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Remote measurement of object orientation is often required in many applications. Out of the six degrees of freedom (DoF) that determine object orientation in space, the roll angle is the most difficult to measure using optical methods. In this letter, we propose a remote Stokes roll-angle sensor that measures roll angles from the detected Stokes vectors of modulated polarized light retroreflected from a sensing unit comprised simply of a retarder and a planar reflection mirror. Experimental results have shown that the proposed sensor can realize absolute roll angle measurement in an unprecedented range of 180° with a maximum absolute error of less than 0.25° and a measurement resolution of better than 0.01°. The proposed sensor adopts a coaxial design and takes the advantages of compactness, simplicity and low cost, and moreover, can be further expanded to a three-DoF angle sensor due to the sensitivity of the sensing unit to other two kinds of angles (pitch and yaw).

A ferroelectric liquid crystal polarization rotator (FLCPR) has been widely used in polarization measurement due to its fast and stable modulation characteristics. The accurate characterization of the modulation performance of FLCPR directly affects the measurement accuracy of the instrument based on liquid crystal modulation. In this study, FLCPR is accurately characterized using a self-developed high-speed Stokes polarimeter. Strong linear and weak circular birefringence are observed during modulation processes, and all the optical parameters of FLCPR are dependent on driving voltage. A dual FLCPR-based Mueller matrix polarimeter is designed on the basis of the Stokes polarimeter. The designed polarimeter combines the advantages of the high modulation frequency of FLCPR and the ultrahigh temporal resolution of the fast polarization measurement system in the Stokes polarimeter. The optimal configuration of the designed polarizer is predicted in accordance with singular value decomposition. A simulated thickness measurement of a 24 nm standard SiO2 thin film is performed using the optimal configuration. Results show that the relative error in thickness measurement caused by using the unsatisfactory modulation characteristics of FLCPR reaches up to −4.34%. This finding demonstrates the importance of the accurate characterization of FLCPR in developing a Mueller matrix polarizer.

With the development of semiconductor manufacturing processes, critical dimension small-angle x-ray scattering (CDSAXS) has been identified as a potential solution for measurement. It is worthy of exploring how to achieve fast parameter extraction. In this paper, we propose a XSCNN model based on deep learning to reconstruct the parameters related to structure and measurement conditions. Simulation experiments performed on a trapezoidal grating have demonstrated that XSCNN can produce satisfactory results. It is expected that deep learning will provide a practical solution in CD-SAXS.

Turbid media will lead to a sharp decline in image quality. Polarization imaging is an effective method to obtain clear images in turbid media. In this paper, we propose an improved method that combines unsupervised learning and polarization imaging theory, which can be applied in a variety of nonuniform optical fields. We treat the background light as a spatially variable parameter, so we designed an end-to-end unsupervised generative network to inpaint the background light, which produces an adversarial loss with the discriminative network to improve the performance. And we use the angle of polarization to estimate the polarization parameters. The experimental results have demonstrated the effectiveness and generalization ability of our method. Compared with other works, our method shows a better real-time performance and has a lower cost in preparing the training dataset.

The low efficiency and dissatisfactory chromaticity remain as important challenges on the road to the OLED commercialization. In this paper, we propose a multi-objective collaborative optimization strategy to simultaneously improve the efficiency and ameliorate the chromaticity of the stratified OLED devices. Based on the formulations derived for the current efficiency and the chromaticity Commission International de L’Eclairage (CIE) of OLEDs, an optical sensitivity model is presented to quantitatively analyze the influence of the layer thickness on the current efficiency and the CIE. Subsequently, an evaluation function is defined to effectively balance the current efficiency as well as the CIE, and a collaborative optimization strategy is further proposed to simultaneously improve both of them. Simulations are comprehensively performed on a typical top-emitting blue OLED to demonstrate the necessity and the effectivity of the proposed strategy. The influences of the layer thickness incorporated in the blue OLED are ranked based on the sensitivity analysis method, and by optimizing the relative sensitive layer thicknesses in the optical views, a 16% improvement can be achieved for the current efficiency of the OLED with desired CIE meantime. Hence, the proposed multi-objective collaborative optimization strategy can be well applied to design high-performance OLED devices by improving the efficiency without chromaticity quality degradation.

Overlay target design is an important issue in overlay metrology, whose aim is to probe the optimal overlay target to achieve good performance on measurement precision and accuracy even in the presence of process variation. In this paper, the target design problem is first formulated as a multiobjective optimization problem and then solved by the multiobjective genetic algorithm. The feasibility of the proposed method is verified based on simulations carried out on two overlay targets. The results reveal that measurements with high precision, accuracy, and process robustness could be achieved on the targets designed by the proposed method.

