Photonic nanostructures have attracted a tremendous amount of attention in the recent past. Via their size, shape and material it is possible to engineer their optical response to user-defined needs. Tailoring of the optical response is usually based on a reference geometry for which subsequent variations to the initial design are applied. Such approach, however, might fail if optimum nanostructures for complex optical responses are searched. As example we can mention the case of complex structures with several simultaneous optical resonances. We propose an approach to tackle the problem in the inverse way: In a first step we define the desired optical response as function of the nanostructure geometry. This response is numerically evaluated using the Green Dyadic Method for fully retarded electro-dynamical simulations. Eventually, we optimize multiple of such objective functions concurrently, using an evolutionary multi-objective optimization algorithm, which is coupled to the electro-dynamical simulations code. A great advantage of this optimization technique is, that it allows the implicit and automatic consideration of technological limitations like the electron beam lithography resolution. Explicitly, we optimize silicon nanostructures such that they provide two user-defined resonance wavelengths, which can be individually addressed by crossed incident polarizations.

There are several applications for diffraction gratings in laser physics like frequency stabilization, wavelength tuning and temporal pulse shaping. Especially the growing market for femtosecond lasers with increasing pulse energies and peak powers boosts the requirement for highly dispersive diffraction gratings with diffraction efficiencies close to unity and highest damage thresholds imposing the use of purely dielectric materials. These advanced requirements also give rise to new challenges for the grating design. Classical design approaches like gold-coated reflection gratings or monolithic transmission gratings are becoming insufficient. Different approaches utilize dielectric multilayer coatings in conjunction with gratings to achieve high transmission or reflection efficiencies together with high damage thresholds. However, to realize a reasonable and robust design, the optimization of the grating and the multilayer stack has to be completed in one step using rigorous methods because interference of multiply diffracted orders contributes to the overall diffraction efficiencies. Moreover, to make these designs feasible for manufacturing, also a tolerancing is necessary. In our contribution, we present self-developed design tools for multilayer gratings where the optimization of both, grating and multilayer stack are combined in one step using Rigorous Coupled Wave Analysis and standard local and global optimization methods like interior point and genetic algorithms. Moreover, a tolerancing routine is included. New designs are presented for multilayer dielectric reflection and transmission gratings based on our approach, including considerations on tolerancing. Gratings etched through multiple layers are proposed to achieve higher bandwidths with top hat diffraction efficiencies.

One of the main problems in the design of AR, VR and MR devices is an estimation of the design result. Base optical characteristics like aberrations or contrast functions are not applicable. On the other hand, the real prototyping of such devices is very expensive. As a result, authors propose to use a virtual prototyping approach as an element of design of AR, VR and MR devices that allows avoiding real prototyping and therefore to reduce design cost. The virtual prototyping approach assembles all elements of the VR, AR or MR system from the system of the virtual image generation to the eye perception. This approach was implemented as a virtual parametric model of that device.

Aspheres in optical design are frequently used to achieve high optical performance in imaging applications. However, manufacturing aspheres involves serious precision and cost issues that must be considered. We show that, by applying a hybrid digital-optical design approach, the amount of the asphericity cost in a single surface may be significantly alleviated without compromising the performance. First, we compute the amount of spherical aberration depending on the optical parameters (conic constant and shape factor), and compute its corresponding point spread function (PSF). From the PSF and the spectral distribution of clean images and noise, we set a statistical observation model for estimating the expected image quality (in mean square error terms) in the image sensor and also in the digitally restored image. In addition, we use a previously proposed metric for quantifying the asphere fabrication cost, to set different cost scenarios. For each of these scenarios, we study how image quality is optimized, before and after digital restoration. Reversely, we find the optical configurations of minimal asphericity cost amongst those providing a very low aberration level. Although here we have limited our study to just on-axis, monochromatic imaging, we show in simulations how our digital-optical combined approach has a high potential for boosting the cost-effectiveness trade-off.

