Imaging of trace species distributions by degenerate four-wave mixing: diffraction effects, spatial resolution, and image referencing

We describe the theory of imaging by degenerate four-wave mixing (DFWM) using a standard diffraction theory of imaging by coherent light. We demonstrate that, even with the phase-conjugating geometry, no aberration correction can be achieved by DFWM imaging. We demonstrate the coherent nature of DFWM image formation using spatially modulated signals generated in flame OH in the phase-conjugating geometry. The intensity distribution in the Fourier plane of a telecentric lens system is shown to be the spatial Fourier transform of the object distribution characteristic of coherent imaging. The brightness of the DFWM signals exceeds that of similar laser-induced fluorescence signals that can be discriminated by restricting the aperture of the imaging system while still allowing a spatial resolution of approximately 70 ?m. DFWM imaging with the forward-folded boxcars geometry is demonstrated and used in a simple referencing scheme to compensate for structure on the images imposed by nonuniformity of the laser beams employed. Images formed in NO are used to illustrate that structure on a scale of less than 100 ?m arising from beam inhomogeneity can be removed by this referencing technique.     

Edge-ringing in Partially Coherent Imaging

A simple condition is shown to be necessary and sufficient to suppress edge-ringing in optical imaging. This criterion is valid in the presence of aberrations and apodization, and for all cases of (spatially stationary) partially coherent illumination. The edge-ringing tendencies of an optical system may be assessed through the use of two new performance functions which form a Fourier-transform pair. One of these performance functions is related to the ‘transmission cross-coefficient’ which appears in the theory of partially coherent imaging. In the coherent limit this performance function reduces to the amplitude transfer function (pupil function), and in the incoherent limit it reduces to the Optical Transfer Function (OTF). The use of this performance function for the general assessment of partially coherent imaging systems is suggested.     

Properties of Output Signal Moments of Optical Processors

General results for the output signal moments are given for both linear and bilinear systems and both space-variant and space-invariant processing. As an example of a bilinear system, a partially coherent system is considered. The properties of intensity moments for a Fourier optical processor and an imaging system with partially coherent illumination are also investigated.     

Coherent-array imaging using phased subarrays. Part I: basic principles

The front-end hardware complexity of a coherent array imaging system scales with the number of active array elements that are simultaneously used for transmission or reception of signals. Different imaging methods use different numbers of active channels and data collection strategies. Conventional full phased array (FPA) imaging produces the best image quality using all elements for both transmission and reception, and it has high front-end hardware complexity. In contrast, classical synthetic aperture (CSA) imaging only transmits on and receives from a single element at a time, minimizing the hardware complexity but achieving poor image quality. We propose a new coherent array imaging method--phased subarray (PSA) imaging--that performs partial transmit and receive beam-forming using a subset of adjacent elements at each firing step. This method reduces the number of active channels to the number of subarray elements; these channels are multiplexed across the full array and a reduced number of beams are acquired from each subarray. The low-resolution subarray images are laterally upsampled, interpolated, weighted, and coherently summed to form the final high-resolution PSA image. The PSA imaging reduces the complexity of the front-end hardware while achieving image quality approaching that of FPA imaging.     

用于分数傅里叶域滤波位相元件设计新算法

基于部分相干成像和分数傅里叶变换理论,建立成像系统的分数傅里叶域滤波模型,提出了可快速设计分数域位相型滤波片的 FrPI 算法。此算法将逆向设计预设初位相与分数傅里叶迭代技术相结合,针对成像系统中不同的设计要求可快速设计出所需的分数域滤波片结构。模拟结果表明,对数值孔径有限的部分相干成像系统,使用新算法设计的分数域滤波片,可有效补偿由于高频损失带来的图像失真,从而使局部线宽偏差和面积偏差分别由滤波前的 36.548nm 和 39.09%下降到了 15.234nm 和 7.72%,明显减少了空间像畸变。     

Correlated imaging with partially coherent light for remote sensing

Based on the extended Huygens–Fresnel integral and the theory of coherence of light field, we have investigated the correlated imaging by using the transverse normalized second-order intensity fluctuation correlation function with partially coherent light radiation. The imaging for a reflected object with relative long distance is determined by the feature of speckle-to-speckle correlation. By using the correlation function, we study the effects of imaging distance, the sizes of object lens and reference lens, the source’s transverse coherent width and its transverse size on the quality of correlated imaging. Numerical results show that the parameters of imaging system and the properties of partially coherent light source have significant influences on the imaging resolution and visibility. For an object lens with large enough diameter, the resolution is determined by the transverse coherent width of light source. On the contrary, it depends on the aperture of object lens. The magnification of the system depends only on the propagation distance. This speckle-to-speckle correlated imaging with unbalanced arms have potential applications in remote sensing due to its unique features.     

