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.     

Variable-radius focused optical vortex with suppressed sidelobes

We propose a design for a phase mask for generating an optical vortex with suppressed sidelobes in the focal plane where the radius of the intensity ring is variable. A radial modulation added to conventional phase mask exp(iltheta) projects the light diffracted from different annular zones into a single intensity ring in the focal plane.     

Scanning two photon fluorescence microscopy with extended depth of field

We describe the design and implementation of a light efficient binary phase-only diffraction optical element which converts a laser beam into an annular ring with the loss of less than 25% of the overall power. The use of annular illumination permits us to obtain an increase in the axial extent of the point spread function of a microscope objective without compromising the lateral resolution. The light efficiency of the system permitted two photon fluorescence images with extended depth of field to be obtained. The combination of two such extended depth of field images obtained at different parallaxes allowed the generation of high resolution two photon stereo pairs.     

Focal shift and focusing properties generation by radial cosine phase masks

Focal shift and focusing properties of Gaussian beams induced by radial cosine phase masks are investigated. Results show that focal shift and the energy distribution among intensity peaks are controlled by two different parameters of the radial cosine phase mask. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift and focal switch may occur, simultaneously, the focal shift direction may change. Moreover, by altering frequency parameter or phase variation parameter of the phase mask will change the energy distributions of maximum intensity peak and other small intensity peaks. And novel focal patterns also evolve considerably, such as from only one peak to six of multiple peaks. The tunable focal shift can be used to construct controllable optical tweezers. In practice, the tunable phase mask can be implemented through liquid crystal spatial light modulator, which can conveniently alter the wavefront phase distribution of the incident laser beam in the control of computer.     

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.     

三环位相型光瞳滤波器的横向超分辨与轴向焦深扩展

用矢量衍射方法分析了线偏振光入射到带有三环位相型光瞳滤波器的高数值孔径物镜时,焦点的轴向和横向光强分布.数值模拟结果表明,高数值孔径物镜聚焦时需同时考虑光强的轴向和横向分布.通过加入三环位相光瞳滤波器,在实现横向超分辨的同时实现了光学系统轴向焦深扩展和轴向光强分布平坦化,并且位相调制深度变化时,会出现轴向焦移现象.对三环位相光瞳滤波器结构进行了优化,得出了优化结果. 关键词： 光学超分辨 扩展焦深 位相型光瞳滤波器 矢量衍射方法     

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。     

Focus depth characteristics of lenses with long focal depth designed by a focal depth function

The validity of a focal length function is investigated in designing optical element with long focal depth and high lateral resolution. The designed lenses with different starting focal length are studied. Two focusing performance measures, focal depth and lateral resolution, are presented. Comparing with the conventional lens and optical element designed by other focal length function, numerical results of the designed optics element indicate that the long focal depth and high lateral resolution are achieved. The validity of the focal length function is confirmed. Meanwhile, the designed optical element is similar with the lens with spherical aberration. It means that one can easily implement long focal depth by applying appropriate phase modulation to a lens with spherical aberration.     

提高微细图形光刻分辨力的相移滤波技术研究

详细研究了提高投影成像光刻分辨力的相移滤波技术的基本理论,给出了理论模型,进行了模拟计算.对不同掩模图形设计制作的不同优化滤波器进行光刻对比实验并取得实验结果.研究表明,相移滤波能显著提高部分相干成像系统光刻分辨力和增大焦深,同时能提高光能利用率,有利于提高光刻生产率,是一种有效提高光刻分辨力和焦深的波前工程技术.     

Focus evolution of Gaussian beam induced by phase plate

In this article, vector diffraction theory is employed to investigate the focusing properties of the Gaussian beam through a phase plate. The phase plate may alter the wavefront phase of an incoming beam by topological charge. Both the circular phase distribution and the annular phase distribution plates are investigated. Numerical simulations show that the focal intensity distribution depends on topological charge. With changing topological charge, focal intensity distribution may evolve into ring shape, and some novel focal spots may occur. Focal intensity distribution evolving process with integer topological charge differs considerably from that with fraction topological charge. When the concentric annular phase plate is placed in the laser path, the focal intensity distribution depends on both the inner radius and topological charge. For small inner radius of the phase plate, doughnut-shape focal pattern occurs. With increasing inner radius, the diameter of the doughnut focal pattern decreases, and doughnut shape disappears slowly in some cases.     