Tandem organic solar cells (OSCs) show great potential due to advantages such as the utilization of wide-spectrum light and low thermalization loss. The current mismatch between sub-cells is one of the major issues reducing the final output efficiency of a tandem device. In this paper, we focus on the current mismatch of tandem OSCs at oblique incidence and aim to reduce its adverse effect on the performances of realistic devices working at varying incident angle. Firstly, we propose an optical analysis method based on the 4×4 matrix formalism to analyze and optimize the performance of tandem solar cells at arbitrary incident angles. Compared with those optimal designs via matching the currents of sub-cells only at normal incidence, the proposed method chooses the optimal structure of the tandem device by maximizing the generated energy density per day with considering the current match at different incident angles during daytime. With the proposed method, a typical tandem organic solar cell is optimized as an example, and the optimized tandem device has a balanced current match at all incident angles during a whole day. Experimental results demonstrate that the generated energy density per day of the optimized tandem device has increased by 4.9% compared to the conventional device optimized only at normal incidence. The proposed method and results are expected to provide some new insights for the performance analysis and optimization of tandem or multi-junction solar cells, especially those devices exhibiting serious current mismatch between sub-cells at varying incident angles in practical applications.

Spatial chirp induced by the misaligned gratings and mirrors in a parallel grating pair pulse stretcher can significantly affect the performance of the output pulses. Firstly, a detailed analysis about the spatial chirp of the stretched pulses caused by the misalignments has been carried out using the ray tracing simulation method. According to the simulation results, an adjustment procedure has been summarized to accurately calibrate these misalignments. The proposed method has been successfully applied in a home-made chirped pulse stretcher. By measuring the output pulse with an imaging spectrometer, the results show the stretched pulse has a good linear temporal chirp and little spatial chirp, which demonstrates the good adjustment of the stretcher.

We propose and demonstrate an all-dielectric metasurface-based roll-angle sensor, in which the roll angle is translated into the change of polarization state of the probe light. A circular polarization beam splitter is designed and fabricated to split the probe light into right-circularly polarized and left-circularly polarized light beams, whose intensities are then collected to estimate the roll angle. The experimental results show that the developed roll-angle sensor has a measurement resolution of 0.1° and a measurement range of 30°. The all-dielectric metasurface-based design promises to substantially reduce the size of the roll-angle sensor and is expected to gain wide applications especially on space-limited occasions.

The development of nanotechnology and nanomaterials has put forward higher requirements and challenges for precision measurement or nanometer measurement technology. In order to cope with this situation, a new type of imaging Mueller matrix ellipsometer (IMME) has been developed. A back focal plane scanning method is designed to make the IMME have the ability to measure multiple incident angles. A two-step calibration method is proposed to ensure the measurement accuracy of IMME. After calibration, the IMME can achieve measurement with wavelengths from 410 nm to 700 nm and incident angles from 0° to 65°. The lateral resolution of the IMME is demonstrated to be 0.8 μm over the entire measurement wavelength range. In addition, a Hadamard imaging mode is proposed to significantly improve the imaging contrast compared with the Mueller matrix imaging mode. Subsequently, the IMME is applied for the measurement of isotropic and anisotropic samples. Experimental results have demonstrated that the proposed IMME has the ability to characterize materials with complex features of lateral micron-distribution, vertical nano-thickness, optical anisotropy, etc., by virtue of its advantages of high lateral resolution and high precision ellipsometric measurement.

Computational super-resolution is a novel approach to break the diffraction limit. The Mueller matrix, which contains full-polarization information about the morphology and structure of a sample, can add super-resolution information and be a promising way to further enhance the resolution. Here we proposed a new approach called Mueller-matrix scattered-field microscopy (MSM) that relies on a computational reconstruction strategy to quantitatively determine the geometrical parameters of finite deep sub-wavelength nanostructures. The MSM adopts a high numerical-aperture objective lens to collect a broad range of spatial frequencies of the scattered field of a sample in terms of Mueller-matrix images. A rigorous forward scattering model is established for MSM, which takes into account the vectorial nature of the scattered field when passing through the imaging system and the effect of defocus in the measurement process. The experimental results performed on a series of isolated Si lines have demonstrated that MSM can resolve a feature size of λ/16 with a sub-7 nm accuracy. The MSM is fast and has a great measurement accuracy for nanostructures, which is expected to have a great potential application for future nanotechnology and nanoelectronics manufacturing.

A single pulse diffraction method to probe the plasma column evolution of the air ionization induced by the femtosecond laser pulse has been proposed. By utilizing a linearly chirped pulse as the probe light, the spatiotemporal evolution spectrum of the plasma column can be acquired in a single measurement. A method based on the Fresnel diffraction integral is proposed to extract the evolution of the phase shift after the probe light is crossing through the plasma column. Results show that the plasma expands rapidly within 7 ps due to the ionization, and then reaches a steady state with a diameter of about 80 μm with the pump pulse energy of 1 mJ. Furtherly, the temporal profile of the free electron density and the refractive index in the plasma region were determined using the corresponding physical models. The single-shot method can be expected to broaden the way for detecting the dynamics of the femtosecond laser-induced plasma.

