Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates.Based on the stationary phase method,the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function.Finally,a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.     

一种基于OTF稳定性的波前编码相位板优化方法

提出了一种简单的可用于光学系统中子午弧矢方向白光OTF稳定性评价的波前编码相位板参量优化方法.该方法仅以标准偏差来评价OTF在目标景深范围内的稳定性,并且结合自适应模拟退火算法在参量空间内优化得到相位板的最佳参量.使用该方法优化得到的相位板参量,可以大幅度提高光学系统的景深,并且可以获得更为清晰、稳定的成像.对应用波前编码技术前后光学系统的成像性能作了比较,并且考察了优化参量的容差性.     

波前编码显微物镜景深扩展的研究

为了解决传统显微物镜景深与分辨率的矛盾,采用波前编码的方法,设计研究了波前编码的10倍显微物镜,结合传统光学设计软件,采用基于MTF一致性的相位板参数的优化方法,实现了在像面附近一定范围内系统的点扩散函数一致性;此外,还设计了扩展三次相位编码板的10倍显微物镜,比较了采用两种不同相位板系统的焦深扩展的效果,结果显示三次相位板的焦深扩展效果较好,可以将传统10倍显微物镜的焦深扩展15倍。成像模拟仿真结果显示滤波后的编码像在±15倍焦深范围内成像清晰,从而扩大了系统的景深。     

可调谐相位板空域频域联合分析

波前编码系统采用在传统光学系统中加入相位板来扩大光学系统的景深而避免传统景深延拓技术的不利影响. 由于相位板的参数不可调, 整个系统的景深延拓扩展率也不能动态可调. 采用两相位板组合的方法可以有效克服这一点. 本文首先从光线差的角度提出了两三次相位板组合下的光线像差分布以及点扩散函数尺寸的具体关系表达式, 直观体现了系统的光线结构, 指出了光线结构和点扩散函数尺寸受两三次相位板的面型和相对位移量的影响. 其次采用稳相法从空间域给出了系统点扩散函数表达式, 依据点扩散函数的振荡性质给出了有效带宽表达式, 提出了点扩散函数在像面的位置会随两相位板面型参数以及相对于光瞳中心的位移量而发生平移. 最后利用菲涅耳积分给出两三次相位板任意面型参数和相对位移组合下的准确光学传递函数. 在得到的调制传递函数中直观体现出了面型参数和相对位移量对调制传递函数和相位传递函数以及有效带宽的影响, 并说明了此系统相位传递函数的非线性性质. 通过空间域与频率域相结合的方法分析验证了传统的两三次相位板组合具有景深可调和带宽可调的性质, 为设计可调谐波前编码系统提供了理论依据.     

波前编码成像系统景深延拓扩展率的研究

研究三次相位板的波前编码光学系统,发现在一定的条件下系统调制传递函数(MTF)对波前编码系统的离焦不敏感,才能得到波前编码系统的景深.对比传统光学系统的景深,得到波前编码系统的景深延拓扩展率的表达式.分析空间频率取值范围和三次相位板系数α,发现当a=20π时,波前编码系统可以将传统光学系统的景深扩大60倍以上.     

Optimized annular phase masks to extend depth of field

A radially symmetric phase mask composed of several annular zones with equal area (called APM) was designed based on the incoherent imaging theory from Fourier Optics. The phase of any ring equals minus of the phase function caused by certain defocus. Another circularly symmetric phase mask similar to the APM (called MQPM) was proposed, except for the different phase function deriving from the quartic phase mask (QPM). For MQPM, there are two differences from an existing phase mask: the selection of the phase parameters and the method to divide the phase mask. An optimization model was developed to obtain optimized parameters of the phase masks. Numerical evaluations show that both APM and MQPM are less insensitive to defocus than QPM, and the defocused optical transfer functions with two phase masks are symmetric about the in-focus plane in the axial direction.     

