Relative Systematic Uncertainty Research Articles

Independent isotopic fission yields of 252Cf spontaneous fission via mass measurements at the FRS Ion Catcher

We present first preliminary results of a novel method for measuring independent isotopic fission yields (IIFYs) of spontaneous fission (SF) via direct mass measurements, at the FRS Ion Catcher (FRS-IC) at GSI. Fission products were generated from a 252Cf source installed in a cryogenic stopping cell, and were identified and counted with the multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) of the FRS-IC, utilizing well-established measurement and data analysis methods. The MR-TOF-MS resolves isobars unambiguously, even with limited statistics, and its non-scanning nature ensures minimal relative systematic uncertainties amongst fission products. The analysis for extracting IIFYs includes isotope-dependent efficiency corrections for all components of the FRS-IC. In particular, we applied a self-consistent technique that takes into account the element-dependent survival efficiencies in the CSC, due to chemical reactions with the buffer gas. Our IIFY results, which cover several tens of fission products in the less-accessible high-mass peak (Z = 56 to 63) down to fission yields at the level of 10−5, are generally similar to those of the nuclear database ENDF/B-VII.0. Nevertheless, they reveal some structures that are not observed in the database smooth trends. These are the first results of a planned campaign to investigate IIFY distributions of spontaneous fission at the FRS-IC. Upcoming experiments will extend our results to wider Z and N ranges, lower fission yields, and other spontaneously-fissioning actinides.

Correcting MAGIC Telescope data taken under non-optimal atmospheric conditions with an elastic LIDAR

The Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes are a system of two Imaging Atmospheric Cherenkov Telescopes (IACTs). IACTs make calorimetric use of the Earth’s atmosphere, which allows them to reach large effective areas, but also makes them strongly dependent on the quality of the atmosphere at the time of the observations. Dust intrusions or clouds obscuring the observed Cherenkov light can then lead to a wrong reconstruction of the gamma-ray data. In order to mitigate this problem, the MPP group built and has been operating a single wavelength elastic LIDAR (LIght Detection And Ranging) system to perform real time ranged-resolved measurements of the aerosol transmission. This information is then used to quantify the quality of the telescope data, as well as to correct the data taken under suboptimal aerosol conditions. In this talk, the correction of atmospherically impaired IACT data will be described and the first systematic evaluation of the correction capabilities of the LIDAR system will be presented. The results describe the impact of the LIDAR corrections for a variety of atmospheric and observational conditions, and therefore contribute to a better understanding of the telescope’s performance and related systematic uncertainties.

Extraction of proton trace anomaly energy from near-threshold $$\phi $$ and $$J/\psi $$ photo-productions

The trace anomalous energy contribution to the proton mass is a very important topic in non-perturbative QCD and hadron physics. In experiments, it is under the hot discussions on how to measure the trace anomalous energy.The QCD interpretation of proton trace anomaly is still not clear.To connect the theory with the experiment,we extract the trace anomaly by analyzing the near-threshold photo-production data of $\phi$ and J/$\psi$ vector mesons. Based on the vector-meson-dominance model and QCD Van der Waals representation, we find that the percentage of trace anomaly in the proton mass ranges from $16\%$ to $24\%$, which is of similar order of magnitude as the 23$\%$ given by Lattice QCD. We also provide the approximate magnitudes of the systematic uncertainties of the extracted results from the model assumptions as well as the data fitting procedures. We give relative statistical uncertainties of 17.2$\%$, 17.7$\%$, 3.6$\%$, and 8.2$\%$, total relative systematic uncertainties of 21.4$\%$, 54.2$\%$, 37.2$\%$, and 25.7$\%$, for the analyses of the GlueX, LEPS, CLAS, and SAPHIR data, respectively. We argue that the near-threshold $\Upsilon$ photo-production experiments are more beneficial for the measurement of trace anomaly in proton mass in the future.

