Recurrent ANN-based modelling of the dynamic evolution of the surface roughness in grinding

Grinding is critical in modern manufacturing due to its capacity for producing high surface quality and high-precision parts. One of the most important parameters that indicate the grinding quality is the surface roughness (R _a). Analytical models developed to predict surface finish are not easy to apply in the industry. Therefore, many researchers have made use of artificial neural networks. However, all the approaches provide a particular solution for a wheel–workpiece pair, not generalizing to new grinding wheels. Besides, these solutions do not give surface roughness values related to the grinding wheel status. Therefore, in this work the modelling of the dynamic evolution of the surface roughness (R _a) based on recurrent neural networks is presented with the capability to generalize to new grinding wheels and conditions taking into account the wheel wear. Results show excellent prediction of the surface finish dynamic evolution. The absolute maximum error is below 0.49 µm, being the average error around 0.32 µm. Besides, the analysis of the relative importance of the inputs shows that the grinding conditions have higher influence than the wheel characteristics over the prediction of the surface roughness confirming experimental knowledge of grinding technology users.

     

Estimation of the minimum machining performance in the abrasive waterjet machining using integrated ANN-SA

In this study, Artificial Neural Network (ANN) and Simulated Annealing (SA) techniques were integrated labeled as integrated ANN-SA to estimate optimal process parameters in abrasive waterjet (AWJ) machining operation. The considered process parameters include traverse speed, waterjet pressure, standoff distance, abrasive grit size and abrasive flow rate. The quality of the cutting of machined-material is assessed by looking to the roughness average value (R_a). The optimal values of the process parameters are targeted for giving a minimum value of R_a. It was evidence that integrated ANN-SA is capable of giving much lower value of R_a at the recommended optimal process parameters compared to the result of experimental and ANN single-based modeling. The number of iterations for the optimal solutions is also decreased compared to the result of SA single-based optimization.     

Simulation of micro-patterns engraved by grinding process with screw shaped wheel

Grinding is an important means of realizing precision and ultra-precision machining of workpiece surface. The surface patterning of workpiece directly affects its mechanical properties such as friction, wear, contact stiffness, fitting property. Therefore, prediction of the geometry of the workpiece surface is very important to evaluate the workpiece quality to perform mechanical function accurately. In this paper using MATLAB simulation, prediction for the geometry pattern of the workpiece according to the developed shape of the grinding wheel dressed by thread cutting was studied. The model for the geometry of the grinding wheel surface was first developed and subsequently, a new simulation model for surface pattern by grinding process was established. The simulation results could be used to optimize the grinding process and to improve the workpiece surface quality or predict the surface pattern by given grinding parameters.     

On-line prediction of micro-turning multi-response variables by machine vision system using adaptive neuro-fuzzy inference system (ANFIS)

In this paper, a new attempt has been made in the area of tool-based micromachining for automated, non-contact, and flexible prediction of quality responses such as average surface roughness (R _a), tool wear ratio (TWR) and metal removal rate (MRR) of micro-turned miniaturized parts through a machine vision system (MVS) which is integrated with an adaptive neuro-fuzzy inference system (ANFIS). The images of machined surface grabbed by the MVS could be extracted using the algorithm developed in this work, to get the features of image texture [average gray level (G _a)]. This work presents an area-based surface characterization technique which applies the basic light scattering principles used in other optimal optical measurement systems. These principles are applied in a novel fashion which is especially suitable for in-process prediction and control. The main objective of this study is to design an ANFIS for estimation of R _a, TWR, and MRR in micro-turning process. Cutting speed (S), feed rate (F), depth of cut (D), G _a were taken as input parameters and R _a, TWR, MRR as the output parameters. The results obtained from the ANFIS model were compared with experimental values. It is found that the predicted values of the responses are in good agreement with the experimental values.     

