Proceedings Volume 9630

Optical Systems Design 2015: Computational Optics

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Proceedings Volume 9630

Optical Systems Design 2015: Computational Optics

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Volume Details

Date Published: 23 October 2015
Contents: 10 Sessions, 32 Papers, 0 Presentations
Conference: SPIE Optical Systems Design 2015
Volume Number: 9630

Table of Contents

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Table of Contents

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  • Front Matter: Volume 9630
  • Imaging Applications I
  • Optical Field Propagation Techniques
  • Applications in Medicine and Energy Harvesting
  • Non-Imaging Applications
  • Imaging Applications II
  • Electromagnetic Field Methods
  • Inverse Imaging Problems
  • Computational Optics
  • Poster Session
Front Matter: Volume 9630
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Front Matter: Volume 9630
This PDF file contains the front matter associated with SPIE Proceedings Volume 9630 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.
Imaging Applications I
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3D imaging and ranging in a snapshot
Imaging samples with a depth in excess of the depth of field of the objective poses a serious challenge in microscopy. The available techniques such as focus-stacking accomplish the task; however, besides necessitating complicated optical and mechanical arrangements, these techniques often exhibit very long acquisition times. As a result, their applicability is limited to static samples. We describe a simple and practical hybrid 3D imaging technique which permits the acquisition of 3D images in a single snapshot. Additionally, the proposed method solves the post-recovery artefact formation problem which plagues hybrid imaging systems; thus, enabling high-quality, artefact-free images to be obtained. Experimental results indicate that this method can yield an image quality comparable to that given by a focus-stack (which can require up to a few hundred snapshots) from a single snapshot.
Large-scale analytical Fourier transform of photomask layouts using graphics processing units
Compensation of lens-heating effects during the exposure scan in an optical lithographic system requires knowledge of the heating profile in the pupil of the projection lens. A necessary component in the accurate estimation of this profile is the total integrated distribution of light, relying on the squared modulus of the Fourier transform (FT) of the photomask layout for individual process layers. Requiring a layout representation in pixelated image format, the most common approach is to compute the FT numerically via the fast Fourier transform (FFT). However, the file size for a standard 26- mm×33-mm mask with 5-nm pixels is an overwhelming 137 TB in single precision; the data importing process alone, prior to FFT computation, can render this method highly impractical. A more feasible solution is to handle layout data in a highly compact format with vertex locations of mask features (polygons), which correspond to elements in an integrated circuit, as well as pattern symmetries and repetitions (e.g., GDSII format). Provided the polygons can decompose into shapes for which analytical FT expressions are possible, the analytical approach dramatically reduces computation time and alleviates the burden of importing extensive mask data. Algorithms have been developed for importing and interpreting hierarchical layout data and computing the analytical FT on a graphics processing unit (GPU) for rapid parallel processing, not assuming incoherent imaging. Testing was performed on the active layer of a 392- μm×297-μm virtual chip test structure with 43 substructures distributed over six hierarchical levels. The factor of improvement in the analytical versus numerical approach for importing layout data, performing CPU-GPU memory transfers, and executing the FT on a single NVIDIA Tesla K20X GPU was 1.6×104, 4.9×103, and 3.8×103, respectively. Various ideas for algorithm enhancements will be discussed.
Automated simulation and evaluation of autostereoscopic multiview 3D display designs by time-sequential and wavelength-selective filter barrier
Mathias Kuhlmey, Silvio Jurk, Bernd Duckstein, et al.
A novel simulation tool has been developed for spatial multiplexed 3D displays. Main purpose of our software is the 3D display design with optical image splitter in particular lenticular grids or wavelength-selective barriers. As a result of interaction of image splitter with ray emitting displays a spatial light-modulator generating the autostereoscopic image representation was modeled. Based on the simulation model the interaction of optoelectronic devices with the defined spatial planes is described. Time-sequential multiplexing enables increasing the resolution of such 3D displays. On that reason the program was extended with an intermediate data cumulating component. The simulation program represents a stepwise quasi-static functionality and control of the arrangement. It calculates and renders the whole display ray emission and luminance distribution on viewing distance. The degree of result complexity will increase by using wavelength-selective barriers. Visible images at the viewer’s eye positon were determined by simulation after every switching operation of optical image splitter. The summation and evaluation of the resulting data is processed in correspondence to the equivalent time sequence. Hereby the simulation was expanded by a complex algorithm for automated search and validation of possible solutions in the multi-dimensional parameter space. For the multiview 3D display design a combination of ray-tracing and 3D rendering was used. Therefore the emitted light intensity distribution of each subpixel will be evaluated by researching in terms of color, luminance and visible area by using different content distribution on subpixel plane. The analysis of the accumulated data will deliver different solutions distinguished by standards of evaluation.