Coherent imaging with two-dimensional focal-plane arrays: design and applications

Scanned, single-channel optical heterodyne detection has been used in a variety of lidar applications from ranging and velocity measurements to differential absorption spectroscopy. We describe the design of a coherent camera system that is based on a two-dimensional staring array of heterodyne receivers for coherent imaging applications. Experimental results with a single HgCdTe detector translated in the image plane to form a synthetic two-dimensional array demonstrate the ability to obtain passive heterodyne images of chemical vapor plumes that are invisible to normal video infrared cameras. We describe active heterodyne imaging experiments with use of focal-plane arrays that yield hard-body Doppler lidar images and also demonstrate spatial averaging to reduce speckle effects in static coherent images.     

Speckle-reduced three-dimensional volume holographic display by use of integral imaging

We propose a method to implement a speckle-reduced coherent three-dimensional (3D) display system by a combination of integral imaging and photorefractive volume holographic storage. The 3D real object is imaged through the microlens array and stored in the photorefractive crystal. During the reconstruction process a phase conjugate reading beam is used to minimize aberration, and a rotating diffuser located on the imaging plane of the lens array is employed to reduce the speckle noise. The speckle-reduced 3D image with a wide viewing angle can be reconstructed by use of the proposed system. Experimental results are presented and optical parameters of the proposed system are discussed in detail.     

Carbon contamination analysis and its effect on extreme ultra violet mask imaging performance using coherent scattering microscopy/in-situ accelerated contamination system

The coherent scattering microscopy/in-situ accelerated contamination system (CSM/ICS) is a developmental metrology tool designed to analyze the impact of carbon contamination on the imaging performance. It was installed at 11B EUVL beam-line of the Pohang Accelerator Laboratory (PAL). Monochromatized 13.5 nm wavelength beam with Mo/Si multilayer mirrors and zirconium filters was used. The CSM/ICS is composed of the CSM for measuring imaging properties and the ICS for implementing acceleration of carbon contamination. The CSM has been proposed as an actinic inspection technique that records the coherent diffraction pattern from the EUV mask and reconstructs its aerial image using a phase retrieval algorithm. To improve the CSM measurement accuracy, optical and electrical noises of main chamber were minimized. The background noise level measured by CCD camera was approximately 8.5 counts (3 sigma) when the EUV beam was off. Actinic CD measurement repeatability was <1 A (3 sigma) at 17.5 nm line and space pattern. The influence of carbon contamination on the imaging properties can be analyzed by transferring EUV mask to CSM imaging center position after executing carbon contamination without a fine alignment system. We also installed photodiode and ellipsometry for in-situ reflectivity and thickness measurement. This paper describes optical design and system performance observed during the first phase of integration, including CSM imaging performance and carbon contamination analysis results.     

激光相干阵列成象雷达系统光束整形的研究

激光相干阵列成象雷达系统中本振光波前与信号光波前匹配与否直接影响系统的灵敏度和分辨力。采用共轭光栅合成技术对相干成象本振光束作整形处理，以适应探测器件列及合成输出满足最佳信噪比条件。     

Optical Bilinear Transformations: General Properties

Because of the quadratic relation between the optical field and intensity, an inherent non-linearity exists in almost all optical systems. A class of non-linear transformations which we call bilinear (quadratic with memory) is defined; its properties and relevance to optical imaging systems are discussed. For space-invariant systems, a generalized transfer function is defined which characterizes the bilinear system completely. We also examine the approximate linearization of bilinear systems for low-contrast images, and the propagation of noise through such systems. Special emphasis is given to the partially coherent system which is but a special case of this general bilinear system.     

Spatial partially coherent imaging

We introduce the partial coherence response function for describing the behaviour of imaging systems under spatial partially coherent illumination in the centre and the diierence coordinates notation. It involves the impulse response of the system and the spatial coherence properties of the illumination. It is shown that this function is the image cross-spectral density for a Young's pair of pinholes attached at the object plane. Furthermore, the partial coherence response function and the partial coherence transfer function constitute a Fourier pair on which the Fourier representation of partially coherent imaging can be based.     