Mueller matrix ellipsometry (MME) is applied to characterize lithographic patterns with natural line edge roughness (LER). A computationally efficient approach based on effective medium approximation is proposed to model the effects of LER in MME measurements. We present both the theoretical and experimental results on lithographic patterns with realistic LER which demonstrate that MME in combination with the proposed effective modeling method is capable of quantifying LER amplitudes. Quantitative comparisons between the MME and scanning electron microscopy measured results also reveal the strong potential of this technique for in-line nondestructive line roughness monitoring.

We derive explicit power dissipation functions for stratified anisotropic OLEDs based on a radiation model of dipole antennas inside anisotropic microcavity. The dipole field expressed by vector potential is expanded into plane waves whose coefficients are determined by scattering matrix method, and then an explicit expression is derived to calculate the energy flux through arbitrary interfaces. Taking advantage of the formulation, we can easily perform quantitative analysis on outcoupling characteristics of stratified anisotropic OLEDs, including outcoupling efficiency, normalized decay rate and angular emission profile. Simulations are carried out on a prototypic stratified OLED structure to verify the validity and capability of the proposed model. The dependencies of the outcoupling characteristics on various emission feature parameters, including dipole position, dipole orientation, and the intrinsic radiative quantum efficiency, are comprehensively evaluated and discussed. Results demonstrate that the optical anisotropy in different organic layers has nonnegligible influences on the far-field angular emission profile as well as outcoupling efficiency, and thereby highlight the necessity of our method. The proposed model can be expected to guide the optimal design of stratified anisotropic OLED devices, and help to solve the inverse outcoupling problem for determining the emission feature parameters.

Optical scatterometry is one of the most important techniques for measuring the critical dimension (CD) and overlay of nanostructures in current semiconductor manufacturing due to its inherent noncontact, nondestructive, time-effective, and relatively inexpensive merits over other metrology techniques, such as scanning electron microscopy (SEM) and atomic force microscopy. Along with the advantages of optical scatterometry, there are some challenges or limitations to this technique with the ever-decreasing dimensions of advanced technology nodes (22 nm and beyond) [1], such as the parameter correlation issue. In addition, optical scatterometry is mostly suitable for measuring repetitive dense structures while infeasible for the measurement of isolated or the general non-periodic structures. To address the challenges or limitations in conventional optical scatterometry, we have developed a novel instrument called the tomographic Mueller-matrix scatterometer (TMS) [2], which is a combination of a dual rotating-compensator Mueller matrix ellipsometer (MME) [3] and a reflection microscope. In this talk, I will present the development of TMS as well as its application for nanostructure metrology. As shown in Fig. 1, the position of the focal point of the light beam on the back focal plane (BFP) of a high-numerical-aperture objective lens OL can be changed by rotating the flat mirror FM, which further leads to the change of illumination direction on the sample. An epi-illumination setup is designed to collect the scattered-field distribution associated with each illumination direction by imaging the BFP of the OL. Thanks to the dual rotating-compensator configuration, a 4-by-4 Mueller matrix associated with each point on the BFP of the OL can be obtained. Since the 16 elements of a Mueller matrix contain all polarization information that one can extract from a linear polarization scattering process, the full polarization properties of the scattered field are thus achieved. Details about the principle as well as the calibration of the TMS can be found in Ref. [4, 5] and are omitted here for the sake of brevity. As a demonstration of the potential of the develop instrument, the TMS was employed for the measurement of a Si grating and a photoresist (PR) grating. For the Si grating, its geometrical profile is characterized by top CD x1, grating height x2, and sidewall angle x3. For the PR grating, its geometrical profile is characterized by top CD x1, grating height x2, sidewall angle x3, and top corner rounding x4. The period of the Si grating is 800 nm, and the nominal dimensions of other structural parameters are x1 = 350 nm, x2 = 470 nm, and x3 = 88 degree, respectively. The period of the photoresist grating is 412 nm, and the nominal dimensions of other structural parameters are x1 = 200 nm, x2 = 311 nm, and x3 = 90 degree, respectively. Figure 2 presents the fitting result of the measured and calculated best-fit Mueller matrices of the Si and PR gratings at different measurement configurations. Good agreement can be observed from this figure for both the two grating samples. References [1] N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, Nat. Electron. 1, 532-547 (2018). [2] Y. Tan, C. Chen, X. Chen, W. Du, H. Gu, and S. Liu, Rev. Sci. Instrum. 89, 073702 (2018). [3] C. Chen, X. Chen, Y. Shi, H. Gu, H. Jiang, and S. Liu, Appl. Sci. 8, 2583 (2018). [4] S. Liu, X. Chen, and C. Zhang, Thin Solid Films 584, 176-185 (2015). [5] C. Chen, X. Chen, H. Gu, H. Jiang, C. Zhang, and S. Liu, Meas. Sci. Technol. 30, 025201 (2019). (See attached documents for the cited figures).

