nan Bayanheshig

Numerical simulation of ultrasonic enhancement on mass transfer in liquid-solid reaction by a new computational model

Mass transfer coefficient is an important parameter in the process of mass transfer. It can reflect the degree of enhancement of mass transfer process in liquid-solid reaction and in non-reactive systems like dissolution and leaching, and further verify the issues by experiments in the reaction process. In the present paper, a new computational model quantitatively solving ultrasonic enhancement on mass transfer coefficient in liquid-solid reaction is established, and the mass transfer coefficient on silicon surface with a transducer at frequencies of 40 kHz, 60 kHz, 80 kHz and 100 kHz has been numerically simulated. The simulation results indicate that mass transfer coefficient increases with the increasing of ultrasound power, and the maximum value of mass transfer coefficient is 1.467 × 10(-4) m/s at 60 kHz and the minimum is 1.310 × 10(-4) m/s at 80 kHz in the condition when ultrasound power is 50 W (the mass transfer coefficient is 2.384 × 10(-5) m/s without ultrasound). The extrinsic factors such as temperature and transducer diameter and distance between reactor and ultrasound source also influence the mass transfer coefficient on silicon surface. Mass transfer coefficient increases with the increasing temperature, with the decreasing distance between silicon and central position, with the decreasing of transducer diameter, and with the decreasing of distance between reactor and ultrasound source at the same ultrasonic power and frequency. The simulation results indicate that the computational model can quantitatively solve the ultrasonic enhancement on mass transfer coefficient.

High-accuracy spectral reduction algorithm for the échelle spectrometer.

A spectral reduction algorithm for an échelle spectrometer with spherical mirrors that builds a one-to-one correspondence between the wavelength and pixel position is proposed. The algorithm accuracy is improved by calculating the offset distance of the principal ray from the center of the image plane in the two-dimensional vertical direction and compensating the spectral line bending from the reflecting prism. The simulation and experimental results verify that the maximum deviation of the entire image plane is less than one pixel. This algorithm ensures that the wavelengths calculated from spectrograms have a high spectral resolution, meaning the precision from the spectral analysis reaches engineering standards of practice.

Controllable morphology and tunable colors of Mg and Eu ion co-doped ZnO by thermal annealing

Mg2+ and Eu3+ co-doped ZnO nanostructures were prepared by an environmentally friendly method. With an increase in the annealing temperature, the Mg2+ and Eu3+ co-doped ZnO nanosheets, composed of aggregated crystallites, experienced structural evolution from individual nanochains to partially sintered short rods and finally smooth nanorods. Consequently, the optical properties of Mg2+ and Eu3+ co-doped ZnO changed accordingly, shown here for white, green and yellow emitting segments. This study on the correlation between the sintered structure and optical properties shows that controlled thermal annealing affects the stress through structural evolution of the Mg2+ and Eu3+ co-doped ZnO nanocrystallites.

Wavelength calibration model for prism-type echelle spectrometer byreversely solving prism’s refractive index in real time

In an echelle spectrometer equipped with a prism cross-dispersion element, wavelength calibration is very difficult because of the complex, nonlinear interaction between the prism and the echelle grating. From the spectrometer geometry and the dispersion equations for the prism and the grating, a detailed mathematical model for wavelength calibration is derived that fits the refractive index of the prism in real time. An expression relating the refractive index, wavelength, and image coordinates is constructed, and standard wavelength sources and image positions are adopted to timely calculate the refractive index, which is affected by ambient factors such as temperature and air pressure. Experimental results indicate that the fitting accuracy of the refractive index in real time approaches 10−4, while the wavelength accuracy approaches 10−3  nm for the entire spectral range.

Real-time monitoring of ruling grating resolution by digital wavefront

In order to solve the problem that the grating quality cannot be monitored directly in real time, we provided a method based on Rayleigh criterion with our designing optical measurement structure to measure yaw and displacement errors of a grating ruling machine feeding system. Gratings are ruled with or without errors correction by the real-time monitoring system . It shows that the resolution obtained without errors correction is reduced from 99.97% to 87.47% of theoretical value, while the resolution obtained with errors correction is stable, remaining at 99.99%–97.21%. The experimental result is that the grating quality can be guaranteed by monitoring grating resolution in real time.