Optimization studies in high speed turning of Ti-6Al-4V

Surface roughness is a major concern to the present manufacturing sector without the wastage of material. Hence, in order to achieve good surface roughness and reduce production time, optimization is necessary. In this study optimization techniques based on swarm intelligence (SI) namely firefly algorithm (FA), particle swarm optimization (PSO) and a newly introduced metaheuristic algorithm namely bat algorithm (BA) has been implemented for optimizing machining parameters namely cutting speed, feed rate, depth of cut and tool flank wear and cutting tool vibrations in order to achieve minimum surface roughness. Two parameters R_a and R_t have been considered for evaluating the surface roughness. The performance of BA algorithm has been compared with FA algorithm and PSO, which is a commonly and widely used optimization algorithm in machining. The results conclude that BA produces better optimization, when compared to FA and PSO. Based on the literature review carried out, this work is a first attempt at using a metaheuristic algorithm namely BA in machining applications.     

虚拟砂轮的开发及其磨削性能分析

采用虚拟现实技术,开发了可交互的虚拟磨削加工环境．以正六面体作为磨粒的基本形态,并将该磨粒随机分布在砂轮基体上,建立虚拟砂轮的仿真物理模型以及磨粒与工件接触的数学模型．以平面磨削为例,进行了不同加工参数下磨削加工过程的动态仿真,测试了虚拟砂轮的磨削性能,并分析了工件表面粗糙度的影响因素．仿真结果与理论分析结果具有一致性,证明了将虚拟现实技术应用于磨削加工机理研究是可行的．     

Remote sensing reflectance and its relationship to optical properties of natural waters

Monte Carlo simulations of photon propagation through natural water have been utilized to determine the sub-surface remote sensing reflectance, R _RSW (the sub-surface value of the ratio of upwelling radiance from the nadir to the downwelling irradiance) as a function of water type (defined by the ratio of the backscattering coefficient to the absorption coefficient Bb/a), solar zenith angle, and incident radiation distribution (direct or diffuse). R _RSW, as opposed to volume reflectance, R _V (the sub-surface value of the ratio of upwelling to downwelling vector irradiance), is directly applicable to remotely sensed data collected over natural waters. It is shown that, for a nadir viewing direction, (a) R _RSW is essentially independent of solar zenith angle and incident radiation distribution and (b) the dominant factor in determining R _RSW is the optical nature of the water body itself (expressed as Bb/a). A relationship between the sub-surface remote sensing reflectance averaged over solar zenith angle between 15° and 89°, R _RSW and water type is found to predict R _RSW with an r.m.s. error of 9 per cent. Also addressed is the determination of the aquatic optical property, Bb/a, from the sub-surface remote sensing reflectance, R _RSW This capability along with the specific absorption and scattering coefficients of aquatic constituents can, through bio-optical models, be used to estimate the concentrations of these aquatic constituents in non-Case I waters. The empirical relationship obtained to estimate Bb/a (with a r.m.s. error of 9·3 per cent) from the nadir value of the sub-surface remote sensing reflectance is Bb/a = 0·0027 + 987R _RSW ? 34·5( R _RSW)² + 1534( R _RSW)³.     

Estimation of solar-induced fluorescence using the canopy reflectance index

This article presents a methodology to quantitatively extract the solar-induced fluorescence (SIF) using the canopy reflectance index. The sensitivity analysis was conducted with a spectral vegetation Fluorescence Model (FluorMOD), and the results demonstrate that Sun zenith angle (θ), fluorescence quantum efficiency (Fi), leaf inclination distribution function (LIDF), leaf temperature (T), leaf area index, and leaf chlorophyll a + b content (chl-a+b) had large effects on the fluorescence radiance at 761 nm (LF,761). Based on the results of the sensitivity analysis, the input parameters θ, Fi, LIDF, T, and chl-a+b varied within a certain range during the generation of the simulated data. Based on the simulated data, R₇₄₀/R₆₃₀, R₆₈₅/R₈₅₀, and R₇₅₀/R₇₁₀ were thought to be the best candidates to extract the fluorescence radiation. The quantitative relationships between the fluorescence retrieved by R₇₄₀/R₆₃₀, R₆₈₅/R₈₅₀, and R₇₅₀/R₇₁₀ and LF,761 were analysed and expressed as functions of θ, Fi, T, and reflectance index. The correlation coefficients (r) between the fluorescence retrieved using R₆₈₅/R₈₅₀, R₇₄₀/R₆₃₀, and R₇₅₀/R₇₁₀ and LF,761 are 0.94, 0.95, and 0.95, respectively, and the root mean square errors (RMSEs) were 0.32, 0.29, and 0.30 W m^?2 μm^?1 sr^?1, respectively. Through comparison with FLD and 3FLD, the method presented in this article yielded better results, and could be used to estimate the fluorescence. This methodology provides new insights into the quantitative retrieval of SIF from the reflectance spectrum.     