We have recently developed a high-numerical-aperture (high-NA) Mueller-matrix ellipsometer (MME). By adopting a high-NA objective lens, the scattered light can be collected and the image with high lateral resolution is acquired to obtain the spatially resolved Mueller matrix of the sample. In this manuscript, we propose a model of the image formation of the high-NA MME based on the rigorous coupled-wave analysis (RCWA) and vector diffraction theory. The proposed imaging formation model consists of four parts: scattering on the sample, collecting by the optical system, propagating in the optical system, and imaging on the image plane. Each part can be modeled and calculated separately. Utilizing the proposed model, we have performed a numerical simulation for two types of gratings. The results reveal the potential of the proposed model in predicting the measured Mueller matrix and analyzing the sensitivity of the high-NA MME to different nanostructures.

Aberration adjustment is of great importance in the lithographic process of integrated circuit manufacturing due to the pressure variance, lens thermal effects, overlay correction, and 3D mask effects. With the objective of removing the crosstalk effect, as well as reducing computational complexity during in-line application, a dominant mode method is proposed to adjust the aberrations of the projection lens for a lithographic tool. Theoretical definitions and corresponding calculations of dominant modes are proposed to select the compensators of the projection lens and to build the control matrix for compensator settings. The proposed method is successfully applied in a practical aberration adjustment of the projection lens in a lithographic tool, and the results demonstrate its feasibility and performance.

As critical dimension shrinks, the image quality of lithographic projection lens is improved gradually. In lithographic tool, vibration is an important factor affecting the image quality of projection lens. The internal vibration of projection lens will change the relative position between the lens elements, reduce the image contrast and process window. There are usually two methods to suppress the internal vibration of lithographic projection lens, isolating the external vibration source and improving the stiffness of the internal structure. Based on the above methods, this paper proposes a dynamic imaging model (DIM) that establishes a precise quantitative relationship between the internal vibration of projection lens and the imaging contrast. The DIM has been used in image performance analysis and the structure design for lithographic projection lens.

Polarization distortion is a phenomenon which the polarization state of output light deviates from the theoretical expectation. Due to the design defects and process limitations, polarization distortion in beam splitter is inevitable, which results in the significant errors in the optical systems. A theoretical analysis method based on Mueller matrix is proposed for characterizing the beam splitter. In the propose approach, polarization distortion in the beam splitter including depolarization, linear and circular birefringence, and linear diattenuation, circular dichroism have been considered. With the proposed method, we can characterize the beam splitters and extract the related effective optical parameters of polarization distortion. The Mueller matrices of two different commonly used beam splitters measured by a commercial Mueller matrix ellipsometer (MME) are consistently fitted by the proposed method and the residual errors have shown the improvement compared to the conventional methods.

Based on the dipole radiation method in anisotropic layer systems, optical formulations are derived to inversely fit the emitter features (including emitter orientation and distribution) of anisotropic OLED from the radiation patterns.

Tandem organic solar cells are optimized based on an optical analysis method considering current mismatch under oblique incidence between two sub-cells to optimized the device structure and obtained higher efficiency.

The development of necessary instrumentation and metrology at the nanoscale, especially fast, low-cost, and nondestructive metrology techniques, is of great significance for the realization of reliable and repeatable nanomanufacturing. In this work, we present the application of a homemade novel optical scatterometer called the tomographic Mueller-matrix scatterometer (TMS), for the measurement of photoresist gratings. The TMS adopts a dual rotating-compensator configuration and illuminates the nanostructure sequentially under test conditions by a plane wave, with varying illumination directions and records. For each illumination direction, the polarized scattered field along various directions of observation can be seen in the form of scattering Mueller matrices. That more scattering information is collected by TMS than conventional optical scatterometry ensures that it achieves better measurement sensitivity and accuracy. We also show the capability of TMS for determining both grating pitch and other structural parameters, which is incapable by current zeroth-order methods such as reflectometry- or ellipsometry-based scatterometry.

Femtosecond laser-induced optical and structural changes inside transparent materials are crucial to ultrafast laser micromachining. In this work, on-axis beam collapse has been predicted by theoretical simulations and further demonstrated by the experimental results where a femtosecond pulse was loosely focused into a fused silica with the energy far above the self-focusing threshold. A detailed discussion of the energy thresholds and the starting locations on the optical axis of beam collapse for different beam waist radiuses is given. In addition, the spatial distribution of the refractive index has been determined using a spectroscopic ellipsometer and a roughly uniform decrease of 0.1 has been observed in the laser-modified region. Further, the relationship between the spatial distribution of the refractive index and the pulse energy density has been discussed quantitatively. The observed modulation of the beam collapse and the refractive index distribution can be expected to be a useful tool for femtosecond laser micromachining.

Dielectric corrugated gratings are of considerable interest due to their applications in acousto-optics, quantum electronics, integrated optics, spectroscopy, and holography integrated optics. Rigorous coupled-wave analysis has been widely used for the analysis of dielectric gratings. However, this approach is not only time-consuming and computer intensive but it also does not really promote the physical understanding of the origin of the observed optical behavior. Here, we use Mueller matrix (MM) spectroscopic ellipsometry to systematically study the sinusoidal polydimethylsiloxane grating. We correlate the observed polarization mixing in the Mueller matrix to the underlying physical origin using the physics-based approach. The calculated MM contour plots obtained from a biaxial Bruggemann effective medium approximation model are completed by the presence of Rayleigh-Woods anomalies. The roles of optical interference, geometric anisotropy, and diffraction orders are respectively identified by their different dispersion behavior, with their interactions and couplings highlighted. Such a straightforward procedure provides a new method for analyzing dielectric gratings, which requires considerably less computer power and is directly linked to the physical interpretations.

