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Annular subaperture stitching interferometry (ASSI) is a common approach for the measurement of aspherical surfaces. A common obstacle of ASSI is the occurrence of lateral displacement errors when the sensor or specimen is repositioned between the subaperture measurements. Our contribution focuses on modeling of the statistical displacement errors. Avirtual experiment is presented simulating the propagation of the displacement errors through a cumulative and a global stitching algorithm to the retrieved surface form. For the considered experimental setup, the uncertainty in lateral position depends on the positioning uncertainties of the employed motion system and the uncertainty in the absolute distance measurement between the sensor and specimen. The lateral displacement uncertainty is determined experimentally employing a calibratable lateral grating. Thus, it is traceable to the SI unit of the length (meter). The experimental results show that the lateral displacement errors may be modeled by a normal distribution, and the results of the virtual experiment indicate that the statistical lateral displacement errors transfer linear through the stitching procedure and also cause a normal distributed topography error. This enables the assignment of an expanded uncertainty to each individual sample point employing the Zernike polynomial expression of the topography measurement.

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The challenges faced in a comparison of measuring the detection efficiency of free-running InGaAs/InP single-photon avalanche detectors (InGaAs/InP SPAD) were studied by four European National Metrology Institutes (NMIs) meeting at a single laboratory. The main purpose of this study is to develop a trustable measurement technique and to provide a snapshot of the methods used by the four NMIs for measuring such photon-counting detectors at telecom wavelengths in order to establish proper procedures for characterising such devices. The detection efficiency measurements were performed using different experimental setups and reference standards with independent traceability chains at the wavelength of 1550 nm. A dedicated model to correct the dead time and dark count effects on the SPAD’s free-running counting process was developed, allowing the correct value of the photon rate impinging on the detector to be recovered from simple ratemeter measurements. The detection efficiency was measured for mean photon number per pulse between 0.01 and 2.4, corresponding to photon rates between approximately 1100 photon/s and 193,000 photon/s, respectively. We found that the measured values reported by the participants are all consistent within the stated uncertainties, proving the consistency of the measurement approach developed.

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We report on the characterization of the angular-dependent emission of single-photon emitters based on single nitrogen-vacancy (NV-) centers in nanodiamond at room temperature. A theoretical model for the calculation of the angular emission patterns of such an NV-center at a dielectric interface will be presented. For the first time, the orientation of the NV-centers in nanodiamond was determined from back focal plane images of NV-centers and by comparison of the theoretical and experimental angular emission pattern. Furthermore, the orientation of the NV-centers was also obtained from measurements of the fluorescence intensity in dependence on the polarization angle of the linearly polarized excitation laser. The results of these measurements are in good agreement. Moreover, the collection efficiency in this setup was calculated to be higher than 80 % using the model of the angular emission of the NV-centers.

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Multiple Aperture Shear-Interferometry (MArS) is a shape measurement technique that uses multi-spot illumination to overcome the problem of a limited observation aperture of conventional interferometric techniques and thus considerably simplifies the measurement of optical aspheres and freeform surfaces. Using a shear interferometry setup, MArS measures the coherence function in order to obtain wave vector distributions created from multi-spot LED illumination reflected by the specimen. Based on the wave vectors we reconstruct the surface topography of aspheric lenses using an inverse ray tracing approach and prior knowledge about the individual source locations. We present the topographic measurement of two aspheric lenses with different global curvature radii measured with the same identical reflection setup. In addition, we examine the achievable accuracy of the wave vector measurement using a single light source to find physical limits of MArS.

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Each mobile telecommunications network requires synchronization between its components. Deutsche Telekom Technik AG has decided to test a method developed by the AGH University of Science and Technology in Krakow, Poland, for the future monitoring of selected points in its network. It is based on optical time transmission (OTT), which has been tested in cooperation with PTB, among others on glass fiber links of Deutsche Telekom AG (DTAG). The results exceed by far the requirements of the International Telecommunication Union (ITU-T) for 5G networks.

