Cross-diffractive optical elements for wide angle geometric camera calibration

Diffractive optical elements (DOEs) can generate multiple two-dimensional (2D) diffraction grids that can be used to calibrate cameras for photogrammetry. However, several factors limit the accuracy and the functionality of this technique. One of the most important is the DOE fabrication itself. A large DOE with wide 2D fan-out grids is very difficult and costly to develop. Consequently, the calibration is limited to small aperture cameras and/or limited angles. To overcome these problems, we present a low cost solution. We propose to use two large, commercially available, crossed phase DOEs that generate 15×15 equally spaced dots. As the DOEs are not perfect, the unwanted secondary diffractive orders are used as calibration targets to expand the calibration field of view. We show that the use of the primary and secondary diffractive orders provides a valuable calibration tool for wide angle aerial cameras.     

螺旋光束经过振幅型衍射光学元件的传输特性及其拓扑电荷数的测量

本文提出了一种利用空间光调制器生成杨氏双缝和三角孔等振幅型衍射光学元件的方法. 利用平面波角谱衍射公式和柯林斯公式研究了螺旋光束经过这两种衍射元件后的传输特性, 并利用杨氏双缝和三角孔实现了螺旋光束拓扑电荷数的测量. 由于空间光调制器可以方便和高精度地改变光学器件的几何尺寸和所在的空间位置, 因此可便捷地实现螺旋光束拓扑电荷数的测量.     

用四台阶相位板产生涡旋光束

涡旋光束的产生与应用是当前光学领域的研究热点. 利用傅里叶级数展开法分析了四台阶相位板的相位结构, 发现四台阶相位板可看作是由一系列不同拓扑荷数的螺旋相位板所组成, 用线偏振光直接照射相位板时, 将产生多级衍射光波, 各级衍射光均为不同拓扑荷数的涡旋光波, 由于多级衍射光波间的干涉导致光强分布偏离轴对称分布, 因而与涡旋光波有一定差距. 在此基础上, 提出了用四台阶相位板产生涡旋光束的新方案, 借助于Mach-Zehnder 干涉仪光路, 两块四台阶相位板产生的衍射光干涉叠加, 通过调节干涉仪光路的相位差, 使一部分衍射级干涉相消, 另一部分衍射级干涉相长, 相互加强, 从而把线偏振光转换为涡旋光束. 数值模拟计算了几种周期数不同的四台阶相位板衍射光强和角动量分布, 并与螺旋相位板进行比较, 证明用简单的四台阶相位板不仅能够获得与用螺旋相位板相同的涡旋光束, 而且可以用周期数较小的四台阶相位板产生具有大拓扑荷数的涡旋光束, 降低了制作相位板的难度.     

Diffraction testing of ultrasonically-produced phase gratings using a double beam illumination method

An optical far-field method is described for studying ultrasonically-produced phase gratings with very small phase variations. An ultrasonic grating is illuminated by two plane waves mutually inclined at an angle properly matched to the diffraction angle of the inspected grating. The expressions for the time-dependent irradiance in the far-field diffraction orders are derived. They enable the extraction of the Raman-Nath parameter of a progressive ultrasonic beam. The application of the technique to pulsed ultrasound beams is proposed.     

一种用于减少相位突变点的衍射光学元件改进设计方法

提出了一种基于数字图像处理技术的用于降低相位突变点的改进型Gerchbery-Saxton(G-S)衍射光学元件设计方法。与普通的G-S衍射光学元件设计算法相比,这种改进型的G-S算法能够使得衍射光学元件的相位分布曲线更加光滑,并且在迭代计算过程中具有更强的收敛能力。利用该种算法获得了由高斯光束变换成空心光束时所需要的衍射光学元件的相位分布,在同样参数条件下,均方根误差为8.31%,优于普通G-S算法的9.46%;并且约有33.2%的像素的相位值得到了改进,从而平滑了衍射光学元件的相位分布曲线,便于实际的微加工。     

A Novel Technique for Measuring Defocus with Phase Shift Gratings on a Photomask

A focus monitor reticle having a novel grating structure is proposed. If a grating pattern has a property of being able to generate asymmetry between positive and negative diffraction orders, a defocus of the grating pattern can be translated to an easily measured pattern shift perpendicular to the optical axis. A possible grating for this purpose is composed of three components: opaque line, naked line and #x03C0;/2-phase-shifted groove. In particular, with their width ratio equivalent to 2/1/1, one of the two first-order beams disappears entirely. Consequently, tilted standing waves are formed by two-beam interference between zeroth-order and the other first-order on the image plane. This paper describes a new technique for measuring a defocus with a phase shift grating object. Good agreement between experimental sensitivities and theoretical expectation verifies that the technique achieves high accuracy of several nanometers or better. Applications of the technique show indicative ability in field curvature and astigmatism of the state-of-the-art scanner.     

