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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Dark Energy Survey Year 1 results: weak lensing mass calibration of redMaPPer galaxy clusters

We constrain the mass-richness scaling relation of redMaPPer galaxy clusters identified in the Dark Energy Survey Year 1 data using weak gravitational lensing. We split clusters into 4 x 3 bins of richness lambda and redshift z for lambda >= 20 and 0.2 <= z <= 0.65 and measure the mean masses of these bins using their stacked weak lensing signal. By modelling the scaling relation as M-200m|lambda, M-0(lambda/40)(F)((1 + /1.35)(G), we constrain the normalization of the scaling relation at the 5.0 per cent level, finding M-0 = [3.081 +/- 0.075(stat) +/- 0.133(sys)] center dot 10(14) M-aS (TM) at lambda = 40 and = 0.35. The recovered richness scaling index is F = 1.356 +/- 0.051 (stat) +/- 0.008 (sys) and the redshift scaling index G = -0.30 +/- 0.30 (stat) +/- 0.06 (sys). These are the tightest measurements of the normalization and richness scaling index made to date from a weak lensing experiment. We use a semi-analytic covariance matrix to characterize the statistical errors in the recovered weak lensing profiles. Our analysis accounts for the following sources of systematic error: shear and photometric redshift errors, cluster miscentring, cluster member dilution of the source sample, systematic uncertainties in the modelling of the halo-mass correlation function, halo triaxiality, and projection effects. We discuss prospects for reducing our systematic error budget, which dominates the uncertainty on M-0. Our result is in excellent agreement with, but has significantly smaller uncertainties than, previous measurements in the literature, and augurs well for the power of the DES cluster survey as a tool for precision cosmology and upcoming galaxy surveys such as LSST, Euclid, and WFIRST

clusters↗
DOE OSTI2016

SU-F-T-288: Impact of Trajectory Log Files for Clarkson-Based Independent Dose Verification of IMRT and VMAT

Purpose: To investigate the effect of the trajectory files from linear accelerator for Clarkson-based independent dose verification in IMRT and VMAT plans. Methods: A CT-based independent dose verification software (Simple MU Analysis: SMU, Triangle Products, Japan) with a Clarksonbased algorithm was modified to calculate dose using the trajectory log files. Eclipse with the three techniques of step and shoot (SS), sliding window (SW) and Rapid Arc (RA) was used as treatment planning system (TPS). In this study, clinically approved IMRT and VMAT plans for prostate and head and neck (HN) at two institutions were retrospectively analyzed to assess the dose deviation between DICOM-RT plan (PL) and trajectory log file (TJ). An additional analysis was performed to evaluate MLC error detection capability of SMU when the trajectory log files was modified by adding systematic errors (0.2, 0.5, 1.0 mm) and random errors (5, 10, 30 mm) to actual MLC position. Results: The dose deviations for prostate and HN in the two sites were 0.0% and 0.0% in SS, 0.1±0.0%, 0.1±0.1% in SW and 0.6±0.5%, 0.7±0.9% in RA, respectively. The MLC error detection capability shows the plans for HN IMRT were the most sensitive and 0.2 mm of systematic error affected 0.7% dose deviation on average. Effect of the MLC random error did not affect dose error. Conclusion: The use of trajectory log files including actual information of MLC location, gantry angle, etc should be more effective for an independent verification. The tolerance level for the secondary check using the trajectory file may be similar to that of the verification using DICOM-RT plan file. From the view of the resolution of MLC positional error detection, the secondary check could detect the MLC position error corresponding to the treatment sites and techniques. This research is partially supported by Japan Agency for Medical Research and Development (AMED)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Improved uncertainty quantification in nondestructive assay for nonproliferation

This paper illustrates methods to improve uncertainty quantification (UQ) for non-destructive assay (NDA) measurements used in nuclear nonproliferation. First, it is shown that current bottom-up UQ applied to calibration data is not always adequate, for three main reasons: (1) Because there are errors in both the predictors and the response, calibration involves a ratio of random quantities, and calibration data sets in NDA usually consist of only a modest number of samples (3–10); therefore, asymptotic approximations involving quantities needed for UQ such as means and variances are often not sufficiently accurate; (2) Common practice overlooks that calibration implies a partitioning of total error into random and systematic error, and (3) In many NDA applications, test items exhibit non-negligible departures in physical properties from calibration items, so model-based adjustments are used, but item-specific bias remains in some data. Therefore, improved bottom-up UQ using calibration data should predict the typical magnitude of item-specific bias, and the suggestion is to do so by including sources of item-specific bias in synthetic calibration data that is generated using a combination of modeling and real calibration data. Second, for measurements of the same nuclear material item by both the facility operator and international inspectors, current empirical (top-down) UQ is described for estimating operator and inspector systematic and random error variance components. A Bayesian alternative is introduced that easily accommodates constraints on variance components, and is more robust than current top-down methods to the underlying measurement error distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Two-pion contribution to hadronic vacuum polarization