Analyzing wavelength behavior of a cubic phase mask imaging system based on modulation transfer function

The wavefront coding technology is an effectively method for extending the depth of field. However, the phase delayed by the phase mask changes with light wavelength, and the chromatic aberration is caused by chromatic dispersion of the optical elements. The modulation transfer function (MTF) of the cubic phase mask (CPM) system is derived with considering the axial chromatic aberration and optical path difference variation with wavelength, and the wavelength behavior of CPM system is analyzed in details. We yield that the MTF is approximately wavelength invariant within a certain frequency bandwidth, and the bandwidth is nearly inverse proportional to wavelength and varies with axial chromatic aberration. The effect induced by dispersion of the CPM material is very weak. If the CPM system is illuminated by wideband spectral light and the ACA exists, then the frequency bandwidth may become narrower than the monochromatic case, and the position of image sensor can be relocated to balance frequency bandwidth among all wavelengths.     

Optical transfer function of an optical system with a vortex phase mask in the presence of primary aberrations

The impact of primary aberrations on the optical transfer function of an optical system with a vortex phase mask has been investigated in detail. The optical transfer function of such a system becomes negative in a certain frequency range even in the absence of aberrations, a feature different from the case of an optical system in which center of the point spread function is bright.     

Analytical and experimental demonstration of depth of field extension for incoherent imaging system with a standard sinusoidal phase mask

The wavefront coding technique is used to enlarge the depth of field（DOF）of incoherent imaging systems. The key to wavefront coding lies in the design of suitable phase masks.To date,numerous kinds of phase masks are proposed.However,further understanding is needed regarding phase mask with its phase function being in a standard sinusoidal form.Therefore,the characteristics of such a phase mask are studied in this letter.Deriving the defocused optical transfer function（OTF）analytically proves that the standard sinusoidal phase mask is effective in extending the DOF,and actual experiments confirm the numerical results.At the same time,with the Fisher information as a criterion,the standard sinusoidal phase mask shows a higher tolerance to focus errors（especially severe focus errors）than the classical cubic phase mask.     

An apodized cubic phase mask used in a wavefront coding system to extend the depth of field

The point spread function (PSF) caused by a wavefront coding system with a cubic phase mask has big side-lobes which leads to bad image restoration. This paper proposes a novel apodized cubic phase mask to suppress the side-lobes of the PSF. Simulated annealing algorithm is used to optimize the cubic and the truncation parameter of the phase mask. The system with the novel phase mask has better performance in the modulation transfer function (MTF) especially in low-and-medium spatial frequency region. The simulation results show that the restored images with the novel phase mask are superior to the one with the classic cubic phase mask in contrast and ringing effect. The experimental results show that the side-lobes of the PSF are suppressed by using the apodized cubic phase mask.     

Optimized free-form phase mask for extension of depth of field in wavefront-coded imaging

To achieve a further extension of the depth of field in wavefront-coded imaging by reducing the impact of focus error in the optical transfer function, we propose the use of a free-form phase mask (FPM) instead of a conventional cubic phase mask (CPM). We optimized the shape of the FPM using the simulated annealing algorithm and confirmed that the optimized FPM provides a much larger focal tolerance and better final images than the CPM in the noise-free case.     

波前编码系统的点扩散函数稳相法分析

本文利用稳相法从本质上分析了三次相位波前编码系统的点扩散函数特性.通过分析三次相位板任意位置掩膜带和点扩散函数的关系,指出点扩散函数和稳相点的关系:两个稳相点引起点扩散函数的振荡,一个稳相点则只会造成点扩散函数的平稳变化.相位掩膜带或相位掩膜对的对称结构是同一区域内存在两个稳相点的必要条件,对称结构的不同位置对应于点扩散函数的不同部分.这种对应关系同时解释了对焦点扩散函数只存在振荡,而离焦点扩散函数却还存在平缓变化区域的本质原因,这是由离焦时光学对称轴和几何对称轴不重合引起的.本文建立了点扩散函数和对称相位掩膜对之间的对应关系,可以有效地指导相位掩膜的加工和检验.     

Phase mask selection in wavefront coding systems: A design approach

A method for optimizing the strength of a parametric phase mask for a wavefront coding imaging system is presented. The method is based on an optimization process that minimizes a proposed merit function. The goal is to achieve modulation transfer function invariance while quantitatively maintaining final image fidelity. A parametric filter that copes with the noise present in the captured images is used to obtain the final images, and this filter is optimized. The whole process results in optimum phase mask strength and optimal parameters for the restoration filter. The results for a particular optical system are presented and tested experimentally in the laboratory. The experimental results show good agreement with the simulations, indicating that the procedure is useful.     

