光学系统设计中全局优化方法的实现

 把变尺度法用于光学优化设计中，同时使用了“逃逸函数”技术, 从而实现了光学系统设计的全局优化。在使用逃逸函数时，两个因子H和W的确定是能否“逃逸”优化“陷井”的关键。用这种技术借助于C语言开发的程序成功地设计了一典型的光学系统。     

逃逸函数算法及其在光学设计中的应用

用阻尼最小二乘法进行光学系统的优化 ,得到的结果往往是评价函数在结构变量空间的一个局部极小值。日本东京工艺大学的一色教授提出了能够跳出此局部极小值继续寻找其它结果的逃逸函数全局优化算法 ,该算法的运行由多个不加或加入逃逸函数的阻尼最小二乘法局部优化组成。描述了逃逸函数的基本原理 ,给出了北京理工大学研制的GOLD软件在加入了这种算法后对光学系统进行全局优化的设计实例。实验证明了逃逸函数算法是提高光学设计效率和质量的一种有效工具。     

混入逃逸函数的实数编码遗传算法优化光学系统

为了得到超多参量光学系统的最佳设计,将标准遗传算法的二进制编码改为实数编码以提高算法的鲁棒性和计算效率,并在评价函数中混入逃逸函数避免优化过程陷入局部极值.用改进后的遗传算法和CODE V对鱼眼镜头光学系统和折反射全景成像系统的设计案例进行光学参量优化,并应用Zemax对两种优化结果进行光线追迹成像模拟.计算结果表明,应用改进遗传算法比混入逃逸函数的遗传算法或CODE V软件优化所得到光学系统的成像质量有明显提高,在优化超多参量光学系统时具有较为理想的鲁棒性和计算效率.     

复杂光学系统的全局优化

逃逸函数法是目前最为实用的光学系统全局优化算法之一。这种全局优化的运行由多个不加或加入逃逸函数的阻尼最小二乘法局部优化组成。探讨了提高其优化效率的方法,提出了两个搜索机制以便提高各个局部优化的效率。首先搜索最佳阻尼因子,从而确定多维结构变量空间中解向量的最优方向;再沿该方向搜索解向量的最优长度。此外,用实验方法确定了逃逸函数的控制参数的最佳缺省值。在此基础上成功地研制了实用化的复杂光学系统全局优化程序。     

应用粒子群算法进行光学自动设计

将粒子群算法用于光学系统的设计优化中,构造相应的数学模型,并编程实现算法.设计了关于曲率半径r、透镜面之间的距离d和玻璃折射率n等光学系统结构参数的适应度函数,用此函数作为评价函数实现对像差的自动校正.给出用粒子群算法进行光学系统设计的实例.结果证明,粒子群算法可以克服以往光学设计中高度依赖初始结构的缺点,可以自由控制结构参数的搜索范围,从而提高光学系统设计的智能化程度.     

基于Wassermann-Wolf方程的共形光学系统设计研究

提出了基于多项式拟合Wassermann-Wolf曲面设计共形光学系统的设计方法，并给出了完整的设计结果.共形光学系统要求导弹整流罩具有流线型几何外观以减少空气阻力，其次考虑导引头的光学系统设计，所以共形整流罩引入的像差通常高达几十甚至一百个波长量级，为导引头光学系统的设计带来了极大的困难.通过多项式拟合Wassermann-Wolf曲面提供共形光学系统初始结构，建立Zernike多项式特殊优化函数取代传统的光学系统评价函数，克服了用传统光学设计方法设计共形光学系统时系统评价函数收敛缓慢的问题，实现了共形光学系统的设计.设计结果表明，系统的调制传递函数在整个目标视场范围内达到了衍射极限.     

用粒子群算法校正三片镜系统的像差（特邀）

提出将粒子群算法用于三片镜光学系统的优化设计。设计了关于曲率半径、透镜面之间的距离、玻璃折射率、系统长度等光学系统结构参数的光学评价函数,用此函数作为粒子群算法中的适应度函数,实现了对光学系统的自动寻优。给出了用粒子群算法进行三片镜光学系统设计过程实例,结果证明：用粒子群算法可以设计出球差、子午场曲、子午光线弥散值都很小的三片镜光学系统;并且用该算法进行光学设计不需要知道系统具体的初始结构,克服了现有光学设计软件高度依赖具体初始结构的缺点,可以自由控制结构参数的搜索范围,从而提高光学系统设计的智能化程度。     