Estimation of chlorophyll‐a concentration in Lake Tai,China using in situ hyperspectral data

Reflectance spectra of water in Lake Tai of East China were measured at 28 monitoring stations with an ASD FieldSpec spectroradiometer at an interval of 1.58 nm over five days in each month from June to August of 2004. Water samples collected at these stations were analyzed in the laboratory to determine chlorophyll‐a (chl‐a) concentration. Twenty‐eight spectral reflectance curves were standardized and correlated with chl‐a concentration. Examination of these curves reveals a peak reflectance at 719 nm. Chl‐a concentration level in the Lake was most closely correlated with the reflectance near 700 nm. If regressed against the reflectance at the wavelength of 667 nm (R ₆₆₇), chl‐a concentration was not accurately estimated at R ² = 0.494. Accuracy of estimation was improved to R ² = 0.817 using the maximum reflectance. A higher accuracy of 0.837 was achieved using the peak reflectance at 719 nm (R ₇₁₉) because it does not drift with the level of chl‐a concentration. The highest accuracy of estimation was achieved at R ² = 0.868 using R ₇₁₉/R ₆₆₇.     

End mill design and machining via cutting simulation

This paper describes a design process for an end mill. A solid model of the designed cutter is constructed together with the computation of the cutter’s geometry, wheel geometry, and wheel positioning data for fabricating end mills with the required cutter geometry. The main idea of the process is to use the cutting simulation method to obtain the machined shape of an end mill by using Boolean operations between a given grinding wheel and a cylindrical workpiece (raw stock). The major design parameters of a cutter, such as rake angle and inner radius, can be verified by interrogating the section profile of its solid model. This study investigates the relationship between various dimensional parameters and proposes an iterative approach to obtain the required geometry of a grinding wheel and cutter location (CL) data for machining an end mill that satisfies the design parameters. This research was implemented using a commercial computer aided design (CAD) system with API function programming and is currently used by a commercial tool maker in Korea. It can eliminate the need to produce a physical prototype during the design stage and can be used in virtual cutting tests and analyses.     

Bio‐optical properties and estimation of the optically active substances in Lake Tianmuhu in summer

Bio‐optical properties in an optically complex and biologically productive region of Lake Tianmuhu were determined in three cruises from June to August 2006. The concentrations of three optically active substances, tripton C _Tripton (calculated from total suspended matter and chlorophyll‐a (Chla) and phaeophytin‐a (Pa)), phytoplankton pigment C _Chla+Pa , and chromophoric dissolved organic matter (CDOM) a _CDOM(440), were predicted from the estimated irradiance reflectance based on in situ measurements and laboratory analyses. The total relative contributions of phytoplankton, tripton, CDOM and pure water over the range of photosynthetically active radiation (PAR) (400–700 nm) were 36.1%, 24.2%, 15.9% and 23.8%, respectively. The dominant contribution of phytoplankton to the total absorption was due to high phytoplankton pigment concentration. The range and variation in irradiance reflectance and diffuse attenuation coefficient derived from a bio‐optical model, based on inherent optical properties, compared well with the measured variability. A reasonably strong relationship (R² = 0.92) was observed between irradiance reflectance at 780 nm R(780) and C _Tripton. For our data set, the best algorithm for C _Chla+Pa used the three‐band reflectance model [R ^?1(688)?R ^?1(717)]×R(747). The a _CDOM(440) could be estimated using the ratio of irradiance reflectance R(682)/R(555). The retrieval accuracy (R²) of tripton, phytoplankton pigment and CDOM was 0.92, 0.87 and 0.91, respectively, while the rms. error was 0.90 mg l^?1 (18.2%), 3.27 µg l^?1 (14.8%) and 0.073 m^?1 (15.3%), respectively. Estimation of the concentrations of the three optically active substances was reasonably accurate based on inherent optical properties measurement.     

