperture synthesis.

The effects of atmospheric disturbances on optical aperture synthesis have been studied by Monte Carlo simulations based on the Kolmogorov theory of refractive-index fluctuations. For the non-redundant masking with τ_c-sized apertures, the simulated fringe amplitude gives an upper bound of the observed fringe amplitude. A smooth transition is seen from the non-redundant masking regime to the speckle regime with increasing aperture size. The fractional reduction of the fringe amplitude according to the bandwidth is nearly independent of the aperture size. The limiting magnitude of optical aperture synthesis with τ_c-sized apertures and that with apertures larger than τ_c are derived.

Monte Carlo simulations are also made to study the sensitivity and resolution of the bispectral analysis of speckle interferometry. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of the heuristic interferometric view of image-forming process in the mid-spatial-frequency range. The signal-to- noise ratio of the bispectrum at arbitrary light levels is derived in the mid-spatial-frequency range.

The non-redundant masking technique is suitable for imaging bright objects with high resolution and high dynamic range, while the faintest limit will be better pursued by speckle imaging.

高频可变间距全息光栅的制作方法的计算机模拟研究

提出了一种制作高频线性可变频率光栅的新方法，并给出了光栅空间频率的表达式．通过在相干的两光路中插入特殊透镜，可以实现线性可变空间频率光栅的制作，而且通过适当地调节实验参数可以改变空间频率的变化率．给出了相应的模拟全息图。

Near-field x-ray phase contrast imaging and phase retrieval algorithm

Theoretical analyses of x-ray diffraction phase contrast imaging and near field phase retrieval method are presented. A new variant of the near field intensity distribution is derived with the optimal phase imaging distance and spatial frequency of object taken into account. Numerical examples of phase retrieval using simulated data are also given. On the above basis, the influence of detecting distance and polychroism of radiation on the phase contrast image and the retrieved phase distribution are discussed. The present results should be useful in the practical application of in-line phase contrast imaging.

The Madden-Julian Oscillation : observation, modeling, and theory

The Madden-Julian Oscillation (MJO) is a pattern of intense rainfall and associated planetary-scale circulations in the tropical atmosphere, with a recurrence interval of 30-90 days. Although the MJO was first discovered 40 years ago, it is still a challenge to simulate the MJO in general circulation models (GCMs), and even with simple models it is difficult to agree on the basic mechanisms. This deficiency is mainly due to our poor understanding of moist convection—deep cumulus clouds and thunderstorms, which occur at scales that are smaller than the resolution elements of the GCMs. Moist convection is the most important mechanism for transporting energy from the ocean to the atmosphere. Success in simulating the MJO will improve our understanding of moist convection and thereby improve weather and climate forecasting.

We address this fundamental subject by analyzing observational datasets, constructing a hierarchy of numerical models, and developing theories. Parameters of the models are taken from observation, and the simulated MJO fits the data without further adjustments. The major findings include: 1) the MJO may be an ensemble of convection events linked together by small-scale high-frequency inertia-gravity waves; 2) the eastward propagation of the MJO is determined by the difference between the eastward and westward phase speeds of the waves; 3) the planetary scale of the MJO is the length over which temperature anomalies can be effectively smoothed by gravity waves; 4) the strength of the MJO increases with the typical strength of convection, which increases in a warming climate; 5) the horizontal scale of the MJO increases with the spatial frequency of convection; and 6) triggered convection, where potential energy accumulates until a threshold is reached, is important in simulating the MJO. Our findings challenge previous paradigms, which consider the MJO as a large-scale mode, and point to ways for improving the climate models.

The modulated grating hologram

A phase and amplitude, off-axis hologram has been synthesized from three computer-generated transmission masks, using a multiple-exposure holographic recording method. Each of the masks controls one fixed-phase component of the complex hologram transmittance. The basic grating is generated optically, relieving the computer of the burden of drawing details the size of each fringe. The maximum information capacity of the computer plotting device can then be applied to the generation of the grating modulation function. By this method large digital holograms (25 mm by 25 mm) have been synthesized in dichromated gelatin. The recording method is applicable to virtually any holographic medium.

The modulated grating hologram was designed primarily for the application of spatial filtering, in which the requirement is a hologram with large dynamic range and large free spectral range. Choice of a low-noise, high-efficiency medium such as dichromated gelatin will allow exceptionally large dynamic range. Independence of the optically-generated carrier grating from the computer-generated modulation functions allows arbitrarily large free spectral range.

The performance of a holographic spatial filter will be limited ultimately by noise originating from imperfections in the holographic medium. The characteristics of this noise are analyzed, and in the case of a high diffraction efficiency hologram are shown to differ significantly from previous analyses. The dominant noise source in holograms of high diffraction efficiency will be scattering of the first order or imaging wave by deformations in the hologram surface or other effects of low spatial frequency. Experimental measurements in various low-noise holographic media verify these predictions.

Multilayer Active Shell Mirrors

This thesis presents a novel active mirror technology based on carbon fiber composites and replication manufacturing processes. Multiple additional layers are implemented into the structure in order to provide the reflective layer, actuation capabilities and electrode routing. The mirror is thin, lightweight, and has large actuation capabilities. These features, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Structural redundancy in the form of added material or support structures is replaced by thin, unsupported lightweight substrates with large actuation capabilities.