The shock etalon method with normal incidence is an effective method to extract the shocked dynamic parameters of transparent materials. In order to eliminate the sample surface reflection, additional efforts on the sample preparation are usually introduced, which may limit the application of the method. Here, we proposed a Brewster incidence method to carry out the shock compression experiment on transparent materials. By utilizing the p-polarized light as the probe pulse at Brewster incidence, the sample surface reflection can be directly eliminated, which consequently simplified the experiment preparations. The errors of the proposed method have been evaluated using a set of virtual experiments. The results show that the shocked dynamic parameters can be accurately and robustly retrieved even when the nominal refractive index of the sample deviates 0.01 from its true value, or the incident angle bias 0.33° from the Brewster angle. Finally, a set of shock compression experiments on a polycarbonate film sample are carried out, and shocked dynamic parameters, such as shock velocity, particle velocity, and shocked refractive index, are successfully measured, for demonstration.

Since the pupil function is defined as a time-invariant system, the traditional partially coherent imaging model is time-consuming to calculate the effect of spatially varying wavefront aberrations on the scanning image. A fast reconstruction method of the aberrated scanning aerial image is presented for the scanning projection lithographic tool. In the proposed method, the principal components (PCs) are used to decompose and reconstruct the aberrated aerial image. Due to the exact quadratic relationship between the PC coefficients and the Zernike coefficients, the integration of the PCs in the intensity domain can be transformed into the integration of quadratic Zernike vectors when reconstructing the scanning aerial image. An integral transfer function is introduced to describe this process. This method can not only reconstruct the aberrated scanning image quickly but can also obtain the explicit relationship between the Zernike coefficients and the aberrated scanning aerial image.

A novel, to the best of our knowledge, optical method using a high-speed polarimetry is proposed for real-time attitude tracking in an ultra-large measurement range. The attitude metrology utilizes the field-of-view effect in birefringent crystals, which is known as the birefringence deviates with the field-of-view angle of polarized light. The basic principle of the metrology is presented via theoretical derivation and has been verified in the static retardance measurement experiments. With a resolution test, a temporal resolution of 0.4 ms per attitude measurement and an angular resolution up to 0.0025°are achieved. With the help of a bubble level, the attitude angles of an object attached with a birefringent wave plate are obtained in the dynamic experiments, which have achieved an accuracy better than 0.02°. Additionally, the angular velocity and acceleration of the real-time measured roll angle can be extracted simultaneously. The experimental results demonstrate that the proposed metrology has great potential and advantages in the real-time attitude sensing.

A high-speed Mueller matrix ellipsometer (MME) based on photoelastic modulator (PEM) polarization modulation and division-of-amplitude polarization demodulation has been developed, with which a temporal resolution of 11 µs has been achieved for a Mueller matrix measurement. To ensure the accuracy and stability, a novel approach combining a fast Fourier transform algorithm and Bessel function expansion is proposed for the in-situ calibration of PEM. With the proposed calibration method, the peak retardance and static retardance of the PEM can be calibrated with high accuracy and sensitivity over an ultra large retardance variation range. Both static and dynamic measurement experiments have been carried out to show the high accuracy and stability of the developed MME, which can be expected to pave the way for in-situ and real-time monitoring for rapid reaction processes.

Nonuniform depolarization properties of SiO 2 thin film, two-dimensional (2D) Si grating, and three-dimensional Si cylinder grating, were systematically investigated by Lu-Chipman decomposition. We find that introducing surface profiles with dimensions comparable to the detecting wavelengths can lead to obvious nonuniform depolarization, and control of the sample azimuth can manipulate the uniformity of the depolarizer components. The results indicate that the 2D nanostructure shows obvious nonuniform depolarization at 0° and 90° azimuths, while almost uniform depolarization at 45° azimuth. These discovered phenomena may give rise to some potential applications, such as the detection of the existence of nanostructures without a priori information about the sample, and the design of a uniform or nonuniform depolarizer.

Although imaging scatterometry has been demonstrated to be a powerful technique for characterization of nano-gratings when high lateral resolution is required, some limits of this novel technique are still undisclosed yet, such as the constraint for the imaging numerical aperture (NA), the number of unit cells for accurate grating reconstruction, and the analyzability of image pixels associated with the grating region. To this end, we establish a vectorial image formation (VIF) model for imaging scatterometry based on the finite-difference time-domain (FDTD) method and vectorial diffraction theory. According to the established VIF model and the simulation results of a Si grating sample with finite numbers of unit cells, we find that accurate grating reconstruction by routine RCWA (rigorous coupled-wave analysis) -based data analysis requires an upper limit for the NA of the employed objective. And enough numbers of unit cells are also required to be covered in the illumination spot. Only in these conditions, the zeroth-order diffraction information of the grating under test can be exclusively and completely collected by the imaging system. Moreover, only the image pixels off the edge of the grating region are analyzable by routine RCWA-based data analysis due to the effect of edge scattering. The required number of grating unit cells and the size of the analyzable region are closely related with the imaging NA and the ratio between the illumination spot size and the size of the grating region D/L. Higher imaging NA or smaller D/L typically requires fewer grating unit cells and meanwhile allows a larger analyzable region. The investigation in this paper promises to provide valuable insights into the application of imaging scatterometry.

