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Register a new userKramers-Kronig Receiver Combined With Digital Resolution Enhancer
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Added by
Menno van den Hout
Publication date
2021
fields
Electronic Engineering
and research's language is
English
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A Kramers-Kronig receiver with a continuous wave tone added digitally at the transmitter is combined with a digital resolution enhancer to limit the increase in transmitter quantization noise. Performance increase is demonstrated, as well as the ability to reduce the number of bits in the digital-to-analog converter.
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Low-loss electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM) probes the valence electron density and relevant optoelectronic properties such as band gap energies and other band structure transitions. The measured spectra can be formulated in a dielectric theory framework, comparable to optical spectroscopies and ab-initio simulations. Moreover, Kramers-Kronig analysis (KKA), an inverse algorithm based on the homonym relations, can be employed for the retrieval of the complex dielectric function (CDF). However, spurious contributions traditionally not considered in this framework typically impact low-loss EELS modifying the spectral shapes and precluding the correct measurement and retrieval of the dielectric information. A relativistic KKA algorithm is able to account for the bulk and surface radiative-loss contributions to low-loss EELS, revealing the correct dielectric properties. Using a synthetic low-loss EELS model, we propose some modifications on the naive implementation of this algorithm that broadens its range of application. The robustness of the algorithm is improved by regularization, appliying previous knowledge about the shape and smoothness of the correction term. Additionally, our efficient numerical integration methodology allows processing hyperspectral datasets in a reasonable amount of time. Harnessing these abilities, we show how simultaneous relativistic KKA processing of several spectra can share information to produce an improved result.
The ultimate precision in any measurement is dictated by the physical process implementing the observation. The methods of quantum metrology have now succeeded in establishing bounds on the achievable precision for phase measurements over noisy channels. In particular, they demonstrate how the Heisenberg scaling of the precision can not be attained in these conditions. Here we discuss how the ultimate bound in presence of loss has a physical motivation in the Kramers-Kronig relations and we show how they link the precision on the phase estimation to that on the loss parameter.
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from superimposition of the original signal with a reference beam. This approach can provide significant advantages in digital holography since it poses less stringent requirements on the reference beam. In particular, it does not require spatial separation between the sought signal and the reference beam. Moreover, the reference beam need not be known precisely, and in fact, may contain severe errors, without leading to a deterioration in the reconstruction quality. Numerical simulations are presented to demonstrate the speed and quality of reconstruction.
In observational radio astronomy, sideband-separating receivers are preferred, particularly under high atmospheric noise, which is usually the case in the sub-millimeter range. However, obtaining a good rejection ratio between the two sidebands is difficult since, unavoidably, imbalances in the different analog components appear. We describe a method to correct these imbalances without making any change in the analog part of the sideband-separating receiver, specifically, keeping the intermediate-frequency hybrid in place. This opens the possibility of implementing the method in any existing receiver. We have built hardware to demonstrate the validity of the method and tested it on a fully analog receiver operating between 600 and 720GHz. We have tested the stability of calibration and performance vs time and after full resets of the receiver. We have performed an error analysis to compare the digital compensation in two configurations of analog receivers, with and without intermediate frequency (IF) hybrid. An average compensated sideband rejection ratio of 46dB is obtained. Degradation of the compensated sideband rejection ratio on time and after several resets of the receiver is minimal. A receiver with an IF hybrid is more robust to systematic errors. Moreover, we have shown that the intrinsic random errors in calibration have the same impact for configuration without IF hybrid and for a configuration with IF hybrid with analog rejection ratio better than 10dB. Compensated rejection ratios above 40dB are obtained even in the presence of high analog rejection. The method is robust allowing its use under normal operational conditions at any telescope. We also demonstrate that a full analog receiver is more robust against systematic errors. Finally, the error bars associated to the compensated rejection ratio are almost independent of whether IF hybrid is present or not.
We use the Kramers-Kronig transform (KKT) with logarithmic kernel to obtain the reflection phase and, subsequently, the complex refractive index of a bulk mirror from reflectance. However, there remains some confusion regarding the formulation for this analysis. Assuming the damped Drude model for the dielectric constant and the oblique incidence case, we calculate the additional terms: phase at zero frequency and Blashke factor and we propose a reformulated KKT within this model. Absolute reflectance in the s-polarization case of a gold film is measured between 40 and 350 eV for various glancing angles using synchrotron radiation and its complex refractive index is deduced using the reformulated KKT that we propose. The results are discussed with respect to the data available in the literature.
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