Optical Field Propagation Techniques
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Approximate solution of Maxwell’s equations by geometrical optics
Ray optics has constituted the fundament of optical modeling and design for more than 2000 years. In recent decades, the introduction of ray tracing software has brought a powerful optical design technology to everybody dealing with optics and photonics. However, with the development and availability of advanced light sources, the capability to produce micro and nano structures, the need for high NA systems, and a boost in the variety of applications and related demands on optical functions, the limitations of ray optics become obvious more often. Optical modeling based on physical optics is required and is the logical next step in the development of optical design. This requires a generalization of ray tracing and its connection with diffractive modeling techniques.
Simulations of general electromagnetic fields propagation through optically anisotropic media
Accurate and flexible simulation techniques for light propagation through components made out of optical anisotropic media are highly demanded. However it is found that most of the existing methods discuss only on specific cases, like for certain types of incident fields, or for certain kinds of anisotropies. We present, based on the previous works of various researchers, a comprehensive numerical approach that deals with arbitrary electromagnetic fields and any kind of optical anisotropy. Various examples are presented to show the validity.
A smooth field decomposition applied to modelling of scattering phenomena
Olga Baladron-Zorita, Huiying Zhong, Michael Kuhn, et al.
In this work the authors investigate the potential of a smooth field decomposition method to improve simulation efficiency in modelling scattering situations. Two examples of particular simulation set-ups are presented and analysed.
A vectorial ray-based diffraction integral for optical systems
Birk Andreas
The propagation of coherent laser light in optical systems is simulated by the vectorial ray-based diffraction integral (VRBDI) method which utilizes vectorial diffraction theory, ray aiming, differential ray tracing and matrix optics. On a global scale the method is not restricted to the paraxial approximation, whereas it is properly used for a local representation of the wavefront close to an aimed detection location. First, the field of a monochromatic continuous wave on an input plane is decomposed into spherical or plane wave components. Then, these components are represented by aimed ray tubes and traced through an optical system. Finally, the contributions are added coherently on an output plane whose position has to be chosen according to ray-aiming requirements. Provided that the apertures in the optical system are large with respect to the wavelength the results are fairly accurate.
Experimental method of optical coherence characterization in phase-space measurement
Jie-En Li, Jhih-Syuan Fu, Ming-Shu Hsiao, et al.
A novel approach of phase-space measurement made its debut with the experimental result. We first designed an experiment based on the Young’s interferometer to characterization the optical coherence property of light source. A well-known algorithm called Hough transformation was applied to deal with the misalignment of micro-lens array by post-processing. The phase-space image of plane wave was then reconstructed from the realigned raw image. Finally, the properties of this system were discussed.
Applications in Medicine and Energy Harvesting
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Untangled modes in multimode fibres for flexible microendoscopy
Martin Plöschner, Tomáš Tyc, Tomáš Čižmár
Small, fibre-based endoscopes have already improved our ability to image deep within the human body. A novel approach introduced recently utilised disordered light within a standard multimode optical fibre for lensless imaging. Importantly, this approach brought very significant reduction of the instruments footprint to dimensions below 100 μm. The most important limitations of this exciting technology is the lack of bending flexibility - imaging is only possible as long as the fibre remains stationary. The only route to allow flexibility of such endoscopes is in trading-in all the knowledge about the optical system we have, particularly the cylindrical symmetry. In perfect cylindrical waveguides we can find optical modes that do not change their spatial distribution as they propagate through. We show that typical fibers retain such highly ordered propagation of light over remarkably large distances, which allows correction operators to be introduced in imaging geometries in order to maintain high-quality performance even in such flexible micro-endoscopes.
Optical properties of textured sheets: an efficient matrix-based modelling approach
Nico Tucher, Johannes Eisenlohr, Peter Kiefel, et al.
A large variety of optical systems incorporate multiple textured surfaces for reflectance reduction, light redirection or absorptance enhancement. One example for such a system is a textured silicon wafer solar cell. We introduce the OPTOS (Optical Properties of Textured Optical Sheets) formalism for the modelling of light propagation and absorption in optically thick sheets with two arbitrary surface textures at the front and rear side, and demonstrate applications.

