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Results for “pseudo-randomness”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sources NASA NTRS DOE OSTI

DOE OSTI2026

Binary pseudo-random array standard for extreme ultraviolet lithography tool characterization

Extreme ultraviolet (EUV) imaging tools play a crucial role in EUV lithography. Achieving high accuracy in EUV metrology is essential for advanced semiconductor manufacturing. A thorough characterization of the instrumentation in use is required. Binary pseudo-random arrays (BPRAs) are an established standard for calibrating and characterizing optical instruments in the frequency domain. Here, we expand the BPRA standard to applications in EUV imaging. To extend the technology to the EUV spectral range, a high-resolution BPRA target with the smallest feature size of 40 nm is developed. The EUV BPRA target establishes an in situ and portable calibration and alignment standard for EUV imaging. The target is patterned by means of electron-beam lithography, using a nickel absorber with a thickness of 39 nm. The substrate is a 4″ silicon wafer with a molybdenum/silicon multilayer coating. To demonstrate the efficacy of the target and develop the instrument calibration protocol, the target is imaged on the Sharp Hyper-NA Actinic Reticle Review Project EUV mask microscope. Power spectral density (PSD) data are presented. The characteristics of the imaging system are imprinted on the PSD. The modulation transfer function is extracted from the PSD data. A partially coherent imaging model is used as a reference to the experimental results.

BPRA↗

DOE OSTI2026

Comparison of theory with the experimental characterization of the spatial frequency response of interferometers using a binary pseudo-random array sample

Experimental evaluations of the surface height response of an interference microscope using a binary pseudo-random array test sample are compared with a theory based on a Fourier optics model. Measurements of key instrument characteristics, including the illumination, imaging, and obscuring apertures of three different Mirau objectives, support the theoretical calculations. Agreement between experimental and theoretical modeling confirms the predictability of the spatial frequency response for the purpose of specification and optimization of instrument configuration for specific metrology tasks. The results also provide confidence in methods of compensating for the decrease in instrument response with spatial frequency.

Calibration↗

DOE OSTI2024

Binary pseudo-random array standards for calibration of 3D optical surface profilers used for metrology with significantly curved x-ray optics

High-accuracy metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate X-ray light with nanometer-scale wavelengths. The current capabilities and possibility for improvements in X-ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. In the case of Fizeau interferometry, metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for measuring slightly curved X-ray optics. However, for even moderately curved aspherical X-ray mirrors the flat-reference calibration is not sufficiently accurate and stitching Fizeau interferometer-based surface metrology is used to mitigate the problem. But still, the retrace and aberration errors, as well as the limited spatial resolution, described with the instrument transfer function (ITF), can be transferred into the optical surface topography of X-ray mirrors obtained in stitching metrology. For ITF calibration, we have developed an original technique, based on test standards structured as two-dimensional (2D) highly-randomized (HR) binary pseudo-random arrays (BPRAs). The technique employs the unique properties of the HR BPRA patterns in the spatial frequency domain., i.e. the inherent 2D power spectral density of the HR BPRA pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. Here, we explore technological, metrological, and analytical aspects essential for calibration of the retrace and aberration errors of Fizeau interferometers using different types of tilted test samples, including a super-polished reference mirror for the re-trace calibration and the uniformly redundant array (URA) BPRA standards for the geometrical distortion (aberration) calibration. While the first method was previously demonstrated by researchers at DIAMOND Light Source, a method based on the URA BPRA is described and demonstrated here for the first time. We outline the design and fabrication process used in fabrication of URA BPRA test standards, and present the results of application of the URA BPRA standards demonstrating the high efficacy of our approach to geometrical distortion calibration of Fizeau interferometers. We also discuss the possible sources of unexpected peculiarities of the systematic errors, including an astigmatic character of the retrace error, observed with Fizeau interferometers at the Advanced Light Source X-Ray Optics Laboratory.

