Showing papers in "Optics and Laser Technology in 2010"

Laser cutting of polymeric materials: An experimental investigation

Abstract: The CO(2) laser cutting of three polymeric materials namely polypropylene (PP), polycarbonate (PC) and polymethyl methacrylate (PMMA) is investigated with the aim of evaluating the effect of the main input laser cutting parameters (laser power, cutting speed and compressed air pressure) on laser cutting quality of the different polymers and developing model equations relating input process parameters with the output. The output quality characteristics examined were heat affected zone (HAZ), surface roughness and dimensional accuracy. Twelve sets of tests were carried out for each of the polymer based on the central composite design. Predictive models have been developed by response surface methodology (RSM). First-order response models for HAZ and surface roughness were presented and their adequacy was tested by analysis of variance (ANOVA). It was found that the response is well modeled by a linear function of the input parameters. Response surface contours of HAZ and surface roughness were generated. Mathematical model equations have been presented that estimate HAZ and surface roughness for various input laser cutting parameters. Dimensional accuracies of laser cutting on polymers were examined by dimensional deviation of the actual value from the nominal value. From the analysis, it has been observed that PMMA has less HAZ, followed by PC and PP. For surface roughness, PMMA has better cut edge surface quality than PP and PC. The response models developed can be used for practical purposes by the manufacturing industry. However, all three polymeric materials showed similar diameter errors tendency in spite of different material properties. (C) 2009 Elsevier Ltd. All rights reserved.

Mach–Zehnder interferometer-based all-optical reversible logic gate

Abstract: In recent years, reversible logic has emerged as a promising computing paradigm having application in low-power CMOS, quantum computing, nanotechnology and optical computing. Optical logic gates have the potential to work at macroscopic (light pulses carry information), or quantum (single photons carry information) levels with great efficiency. However, relatively little has been published on designing reversible logic circuits in all-optical domain. In this paper, we propose and design a novel scheme of Toffoli and Feynman gates in all-optical domain. We have described their principle of operations and used a theoretical model to assist this task, finally confirming through numerical simulations. Semiconductor optical amplifier (SOA)-based Mach–Zehnder interferometer (MZI) can play a significant role in this field of ultra-fast all-optical signal processing. The all-optical reversible circuits presented in this paper will be useful to perform different arithmetic (full adder, BCD adder) and logical (realization of Boolean function) operations in the domain of reversible logic-based information processing.

Synthesis of CdZnO thin film as a potential candidate for optical switches

Abstract: Cadmium doped zinc oxide thin films have been prepared using a thermal decomposition technique. The influence of Cd as a doping agent on the structure, optical and nonlinear optical properties was carefully investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM) and a UV–vis spectrophotometer. A deep correlation has been found between the surface roughness and the optical properties. The roughness is found to deteriorate the nonlinear response, such that the highest nonlinear susceptibility χ (3) is obtained for the smoothest layer. The third-order nonlinear susceptibility χ (3) has been calculated using the Frumer model, and is estimated to be 3.37×10 −10 esu. The dispersion of the refractive index of the prepared thin film is shown to follow the single electronic oscillator model. From the model, the values of oscillator strength ( E d ), oscillator energy ( E o ) and dielectric constant ( e ∞ ) have been determined. The conductivity has been measured as a function of the energy of the photons, revealing marginal change at energies below 3.15 eV, while above this value there is a large increase in the conductivity. This suggests that CdZnO is a potential candidate for applications in optical devices such as optical limiter and optical switching.

A parametric study of pulsed Nd:YAG laser micro-drilling of gamma-titanium aluminide

Abstract: In the present research, Nd:YAG laser micro-drilling of gamma-titanium aluminide, a new material which has performed well in laboratory tests as well as in different fields of engineering, is studied. The effect of different process parameters in the optimization of the process is investigated. The aspects considered are the hole circularity at exit and the hole taper of the drilled hole. Lamp current, pulse frequency, air pressure and thickness of the job are selected as independent process variables. The central composite design (CCD) technique based on response surface methodology (RSM) is employed to plan the experiments to achieve optimum responses with a reduced number of experiments.