For optimizing specific functionalities of optical components which include structures on a micrometer or nanometer scale, typically high-dimensional optimization problems have to be solved. We use Gaussian process regression to this aim. Gaussian processes can be viewed as machine-learning algorithms where results from evaluations at specific points in the parameter space (training data) are used to predict values and their uncertainty in the full parameter space. The forward-problem (evaluation at a given point in parameter space) requires to rigorously solve Maxwell’s equations, i.e. to compute light propagation in a specific setup. We use our finite-element method (FEM) implementation JCMsuite to this aim. The general framework of FEM allows to employ adaptive numerical resolution and accurate geometry modelling for arbitrary shapes. We discuss application of Bayesian optimization for the inverse problem in parameter retrieval from scatterometric data.

The appearance of defects on the photomask is a key challenge in lithographic printing. Printable defects affect the lithographic process by causing errors in both the phase and magnitude of the light and of the sizes and location of the printed features. Presently 193 nm optical inspection tools are still the main ones for detecting pattern defects on EUV masks.1 However, pattern sizes on EUV masks could not be detected due to the resolution limit of 193 nm inspection tools. We propose and investigate the application of Convolutional Neural Networks (CNNs) to characterize and classify defects on lithographic masks. This paper details the training and evaluation of the CNNs to classify defects in simulated aerial images of an EUV setting. The simulation software Dr.LiTHO is used to simulate aerial images of defect-free masks and of masks with different types and locations of defects. Specifically we compute images of regular arrays of squares to be imaged with typical settings of EUV lithography (λ = 13.5 nm, NA= 0.33). We consider five types of absorber defects (extrusion, intrusion, oversize, undersize and center spot). The architecture of the CNN contains 4 convolutional layers (conv. layers) with a mixed size of filter,(3x3) and (5x5). The convolution stride and the spatial padding is 1 pixel for all conv. layers. Spatial pooling is carried out by 4 max-pooling layers. Two separate networks are trained for detection of the defect types and location, whereas a third algorithm combines the results. When an image is presented to the implemented algorithm and trained networks, it will return the defect type with its location. An accuracy of 99.9% on the training set and 99.3% on the test set is achieved for detection of the defect type. The network trained for location detection results in 98.7% training accuracy and 98.0% for the test set. Having a sufficient amount of training images the trained CNNs classify the types of defects and their location in the aerial image with high accuracy. The proposed method can be also applied to other defect types and simulation settings.

The aim of this research is to explore the limits of the basic Ptychography algorithm (FPA) at deep ultra violet (DUV) wavelength of 193 nanometers and for binary and phase shift masks. Furthermore, imaging at high numerical apertures involves polarization effects, which are not covered in the scalar phase retrieval algorithms of FPA. The impact of these effects on FPA is investigated for a test chart with feature sizes close to the resolution limit. The quality of the images before and after applying FPA was measured using different error criteria. The Normalized Image Log Slope (NILS) is the criterion which is most sensitive to the lithographically important change in the edge sharpness of features. The Michelson contrast provides a global assesment of the image contrast. The Mean squared Error (MSE) provides an overall assessment of the image quality with respect to a known object. When FPA is used to recover high resolution images of a phase shift mask, it is found out that the edge sharpness is increased but the overall contrast is declined. Additionally, the printability of side lobes contributed to increase of MSE. After using a rigorous method to compute the mask diffraction spectrum instead of the conventional Fourier transform imaging, it is confirmed that thin object assumption is not at all accurate for high numerical aperture DUV imaging applications. For the first time, the polarization effects at large NAs are introduced to FPA and the output is evaluated. Here, we verified that polarization can be used to increase the edge sharpness at a specific direction.

In signal processing one often faces the phase problem, i.e., when an image is formed information about the phase is lost so that only information about intensity is available. This is often an issue in astronomy, biology, crystallography, speckle imaging, diffractive imaging where the phase of the object must be known. While there have been many approaches how to find a solution to the phase problem, numerical algorithms recovering the phase from intensity measurements become more and more popular. One of such algorithms called PhaseLift has been recently proposed. In this study, we show that even 4 masks may be sufficient for reasonable recovery of the phase. The original wavefront and the recovered wavefront were visually indistinguishable and showed very high correlation. In addition, the four masks are essentially one and the same mask rotated around in steps of 90 degrees. By using just four rotated versions of a single mask, the PhaseLift could be easily implemented in real optical systems thus simplifying the wavefront sensing in astronomy, biology etc.