Search for sterile neutrino oscillations using RENO and NEOS data

We present a reactor model independent search for sterile neutrino oscillation using 2\,509\,days of RENO near detector data and 180 days of NEOS data. The reactor related systematic uncertainties are significantly suppressed as both detectors are located at the same reactor complex of Hanbit Nuclear Power Plant. The search is performed by electron antineutrino\,($\overline{\nu}_e$) disappearance between six reactors and two detectors with baselines of 294\,m\,(RENO) and 24\,m\,(NEOS). A spectral comparison of the NEOS prompt-energy spectrum with a no-oscillation prediction from the RENO measurement can explore reactor $\overline{\nu}_e$ oscillations to sterile neutrino. Based on the comparison, we obtain a 95\% C.L. excluded region of $0.1<|\Delta m_{41}^2|<7$\,eV$^2$. We also obtain a 68\% C.L. allowed region with the best fit of $|\Delta m_{41}^2|=2.41\,\pm\,0.03\,$\,eV$^2$ and $\sin^2 2\theta_{14}$=0.08$\,\pm\,$0.03 with a p-value of 8.2\%. Comparisons of obtained reactor antineutrino spectra at reactor sources are made among RENO, NEOS, and Daya Bay to find a possible spectral variation.

Search for a diffuse flux of cosmic neutrinos with the ANTARES neutrino telescope

An excess of high-energy events has been found in previous ANTARES searches for a diffuse flux of cosmic neutrinos, consistent in spectral slope and normalisation with the cosmic neutrino signal detected by the IceCube Neutrino Observatory. The analysis of ANTARES data can provide valuable information in the study of this high-energy neutrino signal, especially in the case of soft-spectra solutions. To improve previous ANTARES results, a new event selection has been developed for cascade-like events, relying on a boosted decision tree multivariate-analysis technique. This yields a 5-fold increase in event statistics, while also reducing the surviving foregrounds and the related systematic uncertainties. This contribution will report on the status of the analysis and the prospects emerging from the use of this new event sample in the search for a diffuse flux of cosmic neutrinos.

Suppression of free convection effects for spherical 1 kg mass prototype

We investigate the free convection processes in the vicinity of a spherical 1 kg mass standard by two- and three-dimensional direct numerical simulations using a spectral element method. Our focus is on the determination and suppression of updraft forces in a high-precision mass comparator which are caused by temperature differences between mass standard and its environment in the millikelvin range – a source of systematic uncertainties in the high-precison mass determination. A two-dimensional model is presented first, which obtains a good agreement with previous laboratory measurements for the smaller temperature differences up to 15 mK. The influence of different boundary conditions and side lengths of the square domain is discussed for the mass standard positioned in the center of the chamber. The complexity is increased subsequently in configurations with additional built-ins for counter heating in form of planar plates or hemispherical shells above the mass standard. The latter ones lead to a full compensation of the updraft force. Three-dimensional simulations in a closed cubic chamber confirm the two-dimensional findings and additionally reveal complex secondary flow patterns in the vicinity of the mass standard. The reduction of the heat transfer due to the built-ins is also demonstrated by a comparison of the Nusselt numbers as a function of the Rayleigh number in the chosen parameter range. Our simulations suggest that such additional constructive measures can enhance the precision of the mass determination by suppression of free convection and related systematic uncertainties.

Design and performance of an in-vacuum, magnetic field mapping system for the Muon g-2 experiment

The Muon g−2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment, aμ, of the muon with a precision of 140 parts-per-billion. This requires a precise measurement of both the anomalous spin precession frequency, ωa, of muons stored in a magnetic field of 1.45 T, and a precise measurement of that magnetic field in terms of the shielded proton Larmor frequency, ω′p. The measurement of ω′p with a total systematic uncertainty of 70 parts-per-billion involves a combination of various nuclear magnetic resonance (NMR) probes. There are 378 probes mounted in fixed locations that constantly monitor field drifts. A water-based, cylindrical calibration probe provides the calibration in terms of the shielded proton Larmor frequency. A crucial element for the multi-step measurement of ω′p is the regular mapping of the magnetic field over the muon storage region. The former experiment at Brookhaven National Laboratory (BNL) employed an in-vacuum field mapping system equipped with 17 NMR probes, which was developed by the University of Heidelberg. We have refurbished and upgraded this system with new probes and electronics. The upgrades include the addition of 16-bit, 1 MSPS digitization of the NMR signals, which replaced the hardware-implemented zero-crossing counting of the system at Brookhaven. The digitized signals offer new capabilities in the NMR frequency analysis and its related systematic uncertainties. To sustain the higher data rates, a new communication scheme with time-division multiplexing was implemented to separate the important NMR reference clock from the data communication in order to reach the specifications for the accuracy and stability of the reference clock. A new barcode reader provides more precise azimuthal position determination during the measurement and calibration. While the mechanical systems that move the field mapper inside the storage ring have been mostly refurbished from BNL, the motion control system was completely replaced with a custom-built electronics centered around a commercial Galil motion controller. Both the field mapping NMR system and its motion control were successfully commissioned at Fermilab and have been in reliable operation during the first three data taking periods of the experiment at Fermilab. This article will provide the details of the upgrades of the field mapper and its performance.