Measuring method of diffraction efficiency for plane grating based on Fourier spectral technology.

A traditional double monochromatic measurement instrument of diffraction efficiency for a plane grating involves two major problems: one is the differences of output spectrum bandwidths during measurement of a standard reflection mirror and the tested grating; the other is overlapping of diffracted spectra, which influence testing accuracy of diffraction efficiency. In this paper, a new measuring method of diffraction efficiency based on Fourier spectral technology is presented. The mathematical model of diffraction efficiency is first deduced and then verified by ray tracing and Fourier optics simulation. The influences of the moving cube corners tilt error, lateral shift error, and maximal moving distance error on the measurement accuracy are analyzed in detail. The analyses provide theoretical references for designing diffraction efficiency instruments. Compared with the traditional diffraction efficiency measurement instrument with double monochromator structure, our method not only improves the measurement accuracy of diffraction efficiency but also has the advantage of high luminous flux, high spectral resolution, multiwavelength measurement in mean time, and high wavenumber accuracy.

Merit function to design holographic gratings for moderate-resolution monochromators

A merit function is proposed and applied to design holographic concave gratings for moderate-resolution monochromators. To justify the validity of the merit function, imaging properties of gratings used for the coma-correction Seya-Namioka monochromator, designed by the present authors, Noda, and Takahashi, are compared through ray tracing and their aberration-correction mechanisms are also analyzed. The capability of the merit function is well demonstrated in the design of holographic gratings for another two moderate-resolution monochromators with different requirements. All the results obtained show that the merit function is not only straight and effective but also manages to balance various aberrations of the concave holographic grating very well.

Moiré alignment algorithm for an aberration-corrected holographic grating exposure system and error analysis.

To meet the required manufacturing accuracy of high-quality aberration-corrected holographic gratings, we propose a moiré alignment algorithm for the exposure system of holographic gratings. A model holographic grating exposure system is built with multiple degrees of freedom based on optical path function theory. The whole process algorithm is then derived, including the fourth-order orthogonal polynomial of the holographic gratings, fitted aberration coefficients, and an optimized Levenberg-Marquardt algorithm for the exposure systems recording parameters. Finally, the simulated alignment and error analysis of a 2400 gr/mm aberration-corrected holographic gratings exposure system are presented. The proposed moiré alignment algorithm for such exposure systems can effectively improve the alignment accuracy, ensuring better holographic grating aberration correction ability.

Ruling of echelles and gratings with a diamond tool by the torque equilibrium method

Ruling of echelles and gratings by the torque equilibrium method is proposed to eliminate corrugated grating lines, rough blazed grating surfaces, and complex fabrication work such as step-by-step diamond tool deflection. A mathematical model of the torque equilibrium between the diamond tool and the metallic film during the ruling process is deduced to realize optimized diamond tool geometrical parameter design. Then, two echelles with identical areas of 80  mm×100  mm are separately ruled using the traditional deflecting tool ruling method and the proposed method, and the scatter light results for the two echelles are 9.6×10−4 and 3.1×10−4, respectively.

Yaw angle correction of grating line based on single piezoelectric actuator

As the yaw angle of a machine-ruling grating will decline its wavefront quality and influence grating performance and application level, this paper proposes a correction method of single piezoelectric actuator according to the characteristics of the grating machine-ruling process. The method adjusts continuously the displacement of a micro-positioning table to correct the yaw angle error of grating line. Firstly, a real-time displacement correction formula for the micro-positioning table was deduced. Then, the yaw angle of micro-positioning table was measured and analyzed by three interferometers and its main component. Finally, amplification and correction experiments of the yaw angle of grating line were performed. The results show that experiments have basically achieved the expected results. Comparing to the result before yaw angle correction, the corrected yaw angle of grating line for a grating with a width of 10.4 mm and linear density of 600 line/mm has reduced by 64% or more. It concludes that the single piezoelectric actuator approach to the yaw angle correction of grating line effectively reduces yaw angle of grating line and improves the quality of the grating. This method is applicable to the yaw angle correction of machine-ruling grating with a large area.