Optimisation of a low cost SLM for diffraction efficiency and ghost order suppression

Spatial Light Modulators (SLMs) are a powerful tool in many optics laboratories, but due to the technology required for their fabrication, they are usually very expensive. Recently some inexpensive devices have been produced, however their phase shift range is less than 2π, leading to a loss of diffraction efficiency for the SLM. We show how to improve the first order diffraction efficiency of such an SLM by adjusting the blazing function, and obtain a 1.5 times increase in first order diffracted power. Even a perfect SLM with 2π phase throw can produce undesired effects in some situations; for example in holographic optical tweezers it is common to find unwanted “ghost spots” near to the array of first-order spots. Modulating the amplitude, by spatially modulating the blazing function, allows us to suppress the ghost spots. This increases the contrast between desired and unwanted spots by more than an order of magnitude.     

空间层叠矩形阵列式角多路解码光路设计

根据角多路技术原理,提出了一种矩形阵列空间层叠形式的解码光路结构和先分组解码再组内解码的两步解码方式,并针对本实验室的高功率准分子激光系统给出了具体的解码光路设计实例。该方法具有解码精度高,设计误差小,与光路准直、激光参数测量系统等兼容性好,便于加工制作和安装调试等优点。     

Propagation of generalized Mathieu–Gauss beams through paraxial misaligned optical systems

Based on the generalized diffraction integral, we derive an analytical formula for generalized Mathieu–Gauss beams (gMGBs) passing through an apertured misaligned optical system. Furthermore, we use the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions to establish an approximate propagation equation of gMGBs through paraxial circularly apertured optical system. As an example, the propagation of ordinary and modified zeroth order MGBs through a misaligned thin lens is studied numerically.     

环状平顶光束的传输特性研究

利用偏心高斯光束相干叠加方法，建立了柱坐标系下环状平顶光束模型.采用广义强度二阶矩定义，推导出环状光束广义M2因子的解析表达式.利用广义衍射积分理论，给出环状光束经过近轴ABCD光学系统的传输公式，并进一步给出了环状平顶光束修正的菲涅耳数定义.分析了环状平顶光束在自由空间的传输规律.研究结果表明，该模型可统一描述基模高斯光束、环状高斯光束以及环状平顶光束.环状平顶光束的广义M2因子和环状平顶光束的传输特性与其阶数及遮拦比有关.     

紫外衍射微透镜阵列的设计与制备

为了提高紫外焦平面阵列的填充因子,可以通过微透镜阵列与紫外焦平面阵列的集成,以改善紫外焦平面阵列的探测性能。根据标量衍射理论设计了用于日盲型紫外焦平面阵列的128×128衍射微透镜阵列,其工作中心波长为350nm,单元透镜F数为F/3.56。采用组合多层镀膜与剥离的工艺方法制备了128×128衍射微透镜阵列,对具体的工艺流程和制备误差进行了分析,测量了衍射微透镜阵列的光学性能。实验结果表明:衍射微透镜阵列的衍射效率为88%,与理论值95%有偏差,制备误差主要来自对准误差和线宽误差。紫外衍射微透镜阵列具有均匀的焦斑分布,与紫外焦平面阵列单片集成能较好地改善器件的整体性能。     

Designing and fabricating diffractive optical elements with a complex profile by interference

We demonstrate a novel (to our knowledge) method for the design and the fabrication of diffractive optical elements (DOEs) with an arbitrary complex phase profile based on interference. The DOEs are designed to modulate the complex light wave by the analytical formulas, and an asymmetric holographic DOE with cubic phase modulation is fabricated by a two-step exposure technique. The desired Airy beams are produced experimentally, which demonstrates the validity of this method. It is a simple approach with a low cost for the design and the fabrication of DOEs with a large area and arbitrary phase distribution.     

Generalized Helmholtz-Gauss beam and its transformation by paraxial optical systems

We introduce the generalized Helmholtz-Gauss (gHzG) beam and analyze its propagation through optical systems described by ABCD matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive a closed-form expression for the fractional Fourier transform of gHzG beams.     