包含光源面积的整体相位衬度调制传递函数

在部分相干光学理论的基础上,建立了一个整体相位衬度调制传递函数理论模型,模型中包含了光源焦点面积大小对X线相衬成像系统相位调制的影响,并通过数值模拟和数据计算,提出了X线相衬成像系统对光源焦点面积的选择原则,和焦点面积确定条件下的成像参数优化方法,结果表明,这种包含X线光源面积因素的相位衬度调制传递函数模型,更能反映整个系统的光学成像性能,更能有利于成像参数的优化设计。     

Numerical experiment of the Shannon entropy in partially coherent imaging by Koehler illumination to show the relationship to degree of coherence

This paper describes the Shannon entropy in a partially coherent imaging system with Koehler illumination. Numerical simulation shows that the entropy has a one-to-one relationship with the normalized mutual intensity given by the van Cittert-Zernike theorem. Analytical evaluation shows that the entropy is consistent with the definition of coherence and incoherence, which is also verified by numerical simulations. Additional numerical experiments confirm that the entropy depends on the source intensity distribution, polarization state of the source, object, and pupil. Therefore, the entropy quantitatively measures the degree of coherence of the partially coherent imaging system.     

Extreme-ultraviolet lensless Fourier-transform holography

We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed.     

Schlieren systems with coherent illumination for quantitative measurements

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.     

Phase recovery and lensless imaging by iterative methods in optical,X-ray and electron diffraction

Thomas Young's quantitative analysis of interference effects provided the confidence needed to revive the wave theory of light, and firmly established the concept of phase in optics. Phase plays a similarly fundamental role in matter-wave interferometry, for which the field-emission electron microscope provides ideal instrumentation. The wave-particle duality is vividly demonstrated by experimental 'Young's fringes' using coherent electron beams under conditions in which the flight time is less than the time between particle emission. A brief historical review is given of electron interferometry and holography, including the Aharonov-Bohm effect and the electron Sagnac interferometer. The simultaneous development of phase-contrast imaging at subnanometre spatial resolution has greatly deepened our understanding of atomic processes in biology, materials science and condensed-matter physics, while electron holography has become a routine tool for the mapping of electrostatic and magnetic fields in materials on a nanometre scale. The encoding of phase information in scattered farfield intensities is discussed, and non-interferometric, non-crystallographic methods for phase retrieval are reviewed in relationship to electron holography. Examples of phase measurement and diffraction-limited imaging using the hybrid input-output iterative algorithm are given, including simulations for soft X-ray imaging, and new experimental results for coherent electron and visible-light scattering. Image reconstruction is demonstrated from experimental electron and visible-light Fraunhofer diffraction patterns. The prospects this provides for lensless imaging using particles for which no lenses exist (such as neutrons, condensates, coherent atom beams and X-rays) are discussed. These new interactions can be expected to provide new information, perhaps, for example, in biology, with the advantage of less damage to samples.     

Coherent diffractive imaging using short wavelength light sources

Techniques that recover images from diffraction data obtained using coherent short-wavelength light sources are currently under active development for applications in nanotechnology and structural biology. In this review, an outline of paraxial optics is provided in a form that is sufficiently general to incorporate the coherence properties and frequency structure of illumination sources used in diffractive imaging applications. The Fourier phase problem is formulated in the context of imaging algorithms that are designed to obtain uniquely-determined phase distributions from measurements of diffraction data. The properties of several iterative phase retrieval algorithms for both coherent and partially-coherent diffractive imaging applications are presented in a unified formalism, together with a brief discussion of a non-iterative technique. Approaches to diffractive imaging based on Fraunhofer and Fresnel diffraction configurations are compared. Applications are described utilising quasi-monochromatic third-generation synchrotron X-ray sources and polychromatic high-harmonic generation table-top soft X-ray sources. The review concludes with a consideration of proposed applications of diffractive imaging approaches to the determination of biomolecular structures from isolated molecules using fourth-generation X-ray free-electron laser sources.     

Information-based optical design for binary-valued imagery

Applications such as optical data storage, optical computing, and optical interconnects require optical systems that manipulate binary-valued images. Such an optical system can be viewed as a two-dimensional array of binary communication channels. This perspective is used to motivate the use of pagewise mutual information as a metric for optical system analysis and design. Fresnel propagation and coherent imaging both are analyzed in terms of mutual-information transmission. An information-based space-bandwidth product is used to analyze the trade-off between the numerical aperture and the number of image pixels in a coherent 4f system. We propose a new merit function to facilitate information-based optical system design. Information maximization and bit-error-rate minimization both are possible with the new radially weighted encircled-energy merit function. We demonstrate the use of this new merit function through a design example and show that the information throughput is increased by 8% and the bit-error rate is reduced by 36% when compared with systems designed with traditional criteria.