Laser spectroscopy of Nd3+ and Dy3+ ions in lead borate glasses

Abstract: The spectroscopic and laser properties of Nd 3+ and Dy 3+ ions in lead borate glass were studied. Luminescence spectra recorded in the near-infrared and visible ranges correspond to 4 F 3/2 – 4 I J /2 ( J =9, 11, 13) transitions of Nd 3+ and 4 F 9/2 – 6 H J /2 ( J =11, 13, 15) transitions of Dy 3+ , respectively. Luminescence decay curves were analyzed as a function of activator concentration. Luminescence quenching is observed, which is due to Ln–Ln interaction increasing. Several spectroscopic parameters relevant to laser potential of Ln 3+ ions (Ln=Nd, Dy) in lead borate glass were determined. The relatively large values of the quantum efficiency and the room-temperature emission cross-section for the 4 F 3/2 – 4 I 11/2 transition of Nd 3+ at 1061 nm and the 4 F 9/2 – 6 H 13/2 transition of Dy 3+ at 573 nm imply that Ln-doped lead borate glasses can be considered as promising solid-state materials for laser applications.

Laser welding of low carbon steel and thermal stress analysis

Abstract: Laser welding of mild steel sheets is carried out under nitrogen assisting gas ambient. Temperature and stress fields are computed in the welding region through the finite element method. The residual stress developed in the welding region is measured using the XRD technique and the results are compared with the predictions. Optical microscopy and the SEM are used for the metallurgical examination of the welding sites. It is found that von Mises stress attains high values in the cooling cycle after the solidification of the molten regions. The residual stress predicted agreed well with the XRD results.

Optimization of laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy

Abstract: An empirical relationship is developed to predict tensile strength of the laser beam welded AZ31B magnesium alloy by incorporating process parameters such as laser power, welding speed and focal position. The experiments were conducted based on a three factor, three level, central composite face centered design matrix with full replications technique. The empirical relationship can be used to predict the tensile strength of laser beam welded AZ31B magnesium alloy joints at 95% confidence level. The results indicate that the welding speed has the greatest influence on tensile strength, followed by laser power and focal position.

Nonlinear optical and optical power limiting studies on a new thiophene-based conjugated polymer in solution and solid PMMA matrix

Abstract: An experimental investigation of the third-order nonlinear optical properties of new poly{2-{5-[3,4-ditetradecyloxy-5-(1,3,4-oxadiazol-2-yl)thiophen-2-yl]-1,3,4-oxadiazol-2-yl}pyridine} (P) in tetrahydrofuran (THF) solution and in solid poly(methylmethacrylate) (PMMA) matrix, by Z-scan technique is reported. The Z-scan traces reveal that the composite films exhibit large negative nonlinear refractive index of the order 10−10 esu. The excited-state absorption cross-section was found to be larger than the ground-state absorption indicating that the operating nonlinear process is reverse saturable absorption (RSA). The new polymer P exhibits good optical power limiting properties in the nanosecond regime in solution and as well in solid PMMA matrix.

Scintillation effect on intensity modulated laser communication systems—a laboratory demonstration

Abstract: This paper shows the impact of atmospheric turbulence-induced fading on the symbol decision position in the on-off keying (OOK) and the binary phase shift keying (BPSK) subcarrier intensity modulated (SIM) laser communication link. Weak turbulence is simulated in the laboratory using a chamber equipped with heating elements and fans. We have shown that in atmospheric turbulence, it is advantageous to employ modulation schemes such as pulse time and subcarrier intensity modulations that do not directly impress data on the optical irradiance as is the case with the OOK. For the OOK-modulated laser communication system, atmospheric turbulence imposes complexity on the symbol decision subsystem and by extension places a limit on the achievable bit error rate (BER) performance.

Finite element analysis of laser irradiated metal heating and melting processes

Abstract: Laser technology has shown fast growth due to its demands in material processing and manufacturing. Laser material processing includes various applications like cutting, welding, drilling, cladding and surface treatment. In laser surface treatment, the material properties at the surface are altered through surface alloying and transformation hardening. In this study, an enthalpy-based computational model is developed for analyzing laser heating and melting of metals. The solution to the problem is obtained by using a finite element method and validated by comparing the results with that given by an analytical solution to a limiting case problem. A solution algorithm and a computational code are developed to estimate the temperature distribution, solid-liquid interface location and shape and size of the molten pool. The computational model is validated by comparing results with a limiting case analytical model. The study is conducted to analyze the heating rate, the heat affected zone, and the shape and size of the molten pool using a Gaussian laser beam.