基于固定校正元件的椭球形窗口光学系统设计

提出了一种基于非球面固定校正元件的椭球形窗口光学系统设计方法。结合广义科丁顿公式及几何光学原理,推导出非球面校正元件的像散表达式,在此基础上,以消像散和正弦条件作为非球面校正元件像差评价参数,采用最小二乘法拟合出满足消像散及彗差的非球面面形方程。并建立以泽尼克(Zernike)多项式特殊优化函数取代传统的光学系统评价函数,克服了采用传统光学设计方法设计椭球形窗口光学系统时系统评价函数收敛缓慢的问题。成像光学系统设计时通过比对不同材料匹配实现了光学系统的无热化。给出了完整的椭球形窗口光学系统的设计,设计结果表明,系统的调制传递函数在整个扫描视场范围内接近衍射极限。     

自由曲面机载头盔显示器光学系统设计

为了解决传统头盔显示器大出瞳距、大视场与轻型化、小型化间的矛盾,采用径向基函数表征自由曲面设计了一款头盔显示器光学系统。详细论述了径向基函数表征自由曲面的原理,分析了光学系统像差校正方法。在设计中,尝试了一种方法来快速地确定优化起点,分析了该光学系统的成像质量。该光学系统的视场为45°×32°,出瞳大小为15mm,出瞳距为50mm。在奈奎斯特频率处,全视场的调制传输函数(MTF)值大于0.6。在(-22.5°,16°)视场处有最大畸变值-1.54%。系统尺寸56mm×128mm,重量136g。优化设计结果表明,该全息头盔显示光学系统像差小,可以较好地为使用者提供清晰的字符信息或者视频图像。该头盔显示光学系统成像质量好,体积小重量轻,可以应用于新一代机载头盔显示技术。     

不共轴光学系统自动优化中的有关问题

描述不共轴光学系统计算机优化中坐标变换与逆变换、“入瞳”与光线坐标、像面基准与质量函数定义的一致性问题。     

Densities of states and the complex partition function

A Fourier transform technique based on the method of Dubner and Abate is here applied to the energy-level density problem for quantum partition functions. It is shown that, for typical molecular systems at realistic energies, the integrated level count, W(E), is obtainable to near ‘spectroscopic’ accuracy and in reasonable computing time. A smooth Fourier resolution of the simple density function, g(E), is likewise possible. Though somewhat less economical, this procedure entirely removes the slight discrepancies found in the steepest-descent method and can reasonably be claimed to dispose once and for all of the problem of quantum level-density computations in molecular rate theory.     

Magneto-optics of strongly correlated two-dimensional electrons in single heterojunctions

Investigations of two-dimensional (2D) electron systems in semiconductors subjected to a strong perpendicular magnetic field with the use of photoluminescence are reviewed. The foundation of the optical spectroscopy method using the radiative recombination of 2D electrons with photoexcited holes bound to acceptors in a δ-doped monolayer in GaAs/Al _x Ga_1-x As single heterojunctions is presented. Optical spectroscopy studies of the energy spectra of 2D electrons imposed on transverse magnetic fields in the regimes of the integer and fractional quantum Hall effects are discussed. The relationship between the mean energy of the 2D electron gas and the first moment of their radiative recombination is analysed. It is shown that the magnetic field dependence of the first moment provides a method to measure the cyclotron, enhanced spin and quasiparticle energy gaps at the same time. Therefore it is shown how magneto-optics ‘see’ the ground state of interacting 2D electrons in the extreme quantum limit and how an optical ‘tool’ is efficient for the determination of Coulomb gaps of incompressible Fermi fluids in the fractional quantum Hall effect. Finally optical observations and studies of the Wigner crystallization of 2D electrons are presented. The corresponding liquid-solid phase diagram is discussed.     

A method of optical implementation of frequency encoded all optical logic gates based on multiphoton processes in non linear material

A novel frequency encoded all optical logic gates are proposed exploiting multiphoton processes in non linear optical medium. In the frequency encoding of the information the ‘0’ is represented by a frequency ω and ‘1’ is represented by another frequency 2ω. The gates proposed are NOT, OR, AND, NAND and NOR among which NAND and NOR are universal. Using these gates one can generate other important gates and logical function generating all optical devices. Two main three-photon processes, second harmonic generation (SHG) and parametric light generation (PLG) are used to implement the gates and the corresponding appropriate non linear material is LiB₃O₅ (LBO) which has wide operating and transparency range in the wavelength 350–3,200 nm. The source of optical frequency encoded signal may be derived from an external cavity diode laser generating a wavelength 1,560 nm for ω (‘0’ state of information) and its second harmonic 780 nm for 2ω (‘1’ state of information).     