We describe an algorithm of tracing a backward (from camera) ray in a scene which contains birefrigent (uniaxial) media. The physics of scattering of an electromagnetic wave by a boundary between two media is well known and is a base for ray tracing algorithms; but processing of a backward ray differs from scattering of a “natural” forward ray. Say, when a backward ray refracts by a boundary, besides the energy transfer coefficient like for a forward ray one must account for the luminance change due to beam divergence. We calculate this factor and prove it must be evaluated only for the first and the last media along the ray path while the contributions from the intermediate media mutually cancel. In this paper we present a closed numerical method that allows to perform transformation of a backward ray on a boundary between two media either of which can be birefrigent. We hope it is more convenient and ready for usage in ray tracing engines that known publications. Calculation utilizes Helmholtz reciprocity to calculate directions of scattered rays and their polarization (i.e. Mueller matrices) which is advantageous over a straightforward “reverse” of forward ray transformation. The algorithm was integrated in the lighting simulation system Lumicept and allowed for an efficient calculation of images of scenes with crystal elements.

The numerical modeling of light interaction with nanostructured materials is at the heart of many computational photonics studies. A typical example of interest to the present work is the simulation of light trapping in complex photovoltaic devices. This can be a challenging task when the underlying material layers are textured in a very general way. Very often, such studies rely on the Finite Difference Time-Domain (FDTD) method. The FDTD method is a widely used approach for solving the system of time-domain Maxwell equations in the presence of heterogenous media and complex three-dimensional structures. In the classical formulation of the this method, the whole computational domain is discretized using a uniform structured (Cartesian) grid. In this work, we consider an alternative approach by adapting and exploiting a particular finite element method, which is able to deal with topography conforming geometrical models based on non-uniform discretization meshes. The underlying modeling method is known as the Discontinuous Galerkin Time-Domain (DGTD) method. It is a discontinuous finite element type that relies on a high order interpolation of the electromagnetic field components within each cell of an unstructured tetrahedral mesh.

Current EUV exposure systems employ a numerical aperture (NA) of 0.33. This relatively small NA is a consequence of geometrical design limitations of all reflective projection systems with a 4 demagnification in the orthogonal x- and y-directions of the image plane. Anamorphic imaging, which employs different demagnification in horizontal (y) and vertical (x) direction can increase the NA to a value of 0.55. The consequences of using anamorphic high-NA imaging system have to be studied by rigorous methods. Since the range of illumination angles of the anamorphic system is different in x and y directions, one way to understand the involved phenomena, is to investigate and compare the impact of illumination angles for both the high-NA 4 8 anamorphic system at 0.55NA and the lower-NA 4 4 system at 0.33NA. We employ fully coherent that is single source point illumination and imaging to study the impact of the illumination direction on the most relevant lithographic metrics. These metrics include the resulting feature size or critical dimension (CD), the feature position, a local contrast or the normalized image log slope (NILS) and the best-focus position of the projected images. In this study, aerial images from a uniformly-distributed grid of 230 illumination positions were computed and analyzed. The results of the simulation study confirmed that larger illumination angles cause more pronounced shadowing effects and significant variations of the position and feature size versus the illumination direction. The larger demagnification direction of the anamorphic system involves a smaller object-side angular spread of the illumination direction, resulting in less pronounced variation of CD and position versus the illumination direction compared to the isomorphic system. Both systems exhibit a drop of the NILS for more oblique angles. However, the larger image side angles of the high-NA system result in more pronounced polarization effects, which reduce the NILS values compared to that of the lower NA system. The high NA achieved by anamorphic imaging increases the importance of 3D mask effects in EUV lithography. It is not a priori known, which of these 3D mask effects can be attributed to the absorber or the multilayer part of the mask. A hybrid mask simulation approach addresses this question. In the second part of this study, simulations using an hybrid of real and ideal mask elements were performed in an attempt to understand their individual effects of the mask elements and which mask element contributes to which of the observed effects.

