Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes through complex ABCD optical systems

The change of coherence and polarization of an electromagnetic beam modulated by a random anisotropic phase screen passing through any optical system is found within the framework of complex ABCD-matrix theory This means that the formalism can treat imaging and Fourier transform and free-space optical systems, as well as fractional Fourier transform systems, with finite-size limiting apertures of Gaussian transmission shape. Thus, the current paper shall be considered as a continuation, extension, and generalization of a previous work by Shirai and Wolf [J. Opt. Soc. Am. A21, 1907 (2004)]. It will be shown that the inclusion of apertures in the optical system strongly influences not only the propagation of spatial coherence but also the degree of polarization of a propagating field. Analytical expressions of coherence and polarization propagation will be given in terms of the matrix elements for any complex optical system.     

Spatial coherence of backscatter for the nonlinearly produced second harmonic for specific transmit apodizations

To be successful, correlation-based, phase-aberration correction requires a high correlation among backscattered signals. For harmonic imaging, the spatial coherence of backscatter for the second harmonic component is different than the spatial coherence of backscatter for the fundamental component. The purpose of this work was to determine the effect of changing the transmit apodization on the spatial coherence of backscatter for the nonlinearly generated second harmonic. Our approach was to determine the effective apodizations for the fundamental and second harmonic using both experimental measurements and simulations. Two-dimensional measurements of the transverse cross sections of the finite-amplitude ultrasonic fields generated by rectangular and circular apertures were acquired with a hydrophone. Three different one-dimensional transmit apodization functions were investigated: uniform, Riesz, and trapezoidal. An effective apodization was obtained for each transmit apodization by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. Predictions of the spatial coherence of backscatter were obtained using the pulse-echo Van Cittert-Zernike theorem. In all cases the effective apodization at 2f was narrower than the transmit apodization. We demonstrate that certain transmit apodizations result in a greater spatial coherence of backscatter at the second harmonic than at the fundamental.     

Immobilization of biomolecules onto surfaces according to ultraviolet light diffraction patterns

We developed a method for immobilization of biomolecules onto thiol functionalized surfaces according to UV diffraction patterns. UV light-assisted molecular immobilization proceeds through the formation of free, reactive thiol groups that can bind covalently to thiol reactive surfaces. We demonstrate that, by shaping the pattern of the UV light used to induce molecular immobilization, one can control the pattern of immobilized molecules onto the surface. Using a single-aperture spatial mask, combined with the Fourier transforming property of a focusing lens, we show that submicrometer (0.7 μm) resolved patterns of immobilized prostate-specific antigen biomolecules can be created. If a dual-aperture spatial mask is used, the results differ from the expected Fourier transform pattern of the mask. It appears as a superposition of two diffraction patterns produced by the two apertures, with a fine structured interference pattern superimposed.     

Spatial coherence properties of a multiple aperture system an analysis based on the Walsh functions

Abstract

Analysis of the spatial coherence of the light transmitted by an optical device composed of a periodical array of identical apertures is developed by employing an approach based on the properties of the binary Walsh functions. The successive interactions between each aperture, and the mutual intensity characterizing the coherence state of the transmitted light, can be adequately explained through the behaviour of the Walsh-Hadamard spectrum associated with the intensity distribution resulting from the far-field propagated light at the output of the aperture array.     

光学邻近效应与掩模特征尺寸的关系

依据物的空间频谱分布，部分相干成象理论及空间滤波概念，分析了投影光刻中的掩模特征尺寸与光学邻近效应的关系，并通过成象系统的数值孔长对ＯＰＥ的影响的模拟验证了分析结果。     

Effects of source coherence and aperture array geometry on optical sectioning strength in direct-view microscopy

Laser sources offer a possible solution to the problem of low light throughput in direct-view microscopes (DVMs). However, coherent source DVMs have been shown to suffer from problems such as increased sidelobes in the depth response because of coherent cross talk between neighboring apertures. We explore theoretically how source coherence affects the depth responses of DVMs by employing various aperture spacings and number of apertures. We show that, contrary to expectation, closely spaced apertures can result in decreased full width at half-maximum of the depth response curve. We explain this as an effect of destructive interference when cross talk between neighboring apertures occurs. Using apertures arranged in a square grid as an example, we move on to show that the use of aperture arrays that consist of regularly arranged apertures can accentuate the problematic sidelobes of the depth response. We show that arranging pinholes in a rectangular grid rather than a square grid can improve the optical sectioning strength significantly. Finally, by examination of the depth responses corresponding to the infinite-pinhole-array limit, we make some general statements about source coherence and the characteristics of arrays that are likely to perform well.     