Light intensity modulation fiber-optic sensor for curvature measurement

Abstract: A light intensity modulation fiber-optic sensor, which can measure curvature directly, has been developed. It is suitable for the measurement of thin, embedded or highly flexible structures. An experimental analysis on the static and dynamic characteristics of sensor has been undertaken. The results show that the output voltage has polarity and a good linear relationship with curvature when the curvature radius is larger than 60 mm. The mathematical model relating the relative output loss, parameters of sensitive zone’s configuration (depth, number, height and half angle of tooth) and bending radius is described analytically based on the geometric optics. Curvature fiber-optic sensors can be used to build a quasi-distributed fiber-optic sensor system, which can measure curvature and torsion angle simultaneously.

A novel 1D target-based calibration method with unknown orientation for structured light vision sensor

Abstract: The problem associated with calibrating a structured light vision sensor is that it is difficult to obtain the coordinates of the world calibration points falling on the light stripe plane. In this paper, we present a novel method to address this problem by randomly moving a 1D (one-dimension) target within the sensor's view field. At each position where the target is set, the world coordinates with one calibration point on the light stripe plane that can be obtained based on at least three preset known points on the 1D target by a proposed two-stage technique. Thus, as long as the 1D target is at least set at three different positions, not less than three such calibration points can be obtained to perform the structured light vision sensor calibration. The simulation and real experiments conducted reveal that the proposed approach has an accuracy of up to 0.065 mm. The advantages of the proposed method are: (1) 1D target is easily machined with high accuracy, which reduces the cost of the calibration equipment; (2) the method simplifies the calibration operation and can be convenient in on-site calibration; (3) the method is suitable for use in confined spaces.

The effect of concentration on the thermo-optical properties of colloidal silver nanoparticles

Abstract: The thermo-optical properties of colloidal silver nanoparticles (AgNPs) are investigated under a low power laser irradiation at 532 nm. Colloidal AgNPs are synthesized by nanosecond pulsed laser ablation of a pure silver plate in distilled water. The morphology and size of the AgNPs are determined by transmission electron microscopy. Closed Z-scan measurements reveal that nonlocal thermo-optic process is responsible for the nonlinear refractive index of colloid containing different concentrations of silver nanoparticles. The Z-scan behavior of the nanoparticle samples has been investigated based on a nonlocal thermo-optic process and it is shown that the aberrant thermal lens model is in excellent agreement with the experimental results. Z-scan measurement fits have allowed the values of nonlinear refractive index (n2) and thermo-optic coefficients (dn/dt) to be determined at different concentrations of silver nanoparticles. Large enhancement factors were measured for values of n2 and dn/dt of the colloids at higher silver nanoparticle volume fraction. Our results suggest that nonlocal thermal nonlinear processes will play an important role in the development of photonic applications involving metal nanoparticle colloids.

Chaos based multiple image encryption using multiple canonical transforms

Abstract: We propose a new method for multiple image encryption using linear canonical transforms and chaotic maps. Three linear canonical transforms and three chaotic maps are used in the proposed technique. The three linear canonical transforms that have been used are the fractional Fourier transform, the extended fractional Fourier transform and the Fresnel transform. The three chaotic maps that have been used are the tent map, the Kaplan–Yorke map and the Ikeda map. These chaotic maps are used to generate the random phase masks and these random phase masks are known as chaotic random phase masks. The mean square error and the signal to noise ratio have been calculated. Robustness of the proposed technique to blind decryption has been evaluated. Optical implementation of the technique has been proposed. Experimental and simulations results are presented to verify the validity of the proposed technique.