Structured Illumination Microscopy (SIM) is one of the techniques which can surpass the Abbe diffraction limit. It is well suited for living cell imaging due to its high speed and low illumination energy features. For the reconstruction algorithm, a perfect structured illumination pattern is assumed. But in the real experiment, the illumination can be influenced by various effects because of the complexity of the experimental configuration, such as the polarization of the field, the diffraction from an aperture, the inclined illumination on the blazed grating. To analyse the influence of these effects on the final patter in focal plane, we perform a fast-physical optics modeling in the context of field tracing which is fully vectorial. The Local Plane Interface Approximation (LPIA) algorithm, a free space propagation algorithm and the Fourier Modal Method (FMM) are all combined in the calculation. We analyze the contrast and homogeneity of the illumination interference pattern at the sample plane, which should be accounted for in image processing. We find that the above mentioned various effects do influence the contrast and homogeneity of the pattern. We also suggest the parameters of the structured illumination system to obtain best contrast and homogeneity. Finally, the parameters of the optimized system can be obtained to apply to the experimental system.

Based on a rough-surfaced model for a birefringent material with a random interface between its surface and air, we explore the relationship between the correlation area and the spatial degree of polarization of the scattered electric field and the surface-height fluctuations. The statistical properties of the scattered light and the microstructure of the anisotropic material has been investigated based on the coherence matrix. It is shown that achieving depolarization is much more difficult than reducing the coherence for the scattered light introduced by the rough surface of the birefringent material.

We present a numerical approach for the accurate simulation of the complex propagation dynamics of ultrashort optical pulses in nonlinear waveguides, especially valid for few-cycle pulses. The propagation models are derived for the analytical signal, which includes the real optical field, exempt from the commonly adopted slowly varying envelope approximation. As technical basis for the representation of the medium dispersion we use rational Pad´e approximants instead of commonly employed high-order polynomial expansions. The implementation of the propagation equation is based on the Runge-Kutta in the interaction picture method. In addition, our modular approach easily allows to incorporate a Raman response and dispersion in the nonlinear term. As exemplary use-cases we illustrate our numerical approach for the simulation of a few-cycle pulse at various center frequencies for an exemplary photonic crystal fiber and demonstrate the collision of a soliton and two different dispersive waves mediated by their group-velocity event horizon.

further shape or diffuse the light distribution (e.g. in non-imaging luminaires or automotive headlights). While the geometry can be described in a parametric form by mapping the micro-optical features onto an underlying smooth freeform surface, ray-tracing an optical system composed of NURBS or polynomial B-spline surfaces for each optimization step can be costly.

The Fast Fourier Transform (FFT) algorithm makes up the backbone of fast physical optics modeling. Its nu- merical effort, approximately linear on the sample number of the function to be transformed, already constitutes a huge improvement on the original Discrete Fourier Transform (whose own numerical effort depends quadrati- cally on the sample number). However, even this orders-of-magnitude improvement in the number of operations required can turn out to fall short in optics, where the tendency is to work with field components that present strong wavefront phases: this translates, as per the Nyquist-Shannon sampling theorem, into a gigantic sample number. So much so, in fact, that even with the reduced effort of the FFT, the operation becomes impractica- ble. Finding a workaround that allows us to evade, at least in part, the stringent sampling requirements of the Nyquist-Shannon theorem is then fundamental for the practical feasibility of the Fourier transform in optics. In this work we propose, precisely, a way to tackle the Fourier transform that eschews the sampling of second-order polynomial phase terms, handling them analytically instead: it is for this reason that we refer to this method as the “semi-analytical Fourier transform”. We present here the theory behind this concept and show the algorithm in action at several examples which serve to illustrate the vast potential of this approach.

We present the definition of a new quantity, the pupil difference probability density (PDPD), and describe its use in the study of imaging systems. Formally, the PDPD is defined as the probability density that two random points over the pupil, with given separation, have a given wavefront error difference. Under this definition, the PDPD is the one-dimensional Fourier transform, of the error difference variable, of the OTF. Using the PDPD, we show that it is possible to understand how certain sources of error affect the OTF. Further, given its geometric interpretation, this formalism is useful for finding accurate analytic approximations to the OTF.

Although first discovered over a hundred years ago by the scientist of the same name, the Gouy phase anomaly continues to awaken considerable interest in the scientific community. In this work, the authors analyse this phenomenon in the framework provided by the geometric Fourier transform, first introduced byWyrowski [Wyrowski and Hellmann, The geometric Fourier transform, In Proc. DGaO, A37, 2017]. The resulting interpretation of the Gouy effect turns out to be logical, coherent and straight-forward, and beautifully simple, and brings to the fore the vital role of the Gouy phase in the unification of the geometrical and diffractive branches of optics.