We present a detailed analysis of e + e - → π + π - data up to \( \sqrt{s}=1 \) GeV in the framework of dispersion relations. Starting from a family of ππ P -wave phase shifts, as derived from a previous Roy-equation analysis of ππ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the ω meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find a ππ μ | ≤ 1 GeV = 495.0(1.5)(2.1) × 10 -10 and a ππ μ | ≤ 0.63 GeV = 132.8(0.4)(1.0) × 10 -10 . While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the ππ P -wave, valuable input for future global analyses of low-energy ππ scattering, as well as a determination of the pion charge radius, $\langle$$r^{2}_{π}$$\rangle$ = 0 . 429(1)(4) fm 2 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Analytical error bars and RSD for neutron multiplicity counting

This article derives the standard deviation of the moments of neutron multiplicity distributions for both random and (shift register) triggered counting gates by propagating the multinomial distribution of errors in the counting distribution. Exact and approximate analytical formulas for the singles, doubles, and triples error bars are given along with the corresponding RSD (relative standard deviation). These analytical formulas provide a simple way to analyze and predict error bars without needing empirical data or simulations. The comparison of these analytical error bars to actual measurement errors can reveal systematic errors that are not being accounted for in the modeling of the data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

BEYONDPLANCK II. CMB mapmaking through Gibbs sampling

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Time-resolved dosimetry using a pinpoint ionization chamber as quality assurance for IMRT and VMAT

Purpose: To develop a method to verify the dose delivery in relation to the individual control points of intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT) using an ionization chamber. In addition to more effective problem solving during patient-specific quality assurance (QA), the aim is to eventually map out the limitations in the treatment chain and enable a targeted improvement of the treatment technique in an efficient way. Methods: Pretreatment verification was carried out for 255 treatment plans that included a broad range of treatment indications in two departments using the equipment of different vendors. In-house developed software was used to enable calculation of the dose delivery for the individual beamlets in the treatment planning system (TPS), for data acquisition, and for analysis of the data. The observed deviations were related to various delivery and measurement parameters such as gantry angle, field size, and the position of the detector with respect to the field edge to distinguish between error sources. Results: The average deviation of the integral fraction dose during pretreatment verification of the planning target volume dose was −2.1% ± 2.2% (1 SD), −1.7% ± 1.7% (1 SD), and 0.0% ± 1.3% (1 SD) for IMRT at the Radboud University Medical Center (RUMC), VMAT (RUMC), and VMAT at the Wellington Blood and Cancer Centre, respectively. Verification of the dose to organs at risk gave very similar results but was generally subject to a larger measurement uncertainty due to the position of the detector at a high dose gradient. The observed deviations could be related to limitations of the TPS beam models, attenuation of the treatment couch, as well as measurement errors. The apparent systematic error of about −2% in the average deviation of the integral fraction dose in the RUMC results could be explained by the limitations of the TPS beam model in the calculation of the beam penumbra. Conclusions: This study showed that time-resolved dosimetry using an ionization chamber is feasible and can be largely automated which limits the required additional time compared to integrated dose measurements. It provides a unique QA method which enables identification and quantification of the contribution of various error sources during IMRT and VMAT delivery.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Bayesian Inference of High-density Nuclear Symmetry Energy from Radii of Canonical Neutron Stars