Modified astrophysical S-factor of 12C+12C fusion reaction at sub-barrier energies * * Supported by the National Key Research and Development Program of China (2016YFA0400501), National Natural Science Foundation of China (11805291, 11575292, 11475228, 11490564, 11875329), the U.S. Department of Energy ( DE-AC07-05ID14517), Fundamental Research Funds for the Central Universities (18lgpy84), Continuous Basic Scientific Research Project (WDJC-2019-13), CNNC R&D program (FA18000201).

The 12C+12C fusion reaction plays a crucial role in stellar evolution and explosions. Its main open reaction channels include , p, n, and 8Be. Despite more than a half century of efforts, large differences remain among the experimental data of this reaction measured using various techniques. In this work, we analyze the existing data using a statistical model. Our calculation shows the following: 1) the relative systematic uncertainties of the predicted branching ratios decrease as the predicted ratios increase; 2) the total modified astrophysical S-factors (S* factors) of the p and channels can be obtained by summing the S* factors of their corresponding ground-state transitions and the characteristic rays, while taking into account the contributions of the missing channels to the latter. After applying corrections based on branching ratios predicted by the statistical model, an agreement is achieved among the different data sets at Ecm> 4 MeV, while some discrepancies remain at lower energies, suggesting the need for better measurements in the near future. We find that theS* factor recently obtained from an indirect measurement is inconsistent with the direct measurement value at energies below 2.6 MeV. We recommend upper and lower limits for the 12C+12C S* factor based on the existing models. A new 12C+12C reaction rate is also recommended.

Active-sterile neutrino mixing constraints using reactor antineutrinos with the ISMRAN setup

In this work, we present an analysis of the sensitivity to the active-sterile neutrino mixing with the Indian Scintillator Matrix for Reactor Anti-Neutrino (ISMRAN) experimental set-up at very short baseline. In this article, we have considered the measurement of electron antineutrino induced events employing a single detector which can be placed either at a single position or moved between near and far positions from the given reactor core. Results extracted in the later case are independent of the theoretical prediction of the reactor anti-neutrino spectrum and detector related systematic uncertainties. Our analysis shows that the results obtained from the measurement carried out at a combination of the near and far detector positions are improved significantly at higher $\Delta m^{2}_{41}$ compared to the ones obtained with the measurement at a single detector position only. It is found that the best possible combination of near and far detector positions from a 100 MW$_{th}$ power DHRUVA research reactor core are 7 m and 9 m, respectively, for which ISMRAN set-up can exclude in the range 1.4 $eV^{2} \leq \Delta m^{2}_{41} \leq$ 4.0 $eV^{2}$ of reactor antineutrino anomaly region along with the present best-fit point of active-sterile neutrino oscillation parameters. At those combinations of detector positions, the ISMRAN set-up can observe the active sterile neutrino oscillation with a 95$\%$ confidence level provided that $\sin^{2}2\theta_{14}\geq 0.09$ at $\Delta m^{2}_{41}$ = 1 eV$^{2}$ for an exposure of 1 ton-yr. The active-sterile neutrino mixing sensitivity can be improved by about 22\% at the same exposure by placing the detector at near and far distances of 15 m and 17 m, respectively, from the compact proto-type fast breeder reactor (PFBR) facility which has a higher thermal power of 1250 MW$_{th}$.

