KEYWORDS: Signal to noise ratio, Diffraction, Background noise, Interference (communication), Denoising, Analog to digital converters, Analog electronics, Photons, Electrons, Education and training
Diffractive imaging techniques, such as coherent diffraction imaging (CDI), ptychography, and Fourier ptychography, have gained popularity due to their ability to recover the amplitude and phase information of samples simultaneously from the diffracted pattern with super resolution and wide field of view. However, imaging noise can significantly degrade the reconstructions in diffractive imaging. Higher order diffractions, in particular, are sensitive to measurement noise due to their lower signal-to-noise ratios (SNR) compared to lower orders. Existing denoising methods cannot effectively separate signals from detector noise. To address this limitation, we propose a self-adaptive noise minimization approach using a regularized regression method. Our approach involves training a regularized linear regression model to evaluate the power of noise level in the recorded noisy diffraction patterns and the detector's dark noise. This results in a refined pattern with high SNR. We evaluate our approach on synthetic and experimental datasets and compare it with existing noise reduction methods. The results demonstrate that our method significantly outperforms other state-of-the-art methods in terms of both noise reduction and preservation of fine structural details. Moreover, our approach does not require any prior knowledge or assumptions about the noise statistics, making it a robust and versatile method for diffractive imaging applications.
We have recently developed an actinic full-field EUV patterned mask inspection and review system on a tabletop by using a coherent high-harmonic generation (HHG) Extreme Ultra-violet (EUV) source. By adopting a combination of reflective-mode fly-scan scattering detecting and scanning coherent diffraction imaging methods, the actinic defects can be sensitively detected with high throughput and precisely reviewed with a finer resolution. In this work, we propose a model of a two-step EUV mask cross-scale inspection (EMCI) tactic for fast identification of actinic defects and high-resolution review of the EUV mask, which is based on difference analysis of diffracted intensities and precise ptychographic reconstruction of the EUV mask. The proposed EMCI model consists of two steps. In the first step, a fly-scan diffraction difference mapping (FDDM) method is applied to recognize and localize the defects from the EUV mask with full field of view. Thus, a sub-micron resolution defect location map is generated by array to array comparison of the diffracted intensities from the line integral of scanning regions with programmed defects, to regions of defect-free. This FDDM method works particularly in Fourier domain with no need to any form of imaging system, meanwhile, scattering information takes the advantage of high sensitivity to nanoscale defects, so that defects can be recognized and localized with high throughput and robustness. In the second step, with the location information of defects by FDDM, an EUV Ptychography (EUVP) method is applied to do the local review of EUV mask by retrieving the image of both the EUV mask and illumination based on ptychography. In this manuscript, utilizing the proposed EMCI model, we have performed a numerical simulation for EUV patterned mask defect inspection and review. The results reveal the performance of the proposed model in EUV mask metrology. The proposed method is particularly expected to have a remarkable implication for the EUV lithography.
With the maturing of liquid crystal technology, liquid crystal variable retarder (LCVR) has been widely used in optical systems. In practice, it is of great importance to characterize the polarization properties of the LCVR for its control and applications to accurately modulate the polarization state of the light in the optical systems. In this paper, the Mueller matrix ellipsometry (MME) is applied to comprehensively characterize the polarization properties including the retardance and the fast axis azimuth of the LCVR versus the driving voltage, the wavelength, as well as the incidence and the azimuth of the light. An analytical model is constructed to describe the LCVR based on the Mueller matrix calculus, in which the influences of the incidence and the azimuth of the light are considered. A house-developed spectroscopic Mueller matrix ellipsometer is employed to perform the experiments. Simulations and experiments about a commercial LCVR product are presented and discussed to verify the proposed method.
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°.
Mueller matrix ellipsometry has been demonstrated as a powerful tool for nanostructure metrology in high-volume manufacturing. Many factors may induce depolarization effect in the Mueller matrix measurement, and consequently, may lead to accuracy loss in the nanostructure metrology. In this paper, we propose to apply a Mueller matrix decomposition method for the Mueller matrix measurement to separate the depolarization effect caused by the MME system. The method is based on the polar decomposition by decomposing the measured depolarizing Mueller matrix into a sequence of three matrices corresponding to a diattenuator followed by a retarder and a depolarizer. Since the depolarization effects will be only reflected in the depolarizer matrix, the other two matrices are used to extract the structure parameters of the measured sample. Experiments performed on a one-dimensional silicon grating structure with an in-house developed MME layout have demonstrated that the proposed method achieves a higher accuracy in the nanostructure metrology.
Dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) has been designed and applied as a powerful tool for the characterization of thin films and nanostructures. The compensators are indispensable optical components and their performances affect the precision and accuracy of DRC-MME significantly. Biplates made of birefringent crystals are commonly used compensators in the DRC-MME, and their optical axes invariably have tilt errors due to imperfect fabrication and improper installation in practice. The axis tilt error between the rotation axis and the light beam will lead to a continuous vibration in the retardance of the rotating biplate, which further results in significant measurement errors in the Mueller matrix. In this paper, we propose a simple but valid formula for the retardance calculation under arbitrary tilt angle and azimuth angle to analyze the axis tilt errors in biplates. We further study the relations between the measurement errors in the Mueller matrix and the biplate axis tilt through simulations and experiments. We find that the axis tilt errors mainly affect the cross-talk from linear polarization to circular polarization and vice versa. In addition, the measurement errors in Mueller matrix increase acceleratively with the axis tilt errors in biplates, and the optimal retardance for reducing these errors is about 80°. This work can be expected to provide some guidences for the selection, installation and commissioning of the biplate compensator in DRC-MME design.
Optical scatterometry, also referred to as optical critical dimension (OCD) metrology, has been introduced for critical dimension (CD) monitoring and overlay metrology with great success in recent years. Forward modeling to calculate the optical signature from the measured diffractive structure is one of the most important issues in OCD metrology. To simplify the forward modeling approach, such as rigorous coupled-wave analysis (RCWA), the incidence and azimuthal angles are usually assumed to be constant. However, since some focusing elements, such as focusing lens or parabolic mirrors with finite numerical aperture (NA), are always used to gain a sufficient small spot size onto the sample, this assumption is not true in the whole exit pupil of the focusing elements, leading to a modeling error in forward modeling, and finally leading to a fitting error in OCD metrology. In this paper, we propose a correction method with consideration of the effect of NA to decrease the modeling error in the forward modeling. The correction method is an average integral method based on Gaussian quadrature in two dimensions inside a circle, and is performed on forward modeling with varied incidence and azimuthal angles over the exit pupil. Experiments performed on silicon gratings with a Mueller matrix polarimeter have demonstrated that the proposed correction method achieves a higher accuracy in OCD metrology.
Misalignment errors of the composite wave-plate, a typical kind of compensator used in spectroscopic ellipsometers (SE), can lead to spurious oscillations in the SE measurement. In this paper, we construct an equivalent model of the three-inone composite wave-plate through mathematical derivation, and propose a method to analyze and extract the misalignment errors of the composite wave-plate. Obvious oscillations have been observed in the equivalent fast axis azimuth of the composite wave-plate through simulations, and these oscillations can be assigned to the angular misalignment errors between the individual plates of the composite wave-plate. The waveforms and amplitudes of the oscillations in the equivalent fast axis azimuth show high sensitivity to angular misalignment errors. Conversely, angular misalignment errors can be accurately extracted from the oscillations in the equivalent fast axis of the composite wave-plate. It is expected that the proposed method for analysis and extraction of misalignment errors can be used to minimize angular misalignment errors and to improve the alignment procedure of the composite wave-plate.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.