Synthesis, characterization and studies on the nonlinear optical parameters of hydrazones

Abstract: Three hydrazones, 2-(4-methylphenoxy)- N ′-[(1E)-(4-nitrophenyl)methylene]acetohydrazide (compound-1), 2-(4-methylphenoxy)- N ′-[(1E)-(4-methylphenyl)methylene]acetohydrazide ((compound-2) and N ′-{(1E)-[4-(dimethylamino)phenyl]methylene}-2-(4-ethylphenoxy) acetohydrazide(compound-3) were synthesized and their third order nonlinear optical properties were investigated using a single beam z-scan technique with nanosecond laser pulses at 532 nm. Open aperture data obtained from the three compounds indicates two photon absorption at this wavelength. The nonlinear refractive index n 2 , the nonlinear absorption coefficient β , the magnitude of the effective third order susceptibility χ (3) , the second order hyperpolarizability γ h and the coupling factor ρ have been estimated. The values obtained are comparable with the values obtained for 4-methoxy chalcone derivatives and dibenzylidene acetone derivatives. Among the compounds studied, compounds-1 and 3 exhibited the better optical power limiting behaviour at 532 nm. Our studies suggest that compounds-1, 2 and 3 are potential candidates for optical device applications such as optical limiters and optical switches.

Synthesis and optical characterization of nanocrystalline CdTe thin films

Abstract: From several years the study of binary compounds has been intensified in order to find new materials for solar photocells. The development of thin film solar cells is an active area of research at this time. Much attention has been paid to the development of low cost, high efficiency thin film solar cells. CdTe is one of the suitable candidates for the production of thin film solar cells due to its ideal band gap, high absorption coefficient. The present work deals with thickness dependent study of CdTe thin films. Nanocrystalline CdTe bulk powder was synthesized by wet chemical route at pH≈11.2 using cadmium chloride and potassium telluride as starting materials. The product sample was characterized by transmission electron microscope, X-ray diffraction and scanning electron microscope. The structural characteristics studied by X-ray diffraction showed that the films are polycrystalline in nature. CdTe thin films with thickness 40, 60, 80 and 100 nm were prepared on glass substrates by using thermal evaporation onto glass substrate under a vacuum of 10 −6 Torr. The optical constants (absorption coefficient, optical band gap, refractive index, extinction coefficient, real and imaginary part of dielectric constant) of CdTe thin films was studied as a function of photon energy in the wavelength region 400–2000 nm. Analysis of the optical absorption data shows that the rule of direct transitions predominates. It has been found that the absorption coefficient, refractive index ( n ) and extinction coefficient ( k ) decreases while the values of optical band gap increase with an increase in thickness from 40 to 100 nm, which can be explained qualitatively by a thickness dependence of the grain size through decrease in grain boundary barrier height with grain size.

Thermal annealing effect of on optical constants of vacuum evaporated Se75S25−xCdx chalcogenide thin films

Abstract: Chalcogenide glasses are interesting materials due to their infrared transmitting properties and photo induced effects exhibited by them. Thin films with thickness of 3000 A of the glasses Se75S25-xCdx with x=6, 8 and 10 at% prepared by melt quench technique were evaporated by thermal evaporation onto glass substrates under a vacuum of 10-6 Torr. The optical constants (absorption coefficient, refractive index and extinction coefficient) of as-prepared and annealed films have been studied as a function of photon energy in the wave length region 400-1000 nm. Analysis of the optical absorption data shows that the rule of non-direct transitions predominates. It has been found that the absorption coefficient and optical band gap increase with increasing annealing temperatures. The refractive index (n) and the extinction coefficient (k) were observed to decrease with increasing annealing temperature.

Atmospheric turbulence and numerical evaluation of bit error rate (BER) in free-space communication

Abstract: Bit error rate (BER) is an important parameter in free-space optical (FSO) communication. This paper presents the numerical evaluation of BER by studying the propagation of an initial Gaussian laser beam through turbulent atmosphere. Beam scintillation, spreading and wandering were considered as the atmospheric turbulent effects on the laser beam degradation. Different turbulent conditions and laser beam characteristics were applied to the calculations. The results show that the BER can be influenced considerably by atmospheric turbulence. According to these results the laser beam size and wavelength have also significant effects in the BER values.

Detection of liquid-level variation using a side-polished fiber Bragg grating

Abstract: A liquid-level sensor based on a side-polished fiber Bragg grating (FBG) is proposed and experimentally demonstrated. The sensor can detect height variation of liquids of arbitrary refractive index (RI). For liquids with RI lower than that of fiber core, liquid-level variation can be monitored by the peak power difference of the grating segments surrounded by the liquid and air. For liquids with RI higher than that of fiber core, liquid-level information can be obtained from the influence of the shortening of the effective length of the immersed grating segment upon the reflection spectrum.