Propagation of statistical uncertainties in covariant density functional theory: Ground state observables and single-particle properties

Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in covariant density functional theory (CDFT) for the first time. In this study we consider only covariant energy density functionals with non-linear density dependency. Statistical errors for binding energies and neutron skins significantly increase on approaching two-neutron drip line. On the contrary, such a trend does not exist for statistical errors in charge radii and two-neutron separation energies. The absolute and relative energies of the single-particle states in the vicinity of the Fermi level are characterized by low statistical errors ($\sigma(e_i)\sim 0.1$ MeV). Statistical errors in the predictions of spin-orbit splittings are rather small. Statistical errors in physical observables are substantially smaller than related systematic uncertainties. Thus, at the present level of the development of theory, theoretical uncertainties at nuclear limits are dominated by systematic ones. Statistical errors in the description of physical observables related to the ground state and single-particle degrees of freedom are typically substantially lower in CDFT as compared with Skyrme density functional theory. The correlations between the model parameters are studied in detail. The parametric correlations are especially pronounced for the $g_2$ and $g_3$ parameters which are responsible for the density dependence of the model. The accounting of this fact potentially allows to reduce the number of free parameters of non-linear meson coupling model from six to five.

Calibration and Reconstruction of the Daya Bay Antineutrino Detector

The Daya Bay Reactor Neutrino Experiment has produced the most precise measurements to date of the mixing angle θ13 and the mass-squared difference in the electron antineutrino disappearance channel. In addition, the experiment has published a precision measurement of the reactor antineutrino flux and spectrum. Energy calibration and reconstruction are crucial to all of these measurements. Various approaches are used to understand the detector non-linearity, non-uniformity, energy scale and the related systematic uncertainties. The uncertainty of the detector-uncorrelated energy scale and the absolute energy response are less than 0.2% and 1%, respectively. Nevertheless, these uncertainties are among the leading contributors to the overall systematic uncertainties leading contributors of the systematic uncertainties and will continue to be studied.

Beam energy measurement system for BEPCII

The beam energy measurement system for BEPCII is described. The system is based on measuring the energies of Compton back-scattered photons. The relative systematic uncertainty of the beam energy determination is estimated as 2 × 105. The upgrade of the system guarantees a smooth and efficient measurement of beam energy at BEPCII and enables accurate offline energy values for further physics analysis at BESIII.

Design and construction of a high-energy photon polarimeter

We report on the design and construction of a high-energy photon polarimeter for measuring the degree of polarization of a linearly-polarized photon beam. The photon polarimeter uses the process of pair production on an atomic electron (triplet production). The azimuthal distribution of scattered atomic electrons following triplet production yields information regarding the degree of linear polarization of the incident photon beam. The polarimeter, operated in conjunction with a pair spectrometer, uses a silicon strip detector to measure the recoil electron distribution resulting from triplet photoproduction in a beryllium target foil. The analyzing power ΣA for the device using a 75 μm beryllium converter foil is about 0.2, with a relative systematic uncertainty in ΣA of 1.5%.

CTA Atmospheric Calibration

The main contribution to the systematic uncertainties of Atmospheric Imaging Cherenkov Telescopes (IACTs) currently stems from the uncertainty in the determination of atmospheric properties for a given moment of observation. This technique uses the atmosphere as a calorimeter of gamma-ray induced atmospheric air showers and measures the amount of Cherenkov light collected by large mirrors and focused towards a pixellized camera. Atmospheric conditions affect the measured Cherenkov light yield in several ways: the air-shower development itself, the variation of the Cherenkov angle with altitude and the loss of photons due to scattering and absorption of Cherenkov light. Although IACTs use to be located at astronomical sites, characterized by extremely clear atmospheric conditions, the local atmosphere should be continuously monitored, in terms of molecular density profiles, aerosol extinction profiles, and clouds. Moreover, a general understanding of the site and particularly aerosol climatology is desirable for a robust interpretation of the sensing instruments’ data. Here, the strategy of the Cherenkov Telescope Array (CTA) on atmospheric monitoring is presented, designed to ensure that the related systematic uncertainties are brought down by at least a factor of two with respect to current installations. Additionally, a more intelligent scheduling scheme is aimed at, where source observations are selected using dedicated auxiliary atmospheric monitoring instruments and taking into account the feasibility of a later analysis according to the underlying scientific case. This plan should reduce data loss during offline data selection and enhance the effective duty cycle of the CTA.

