Restoration of Hardware Function of Spectral Colorimeters Using Regularization Methods

The problem of determining the spectral characteristic of a controlled sample under conditions of limited a priori information using regularization methods is considered in the paper. A change in the state of the surface of optical elements significantly increases the light scattering, so it is necessary regularly to take into account the amount of scattered light in the light flux reflected from the surface and the measured and comparative samples. The conversion of the light flux into the electrical signal of the photodetector can also occur non-linearly. This requires the development of such measurement method that considers both the scattered light and various non-linearities of the measuring circuit. It is known that the mathematical model of measurement is described by the Fredholm integral equation of the first kind, its solution under the accepted assumptions is recommended to be sought in the form of a matrix equation using a recurring procedure. With regard to the fact that the estimation of the initial data errors in the equation is associated with certain difficulties, in the case under consideration, it is advisable to determine the regularization parameter based on the method of quasi-optimality. A characteristic disadvantage of the known analytical and experimental methods for determining the hardware function of a spectral device is that they do not take into account its change during operation. Since the actual hardware function of the device usually differs from the Gaussian curve, the use of hardware functions in the form of analytical dependencies does not always give the desired result, and for experimental methods, special equipment with a quasi-monochromatic radiation source is required. An algorithm for restoring the hardware function of a spectral device based on regular methods for solving ill-posed problems is proposed. The estimation of the matrix operator of the hardware function is proposed to be obtained on the basis of explicit least squares estimation algorithms. The expediency of choosing a value of the regularization parameter that minimizes the accepted characteristic of the accuracy of the solution is indicated.

Piecewise Parabolic Approximate Computation Based on an Error-Flattened Segmenter and a Novel Quantizer

This paper proposes a novel Piecewise Parabolic Approximate Computation method for hardware function evaluation, which mainly incorporates an error-flattened segmenter and an implementation quantizer. Under a required software maximum absolute error (MAE), the segmenter adaptively selects a minimum number of parabolas to approximate the objective function. By completely imitating the circuit’s behavior before actual implementation, the quantizer calculates the minimum quantization bit width to ensure a non-redundant fixed-point hardware architecture with an MAE of 1 unit of least precision (ulp), eliminating the iterative design time for the circuits. The method causes the number of segments to reach the theoretical limit, and has great advantages in the number of segments and the size of the look-up table (LUT). To prove the superiority of the proposed method, six common functions were implemented by the proposed method under TSMC-90 nm technology. Compared to the state-of-the-art piecewise quadratic approximation methods, the proposed method has advantages in the area with roughly the same delay. Furthermore, a unified function-evaluation unit was also implemented under TSMC-90 nm technology.

A method for recognizing the muon flux intensity modulations using the normalized variation functions for the URAGAN hodoscope matrix data

<p>Muon flux intensity modulation (MFIM) recognition is a relevant solar-terrestrial physics problem. The considered MFIM, recorded on the Earth's surface, are caused by extreme heliospheric events – the geoeffective solar coronal mass ejections.</p><p>The URAGAN muon hodoscope (MH), developed by NRNU MEPhI, a computerized device that measures the intensities of muon fluxes, is used. In the MH, the number of muons falling per unit time on the MH aperture is calculated for the selected system of zenith and azimuthal angles. MH matrix data time series are formed. In the MH data, there are angular modulations due to the action of the hardware function HF, temporal modulations due to atmospheric disturbances and noise: the values of these modulations significantly exceed the values of MFIM of cosmic origin. This circumstance prevents effective MFIM recognition.</p><p>A method for MFIM recognition is proposed, based on the mathematical apparatus of the introduced normalized variation functions for MH matrix data, and focused on overcoming the noted circumstance.</p><p>A two-dimensional normalized HF is defined for MH. A quite realistic hypothesis is accepted about the initialiy uniform muon flux intensity distributions on a small reference time interval, where there are no extreme heliospheric events and the corresponding reference MH data do not contain significant MFIMs. The estimation of the two-dimensional normalized HF is carried out on the basis of a multiparameter model and its optimization fit to the reference MH data. In order to reduce noise errors, the estimate of the two-dimensional normalized HF is subjected to two-dimensional filtering and subsequent threshold filtering.</p><p>Two-dimensional functions of variations of matrix MH datas with respect to two-dimensional normalized AF are calculated. The normalized variation functions are calculated by dividing the two-dimensional functions of variations of matrix MH data by the two-dimensional normalized HF. MFIM recognition method was tested on model and experimental MH data.</p><p>A time series of model matrix MH data containing model MFIM was generated. Testing led to a conclusion that it is possible to recognize MFIM with decreases of about 2-3%. A time series of experimental matrix MH data was generated, in which the model MFIM-containing areas were made. Testing led to a conclusion that it is possible to recognize MFIM with the magnitudes of the decreases almost commensurate with the decreases for the case of model MH data.</p><p>The proposed MFIM recognition method based on the normalized variation functions for matrix MH data has a favorable perspective for its application in solving problems of geomagnetic storm early diagnostics.</p>

Restoring Missing Fragments of a Distorted Image Due to Defocusing or Blur of a Known Hardware Function

In this paper, a comparative analysis of the methods for recovering images distorted by defocusing or blurring from incomplete data is performed using examples. Incomplete data means the absence of any image fragments that were retouched using different types of interpolation - linear, spline and the interpolation method for the sequential calculation of the Fourier spectrum (IMSCS) developed by us. Then, the famous deconvolution method, the Wiener Filter (WF), was applied to the entire image. Analysis of the quality of restoration, carried out on the example of aerospace images, suggests that using IMSCS to fill in missing fragments (gaps) is either preferred or no less competitive than alternative methods. This is a consequence of the fact that IMSCS does not just retouch the gap, but also tries to reconstruct the lost data.

Expansion of the analyte concentration range using self-absorption lines

The width of a spectral line in atomic emission spectral analysis with arc radiation sources is, as a rule, much smaller than the hardware function of the spectral device. Thus, the spectral line shape is determined by the hardware function of the spectral device and can be approximated, for example, by the Voigt function. However, when analyzing standard samples with a wide range of element concentrations, the problem of self-absorption often occurs, due to which the analytical line has to be changed, which is not always possible. We propose to modify the Voigt function by adding a factor that describes self-absorption, by analogy with the Bouguer-Lambert law. The possibility of using the proposed function was evaluated in analysis of standard samples of rocks, ores and sandstones on a Grand-Potok spectral system with a MAÉS analyzer and BLPP-2000 linear photodetector arrays. The use of proposed approximating function is shown to provide an increase in the working range of the calibration curves of Cu 327.3954 nm, Cu 324.7532 nm, Pb 287.3311 nm, Ni 305.0818 nm, and Mo 313.2594 nm by 1 – 3 orders of magnitude.