Correcting non-linear lens distortion in cameras without using a model

Abstract: Camera lens distortion calibration is the first step in resolving any metric application with a camera. To date, lens distortion was corrected using some existing lens distortion non-metric or self-calibration methods. Using a lens distortion model means defining a global rule to correct the entire image. This global rule does not take into account particular lens distortion effects not represented by the model. Moreover, to calibrate the model, only some features of the scene such as straight lines, circles or vanishing points are used. Since only the feature of the scene used to calibrate the model is guaranteed by the distortion rectification, it is certain that the model will not be precise. The result is an approximation of the real image distortion. To improve the lens distortion rectification, a method without using a model is proposed. Using a set of control points distributed across the entire image, they are corrected to assure all the restrictions of the scene. With both sets of points, the points detected in the image and the undistorted ones, image local transformations are defined considering only nearby control points. Rather than calibrating a global model, local functions are characterized. The distortion correction is defined by a rectification surface composed of local surface patches each influenced by nearby control points. This method is more sensitive to local deformations and allows the image to be corrected in accordance with its distortion.

Study on fast linear scanning for a new laser scanner

Abstract: In the field of lidar system design, there is a need for laser scanners that offer fast linear scanning, are small size and have small a rotational inertia moment. Currently, laser scanners do not meet the above needs. A new laser scanner based on two amplified piezoelectric actuators is designed in this paper. The laser scanner has small size, high mechanical resonance frequencies and a small rotational inertia moment. The size of the mirror is 20 mm×15 mm. To achieve fast linear scanning performance, an open-loop controller is designed to compensate the hysteresis behavior and to restrain oscillations that are caused by the mechanical resonances of the scanner's mechanical structure. By comparing measured scanning waveforms, nonlinearities and scan line images between the uncontrolled and controlled scanner, it was found that the scanning linearity of linear scanning was improved The open-loop controlled laser scanner realizes linear scanning at 250 Hz with optical scan angle of ±12 mrad.

Dual beam method for laser welding of galvanized steel: Experimentation and prospects

Abstract: Laser welding of zinc-coated steel sheets in lap configuration poses a challenging problem, because of the zinc vapours spoiling the quality of the weld. In continuation to the earlier work, the novel solution of dual laser beam method for lap welding of galvanized steel sheets is discussed here in view of the recently obtained observations and ensuing concerns. In this method the precursor beam cuts a slot, thus making an exit path for the zinc vapours, while the second beam performs the needed welding. The metallurgical analysis of the welds is encouraging showing absence of zinc in the welded area. In the current work on this technique, new experimental results have been obtained verifying the earlier observations. Along with this, the possibility of using a transversely split-up beam for the welding purposes with this approach is discussed and analyzed in this paper. This new technique is expected to be very useful in prospective industrial applications requiring higher welding throughput along with the needed quality.

Laser removal of TiN coatings from WC micro-tools and in-process monitoring

Abstract: Current environmental challenges require sustainable and extended use and re-use of materials. For example, the service life of engineering tooling can be extended by using thin film coatings such as titanium nitride (TiN). However, when errors arise in the coating process or when the tooling needs to be re-used it is necessary to remove the coating. Decoating is also useful when a large batch of cutting tools needs to be re-directed for a different application, which requires a new generation of coating. Existing technology uses chemical methods which are not environmentally friendly or ideal for selective removal. In this work, excimer laser striping of TiN from coated tungsten carbide (WC) micro-tools has been demonstrated as a viable alternative to chemical methods. Also, in order to raise the integrity of the decoating process and to make the process more accurate and reliable, two online monitoring systems were developed exploiting probe beam reflection (PBR) and laser plume emission spectroscopy (PES). The online monitoring system facilitated a simultaneous prediction of surface elements as coating layers are progressively removed and ensures better control over the laser irradiation process so as to avoid under or over stripping of the coating.

Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system

Abstract: A highly stabilised vibration-displacement measurement system, which employs fiber Bragg gratings (FBGs) to interleave two fiber Michelson interferometers that share the common-interferometric-optical path, is presented. The phase change in the interferometric signals of the two fiber Michelson interferometers have been tracked, respectively, with two electronic feedback loops. One of the fiber interferometers is used to stabilise the system by the use of an electronic feedback loop to compensate the environmental disturbances. The second fiber interferometer is used to perform the measurement task and employs another electronic feedback loop to track the phase change in the interferometric signal. The measurement system is able to measure vibration-displacement and provide the sense of direction of the displacement. The frequency range of the measured vibration-displacement is from 0.1 to 200 Hz and the measurement resolution is 10 nm.