In contrast to many optical simulation techniques, which are tailored to specific surface morphologies, the OPTOS formalism is a matrix-based method that allows including textures that are described by different optical modelling techniques (e.g. ray optical or wave optical) within one simulation tool. It offers the computationally efficient simulation of light redistribution and non-coherent propagation inside thick sheets. After calculating redistribution matrices for each individual surface texture with the most appropriate technique, optical properties of the complete textured sheet, like e. g. angle dependent reflectance, transmittance or depth resolved absorptance, can be determined via iterative matrix multiplications (for propagation and redistribution) with low computational effort.

In this work, we focus on textured wafer-based silicon solar cells as application examples for the OPTOS formalism. The simulation enables us to investigate and optimize combinations of front and rear textures on solar cells in order to increase the photocurrent generation. A solar cell with inverted pyramid front side and a diffractive grating at the rear is found to show similar light trapping properties as one with Lambertian scattering at the rear.
Optical tomography by means of regularized MLEM
Charles L. Majer, Tina Urbanek, Jörg Peter
To solve the inverse problem involved in fluorescence mediated tomography a regularized maximum likelihood expectation maximization (MLEM) reconstruction strategy is proposed. This technique has recently been applied to reconstruct galaxy clusters in astronomy and is adopted here. The MLEM algorithm is implemented as Richardson-Lucy (RL) scheme and includes entropic regularization and a floating default prior. Hence, the strategy is very robust against measurement noise and also avoids converging into noise patterns. Normalized Gaussian filtering with fixed standard deviation is applied for the floating default kernel. The reconstruction strategy is investigated using the XFM-2 homogeneous mouse phantom (Caliper LifeSciences Inc., Hopkinton, MA) with known optical properties. Prior to optical imaging, X-ray CT tomographic data of the phantom were acquire to provide structural context. Phantom inclusions were fit with various fluorochrome inclusions (Cy5.5) for which optical data at 60 projections over 360 degree have been acquired, respectively. Fluorochrome excitation has been accomplished by scanning laser point illumination in transmission mode (laser opposite to camera). Following data acquisition, a 3D triangulated mesh is derived from the reconstructed CT data which is then matched with the various optical projection images through 2D linear interpolation, correlation and Fourier transformation in order to assess translational and rotational deviations between the optical and CT imaging systems. Preliminary results indicate that the proposed regularized MLEM algorithm, when driven with a constant initial condition, yields reconstructed images that tend to be smoother in comparison to classical MLEM without regularization. Once the floating default prior is included this bias was significantly reduced.
Non-Imaging Applications
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Simulation of laser radar tooling ball measurements: focus dependence
Daniel G. Smith, Anthony Slotwinski, Thomas Hedges
The Nikon Metrology Laser Radar system focuses a beam from a fiber to a target object and receives the light scattered from the target through the same fiber. The system can, among other things, make highly accurate measurements of the position of a tooling ball by locating the angular position of peak signal quality, which is related to the fiber coupling efficiency. This article explores the relationship between fiber coupling efficiency and focus condition.
Wave optics analysis of corner-cube retro-reflectors in near-to-eye displays based on scanning laser projectors
Seyedmahdi Kazempourradi, Erdem Ulusoy, Sven Holmstrom, et al.
In near to eye displays based on scanning laser projectors, retro-reflectors seem as convenient image relay components since they can ideally be placed at any location on the scanned beam path. In case of practical retro reflectors though, such as corner cube retro-reflectors (CCRs), the relayed image suffers from loss in quality and resolution due to the positional shift in the retro-reflected rays and the diffraction effects. We perform a wave optics simulation to analyze the image relay performance of a CCR. Our model assumes that the scanned spot of the projector is imaged by the CCR into an array of spots, which superpose and interfere to yield the effective scan spot seen by an eye looking at the CCR. The results indicate that the CCR results in a significant broadened spot size. Experimental results verify the simulation model in terms of achievable resolution and image quality.
Comparison of modelling techniques for multimode fibers and its application to VCSEL source coupling
Huiying Zhong, Site Zhang, Rui Shi, et al.
Ray tracing and split-step method are the most efficient techniques to model multi-mode fiber. In this work, we also propose a geometrical optics based approach, which is beyond ray tracing. This approach, which is mathematically based on Runge-Kutta methods, handles not only ray information but light field information, e.g. amplitude and polarization. Then we discuss and compare the different techniques by the example of coupling of a VCSEL source into a multi-mode fiber.
Imaging Applications II
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Systematic investigation of the principal and first secondary maxima of ultrashort optical pulses focused by a high numerical aperture aplanatic lens
Norbert Lindlein, Florian Loosen, Sebastian Fries
The electromagnetic field in the focus of an ideal aplanatic lens with high numerical aperture, which is illuminated by an ultrashort optical pulse and plane wave front, is simulated by taking the vectorial Debye integral and the coherent superposition of a frequency spectrum of monochromatic waves. The behavior of the principal maxima and the first secondary maxima as function of the numerical aperture (NA) and the pulse duration T is investigated systematically for light incident with linear polarization. First, one would not expect remarkable deviations from the stationary case. But also this simple system of an ideal aplanatic lens without any chromatic or monochromatic aberrations (of course only simple from the point of theory, but not at all from the point of practical realization) shows some remarkable results.