Study of the polarimetric performance of a Si/CdTe semiconductor Compton camera for the Hitomi satellite

Gamma-ray polarization offers a unique probe into the geometry of the γ-ray emission process in celestial objects. The Soft Gamma-ray Detector (SGD) onboard the X-ray observatory Hitomi is a Si/CdTe Compton camera and is expected to be an excellent polarimeter, as well as a highly sensitive spectrometer due to its good angular coverage and resolution for Compton scattering. A beam test of the final-prototype for the SGD Compton camera was conducted to demonstrate its polarimetric capability and to verify and calibrate the Monte Carlo simulation of the instrument. The modulation factor of the SGD prototype camera, evaluated for the inner and outer parts of the CdTe sensors as absorbers, was measured to be 0.649–0.701 (inner part) and 0.637–0.653 (outer part) at 122.2keV and 0.610–0.651 (inner part) and 0.564–0.592 (outer part) at 194.5keV at varying polarization angles with respect to the detector. This indicates that the relative systematic uncertainty of the modulation factor is as small as ∼3%.

Precise determination of micromotion for trapped-ion optical clocks

As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low 10−18 range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in the commonly encountered regime where the transition linewidth is comparable to the rf drive frequency. We show that a fractional frequency uncertainty due to the 2nd-order Doppler shift below |Δν/ν|=1×10−20 can be achieved. The quantitative evaluation is verified in an interleaved measurement with the conceptually simpler resolved sideband method. If not performed deep within the Lamb-Dicke regime, a temperature-dependent offset at the level of 10−19 is observed in resolved sideband measurements due to sampling of intrinsic micromotion. By direct comparison with photon-correlation measurements, we show that the simple to implement parametric heating method is sensitive to micromotion at the level of |Δν/ν|=1×10−20 as well.

High-accuracy determination of theU238/U235fission cross section ratio up to≈1GeV at n_TOF at CERN

The U238 to U235 fission cross section ratio has been determined at n_TOF up to ≈1 GeV, with two different detection systems, in different geometrical configurations. A total of four datasets has been collected and compared. They are all consistent to each other within the relative systematic uncertainty of 3–4%. The data collected at n_TOF have been suitably combined to yield a unique fission cross section ratio as a function of neutron energy. The result confirms current evaluations up to 200 MeV. Good agreement is also observed with theoretical calculations based on the INCL++/Gemini++ combination up to the highest measured energy. The n_TOF results may help solve a long-standing discrepancy between the two most important experimental datasets available so far above 20 MeV, while extending the neutron energy range for the first time up to ≈1 GeV.1 MoreReceived 27 November 2014DOI:https://doi.org/10.1103/PhysRevC.91.024602This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

Calculation of the detection limit in radiation measurements with systematic uncertainties

The detection limit (LD) or Minimum Detectable Activity (MDA) is an a priori evaluation of assay sensitivity intended to quantify the suitability of an instrument or measurement arrangement for the needs of a given application. Traditional approaches as pioneered by Currie rely on Gaussian approximations to yield simple, closed-form solutions, and neglect the effects of systematic uncertainties in the instrument calibration. These approximations are applicable over a wide range of applications, but are of limited use in low-count applications, when high confidence values are required, or when systematic uncertainties are significant. One proposed modification to the Currie formulation attempts account for systematic uncertainties within a Gaussian framework. We have previously shown that this approach results in an approximation formula that works best only for small values of the relative systematic uncertainty, for which the modification of Currie׳s method is the least necessary, and that it significantly overestimates the detection limit or gives infinite or otherwise non-physical results for larger systematic uncertainties where such a correction would be the most useful. We have developed an alternative approach for calculating detection limits based on realistic statistical modeling of the counting distributions which accurately represents statistical and systematic uncertainties. Instead of a closed form solution, numerical and iterative methods are used to evaluate the result. Accurate detection limits can be obtained by this method for the general case.