Polarization phase in aberration compensation

A phase/amplitude mask on the aperture of an imaging system results in a pupil function that is multiplicative with the lens function, resulting in a morphological transformation of the imaging wavefront. It was shown that such amplitude and phase functions can be implemented using polarization masks, with the advantage that the phase and amplitude can be controlled in real time and in some cases, independently of each other. The phase and amplitude variation over the mask can be controlled either by changing the polarization of the mask or by changing the input beam parameters. Wavefront tailoring using polarization-masked apertures is therefore feasible and may be utilized for focal shift and partial aberration compensation. For complete compensation of aberration, the phase distribution over the mask should be conjugate to that of the phase error of the aberrant wavefront, which necessitates the use of a continuously variable polarization mask. Since such a mask is difficult to implement, we have considered polarizing masks consisting of discrete polarized zones on the lens aperture, leading to polarization phase steps on the exit pupil of the imaging system. The simulation results presented in this paper show that effects of focal shift, partial compensation of primary spherical aberration and astigmatism can indeed be achieved by the proper use of polarization masked apertures.     

Optimized phase pupil masks for extended depth of field

By properly designing a phase pupil mask to modulate or encode the optical images and then digitally restoring them, one can greatly extend the depth of field and improve image quality. The original works done by Dowski and Cathey introduce the use of a cubic phase pupil mask to extend the depth of field. The theoretical and experimental researches all verified its effectiveness. In this paper, we suggest the use of an exponential phase pupil mask to extend the depth of field. This phase mask has two variable parameters for designing to control the shape of the mask so as to modulate the wave-front more flexible. We employ an optimization procedure based on the Fisher information metric to obtain the optimum values of the parameters for the exponential and the cubic masks, respectively. A series of performance comparisons between these two optimized phase masks in extending the depth of field are then done. The results show that the exponential phase mask provide slight advantage to the cubic one in several aspects.     

Focal depth and focal splitting of truncated hyperbolic-cosine-Gaussian beam induced by phase plate

Focal depth and focal splitting of hyperbolic-cosine-Gaussian beams induced by a phase plate were investigated. The pure phase plate consists of three concentric zones: a center circle zone, an inner annular zone and an outer annular zone. The phase variance of the inner annular zone is adjustable. Simulation results show that the focal depth can be adjusted by changing the radii of zones. With the increase of the inner radius of the outer annular zone, the focal spot broadens along the optical axis and splits into two peaks. Then the two peaks combine back into one peak. There are two critical values for the inner radius of the outer annular zone, at which focal spot changes sharply. The tunable range of the focal depth varies considerably. The phase variance of the inner annular zone affects focal depth also; when the phase variance is π, the effect attains maximum. The parameters of cosh parts of the beam affect both focal splitting and focal depth evidently; focal splitting disappears with increasing parameters of cosh parts, and focal depth increases with increasing the parameters of cosh parts in both the low and the high numerical-aperture optical systems.     

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.     

Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system

Wave-front coding is a well known technique used to extend the depth of field of incoherent imaging system. The core of this technique lies in the design of suitable phase masks, among which the most important one is the cubic phase mask suggested by Dowski and Cathey (1995) [1]. In this paper, we propose a new type called cubic sinusoidal phase mask which is generated by combing the cubic one and another component having the sinusoidal form. Numerical evaluations and real experimental results demonstrate that the composite phase mask is superior to the original cubic phase mask with parameters optimized and provides another choice to achieve the goal of depth extension.     