Munechika, Keiko↗

DOE OSTI2025

Topography restoration in white-light interferometry using an instrument transfer function evaluated with binary pseudo-random arrays

Accurate knowledge of the instrument transfer function (ITF) is vital for topography measurements using white-light interferometry (WLI). To this end, we derive a complete set of analytical expressions for the power spectral density (PSD) of a discretely sampled binary pseudo-random array (BPRA) as a theoretical benchmark. We then determine the ITF by comparing this theoretical PSD with the measured PSD of the BPRA. For the Zygo ZeGage Pro HR with a objective, the determined ITF closely matches the nominal modulation transfer function (MTF). Accordingly, we integrate the nominal MTF into Fourier-domain restoration filters and apply them to practical WLI topography data, yielding restored topographies that show improved agreement with atomic force microscopy measurements. Overall, our integrated BPRA-based ITF measurement and filtering methodology offers a robust yet practical means of characterizing WLI performance and enhancing the accuracy of surface measurements.

Hirose, Shigenobu [Japan Agency for Marine Earth S↗

DOE OSTI2025

Multi-mode THz quantum-cascade VECSELs based on disordered metasurfaces

Quantum-cascade vertical-external-cavity surface-emitting-lasers (VECSELs) based on disordered amplifying metasurfaces are demonstrated and explored as potential broadband, multi-mode THz sources. The disorder is introduced along one spatial axis of the metasurface by pseudo-randomly varying the width of its resonant ridge antennas. Compared to a quantum-cascade (QC) VECSEL based on a uniform metasurface, the disordered structure supports much more localized transverse modes with reduced spatial overlap within the QC gain material. This localization is hypothesized to facilitate the spatial hole burning of the gain material and, therefore, enable multi-mode lasing, particularly for short cavities on the order of a few wavelengths. Several devices have been fabricated and shown to differ from uniform QC-VECSELs in a few key ways, possessing highly nonlinear light-current characteristics, angle-dependent emission spectra and broadband multi-mode lasing. At most, 17 modes are simultaneously observed, spanning 680 GHz. The number of VECSEL modes is shown to have an inverse relationship with the cavity length, which is attributed to increased diffractive losses in the open plano-plano cavity. As the cavity length is tuned, the device emits over a quasi-continuous band from 3.15 to 3.97 THz or up to 4.24 THz with a longitudinal mode hop.

Morag, Eilam [Univ. of California, Los Angeles, CA↗

DOE OSTI2025

Effects of Central Cut Width on the Dynamical Characteristics of Box Assembly Structure

An investigation into the Box Assembly with Removable Component (BARC) structure is conducted by utilizing computational simulations and experimental structural testing in order to determine the complex dynamical responses instigated by the central cut of the system. Because the dynamics of the BARC system is complex, this study focuses primarily on analyzing the behavior of the box assembly (BA) system. The investigation explores the dynamics of the BA system by varying the central cut widths, ranging from a cut as wide as 0.5” cut to a 0.25” cut system, as well as a 0.1” cut and a system with no cut at all. Experimental testing is performed on each system including a free vibration test using an impact hammer to excite and identify the dominant frequencies of each structure. This testing is followed by pseudo-random vibration tests and swept sinusoidal excitation tests to determine the nonlinear aspects of these systems, such as the possible existence of nonlinear softening, hardening, and/or damping. The results show that nonlinear softening and nonlinear damping are present in each system. The no-cut system demonstrated the highest peak frequencies throughout all the tests, being the most rigid structure. The 0.25” cut system was shown to have the highest peak frequencies among all the cut systems in both the finite elemenet analysis (FEA) and impact testing. This trend did not continue, though, in the random and harmonic testing, possibly due to the added stiffness of the test setup with the slip table and stinger. The results show the importance of accurately measuring the central cut width and how possible geometric uncertainties change the overall dynamical behaviors of complex systems, such as natural characteristics, nonlinear responses, coupling of modes, and oscillating amplitudes.

Padilla, Christopher (ORCID:000900033446732X)↗

DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗

DOE OSTI2025

Simulation of a Wireless Authentication Protocol

Abstract—A wireless authentication protocol that employs timeslots and associated frequency-channels (APEC) is simulated using Python as the simulation environment and implemented into radio hardware as a proof of concept. The APEC protocol does not rely on the use of challenge-response, multifactor authentication schemes but relies instead on the physical properties of a wireless signal. The APEC protocol provides opportunities for real-time deployment in cell phone network infrastructure, as well as in adverse civil and military applications. Description of the APEC implementation and the corresponding results of the simulation study are presented.

42 - ENGINEERING↗