The radius R 1.4 of neutron stars (NSs) with a mass of 1.4 M ⊙ has been extracted consistently in many recent studies in the literature. Using representative R 1.4 data, we infer high-density nuclear symmetry energy E sym (ρ) and the associated nucleon specific energy E 0 (ρ) in symmetric nuclear matter (SNM) within a Bayesian statistical approach using an explicitly isospin-dependent parametric equation of state (EOS) for nucleonic matter. We found the following. (1) The available astrophysical data can already significantly improve our current knowledge about the EOS in the density range of ρ 0 - 2.5ρ 0 . In particular, the symmetry energy at twice the saturation density ρ 0 of nuclear matter is determined to be E sym (2ρ 0 )=${39.2}_{-8.2}^{+12.1}$ MeV at a 68% confidence level. (2) A precise measurement of R 1.4 alone with a 4% 1σ statistical error but no systematic error will not greatly improve the constraints on the EOS of dense neutron-rich nucleonic matter compared to what we extracted from using the available radius data. (3) The R 1.4 radius data and other general conditions, such as the observed NS maximum mass and causality condition, introduce strong correlations for the high-order EOS parameters. Consequently, the high-density behavior of E sym (ρ) inferred depends strongly on how the high-density SNM EOS E 0 (ρ) is parameterized, and vice versa. (4) Finally, the value of the observed maximum NS mass and whether it is used as a sharp cutoff for the minimum maximum mass or through a Gaussian distribution significantly affects the lower boundaries of both E 0 (ρ) and E sym (ρ) only at densities higher than about 2.5ρ 0 .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

TU-H-CAMPUS-TeP2-04: Measurement of Stereotactic Output Factors with DNA Double-Strand Breaks

Purpose: Radiotherapy treatment is specified by radiation dose prescriptions, but biological DNA damage actually controls treatment effectiveness. It is impractical to directly measure dose in the clinic, so we measure quantities, such as collected charge, and calculate the relationship to dose. At small fields, such as those in stereotactic radiosurgery (SRS), charged-particle equilibrium (CPE) breaks down and the accuracy of the measurement for delivered dose decreases. By measuring DNA double-strand breaks (DSB) directly, we believe treatment accuracy could improve by providing a more meaningful measurement. Methods: A DNA dosimeter, consisting of magnetic streptavidin beads attached to 4 kilobase pair DNA strands labeled with biotin and fluorescein amidite (FAM) on opposing ends, was suspended in phosphate-buffered saline (PBS). Twenty µL samples were placed in plastic micro-capillary tubes inside a water tank setup and irradiated with 10 cm, 3 cm, 1.25 cm, 0.75 cm, and 0.5 cm radiation field sizes, where the three smallest sizes were cones. After irradiation, the dosimeters were mechanically separated into beads (intact DNA) and supernatant (broken DNA/FAM) using a magnet. The fluorescence was read and the probability of DSB was calculated. This was used to calculate the output factor for an SRS beam and compared to that measured using a diode detector. Results: The output factors relative to a 10 cm field were 0.89±0.07, 0.76±0.08, 0.59±0.04, and 0.78±0.12 for the field sizes of 3 cm, 1.25 cm, 0.75 cm, and 0.5 cm, respectively. Some of the diode measurements do not fall within these uncertainties. Conclusion: This was the first attempt to measure output factors in a water tank with the DNA dosimeter. Although differences compared to the diode were observed, the uncertainty analysis ignored systematic errors. For future work, we will repeat this experiment to quantify and correct systematic errors, such as those caused by positional alignment and sample contamination. This work was funded in part by CPRIT (RP140105).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Process-oriented evaluation using ARM observations to improve clouds and radiation in a global atmospheric model

The goal of the research is to improve understanding of cloud, radiation and precipitation processes and their representation in numerical models for weather and climate using observations from the ARM/ASR program. Global models need to represent all cloud types across different weather regimes from the tropics to the poles and ARM provides long-term observations at different geographical sites that cover these different regimes. Combined with satellite data to give a global context, the observations are used to evaluate the systematic errors in a global model for predictions of cloud, radiation and precipitation. The focus is on understanding the links to underlying physical processes to pinpoint the sources of error and improve the model representation of these processes. The research covers boundary layer cloud over the continental U.S., marine stratocumulus and shallow cumulus in the subtropics, mixed-phase clouds over the Arctic and Southern Ocean, and high-altitude cirrus ice clouds in the tropics. The model used is the operational global weather prediction system at the European Centre for Medium-range Weather Forecasts (ECMWF). The research has led to numerous developments, several of which have been implemented operationally leading to improvements in everyday forecasts. Many of the systematic errors are common across different modelling systems and the wider implications from the research for other weather and climate models are highlighted.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Detection of the pairwise kinematic Sunyaev-Zel'dovich effect with BOSS DR11 and the Atacama Cosmology Telescope