Composite waveplates (CWs) consisting of multiple single waveplates are basic polarization elements and widely used to manipulate the polarized light in optical systems, and their performances affect the final accuracy and precision significantly. This research proposes a method for the comprehensive characterization of an arbitrary CW based on spectroscopic Mueller matrix polarimetry. An analytical model is established to describe a general CW by extending Jones’ equivalent theorem with Mueller matrix calculus. In this model, an arbitrary CW is optically equivalent to a cascaded system consisting of a linear retarder with slight diattenuation followed by an optical rotator, and its polarization properties are completely described by four polarization parameters, including the retardance, the fast axis azimuth, the rotation angle, and the diattenuation angle. Analytical relations between the polarization properties, the structure, and the Mueller matrix of the CW are then derived from the established model. By the proposed method, the polarization parameters of an arbitrary CW can be comprehensively characterized over an ultra-wide spectral range via only one measurement. Moreover, the actual structure of the CW, including the thicknesses and fast axis azimuths of the single waveplates, as well as the axis alignment errors, can be completely reconstructed from the polarization spectra. Experiments performed with a house-developed broadband Mueller matrix polarimeter on three typical CWs including a compound zero-order waveplate, an achromatic waveplate and a specially designed biplate have demonstrated the capability of the proposed method.

In this paper, we describe the development of a novel instrument, tentatively called tomographic Mueller-matrix scatterometer (TMS), which enables illuminating sequentially a sample by a plane wave with varying illumination directions and recording, for each illumination, the polarized scattered field along various directions of observation in the form of scattering Mueller matrices. The incidence angle is varied from 0° to 65.6° with the rotation of a flat mirror that changes the position of the focal point of a light beam on the back focal plane of a high numerical aperture objective lens. The scattering Mueller matrices are collected over a wide range of scattering angles (0°–67°) and azimuthal angles (0°–360°). The developed instrument was then applied for the measurement of nanostructures in combination with an inverse scattering problem solving technique. The experiment performed on a periodic nanostructure preliminarily demonstrates the performance of TMS as well as its potential in nanostructure metrology. It is expected that the TMS would be a powerful tool for characterizing the polarized scattered-field distributions and measuring nanostructures in nanomanufacturing.

This paper presents a comprehensive approach to control flat panel display (FPD) lithographic tool exposure process based on projection lens thermal behavior. Lithographic tool can maintain enough process window and high throughput for large DOSE exposure on this control method. In some FPD lithographic process layers, the exposure tool would generate huge thermal aberration, such as focal plane and magnification drift, because of the large DOSE. This control method includes several technics such as high accuracy patterning quality prediction, high accuracy thermal aberration prediction, aberration correction and equipment process adaptive management. In exposure process, the lithographic tool can adjust the internal parameters and working sequences in real time to maintain the aberration level and tact time. Based on this method, the FPD lithographic tool is applicable for high resolution and high DOSE processes with high manufacturing efficiency.

Muller matrix ellipsometry is introduced as a nondestructive method to measure the fabrication process of grating upon holography, with which the exact widths and refractive indices, nanoparticle fractions of bright and dark regions are achieved.

In this work, we combine conventional boundary element method (BEM) with the reduced-basis method (RBM) and propose a reduced-basis boundary element method (RB-BEM) to realize efficient modeling for parameterized electromagnetic scattering problems of dielectric scatterers. The RB-BEM allows for splitting the modeling process into a parameter-independent offline part and parameter-dependent online part, and replacing the high-dimensional original model obtained by conventional BEM with a low-dimensional reduced-basis model to improve computational efficiency of the online part. We also propose an improved greedy algorithm based on multi-grid to improve the computational efficiency of the offline part. The numerical experiments indicate that the efficiency of the improved greedy algorithm is several times higher than that of the standard one, and the solving efficiency of the reduced-basis model is several times to dozens of times higher than that of the original model with a prescribed approximation accuracy.

Ellipsometric scatterometry has gained wide industrial applications in semiconductor manufacturing after ten years of development. Among the various types of ellipsometers, Mueller matrix ellipsometer (MME) can provide all 16 elements of the 4 by 4 Mueller matrix, and consequently, MME-based scatterometry can acquire much more useful information about the sample and thereby can achieve better measurement sensitivity and accuracy. In this paper, the basic principles and instrumentation of MME are presented, and the data analysis in MME-based nanostructure metrology is revisited from the viewpoint of computational metrology. It is pointed out that MME-based nanometrology is essentially a computational metrology technique by modeling a complicated forward process followed by solving a nonlinear inverse problem. Several case studies are finally provided to demonstrate the potential of MME in nanostructure metrology.