Optical simulations are a crucial part in designing and understanding new solar cell devices to help with the transition to more environmentally friendly energy generation. We present a multicore wavefront diamond blocking scheme with multi-dimensional cache block sharing for our hybrid-parallel (MPI+OpenMP) optical solar cell simulation code utilizing the Time Harmonic Inverse Iteration Method (THIIM) to discretize Maxwell’s equations. This approach allows to decouple the code from the main memory bandwidth bottleneck and achieves a single node speed-up of up to three compared to an optimal implementation with pure spatial blocking and a multi node speed-up of up to two even with large numbers of compute nodes.

A ray tracing model for thermal effects solid-state single-pass amplifiers is presented, which is able to simulate thermal lensing, depolarization and beam quality degradation. The ray tracing algorithm is based on alternatively evaluating the axial and radial gradient and thereby finding the trajectory in thermally influenced media. This enables to find the focal length distribution of the system. Additionally, to the position of the rays, its phase is also determined, which enables to reconstruct the wavefront of the beam after passing through the crystal. This wavefront is used for a Zernike polynomial analysis to determine spherical aberration, which is linked to the beam quality of the passing beam. Furthermode the total depolarization is obtained by finding the change of polarization for each ray separately. The simulation for thermal lensing is compared with a single-pass Nd:YVO4 system, the beam degradation is compared with a Nd:YVO₄-MOAP system. Both show good agreement with the simulation data, as long as the gain of the system is homogeneous.

Point diffraction interferometry is a promising method for spherical or aspherical measurement with nanometer or even sub-nanometer accuracy. As the accuracy of a PDI is mainly depends on its diffraction reference wavefront, an accurate estimation of the diffraction wavefront error plays a critical role for system’s design and optimization. Although, various error factors may affect the quality of this diffraction wavefront, alignment error of the focusing spot to the pinhole is the decisive one. The common analyses for the diffraction wavefront error mainly based on plane wave approximation of the incidence beam can’t be used to analyze the influence of the misalignment error. Meanwhile, most of these analyses are limited to two-dimensional analysis and therefore is not enough to show the complete error distribution. In this paper, a three-dimensional (3-D) analysis based on Gaussian incidence is developed, and the influences of lateral shift, defocus and tilt alignment errors of focusing spot to the pinhole are analyzed. Here, a 3-D analysis model of diffraction wavefront was established based on Rayleigh-Sommerfeld diffraction theory of a Gaussian incidence for error analysis of various alignment errors. After that, 3-D diffraction wavefront error distribution and the peak-valley (PV) comprehensive evaluation result in different lateral shift, defocuses, and tilt alignment errors were acquired through numerical simulation. The achieved results will be benefit for choosing the pinhole parameters and theoretically accuracy evaluation of diffraction wavefront for nano profilometry.

In order to accomplish the software definition micro-nano satellite demands, which includes that its payload functions and parameters could be reconstructive and controllable by uploading software as needs, we have to break through the design limitations between traditional satellite platform and ordinary optical camera, one new type of optical imaging camera technology is developed based on software definition micro-nano satellite here. we gave full consideration to the possible development joint designing space between the software and the hardware of the payload. Then we analyze the influence of sub-pixel information, satellite platform parameters, optical system parameters, detector parameters, noise and atmosphere on image data processing, especially the super-resolution reconstruction. we establish the physical model and the error model according to the physical mechanism of each factor, as a priori information of the reconstruction method, we apply these prior information constraints in favor of super-resolution to the design of the camera, enabling the images captured by the camera to match the super resolution method very well. This method can simultaneously improve visual resolution and substantial resolution, while maintaining the ability of suppressing noise and may reduce the size and development difficulty of traditional cameras. At the same time, we also carry out high dynamic range imaging technology based on the definition of CMOS software, which assists multi frame image superposition, and fit in the image processing algorithm, breaking through the digital dynamic range enhancement technology, and realizing the ability of high dynamic range clear imaging over high performance CCD. We have developed a general purpose computing optical imaging camera, which integrates the super resolution imaging, dynamic range enhanced imaging, video imaging and other multi intelligent controllable imaging modes. Finally we have completed the related camera integration, testing and experiment.