Nano-fabrication with a flexible array of nano-apertures

We report fabrication and use of a flexible array of nano-apertures for photolithography on curved surfaces. The batch-fabricated apertures are formed of metal-coated silicone tips. The apertures are formed at the end of the silicone tips by either electrochemical etching of the metal or plasma etching of a protective mask followed by wet chemical etching. The apertures are as small as 250 nm on substrates larger than several millimeters. We demonstrate how the nano-aperture array can be used for nano-fabrication on flat and curved substrates, and show the subsequent fabrication steps to form large arrays of sub-micron aluminum dots or vertical silicon wires.     

Polarization-based compensation of astigmatism

One approach to aberration compensation of an imaging system is to introduce a suitable phase mask at the aperture plane of an imaging system. We utilize this principle for the compensation of astigmatism. A suitable polarization mask used on the aperture plane together with a polarizer-retarder combination at the input of the imaging system provides the compensating polarization-induced phase steps at different quadrants of the apertures masked by different polarizers. The aberrant phase can be considerably compensated by the proper choice of a polarization mask and suitable selection of the polarization parameters involved. The results presented here bear out our theoretical expectation.     

Experimental geometry for simultaneous beam characterization and sample imaging allowing for pink beam Fourier transform holography or coherent diffractive imaging

One consequence of the self-amplified stimulated emission process used to generate x rays in free electron lasers (FELs) is the intrinsic shot-to-shot variance in the wavelength and temporal coherence. In order to optimize the results from diffractive imaging experiments at FEL sources, it will be advantageous to acquire a means of collecting coherence and spectral information simultaneously with the diffraction pattern from the sample we wish to study. We present a holographic mask geometry, including a grating structure, which can be used to extract both temporal and spatial coherence information alongside the sample scatter from each individual FEL shot and also allows for the real space reconstruction of the sample using either Fourier transform holography or iterative phase retrieval.     

A mathematical model for wet-chemical diffusion-controlled mask etching through a circular hole

Asymptotic solutions are presented for diffusion-controlled wet-chemical etching through a round hole in a mask. The three-dimensional diffusion field is assumed to be axisymmetric and fully developed. Two time regimes are considered. The first applies when the etched depth is small in comparison with the width of the mask opening. In the second, the depth of etching is much greater than the width of the mask opening. Explicit solutions are found for the shape of the etched surface as a function of the physical parameters. Among other things it is found that, as long as the etched pits are shallow, etching through small apertures is faster than through larger ones. The opposite is true for deep pits.     

Optical Synthetic Aperture Analogues of Two Radio Interferometers

Experimental and theoretical results are given for the one and two-dimensional Covington-Drane optical synthetic apertures and the thin annular aperture. The segmented thin annulus is also discussed as a special case of the thin continuous annulus. Experiments are performed by masking a diffraction-limited lens with the appropriate pupil function and then measuring the imaging characteristics of the aperture. All the synthetic apertures are shown to have the full synthetic MTF's predicted by the theory. The Covington-Drane doubles the resolution of the central aperture and the thin annular apertures synthesize the full lens spatial frequency response. Optical processing of synthetic aperture photography is discussed and examples of inverse spatial filters are given.     

Liquid-crystal projection image depixelization by spatial phase scrambling

A technique that removes the pixel structure by scrambling the relative phases among multiple spatial spectra is described. Because of the pixel structure of the liquid-crystal-display (LCD) panel, multiple spectra are generated at the Fourier-spectrum plane (usually at the back focal plane of the imaging lens). A transparent phase mask is placed at the Fourier-spectrum plane such that each spectral order is modulated by one of the subareas of the phase mask, and the phase delay resulting from each pair of subareas is longer than the coherent length of the light source, which is approximately 1 μm for the wideband white light sources used in most of LCD's. Such a phase-scrambling technique eliminates the coherence between different spectral orders; therefore, the reconstructed images from the multiple spectra will superimpose incoherently, and the pixel structure will not be observed in the projection image.     

Optimization of a beam delivery system for a short-pulse KrF laser used for material ablation

We present an optical arrangement for spatial homogenization of an UV beam carrying a short pulse (500 fs) to be used for material ablation. Conventional cylindrical fly's eye lens homogenizers (CFELH's) introduce unwanted interference effects into a beam caused by the high spatial coherence of short pulses. To prevent the disturbing effect of these intensity modulations, one can couple a low-loss distributed delay device to the CFELH. With the new design an intensity nonuniformity of <+/-5% rms can be obtained. High-resolution images of the beam profile show complete removal of the interference modulation. The pulse duration after homogenization is 12.5 ps. We performed preliminary ablation experiments in polyimide samples both by direct irradiation and by mask imaging. Uniformity and edge quality of the results are more than satisfactory, and the undesirable structure caused by interference is completely removed.     