Color filters based on metasurfaces have been widely investigated due to their advantages of high efficiency, flexible transfer characteristics and compactness. Nowadays, most of them have been developed only for controlling color hue and the output of most color filters is fixed, while another two elements of the color, namely saturation and value, are rarely considered. However, color saturation and color value signifying attribute of visual perception are essential in optimizing color response of color filters, and developing color filters with controllable output can make color filter-based devices more flexible. Here, we propose three kinds of color filters based on all-dielectric metasurfaces to control color hue, saturation and value (HSV) at the visible region, respectively. Designed with principle of the magnetic resonances and the structural anisotropy, the output of proposed color filters could be dynamically modulated by changing polarization state of incident light. The proposed polarization-dependent color filters are expected to gain novel applications for security tags, polarization imaging and optical data storage.

Recently, the Mueller matrix polarimeter (MMP) has been introduced for critical dimension and overlay metrology. In practice, the measurement process invariably has errors. These errors, which can be generally categorized into random and systematic errors, have great influences on the final precision and accuracy of the extracted structural parameters. In this paper, we present detailed formulations for the propagation and estimation of random and systematic errors in grating reconstruction using a dual-rotating compensator MMP (DRC-MMP). We derive a generalized first-order error propagating formula, which reveals the mechanism of error propagation in grating reconstruction using the DRC-MMP. According to this first-order error propagating formula and the measurement principle of the DRC-MMP, we then derive detailed formulations for the estimation of random and systematic errors that are propagated into the final extracted structural parameters. Simulations performed on silicon grating samples have demonstrated the validity of the present theoretical derivations.

Recently, ellipsometry-based scatterometry has gained more and more attention in semiconductor manufacturing. Among the various types of ellipsometry, Mueller matrix polarimetry (MMP) can obtain up to 16 quantities of a 4×4 Mueller matrix, and consequently, MMP-based scatterometry can acquire much more useful information about the sample. In this paper, the basic principle and instrumentation of MMP are presented, and then the fundamental concept of computational metrology is introduced. Several case studies are finally provided to demonstrate the potential of MMP in nanostructure metrology.

We propose a universal method for optimal design of a wide field-of-view (FOV) angle linear retarder with an ultra-flat retardance response based on paired positive/negative birefringent plates. The mechanism and rules for the FOV effect compensation are revealed to determine the structure of the proposed retarder by introducing the partial derivative of refractive index with respect to the incident angle. A concrete example based on quartz/sapphire plates is designed and manufactured as a proof-of-concept of the proposed method. The maximum deviation in the retardance of the optimally designed quartz/sapphire wide FOV angle retarder over the concerned FOV angles (incidence: -20°-20°; azimuth: 0°-360°) is only 0.08°, which has been reduced by 3 orders of magnitude compared with the common quartz retarder.

Liquid crystal variable retarders (LCVRs) have been widely used as a transmissive element with electrically tunable optical phase retardance in polarimetric optical systems. Since the responsive characteristics of the LCVRs depend on the modulation processes, accurately and rapidly characterizing LCVRs is of great significance for the performance improvement of the optical system with LCVRs. Firstly, we proposed a Mueller matrix based model to characterize an LCVRs with considerations of both linear birefringence (LB) and circular birefringence (CB), with which the LCVRs is described by several driving voltage-dependent optical parameters such as retardance, azimuth, relative transmittance and optical rotation angle. The experimental results show that the Mueller matrices of the LCVRs measured by a commercial Mueller matrix ellipsometer are consistently fitted by the proposed method, and the improvement of the proposed characterization method can be read from the 15 times reduced average residual errors of the reconstructed Muller matrix compared to the matrix reconstructed with the conventional characterization methods. Through several typical dynamic measurement experiments using a high-speed Stokes polarimeter with a temporal resolution of several nanoseconds, we demonstrated the driving-voltage-dependence of these optical parameters as well as the existence of both LB, CB and depolarization properties in the LCVRs modulation processes. Based on the analysis of the extracted optical parameters, we have obtained the continuous modulation characteristics and step response characteristics of LCVRs. Additionally, a comparison between the Mueller matrices of air measured with the proposed and conventional characterization method has been carried out to demonstrate the fidelity of the proposed method as well.

Volume grating is a key optical component due to its comprehensive applications. Other than the common grating structures, volume grating is essentially a predesigned refractive index distribution recorded in materials, which raises the challenges of metrology. Although we have demonstrated the potential application of ellipsometry for volume grating characterization, it has been limited due to the absence of general forward model reflecting the refractive index distribution. Herein, we introduced a distributed dielectric constant based rigorous coupled-wave analysis (RCWA) model to interpret the interaction between the incident light and volume grating, with which the Mueller matrix can be calculated. Combining with a regression analysis with the objective to match the measured Mueller matrices with minimum mean square error (MSE), the parameters of the dielectric constant distribution function can be determined. The proposed method has been demonstrated using a series of simulations of measuring the volume gratings with different dielectric constant distribution functions. Further demonstration has been carried out by experimental measurements on volume holographic gratings recorded in the composite of polymer and zinc sulfide (ZnS) nanoparticles. By directly fitting the spatiotemporal concentration of the nanoparticles, the diffusion coefficient has been further evaluated, which is consistent to the result reported in our previous investigations.