Appearance of fractional vortex dipoles by using spiral linear zone plate

We present a novel technique based on linear zone plate (LZP) by which linear singularities regarded as fractional vortex dipoles are efficiently generated. Our approach requires applying spiral phase to a LZP, so fractional vortex dipoles are then acquired. By also implementing transverse phase shift to the spiral LZP, we are able to equally divide the number of the produced dark beams carrying mixed phase dislocations into two transverse separate parts. As a result, by varying a so called the controlling parameter the lateral positions of the focused fractional vortex dipoles are changed. Since we are able to generate dark beams in different and specific linear positions, therefore we suggest these features will be of great interest in one-dimensional optical trapping. All results are completely verified by experimental works.     

Decomposition of acoustic fields in quantised Bessel beams

Bessel beams are non-diffracting solutions to the wave equation, which become limited diffraction beams when implemented on finite apertures. In previous work we have applied Fourier-Bessel theory to deduce theoretically that the quantization of the Bessel beam profile on annular arrays results in a field which is a sum of limited diffraction fields. Here we demonstrate this for a five-ring, 20-mm diameter, 2.5-MHz transducer. The quantized field comprises a weighted sum of a main component corresponding to the desired field, along with three other major components and 28 lesser components representing undesired field components. The three major components correspond to limited diffraction beams with narrower beamwidths and shorter depths of field than the desired beam, and we show that these account for most of the discrepancies between the desired field and actual quantized field. An estimate and an interpretation of the number of field components as a function of the wavenumber are also given.     

Generation of radially polarized light beams of high quality using a step-index optical fiber

We present an experimental setup to generate radially polarized beams without using high-cost optical elements. In the setup a four-segment polarization converter is used in front of the fiber to produce a pseudo radially polarized beam. A traditional step-index fiber which supports only LP₀₁ and LP₁₁ modes is then used as a mode-cleaning device. A commercial mechanical fiber-squeezer polarization controller is applied to produce adequate pressure and twist onto the fiber. The four-segment polarization converter and the fiber squeezer polarization controller are adjusted by turns for improving the beam quality in intensity and polarization. Additionally, several methods of characterizing the polarization properties of radially polarized beams are reviewed. One of the latest methods is applied for characterizing the polarization properties of the radially polarized beams produced by using our technique. The results show the highquality of the obtained beams.     

Self-diffraction and Z-scan studies in organic dye doped thin films

Self-diffraction in Acid Red 87 (eosin Y) dye doped thin films is studied using argon ion laser (514.5 nm). Growth of self-diffraction grating is monitored by measuring intensities of various diffraction orders. This study has resulted in the observation of phase variation between the contributing beams in any diffracted order. This change of phase is measured at various stages of grating formation. Due to self-phase modulation, circular concentric rings pattern is obtained in the far field. The observed fluctuation in this pattern may be due to the phase variation between the contributing beams in any diffracted order. Z-scan technique is used to study the optical non-linearity of the sample.     

Theoretical conversion of the hypergeometric-Gaussian beams family into a high-order spiraling Bessel beams by a curved fork-shaped hologram

Based on the process of the Fresnel diffraction, the possibility of generating a new type of laser beams family by illuminating a curved fork-shaped hologram, with an input hypergeometric-Gaussian beams family of orders n and m is studied in this paper. The theoretical and the numerical results showed that, at the output plane, a high order spiraling Bessel vortex beam is produced. This vortex beam is divergence or non-divergence depending upon the waist position of the input hypergeometric-Gaussian beams, regarding the plane where the curved fork-shaped hologram is situated. Analytical expressions of the amplitude and the intensity distribution of the diffracted wave field are calculated and deduced using the stationary phase method. The actual work generalizes also the Fresnel diffraction study of some subfamilies of the hypergeometric-Gaussian beams family, such as: fundamental Gaussian, hollow Gaussian, modified quadratic Bessel–Gaussian and elegant Laguerre–Gaussian beams.     

用于并行激光直写的连续深浮雕衍射透镜阵列研究

研究了一种用于并行激光直写的连续深浮雕衍射透镜阵列方法.该方法采用连续浮雕衍射透镜阵列替换传统并行激光直写中的物镜阵列,在兼顾系统分辨力基础上,克服了波带片等衍射透镜阵列衍射效率低的缺点|同时因采用深浮雕结构优化环带宽度,可降低阵列的制作难度.针对并行激光直写系统阵列F/#小的特点,在建立连续深浮雕衍射透镜阵列非旁轴近似聚焦模型基础上,设计、制作和测试了波长为441.6 nm,F/#为7.5的连续深浮雕衍射透镜阵阵列.测试结果表明：该阵列的衍射效率优于70%,远高于波带片阵列的40%.