If the NA (in vacuum) tends to the limiting case of 1.0 the maximum value of |E|2 increases faster than expected from the scalar theory (Airy disc) with a maximum deviation of about 13%. The second effect really comes from very short pulses, i.e. very small values T. Then, the value of |E|2 compared to the expected linear increase with 1/T decreases slightly (only less than 2%), but systematically for all NAs.

Even more interesting is the dependence of the height of the first secondary maxima along the x-axis and y-axis on the NA and 1/T. It can be seen that along both axes the first secondary maxima nearly vanish for very short pulses, i.e. large values 1/T.
Micro-optical freeform elements for beam-shaping
Thin optical beam-shaping elements that are able to produce good quality images and that are operational with different light sources are studied in this work. The influence of the design approach on the smoothness of their surface and on the image quality will be evaluated.
Introducing free-function camera calibration model for central-projection and omni-directional lenses
M. Nekouei Shahraki, N. Haala
To ensure making valid decisions with high accuracy in machine vision systems such as driver-assistant systems, a primary key factor is to have accurate measurements, which means that we need accurate camera calibration for various optical designs and a very fast approach to analyse the calibration data in real-time. Conventional methods have specific limitations such as limited accuracy, instability by using complex models, difficulties to model the local lens distortions and limitation in real-time calculations that altogether show the necessity to introduce new solutions.

We introduce a new model for lens distortion modelling with high accuracies beyond conventional models while yet allowing real-time calculation. The concept is based on Free-Function modelling in a posterior calibration step using the initial distortion estimation and the corresponding residuals on the observations as input information.

Free-Function model is the technique of numerically and locally modelling the lens distortion field by assuming unknown functions in our calibration model. This increases the model’s flexibility to fit to different optical designs and be able to model the very local lens distortions. Using the Free-Function model one can observe great enhancements in accuracy (in comparison with classical models). Furthermore, by increasing the number of control points and improving their distribution the quality of lens modelling would be improved; a characteristic which is not present in the classical methods.
Electromagnetic Field Methods
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Fast integral methods for integrated optical systems simulations: a review
Boundary integral equation methods (BIM) or simply integral methods (IM) in the context of optical design and simulation are rigorous electromagnetic methods solving Helmholtz or Maxwell equations on the boundary (surface or interface of the structures between two materials) for scattering or/and diffraction purposes.

This work is mainly restricted to integral methods for diffracting structures such as gratings, kinoforms, diffractive optical elements (DOEs), micro Fresnel lenses, computer generated holograms (CGHs), holographic or digital phase holograms, periodic lithographic structures, and the like. In most cases all of the mentioned structures have dimensions of thousands of wavelengths in diameter. Therefore, the basic methods necessary for the numerical treatment are locally applied electromagnetic grating diffraction algorithms.