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For the analysis of measured data in spectroscopic Mueller matrix ellipsometry (MME) there exist some commonly used optimization techniques to calculate for example layer thicknesses of samples under test. Concentrating on metrological aspects of MME we identified a non-optimal treatment of depolarization in all these techniques. Therefore, we recently developed an improved optimization method to take depolarization in MME adequately into account. In a further step we also included statistical measurement noise and derived a likelihood function, which enabled us to apply both the maximum likelihood method and Bayesian statistics as well as the Bayesian information criterion for the data evaluation. In this paper we concentrate on the application of this new method for measurements of SiO2-layer thicknesses on silicon. With a state-of-the-art SENTECH SENresearch 4.0 Mueller ellipsometer we measured different SiO2-layer thickness standard samples with calibrated thicknesses between about 6 nm and 1000 nm. The MME results are compared to the calibration data. For all samples an SiO2-SiO double-layer-model turned out to be optimal. The measured total oxid layer thicknesses match excellently with the calibration values within the estimated uncertainties. All results are presented here. It is a first comparison with traceable reference measurements demonstrating the validity of our novel MME analysis method.

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We demonstrate the retrieval of deep subwavelength structural information in nano-optical polarizers by scatterometry of quasi-bound states in the continuum (quasi-BICs). To this end, we investigate titanium dioxide wire grid polarizers for application wavelengths in the deep ultraviolet (DUV) spectral range fabricated with a self-aligned double-patterning process. In contrast to the time-consuming and elaborate measurement techniques like scanning electron microscopy, asymmetry induced quasi-BICs occurring in the near ultraviolet and visible spectral range provide an easily accessible and efficient probe mechanism. Thereby, dimensional parameters are retrieved with uncertainties in the sub-nanometer range. Our results show that BICs are a promising tool for process control in optics and semiconductor technology.

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Accurate bidirectional measurements are performed at PTB using UV-microscopy. For this purpose, edge detection algorithms based on the rigorous calculation of the optical imaging problem are employed. Hence, all the parameters of the imaging system and the object must be considered due to their specific impact on theimage formation. In order to further improve the model-based edge detection the small but inevitable optical aberrations of the imaging optics must be included into the simulations.For the determination of the aberrations, microscopic images of state-of-the-art line gratings (shapes verified by AFM) are measured in the focus and several afocal planes of the microscope. This procedure is similar to a phase retrieval method with the only difference that  usually  idealized  pinholes  are  measured  there.  A  particle  swarm  optimisation  (PSO)  method  is  developed  to  determine  the aberration of the used microscope in terms of Zernike polynomials. Therefore, the particles of the PSO are evenly spread over the parameter space that has been expanded by the Zernike polynomials. The optimisation problem consists of the minimization of the difference between the microscopic images in different focal planes and their respective simulated microscopic images. Because the illumination, imaging, and object parameters of the measured and the simulated microscopic images are identical, only a change of the Zernike polynomialsis responsible for a minimization during an iteration of the PSO. First results show, that when convergence is  achieved,  the  difference  between  the  images  is  very  small.  The  particle  responsible  for  the  minimum  then  holds  the  Zernikepolynomials, which characterize the aberrations of the used microscope.

(J. Krüger, FB 4.2, jan.krueger@ptb.de)

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The Physikalisch-Technische Bundesanstalt has developed a reference setup for measuring the modulation transfer function (MTF) of camera lenses with the goal of reaching an expanded measurement uncertainty of 0.01 (coverage probability of 95%) for various measurement configurations. We present optomechanical simulations of the setup behavior, which are used to investigate the influence of the combined mechanical misalignments on the MTF depending on the lens under test. The investigations are carried out as part of Monte Carlo studies for different sample lenses and field heights considering the correlations between the effects of different positioning errors on the MTF measured. The results of the sensitivity analyses have allowed appropriate alignment strategies to be identified that significantly reduce the uncertainty contribution of the positioning errors. By implementing these strategies, the target measurement uncertainty can be achieved for most of the desired measurement configurations. In addition, the comparison of three different sample lenses shows that the MTF sensitivity to misalignments strongly depends on the characteristics of the lens to be measured.

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