Gamma-telescopes Fermi/LAT and GAMMA-400 Trigger Systems Event Recognizing Methods Comparison

Usually instruments for high-energy γ-quanta registration consists of converter (where γ-quanta produced pairs) and calorimeter for particles energy measurements surrounded by anticoincidence shield used to events identification (whether incident particle was charged or neutral). The influence of pair formation by γ-quanta in shield and the backsplash (moved in the opposite direction particles created due high energy γ-rays interact with calorimeter) should be taken into account. It leads to decrease both effective area and registration efficiency at E>10GeV. In the presented article the event recognizing methods used in Fermi/LAT trigger system is considered in comparison with the ones applied in counting and triggers signals formation system of gamma-telescope GAMMA-400.The GAMMA-400 (Gamma Astronomical Multifunctional Modular Apparatus) will be the new high-apogee space γ-observatory. The GAMMA-400 consist of converter-tracker based on silicon-strip coordinate detectors interleaved with tungsten foils, imaging calorimeter make of 2 layers of double (x, y) silicon strip coordinate detectors interleaved with planes of CsI(Tl) crystals and the electromagnetic calorimeter CC2 consists only of CsI(Tl) crystals. Several plastics detections systems used as anticoincidence shield, for particles energy and moving direction estimations. The main differences of GAMMA-400 constructions from Fermi/LAT one are using the time-of-flight system with base of 50cm and double layer structure of plastic detectors provides more effective particles direction definition and backsplash rejection. Also two calorimeters in GAMMA-400 composed the total absorbtion spectrometer with total thickness ∼ 25 X0 or ∼1.2 λ0 for vertical incident particles registration and 54 X0 or 2.5 λ0 for laterally incident ones (where λ0 is nuclear interaction length). It provides energy resolution 1-2% for 10 GeV–3.0×103 GeV events while the Fermi/LAT energy resolution does not reach such a value because of its calorimeter thickness is only ∼10 X0 and energy of registered particles is defined by shower profile analysis. Less than 3% photons will be wrongly recognized as electrons or protons in double-layer ACtop taking into account both temporal and amplitude trigger marker analysis methods during onboard processing in the counting and triggers signals formation system of GAMMA-400. The proton rejection factor will be ∼10-5.The Fermi/LAT based on a 4 × 4 array of identical towers each contains a tracker, calorimeter and data acquisition module. Each tracker consists of 18 x-y silicon-strip layers. The calorimeter in each tower made of eight layers in a hodoscopic arrangement for measure the three-dimensional profiles of showers permits corrections for energy leakage and enhances the capability to discriminate hadronic cosmic rays. The each layer consists of 12 CsI(Tl) based bars. The segmented anticoincidence shield covers the array of towers. Unfortunately, several types of biases lead to systematic effects caused high values of relative systematic uncertainties of the exposure, the number of signal events, the induced fractional signal and so on. For example non confirmed announcement of ∼133GeV line detection and lost sources in different Fermi catalogues (1FGL, 2FGL, 3FGL) – just well seen in 2FGL Cygnus X−3 (J2032.1+4049) does not appear in 3FGL. It allows to conclude sufficient biases in LAT characteristics obtained methods and event recognized algorithms. Now Fermi/LAT operates during ∼ 7 years but effective caveats methods continuously to be proposed. Respectively, continuation of measurements with use of other telescopes is necessary, and realization of GAMMA-400 will allow improving the results.

Miniaturization of an interferometric distance sensor employing diffractive optics

Abstract In order to improve safety, lifetime and energy efficiency of turbo machines, the behavior of the turbine blades has to be monitored during operation. This is a great challenge for metrology, since small, robust and non-contact position measurement techniques are required that offer both micrometer accuracy and microsecond temporal resolution. The Laser-Doppler-Distance (LDD) -Sensor proved to be an adequate technique to perform such measurements. However, the usage in turbo machines requires a miniaturized and temperature-stable sensor-head. In this paper we introduce a miniaturized design of the LDD-sensor that is based on common-path detection. First results indicated that the numerical aperture of the common-path detection is small in comparison to former implementations that used separate paths for illumination and detection. We find that decreasing the numerical aperture strongly increases the systematic measurement uncertainty. For this purpose a novel diffractive optical element containing a diffracting-lens was designed and used to increase the numerical aperture of the common-path detection without affecting the sensor size. Experiments prove that the new element reduces the relative systematic measurement uncertainty by a factor of ten. The mean systematic position measurement uncertainty amounts to Δz mean≈16 μm. The resulting sensor has dimensions of 25×25×60 mm3, offers temperature-stability and achieves micrometer resolution.