基于光束扫描宽化技术的激光掩模微加工系统

利用Nd∶KGW激光器,采用光束扫描宽化技术和掩模微缩成像方法研制了用于微打标及微型零件雕刻成形的激光掩模微加工系统。系统采用计算机打印的塑料胶片或液晶作掩模,光束扫描面积为（有效掩模面积）30 mm×30 mm。微缩成像系统的缩小倍率分别为8～10倍（f=100 mm透镜）和15～20倍（f=50 mm透镜）。对该系统的加工尺寸和加工精度进行了分析。实验结果表明：系统达到的最小标刻宽度和加工图形精度均为10μm,与分析结果一致。系统的单次加工深度为0.07～0.1μm,最大加工深度为200μm,可满足工业微加工技术的基本要求。     

Transverse superresolution and focal shift with rotational tunable phase mask

This paper reports the imaging characteristics of an optical system can be modified by our designed polarization pupil mask. The novel rotational symmetric polarization pupil mask design based on combination of half-wave and quarter-wave plates is introduced for realizing the focal shift and extending focal depth of an optical system and the procedure for designing is presented. Numerical results show when an appropriate rotational symmetric polarization pupil mask is used as an apodizer in the optical imaging system, it not only can effectively achieve the continuously focal shift in a small range and extend focal depth of the optimized system, but also can evidently increase the transverse resolution of the optimized system at the genuine focal plane.     

Focusing properties of the hyperbolic-cosine-Gaussian beam induced by phase plate

Focusing properties of hyperbolic-cosine-Gaussian beam induced by phase plate were investigated theoretically in this Letter. The phase plate consists of three concentric zones: center circle zone, inner and outer annular zones with 0, π, 0 phase variations, respectively. Numerical simulations show that the evolution of the focal shape is altered considerably by changing the radii of zones and the decentered parameters in cosh parts of the light beam. Increase inner radius of the outer annular zone, focal spot broadens along optical axis, splits into two peaks, and then the two peaks combine back into one peak. In this process, the focal depth increases and then decreases three times, so three focal depth peaks occur. And the distance between the two peaks for bigger inner radius of outer annular zone is very small. With decreasing decentered parameters in cosh part of the beam, position of the three focal depth peaks shift toward to small radius, and the peak values also fall simultaneously.     

Focal shifting of transversely polarized beam using cosine phase plate

Focal shift of transversely polarized beams induced by cosine phase masks are investigated theoretically by vector diffraction theory. Results show that when the transversely polarized beam with radial cosine wavefront phase is focused, the focal pattern differs considerably with frequency parameter in the cosine function term. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift may occur, simultaneously, the focal shift direction may change. Moreover, by altering frequency parameter or phase variation parameter of the phase mask will change the energy distributions of maximum intensity peak and other small intensity peaks. And novel focal patterns also evolve considerably, such as from only one peak to five of multiple peaks. The tunable focal shift can be used to construct controllable optical tweezers.     

Excimer laser patterned dielectric masks for the fabrication of diffractive optical elements by laser ablation

Masks for laser processing are generated by laser ablation patterning of dielectric layer systems. The application of these masks for the rapid fabrication of diffractive optical elements (DOEs) is presented. The diffractive optical elements are designed as phase-only elements, assuming an illumination with a plane wave. A continuous phase function is calculated using an iterative Fourier transform algorithm (IFTA). This continuous phase function is reduced to two or four levels by an iterative Fourier quantisation algorithm (IFQA) that is able to include focal power. The fabrication of the DOE is performed in a two-step process. First, a binary amplitude mask (or a set of masks for multi-level DOEs) is made by structured ablation of a highly reflective dielectric coating (HR 248 nm) from a fused silica substrate. This is accomplished by using an ArF excimer laser emitting at 193 nm, a wavelength that is sufficiently absorbed in the HfO₂/SiO₂-dielectric layer system, leading to precisely ablated mask structures. In the second step, this mask is used in a 4:1 projection configuration to generate a surface profile in a polymer substrate by ablation at 248 nm. The depth modulation can be defined by adjusting laser fluence and pulse number. Examples of DOEs ablated in polycarbonate are shown and their performance is characterised.