Relevance of mask-roughness-induced printed line-edge roughness in recent and future extreme-ultraviolet lithography tests

The control of line-edge roughness (LER) of features printed in photoresist poses significant challenges to next-generation lithography techniques such as extreme-ultraviolet (EUV) lithography. Achieving adequately low LER levels requires accurate resist characterization as well as the ability to separate resist effects from other potential contributors to LER. One potentially significant contributor to LER arises from roughness on the mask coupling to speckle in the aerial image and consequently to LER in the printed image. Here I numerically study mask surface roughness and phase roughness to resist LER coupling both as a function of illumination coherence and defocus. Moreover, the potential consequences of this mask effect for recent EUV lithography experiments is studied through direct comparison with experimental through-focus printing data collected at a variety of coherence settings. Finally, the effect that mask roughness will play in upcoming 0.3-numerical-aperture resist testing is considered.     

CCD实时图像采集处理系统测量光场相干性

本文描述了用CCD摄像机及DIP图像处理系统在双频光栅剪切干涉光路中测量光场相干性的原理和实测结果,以及讨论实验光路中逶镜非准直因素对测量结果的影响。     

Simultaneous measurement of out-of-plane displacement and slope using a multiaperture DSPI system and fast Fourier transform

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second after loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center.     

Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence

The lognormal (LN) and gamma-gamma (GG) distributions are compared to simulated and experimental data of the irradiance fluctuations of a Gaussian beam wave propagating through the atmosphere along a horizontal path, near the ground, in the moderate-to-strong turbulence regime. Irradiance data were collected simultaneously at three receiving apertures of different sizes. Atmospheric parameters were inferred from the measurements and scintillation theory and were used to develop the parameters for the theoretical probability density functions. Numerical simulations were produced with the same C(n)(2) value as the experimental data. Aperture-averaging effects were investigated by comparing the irradiance distributions for the three apertures at two different values of the structure parameter C(n)(2), and, hence, different values of the coherence radius rho(0). For the moderate-to-strong fluctuation regime, the GG distribution provides a good fit to the irradiance fluctuations collected by finite-sized apertures that are significantly smaller than rho(0). For apertures larger than or equal to rho(0), the irradiance fluctuations appear to be LN distributed.     

Digital speckle pattern interferometry using spatial phase shifting: influence of intensity and phase gradients

Spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS) provides the phase information due to the object displacement from two images, one stored before and other after loading. The technique needs a carrier fringe system. The double aperture mask in front of the imaging system is one of the methods for introducing the spatial carrier frequency for phase evaluation. The size of the apertures and their separation are important criteria to obtain appropriate phase shift/column within the desired size of the speckle for phase retrieval. The assumptions of constant intensity and phase on adjacent pixels of the camera while calculating phase in spatial phase shifting (SPS) are not met as the speckled object wave contains intensity and phase gradients, resulting in distortions in the calculated phase profiles. In this paper we discuss a strategy to overcome these problems. The contrast of the correlation fringe obtained using this approach is much improved. It also eliminates the distortion in the unwrapped phase map like wave ripples. The experimental results on an edge clamped circular plate loaded at the center are presented.     

Phase-only optical decryption of a fixed mask

We present a system for the implementation of phase-only optical decryption of an encrypted fixed phase mask. We achieve decryption by superimposing a decrypting phase key, implemented on a phase-only spatial light modulator with an encrypted phase mask in two equivalent image planes in an optical system. The decrypted phase information is retrieved by the generalized phase-contrast technique. We have constructed a compact experimental system that uses a 635-nm diode laser in which a fixed encrypted 0/pi binary phase mask is decrypted by a binary phase key produced electronically on the spatial light modulator. The key is aligned by electronic scrolling of its position with respect to the mask.     

Effect of mask-roughness on printed contact-size variation in extreme-ultraviolet lithography

Relying on reflective mask technology, extreme-ultraviolet (EUV) lithography is particularly vulnerable to mask substrate roughness. Previous research has shown mask roughness to play a significant role in printed line-edge roughness (LER). Here the analysis of mask-roughness effects is extended to printed contact-size variations. Unlike LER, illumination partial coherence is found to have little affect on the results for contacts that are near the diffraction limit. Analysis shows that, given the current state-of-the-art EUV mask, mask roughness has a significant effect on the process window for small contacts. The analysis also shows that a significant portion of the contact-size variation observed in recent 0.1-numerical-aperture EUV exposures can be attributed to the mask-roughness effect studied here.