Optimal key mask design for optical encryption based on joint transform correlator architecture

We examine perfect recovery in the optical encryption system based on joint transform correlator architecture, which requires the key mask to be space-limited and phase-only in the frequency domain. Accordingly, a discrete sinc function interpolation is used to generate a binary phase difference mask for image encryption and decryption. Furthermore, the optimal binary phase difference mask is derived from the interpolation process best approximating the ideal sinc function interpolation. The simulation results confirm better recovery of the decrypted image for applying the proposed key masks to the optical encryption system. Especially, the optimal binary phase difference mask significantly enhances the recovery performance.     

波前编码系统相位板视场效应的消除

通过在光学系统的光阑面上加入一个非球面相位板,使得光学系统的成像对离焦不敏感.但当入射视场角较大时,图像的边缘发生变形且难以恢复.针对此问题,提出了两种解决方案,方案一是把相位板移至光路中光线较为平缓的区域,但不是系统的光阑位置;方案二是保持相位板位置不变,优化整个光学系统,使相位板前的光线能够平缓地入射到相位板.实验中对一个EFL=12.5 mm,F/#=1.3,半视场角为13.5°的波前编码实际系统进行仿真比较,得出方案二可以有效地消除波前编码相位板引入的视场效应.     

Problems on fabrication of computer-generated holograms for testing aspheric surfaces

Interferometric optical testing using computer-generated hologram （CGH） can give highly accurate measurement of aspheric surfaces has been proved. After the system is designed, a phase function is obtained according to the CGH＇s surface plane. For the requirement of accuracy, an optimization algorithm that transfers the phase function into a certain mask pattern file is presented in this letter, based on the relationship between the pattern error of CGH and the output wavefront accuracy. Then the writing machine is able to fabricate such a mask with this kind of file. With that mask, an improved procedure on fabrication of phase type CGH is also presented. Interferometrie test results of an aspherie surface show that the whole test system obtains the demanded accuracy.     

波前编码系统景深延拓性能研究

波前编码景深延拓技术是在非相干光学系统的出瞳处加入三次位相板,对成像进行解码处理而获得清晰图像以扩大光学系统景深的技术.文章通过深入研究波前编码光学成像系统的调制传递函数(MTF),分析离焦量和位相板的调制系数对MTF的影响,并通过数值计算和曲线拟合得到位相板调制系数、系统带宽、景深延拓性能之间的关系.该研究成果为位相板的调制系数的选择和景深延拓光学系统的设计提供依据. 关键词： 波前编码 景深延拓 调制传递函数 三次位相板     

Multiple image encryption using an aperture-modulated optical system

A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method.     

Multiple-beam optical tweezers generated by the generalized phase-contrast method

We demonstrate the application of the generalized phase-contrast (GPC) method to the implementation of a multiple-beam optical tweezer system. Experimental results show the generation of four optical tweezers from a fixed phase mask in conjunction with a GPC system to trap and hold 1-microm-sized polystyrene beads in solution.     

基于联合菲涅耳变换相关器和矢量分解的光学加密方法研究

为提高光学图像加密系统的安全性,利用双光楔联合菲涅耳变换相关器和矢量分解设计了一种非线性光学图像加密系统。通过矢量分解将原始图像分解为两个相位模板,其中一个相位模板f1(x)放置于双光楔联合菲涅耳变换相关器物窗口实现图像加密;携带另一相位模板f2(x)信息的光束与解密系统输出的携带f1(x)信息的光束相干叠加得到解密图像。数值模拟了加密系统的加、解密过程,对于灰度图像和二值图像,当光楔楔角为1.8°和相位模板f1(x)与密钥k(x)的中心间距为18 mm时,解密图像与原始图像的相关系数分别为0.812 7和0.810 9;分析了密钥模板相位分布错误对解密效果的影响,验证了加密方法的可行性。模拟分析表明,密钥k(x)的位置和光楔楔角作为附加的密钥参量,有效扩展了加密系统密钥空间,并能抵御唯密文攻击、已知明文攻击和选择明文攻击。