Interestingly, integral methods belong to the first electromagnetic methods investigated for grating diffraction. The development started in the mid 1960ies for gratings with infinite conductivity and it was mainly due to the good convergence of the integral methods especially for TM polarization. The first integral equation methods (IEM) for finite conductivity were the methods by D. Maystre at Fresnel Institute in Marseille: in 1972/74 for dielectric, and metallic gratings, and later for multiprofile, and other types of gratings and for photonic crystals. Other methods such as differential and modal methods suffered from unstable behaviour and slow convergence compared to BIMs for metallic gratings in TM polarization from the beginning to the mid 1990ies.

The first BIM for gratings using a parametrization of the profile was developed at Karl-Weierstrass Institute in Berlin under a contract with Carl Zeiss Jena works in 1984–1986 by A. Pomp, J. Creutziger, and the author. Due to the parametrization, this method was able to deal with any kind of surface grating from the beginning: whether profiles with edges, overhanging non-functional profiles, very deep ones, very large ones compared to wavelength, or simple smooth profiles. This integral method with either trigonometric or spline collocation, iterative solver with O(N2) complexity, named IESMP, was significantly improved by an efficient mesh refinement, matrix preconditioning, Ewald summation method, and an exponentially convergent quadrature in 2006 by G. Schmidt and A. Rathsfeld from Weierstrass-Institute (WIAS) Berlin.

The so-called modified integral method (MIM) is a modification of the IEM of D. Maystre and has been introduced by L. Goray in 1995. It has been improved for weak convergence problems in 2001 and it was the only commercial available integral method for a long time, known as PCGRATE.

All referenced integral methods so far are for in-plane diffraction only, no conical diffraction was possible. The first integral method for gratings in conical mounting was developed and proven under very weak conditions by G. Schmidt (WIAS) in 2010. It works for separated interfaces and for inclusions as well as for interpenetrating interfaces and for a large number of thin and thick layers in the same stable way. This very fast method has then been implemented for parallel processing under Unix and Windows operating systems.