Numerical analysis and optimization of a dual-concentric-core photonic crystal fiber for broadband dispersion compensation

Abstract: In this article, a novel dual-concentric-core photonic crystal fiber (DC-PCF) for dispersion compensation is presented. The proposed DC-PCF has relatively high negative dispersion over a wide wavelength range, which covers E, S, C, L and U telecommunication wavelength bands. The validity of the proposed design is carried out by employing a 2-D finite difference frequency domain method (FDFD) with perfectly matched layers (PML). By using the numerical method, the dispersion profile of the DC-PCF is optimized in terms of three air-hole diameters to achieve desirable negative dispersion. The influence of the location of ring-core, the number of air-hole rings on dispersion and loss characteristics are also studied.

Estimation of laser solid forming process based on temperature measurement

Abstract: By using a moving disc heat source model, an analytical model was developed to describe laser solid forming (LSF) process with the feedback of the surface temperature of the molten pool, which can be used to estimate the geometric characterizations (width and height) of the clad layer rapidly. An on-line temperature measurement system was established and some single-pass cladding experiments were conducted while the molten pool temperature was monitored. It was found that the estimated geometric characterizations agreed well with the experimental results. In addition, the power consumed by conduction, convection, radiation, evaporation and absorption during LSF were also estimated by the model. It was shown that the majority of the total absorbed power was conducted to the substrate. The effective model can not only be used to optimize the processing parameters but also potentially applied to the real-time feedback control.

High resolution temperature insensitive interrogation technique for FBG sensors

Abstract: In this letter, we propose a high resolution temperature insensitive interrogation technique for FBG sensors where one FBG acts as an edge filter to interrogate a separate FBG sensor. A high resolution of better than 5 μe in strain measurement range from 0 to 1100 μe and the best resolution of better than 1 μe were verified by experiments. An error of only ±2.2 μe is achieved over a temperature range from 15 to 50 °C, indicating that this strain interrogation technique is temperature insensitive. Using an altered system configuration, the temperature was also measured simultaneously with a resolution better than 0.2 °C.

Thermal fatigue resistance of non-smooth cast iron treated by laser cladding with different self-fluxing alloys

Abstract: In order to enhance the thermal fatigue resistance of gray cast iron with non-smooth surface further, the non-smooth units in samples’ surface layer were fabricated by laser cladding with Fe-based, Ni-based and Co-based self-fluxing alloy powders, respectively, instead of laser melting technique. The microstructure, phase structure, microhardness and thermal fatigue behaviors were investigated by means of scanning electron microscope, X-ray diffraction and Vickers microhardness tester, as well as self-restrain thermal fatigue test. The results indicated that laser cladding with self-fluxing alloy powders was beneficial to reinforcing the units so as to enhance the thermal fatigue resistance of non-smooth samples further. Of all samples tested, those treated by laser cladding with Co-based (Co50) alloy had the best thermal fatigue resistance.

Detection of physical defects in solar cells by hyperspectral imaging technology

Abstract: A hyperspectral imaging system is developed and is used to identify cracks and fracture defects in solar cells. The basic principles and key technologies of this system are presented, along with a characterization of its performance. The system can provided both single-band images and spectrums of solar cells by laser scanning and hyperspectral imaging. The spectral angle mapper algorithm is used to identify cracks on the surface of solar cells. Experiment results show that this is a non-contact, no-destructive method for detecting cracks in solar cells.

Color image encryption based on interference and virtual optics

Abstract: We propose two approaches to encrypt color images based on interference and virtual optics. In the first method, a color image is first decomposed into three independent channels, i.e., red, green and blue. Each channel of the input image is encrypted into two random phase-only masks based on interference. In the second method, a color image is first converted into an image matrix and a color map, and only the image matrix is encrypted into random-phase masks based on interference. After the phase masks are retrieved, a concept based on virtual optics is further applied to enhance the security level. Numerical simulations are demonstrated to show the feasibility and effectiveness of the proposed methods.