Here, we present a new measurement of the kinematic Sunyaev-Zel'dovich effect using data from the Atacama Cosmology Telescope (ACT) and the Baryon Oscillation Spectroscopic Survey (BOSS). Using 600 square degrees of overlapping sky area, we evaluate the mean pairwise baryon momentum associated with the positions of 50,000 bright galaxies in the BOSS DR11 Large Scale Structure catalog. A non-zero signal arises from the large-scale motions of halos containing the sample galaxies. The data fits an analytical signal model well, with the optical depth to microwave photon scattering as a free parameter determining the overall signal amplitude. We estimate the covariance matrix of the mean pairwise momentum as a function of galaxy separation, using microwave sky simulations, jackknife evaluation, and bootstrap estimates. The most conservative simulation-based errors give signal-to-noise estimates between 3.6 and 4.1 for varying galaxy luminosity cuts. We discuss how the other error determinations can lead to higher signal-to-noise values, and consider the impact of several possible systematic errors. Estimates of the optical depth from the average thermal Sunyaev-Zel'dovich signal at the sample galaxy positions are broadly consistent with those obtained from the mean pairwise momentum signal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A Point Kinetics Model for Estimating Neutron Multiplication of Bare Uranium Metal in Tagged Neutron Measurements

An extension of the point kinetics model is developed in this paper to describe the neutron multiplicity response of a bare uranium object under interrogation by an associated particle imaging deuterium-tritium (D-T) measurement system. This extended model is used to estimate the total neutron multiplication of the uranium. Both MCNPX-PoliMi simulations and data from active interrogation measurements of highly enriched and depleted uranium geometries are used to evaluate the potential of this method and to identify the sources of systematic error. The detection efficiency correction for measured coincidence response is identified as a large source of systematic error. If the detection process is not considered, results suggest that the method can estimate total multiplication to within 13% of the simulated value. Values for multiplicity constants in the point kinetics equations are sensitive to enrichment due to (n, xn) interactions by D-T neutrons and can introduce another significant source of systematic bias. This can theoretically be corrected if isotopic composition is known a priori. Finally, the spatial dependence of multiplication is also suspected of introducing further systematic bias for high multiplication uranium objects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Modelling the BAO feature in bispectrum

We investigate how well a simple leading order perturbation theory model of the bispectrum can fit the baryon acoustic oscillation (BAO) feature in the measured bispectrum monopole of galaxies. Previous works showed that perturbative models of the galaxy bispectrum start failing at the wavenumbers of k ∼ 0.1 h Mpc −1 . We show that when the BAO feature in the bispectrum is separated, it can be successfully modelled up to much higher wavenumbers. We validate our modelling on GLAM simulations that were run with and without the BAO feature in the initial conditions. We also quantify the amount of systematic error due to BAO template being offset from the true cosmology. We find that the systematic errors do not exceed 0.3 per cent for reasonable deviations of up to 3 per cent from the true value of the sound horizon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Measurements of Effective Optical Depth in the Lyα Forest from the BOSS DR12 Quasar Sample

We measure the effective optical depth in the Lyα forest using 40,035 quasar spectra from the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey of Sloan Digital Sky Survey IV. A rigorous selection based on spectral index and the equivalent width of the C iv emission line is applied to choose seven uniform samples with minimal intrinsic variations across redshifts. Modeling the redshift evolution of the effective optical depth with a power law, ${\tau }_{\mathrm{eff}}={\tau }_{0}{(1+z)}^{\gamma },$ produces ${\tau }_{0}=(5.54\pm 0.64)\times {10}^{-3}$ and $\gamma =3.182\pm 0.074$. The 2.2% precision estimate on γ is dominated by systematic errors, likely arising from the bias and uncertainties in spectral index estimates. Even after incorporating the systematic errors, this work provides the most precise estimates of optical depth parameters to date. Finally, using the reconstructed Lyα forest continuum to directly measure the transmitted flux ratio as a function of redshift, we find deviations of less than 2.5% from the predictions from the global model and no convincing evidence for signal associated with He ii reionization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spectral Fidelity of Earth's Terrestrial and Aquatic Ecosystems

The Surface Biology and Geology (SBG) investigation will create global maps of spectral surface reflectance and emissivity at a cadence of 16 days or better, with coverage to address global questions about Earth's geology, cryosphere and ecosystems. The revolutionary potential poses a commensurate challenge: creating contiguous maps free from regional biases induced by atmosphere, observation geometry, or inversion error. This will require an accurate calibration with precise knowledge of each channel's spectral response. In this work, we quantify the impact of spectral calibration on SBG's aquatic and terrestrial ecosystem objectives. We find that contemporary algorithms for ecosystem trait retrieval demand more accurate spectral calibration than historical missions. Errors due to drift or spatial nonuniformity in the wavelength calibration that have previously been considered acceptable can cause systematic errors larger than the instrument noise and of the same order as the variability SBG aims to measure. Moreover, their impact on atmospheric correction can induce climate-dependent systematic errors that thwart comparisons between ecosystems. These results underscore the importance of spectral response accuracy in SBG mission design.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