Several studies motivated by the desire to improve as-manufactured figure quality are performed. Firstly, imperfections in thin CFRP laminates and their effect on post-cure shape errors are studied. Numerical models are developed and compared to experimental measurements on flat laminates. Techniques to mitigate figure errors for thicker laminates are also identified. A method of properly integrating the reflective facesheet onto the front surface of the CFRP substrate is also presented. Finally, the effect of bonding multiple initially flat active plates to the backside of a curved CFRP substrate is studied. Figure deformations along with local surface defects are predicted and characterized experimentally. By understanding the mechanics behind these processes, significant improvements to the overall figure quality have been made.

Studies related to the actuation response of the mirror are also performed. The active properties of two materials are characterized and compared. Optimal active layer thicknesses for thin surface-parallel schemes are determined. Finite element simulations are used to make predictions on shape correction capabilities, demonstrating high correctabiliity and stroke over low-order modes. The effect of actuator saturation is studied and shown to significantly degrade shape correction performance.

The initial figure as well as actuation capabilities of a fully-integrated active mirror prototype are characterized experimentally using a Projected Hartmann test. A description of the test apparatus is presented along with two verification measurements. The apparatus is shown to accurately capture both high-amplitude low spatial-frequency figure errors as well as those at lower amplitudes but higher spatial frequencies. A closed-loop figure correction is performed, reducing figure errors by 94%.

利用二维光谱色散和透镜列阵改善靶面辐照均匀性

利用二维光谱色散平滑技术和透镜列阵(LA)来改善激光驱动器中靶面的辐照均匀性。通过消衍射透镜列阵可得到包络陡峭且中小空间尺度均匀性较好的焦斑。当在光路中加入二维光谱色散平滑单元后,光束在两个互相垂直的方向发生光谱色散,多光束干涉所引起的细密条纹也将在很大程度上被抹平,如果把横向热传导平滑效应也考虑在内,高空间频率的强度波动可进一步被消除。二维理论模拟结果表明采用该方案可获得顶部平坦边缘陡峭的焦斑,而且该方案无需仔细调整靶面的位置,实际应用较方便。

傅立叶分解法荧光层析成像

本文提出一种基于结构光照明和傅立叶分解方法的荧光层析成像技术，该技术首先将激发光的强度沿着光轴方向调制成余弦函数，然后用此激发光对样品作传统的二维扫描，在每一个扫描位置余弦函数的频率在一定的范围内扫描，同时一一对应地记录下所发出的荧光强度。只要对所纪录的荧光序列做一个简单的傅立叶变换，即可以得到此位置样品沿着光轴方向的荧光团分布。这样通过一个传统的二维扫描，就可以得到一个三维的阳样品分布。

New approach to superresolution

We propose a new method to increase the resolution of an optical system by modifying part of the spatial-frequency spectrum, viz., displacing the lower-frequency light to a high-frequency band, which makes the central maximum in the diffraction pattern narrower and increases the depth of focus. Simulation results show that this kind of apodizer (the term apodization was originally used to describe ways to reduce the sidelobes of the PSF, but in this paper, we use it in a wider sense) is superior to the phase-shifting ones. (C) 2001 Society of Photo-Optical Instrumentation Engineers.

Super-resolution scanning laser microscopy with a third-order optical nonlinear thin film

In a configuration of optical far-field scanning microscopy, super-resolution achieved by inserting a third-order optical nonlinear thin film is demonstrated and analyzed in terms of the frequency response function. Without the thin film the microscopy is diffraction limited; thus, subwavelength features cannot be resolved. With the nonlinear thin film inserted, the resolution is dramatically improved and thus the microscopy resolves features significantly smaller than the smallest spacing allowed by the diffraction limit. A theoretical model is established and the device is analyzed for the frequency response function. The results show that the frequency response function exceeds the cutoff spatial frequency of the microscopy defined by the laser wavelength and the numerical aperture of the convergent lens. The main contribution to the improvement of the cutoff spatial frequency is from the phase change induced by the complex transmission of the nonlinear thin film. Experimental results are presented and are shown to be consistent with the results of theoretical simulations.

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r) similar to E-2(r). For ultrathin films of thickness d << lambda the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region. (C) 2007 Published by Elsevier B.V.

汉语发展性阅读障碍儿童的视觉大细胞通路特点

Developmental dyslexia (DD) is a common kind of learning disorder, which affects 5-18% of people. It seems important to explore the deficit in visual magnocellular pathway in Chinese developmental dyslexia, for many researches demonstrated that one of the core deficits of Chinese developmental dyslexia was orthographic deficit which was associated with the deficit in visual magnocellular pathway. Two studies were done to detect the differences among Chinese developmental dyslexics, average readers of the same chronological age (CA controls) and average readers of the same reading level (RL controls) in reaction time, accuracy and visual mismatch negativity (vMMN) elicited by the moving gratings responded by visual magnocellular pathway. There were two grating-conditions which were low contrast/low spatial frequency condition and high contrast/high spatial frequency condition respectively. In ERP study, a modified “cross-modal delayed response” paradigm was used to elicit the vMMN. The results showed that the developmental dyslexics responded slower than CA controls, had more errors than RL controls, and had smaller amplitudes of vMMNs than the two controls in visual magnocellular pathway condition, but not in control condition. That is to say, Chinese developmental dyslexics had deficits in visual magnocellular pathway.

Optical determination of fractal dimensions using Fourier transforms

R. Zwiggelaar and C.R. Bull, 'Optical determination of fractal dimensions using Fourier transforms', Optical Engineering 34 (5), 1325-1332 (1995)