This work gives an overview over the most important BIMs for grating diffraction. It starts by presenting the historical evolution of the methods, highlights their advantages and differences, and gives insight into new approaches and their achievements. It addresses future open challenges at the end.
Reduced basis method for Maxwell's equations with resonance phenomena
Martin Hammerschmidt, Sven Herrmann, Jan Pomplun, et al.
Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwell's equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwell's equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field.
Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures
Sven Burger, Philipp Gutsche, Martin Hammerschmidt, et al.
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computations on meshes with strong variations in element sizes. This enables to use precise geometry resolution of the rough textures. Convergence to highly accurate results is observed.
Combining ray-tracing and FDTD to enable the simulation of complex optical devices in an iterative simulation process with reduced simulation effort
Claude Leiner, Wolfgang Nemitz, Susanne Schweitzer, et al.
The development of photonic multi-scale devices with tailor-made optical properties requires the control and the manipulation of light propagation within structures of different length scales, ranging from sub-wavelength to macroscopic dimensions. Unfortunately, applications of common optical simulation methods are usually restricted to particular size regimes. For this reason, a complete optical simulation of multi-scale devices can only be conducted by combining different simulation methods. In our previous work we already introduced an interface method that uses the Poynting vector to bridge between classical Ray-Tracing and the Finite-Difference-Time-Domain method to enable the simulation of suchlike devices. In this contribution we present and discuss a method to reduce the simulation effort and time consumption of this interface simulation process. This approach is based on an FDTD simulation concept for creating the matrices containing probability density distributions that are needed for the FDTD-RT interface simulations by using broadband frequency sources. With this new FDTD simulation concept, the number of simulations needed to create these matrices can be significantly decreased.
Topology optimized design of carpet cloaks based on a level set approach
Garuda Fujii, Masayuki Nakamura
This paper presents topology optimized designs of carpet cloaks made of dielectrics modeled by a level set boundary expression. The objective functional, evaluating the performance of the carpet cloaks, is defined as the integrated intensity of the difference between electric field reflected by the flat plane and that controlled by a carpet cloak covering a bump. The dielectric structures of carpet cloak are designed to minimize the objective functional value and, in some cases, the value reach 0.34% of that when a bare bump exists. Dielectric structures of carpet cloaks are expressed by level set functions given on grid points. The function becomes positive in dielectrics, negative in air and zero on air-dielectric interfaces and express air-dielectric interfaces explicitly.
Inverse Imaging Problems
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Single emitter localization analysis in the presence of background
S. Stallinga
Localization microscopy for imaging at the nano-scale relies on the quality of fitting the emitter positions from the measured light spots. The type and magnitude of the noise in the detection process, the background light level and the Point Spread Function model that is used in the fit are of paramount importance for the precision and accuracy of the fit. We present several developments on the computational methods and performance limits of single emitter localization, targeting specifically these three aspects.
Analysis for simplified optics coma effection on spectral image inversion of coded aperture spectral imager
As a novel spectrum imaging technology was developed recent years, push-broom coded aperture spectral imaging (PCASI) has the advantages of high throughput, high SNR, high stability etc. This coded aperture spectral imaging utilizes fixed code templates and push-broom mode, which can realize the high-precision reconstruction of spatial and spectral information. But during optical lens designing, manufacturing and debugging, it is inevitably exist some minor coma errors. Even minor coma errors can reduce image quality. In this paper, we simulated the system optical coma error’s influence to the quality of reconstructed image, analyzed the variant of the coded aperture in different optical coma effect, then proposed an accurate curve of image quality and optical coma quality in 255×255 size code template, which provide important references for design and development of push-broom coded aperture spectrometer.
High-resolution microscopy with low-resolution objectives: correcting phase aberrations in Fourier ptychography
Pavan Chandra Konda, Jonathan M. Taylor, Andrew R. Harvey
The spatial resolution of a microscope is inversely proportionate to the sum of the objective numerical aperture (NA) and the illumination NA. Fourier Ptychography (FP) microscopy achieves high-resolution, wide-field imaging by the use of a low-NA, wide-field objective combined with time-sequential synthesis of high NA illumination using an array of LEDs. We describe reconstruction algorithms based on Fresnel propagation, rather than the traditional Fraunhofer propagation, which enables more accurate representation of LED illumination and hence reduced aberration in the image reconstruction. This also enables the new technique of Multi-Aperture Fourier Ptychography in the near-field. In this work the implementation of this algorithm is described together with some experimental results. The performance of this algorithm is validated by comparing to Fraunhofer based algorithm. More sophisticated update functions in the reconstruction procedures developed for FP are implemented with this algorithm and their performance is validated. The pupil phase can also be reconstructed during the reconstruction procedure hence allowing us to correct for the aberrations in the optical system without the need of any additional measurements.
Application of Principal Component Analysis to EUV multilayer defect printing
This paper proposes a new method for the characterization of multilayer defects on EUV masks. To reconstruct the defect geometry parameters from the intensity and phase of a defect, the Principal Component Analysis (PCA) is employed to parametrize the intensity and phase distributions into principal component coefficients. In order to construct the base functions of PCA, a combination of a reference multilayer defect and appropriate pupil filters is introduced to obtain the designed sets of intensity and phase distributions. Finally, an Artificial Neural Network (ANN) is applied to correlate the principal component coefficients of the intensity and the phase of the defect with the defect geometry parameters and to reconstruct the unknown defect geometry parameters.