The calibration of the polarization effect of a high-numerical-aperture (high-NA) objective lens (OL) is of great significance for high-precision polarized light micro-imaging. In this work, we propose a method to calibrate the polarization effect of a high-NA OL with Mueller matrix polarimetry in a retro-reflection configuration by using a spherical mirror as the reference sample. We present the calibration details in both the conoscopic and orthoscopic illumination modes. A high-NA OL with a NA of 0.95 is exemplified to demonstrate the capability of the proposed calibration method, and the experiments performed on two standard SiO2/Si thin film samples with thicknesses of 25 nm and 100 nm verify the calibrated results. Compared with the existing calibration methods, the proposed method is simpler and more efficient for implementation, and moreover, the calibrated Mueller matrices contain all the polarization information of the high-NA OL under test. It is therefore expected that the proposed calibration method could provide a more complete polarization characterization of the high-NA OL.

The biplate that consists of two single wave plates made from birefringent materials with their fast axes oriented perpendicular to each other is one of the most commonly used retarders in many optical systems. The internal alignment of the optical axes of the two single wave plates is a key procedure in the fabrication and application of a biplate to reduce the spurious artifacts of oscillations in polarization properties due to the misalignment error and to improve the accuracy and precision of the systems using such biplates. In this paper, we propose a method to accurately align the axes of an arbitrary biplate by minimizing the oscillations in the characteristic parameter spectra of the biplate detected by a spectroscopic Mueller matrix ellipsometer (MME). We derived analytical relations between the characteristic parameters and the misalignment error in the biplate, which helps us to analyze the sensitivity of the characteristic parameters to the misalignment error and to evaluate the alignment accuracy quantitatively. Experimental results performed on a house-developed MME demonstrate that the alignment accuracy of the proposed method is better than 0.01° in aligning the optical axes of a quartz biplate.

The diagnosis and control of the polarization aberrations is one of the main concerns in a hyper numerical aperture (NA) lithography system. Waveplates are basic and indispensable optical components in the polarimetric diagnosis tools for the immersion lithography system. The retardance of a birefringent waveplate is highly sensitive to the incident angle of the light, which makes the conventional waveplate not suitable to be applied in the polarimetric diagnosis for the immersion lithography system with a hyper NA. In this paper, we propose a method for the optimal design of a wideview- angle waveplate by combining two positive waveplates made from magnesium fluoride (MgF2) and two negative waveplates made from sapphire using the simulated annealing algorithm. Theoretical derivations and numerical simulations are performed and the results demonstrate that the maximum variation in the retardance of the optimally designed wide-view-angle waveplate is less than ± 0.35° for a wide-view-angle range of ± 20°.

The lithographic performance of a photomask is sensitive to shape uncertainty caused by manufacturing and measurement errors. This work proposes incorporating the photomask shape uncertainty in computational lithography such as inverse lithography. The shape uncertainty of the photomask is quantitatively modeled as a random field in a level-set method framework. With this, the shape uncertainty can be characterized by several parameters, making it computationally tractable to be incorporated in inverse lithography technique (ILT). Simulations are conducted to show the effectiveness of using this method to represent various kinds of shape variations. It is also demonstrated that incorporating the shape variation in ILT can reduce the mask error enhancement factor (MEEF) values of the optimized patterns, and improve the robustness of imaging performance against mask shape fluctuation.

Optical scatterometry is a model based technique, which conventionally requires minimization of a predefined least square function. This minimization relies heavily on the measurement configuration: wavelength, incident angle, azimuthal angle, and sample position, which brings up the question of how to find the configuration that maximizes measurement accuracy. We propose a general measurement configuration optimization method based on error propagation theory and singular value decomposition, by which the measurement accuracy can be approximated as a function of a Jacobian matrix with respect to the measurement configurations. Simulation and experiments for a one-dimensional trapezoidal grating establishes the feasibility of the proposed method.

In this paper, wavelengths parallel swept technique is proposed by using an optical swept loop outside the laser cavity. A frequency shifter controlled by RF signal in the loop shifts the frequencies of the incident optical signals simultaneously with a constant value in every circulation. Experimentally, the outputs of two distributed feed back (DFB) lasers were parallel swept by using the optical swept loop. The swept step is tunable from 300MHz(24pm) to 15GHz(0.12nm) depending on the electro-optical bandwidth of the frequency shifter used in our experiments. Dual-wavelength swept output at 214 kHz swept rate with 0.08nm swept step and 122 kHz swept rate with 0.04nm swept step were achieved respectively. The swept span of the swept source was 1.6nm with a flatness of ±1.5dB.