SU-E-J-37: Combining Proton Radiography and X-Ray CT Information to Better Estimate Relative Proton Stopping Power in a Clinical Environment

Purpose: In standard proton therapy clinical practice, proton stopping power uncertainties are in the order of 3.5%, which affects the ability of placing the proton Bragg peak at the edge of the tumor. The innovating idea of this project is to approach the uncertainty problem in RSP by using combined information from X-ray CT and proton radiography along a few beam angles. In addition, this project aims to quantify the systematic error introduced by the theoretical models (Janni, ICRU49, Bischel) for proton stopping power in media. Methods: A 3D phantom of 36 cm3 composed of 9 materials randomly placed is created. Measured RSP values are obtained using a Gammex phantom with a proton beam. Theoretical RSP values are calculated with Beth-Block equation in combination with three databases (Janni, ICRU49 and Bischel). Clinical RSP errors are simulated by introducing a systematic (1.5%, 2.5%, 3.5%) and a random error (+/−0.5%) to the theoretical RSP. A ray-tracing algorithm uses each of these RSP tables to calculate energy loss for proton crossing the phantom through various directions. For each direction, gradient descent (GD) method is done on the clinical RSP table to minimize the residual energy difference between the simulation with clinical RSP and with theoretical RSP. The possibility of a systematic material dependent error is investigated by comparing measured RSP to theoretical RSP as calculated from the three models. Results: Using 10,000 iterations on GD algorithm, RSP differences between theoretical values and clinical RSP have converged (<1%) for each error introduced. Results produced with ICRU49 have the smallest average difference (0.021%) to the measured RSP. Janni (1.168%) and Bischel (−0.372%) database shows larger systematic errors. Conclusion: Based on these results, ray-tracing optimisation using information from proton radiography and X-ray CT demonstrates a potential to improve the proton range accuracy in a clinical environment.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2015

RED NOISE VERSUS PLANETARY INTERPRETATIONS IN THE MICROLENSING EVENT OGLE-2013-BLG-446

For all exoplanet candidates, the reliability of a claimed detection needs to be assessed through a careful study of systematic errors in the data to minimize the false positives rate. We present a method to investigate such systematics in microlensing data sets using the microlensing event OGLE-2013-BLG-0446 as a case study. The event was observed from multiple sites around the world and its high magnification (A{sub max} ∼ 3000) allowed us to investigate the effects of terrestrial and annual parallax. Real-time modeling of the event while it was still ongoing suggested the presence of an extremely low-mass companion (∼3M{sub ⨁}) to the lensing star, leading to substantial follow-up coverage of the light curve. We test and compare different models for the light curve and conclude that the data do not favor the planetary interpretation when systematic errors are taken into account.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Raytracing the long trace profiler

The optical design of the Long Trace Profiler optical system is explored with a commercial raytrace program, Zemax OpticStudio™ (ZOS)1, with the intent of finding and correcting sources of systematic error. ZOS provides both geometric raytracing tools and physical optics Gaussian beam propagation and diffraction image calculation tools, and two design modes, sequential component (SC) and non-sequential component (NSC) that are optimized for different aspects of the design process. The original LTP-II system employs a singlet lens with a 1250 mm focal length. It is optimized to provide minimum distortion over a surface slope angle range of ±5 mrad. Using the ZOS tools, we are able to simulate ghost rays that produce distortion in the beam spot image and can minimize the distortion by deliberate misalignment of the beamsplitter (BS) components. Unfortunately, the reference beam is compromised because of the component tilts. The most recent LTP500 system design simplifies the optical system and makes the reference beam usable again, even with misalignment of the polarizing beamsplitter (PBS). Two lenses are designed for the LTP500 - a cemented doublet that has been fabricated, and a singlet with one aspheric surface. Both have focal distances of 500 mm with an expanded angular measurement range of ±10 mrad. The aspheric singlet provides superior performance. ZOS allows the import of wavefront measurement data produced by commercial interferometer software. We apply the wavefront error measurement from the cemented doublet to the model to show that the 19nm RMS wavefront error needs to be improved by at least a factor of ten in order to reduce the systematic error to a level that will allow the LTP to approach its design limit of a few tens of nanoradians.

Takacs, Peter Z.↗