The interaction between first excited state hydrogen atoms and a different non-degenerate atom: an example of second-order resonance forces

The interaction of a first excited state hydrogen atom with a different non-degenerate atom is considered in the R ^-1 multiple approximation. The interaction energies for the Π states arising from this interaction have the form usually associated with second-order dispersion energies while those for the Σ states behave quite differently as a function of R. Because of a second-order ‘resonance within one molecule effect’ the second-order Σ-state energies do not possess single R ^-1 expansions that are formally valid for all values of R consistent with the multipole treatment. The expansions of these Σ-state energies, that are valid for ‘small’ R, contain terms varying as both even and odd powers of R ^-1; the lead R ^-7 ‘odd’ term competes strongly with the usual R ^-6 dispersion energy. The expansions that are valid for ‘large’ R contain terms varying as even powers of R ^-1 only and usually have little physical meaning. The He(¹S)-H(n=2) interaction is considered as a specific example of these results and the interaction energies for this system are evaluated through O(R ^-8) by using one-centre pseudostate methods. The general significance of the results is also discussed briefly.     

Design of Plane-Symmetric Low <Emphasis Type="Italic">F</Emphasis>-number Reflective System Based on Perturbation Aberration Model

All-reflective optical systems have theoretically no chromatic aberration and are suitable for wide spectral application, but co-axial reflective systems are difficult to design as low F-number optical systems. In this paper, the aberration of plane-symmetric optical systems with low F-number is analyzed based on the wavefront derived from optical path length. Up to third-order aberrations are classified into three categories by their characteristics. The reduction method of the dominant aberration, astigmatism-like aberration, is proposed. In the method, the Gauss image plane is modeled by means of a simplified mirror surface with third-order approximation. Because the system is plane-symmetric, symmetric cross section and asymmetric cross section are modelled differently. The design example of a three-mirror system with F/2 is shown.     

A partitioned density functional theory of freezing: application to soft spheres

A non-perturbative density functional theory (DFT) for inhomogeneous fluids is developed by partitioning the functional into short range (‘entropic’) and long range (‘energetic’) contributions. The short range part is treated using standard weighted density functional techniques and the long range contribution is evaluated exactly. This method, which is a generalization of a method due to Likos, C., and Senatore, G., 1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of a reference system. Results are presented for the calculation of the crystal-/fluid phase coexistence for systems interacting with inverse-power potentials of the form r ^-n , where n = 4, 6 and 12. These results show that this non-perturbative DFT is capable of predicting the freezing of long range inverse power systems (n = 4, 6) into a body-centredcubic lattice. Improvements over earlier methods also are noted in the current results for the solid structure as measured by the Lindemann ratio.     

Simple model for electron inelastic mean free paths: Application to condensed organic materials

A simple, ‘one-mode’ approximation for the wavevector- and frequency-dependent energy-loss function is employed to derive an expression for the electron inverse mean free path, λ_v^?1, including the effect of exchange between the incident electron and the electrons in the medium. Relation to optical data is made by averaging λ_v^?1, over the optical oscillator strength distribution, which is proportional to ωIm[— 1/?(ω)]. For materials for which the optical oscillator strength distribution may be approximated by a single, Drude-type function, especially organic materials, the general results may be cast in a particularly simple form. Using a few constants derived from optical data for a given material, electron mean free paths in that material can be predicted for electron energies ? 150 eV. An approximate expression is also deduced for estimating electron mean free paths in materials for which no optical data are available. Mean free paths determined using this approximate expression agree well with those obtained in our earlier ‘universalcurve’ predictions. For polyethylene, the excellent agreement between results from the model presented here and those from a more detailed insulator model gives additional support for this simple theoretical approach. Agreement between theoretical predictions and experimental measurements of electron mean free paths in organic compounds, which in some cases is quite good, is on the whole less than satisfactory.     

On the kinetic theory of diffusion,self-diffusion and thermal diffusion in adsorbed gases

Phosphorescence microwave double resonance experiments are reported on Zn porphin at 1·2 K. In glassy solution very broad resonance transitions are observed. However, for Zn porphin in a crystalline n-octane matrix—a system known for its sharp optical spectra (Shpolskii effect)—three pairs of microwave transitions with widths of a few MHz are found, all of them corresponding to a decrease in phosphorescence intensity. By studying the behaviour of the signals for various methods of preparation of the sample and as a function of the optical bandwidth of excitation and detection, one pair of transitions could be assigned to monomeric solute molecules. The corresponding zero-field splittings are |X - Z| = 1355, |Y - Z| = 806 MHz. It was further established that by ‘pumping’ either of these transitions a third one can be detected at the difference frequency, so that the order of the levels must be X> Y>Z (or reverse). The results indicate that the molecule no longer possesses a four-fold axis in the excited state. What one observes must be the lowest vibronic level of a Jahn-Teller unstable state, the degeneracy of which is removed by an anisotropic crystal field. From some preliminary E.S.R. experiments on zinc porphin in an EPA glass at 77K it is concluded that Z corresponds to that component where the angular momentum lies in the molecular plane; for a ππ* electronic state this is expected to be the lowest in energy of the three.