Computational Optics
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A Wigner-based ray-tracing method for imaging simulations
B. M. Mout, M. Wick, F. Bociort, et al.
The Wigner Distribution Function (WDF) forms an alternative representation of the optical field. It can be a valuable tool for understanding and classifying optical systems. Furthermore, it possesses properties that make it suitable for optical simulations: both the intensity and the angular spectrum can be easily obtained from the WDF and the WDF remains constant along the paths of paraxial geometrical rays. In this study we use these properties by implementing a numerical Wigner-Based Ray-Tracing method (WBRT) to simulate diffraction effects at apertures in free-space and in imaging systems. Both paraxial and non-paraxial systems are considered and the results are compared with numerical implementations of the Rayleigh-Sommerfeld and Fresnel diffraction integrals to investigate the limits of the applicability of this approach. The results of the different methods are in good agreement when simulating free-space diffraction or calculating point spread functions (PSFs) for aberration-free imaging systems, even at numerical apertures exceeding the paraxial regime. For imaging systems with aberrations, the PSFs of WBRT diverge from the results using diffraction integrals. For larger aberrations WBRT predicts negative intensities, suggesting that this model is unable to deal with aberrations.
Computer holography as an application of computational optics
Several techniques are reviewed in high-definition computer holography. These techniques are based on numerical techniques in wave optics. For example, the polygon-based method based on propagation between tilted planes is used for calculating the field of polygonal surface sources of light. Numerical propagation of large-scaled field is also implemented by using the technique of off-axis propagation. The silhouette method for occlusion processing is based on the angular spectrum method for propagation between parallel planes. The relation between computer holography and computational optics are presented and several high-definition CGHs using these techniques are demonstrated for verifying the techniques.
Poster Session
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Design and implementation of a Cooke triplet based wave-front coded super-resolution imaging system
Hui Zhao, Jingxuan Wei
Wave-front coding is a powerful technique that could be used to extend the DOF (depth of focus) of incoherent imaging system. It is the suitably designed phase mask that makes the system defocus invariant and it is the de-convolution algorithm that generates the clear image with large DOF. Compared with the traditional imaging system, the point spread function (PSF) in wave-front coded imaging system has quite a large support size and this characteristic makes wave-front coding be capable of realizing super-resolution imaging without replacing the current sensor with one of smaller pitch size. An amplification based single image super-resolution reconstruction procedure has been specifically designed for wave-front coded imaging system and its effectiveness has been demonstrated experimentally. A Cooke Triplet based wave-front coded imaging system is established. For a focal length of 50 mm and f-number 4.5, objects within the range [5 m, ∞] could be clearly imaged, which indicates a DOF extension ratio of approximately 20. At the same time, the proposed processing procedure could produce at least 3× resolution improvement, with the quality of the reconstructed super-resolution image approaching the diffraction limit.
Investigation of light propagation methods used to calculate wave-optical PSF
Shuma Horiuchi, Shuhei Yoshida, Manabu Yamamoto
In this study, we investigated the suitability of various light propagation methods and their usefulness in terms of calculating the wave-optical point spread function (PSF) of an optical imaging system. To analyze an aberration in an optical imaging system in order to obtain its PSF, light propagation methods are widely used to obtain the light intensity distribution on the observation plane. Both the Fresnel-Kirchhoff and Rayleigh-Sommerfeld diffraction formulae are commonly used in light propagation simulations. Recently, there have been many reports concerning light propagation methods in the field of digital holography. These methods are based on the Rayleigh-Sommerfeld diffraction formula and use discrete Fourier transformation. These methods are referred to as the angular spectrum and Fresnel diffraction methods. In this study, these propagation methods are evaluated in terms of the degree of accuracy offered and their associated calculation costs. In order to demonstrate and investigate the features of these propagation methods, we employed a Tessar lens system, which is composed of four lenses. The wavefront aberration of the lens system is obtained by a ray tracing simulation and is used to generate the generalized pupil function. Next, the Rayleigh- Sommerfeld diffraction formula and the light propagation method based on this formula are used to calculate the waveoptical PSF using the pupil function. We applied these simulation methods to various recently proposed propagation methods and discussed the suitability of the various light propagation methods under consideration for calculating the wave-optical PSF.
Cylindrical plasmonic microcavity and its excitation
Cylindrical plasmonic microcavity structure is considered. The system consists of a cylindrically curved metallic structure placed above the flat metallic surface, supporting Surface Plasmon Polariton (SPP) propagation, and they are separated by dielectric gap. The active coupling between SPP resonant modes and SPP modes propagating over the flat metallic surface is demonstrated. The excitation efficiency dependence on structure’s geometric and electrodynamics parameters of plasmonic microcavity is investigated. The possibility of controlling (or modulating) resonant SPP modes by varying different parameters such as minimal distance between cylindrical metallic and flat surfaces, relative permittivity of the dielectric gap, as well as working wavelengths are shown. The quality factor of metallic (as the metal is chosen gold: Au) cylindrical plasmonic microcavity is estimated Q ≈ 90, for fixed values of working wavelength: λ0=690 nm, relative permittivity of the dielectric media εd =3, and the radius of cylinder R=2.5 μm. Considered structure shows strong dependence on the relative permittivity of the dielectric media, the change of third decimal of εd brings to the significant change (up to three times) of microcavity excitation efficiency. Such phenomena can be successfully used for sensors construction based on plasmonic structures.