凸轮轴磨床工件旋转轴转速预测算法的研究

采用三次B样条曲线插补的凸轮磨削加减速能力不足,易产生过磨和少磨。根据凸轮磨削的数学模型,分析了砂轮进给轴运动的理论与实际速度、加速度、加加速度,提出了一种预测工件旋转轴转速的加工方法,在速度变化剧烈处自动降低工件旋转轴转速,以避免加速度和加加速度的变化对伺服系统造成的机械冲击,利用Matrix VB控件编程技术,设计了凸轮轴磨削软件,并将其移植到YTMK-CNC8326全数控高速凸轮轴磨床中。测试表明,采用该方法磨削的凸轮轴型线误差小于±0.01mm,工件表面粗糙度得到明显改善,实现了凸轮轴的精密加工。     

Correlation between soil apparent electroconductivity and plant hyperspectral reflectance in a managed wetland

The apparent electrical conductivity (σ_a) of soil is influenced by a complex combination of soil physical and chemical properties. For this reason, σ_a is proposed as an indicator of plant stress and potential community structure changes in an alkaline wetland setting. However, assessing soil σ_a is relatively laborious and difficult to accomplish over large wetland areas. This work examines the feasibility of using the hyperspectral reflectance of the vegetation canopy to characterize the σ_a of the underlying substrate in a study conducted in a Central California managed wetland. σ_a determined by electromagnetic (EM) inductance was tested for correlation with in-situ hyperspectral reflectance measurements, focusing on a key waterfowl forage species, swamp timothy (Crypsis schoenoides). Three typical hyperspectral indices, individual narrow-band reflectance, first-derivative reflectance and a narrow-band normalized difference spectral index (NDSI), were developed and related to soil σ_a using univariate regression models. The coefficient of determination (R ²) was used to determine optimal models for predicting σ_a, with the highest value of R ² at 2206 nm for the individual narrow bands (R ²?=?0.56), 462 nm for the first-derivative reflectance (R ²?=?0.59), and 1549 and 2205 nm for the narrow-band NDSI (R ²?=?0.57). The root mean squared error (RMSE) and relative root mean squared error (RRMSE) were computed using leave-one-out cross-validation (LOOCV) for accuracy assessment. The results demonstrate that the three indices tested are valid for estimating σ_a, with the first-derivative reflectance performing better (RMSE?=?30.3 mS m^?1, RRMSE?=?16.1%) than the individual narrow-band reflectance (RMSE?=?32.3 mS m^?1, RRMSE?=?17.1%) and the narrow-band NDSI (RMSE?=?31.5 mS m^?1, RRMSE?=?16.7%). The results presented in this paper demonstrate the feasibility of linking plant–soil σ_a interactions using hyperspectral indices based on in-situ spectral measurements.     

Accurate robotic belt grinding of workpieces with complex geometries using relative calibration techniques

Robotic belt grinding operations are performed by mounting a workpiece to the end effector and commanding it to move along a trajectory while maintaining contact with the belt grinding wheel. A constant contact force throughout the grinding process is necessary to provide a smooth finish on the workpiece, but it is difficult to maintain this force due to a multitude of installation, manipulation, and calibration errors. The following describes a novel methodology for robotic belt grinding, which primarily focuses on system calibration and force control to improve grinding performance. The overall theory is described and experimental results of turbine blade grinding for each step of the methodology are shown.     

Estimation of chlorophyll-a concentration in waters over the continental shelf of the Bay of Biscay: a comparison of remote sensing algorithms

Ocean colour imagery is used increasingly as a tool to assess water quality via chlorophyll-a concentration (chl-a) estimations in European waters. The Bay of Biscay is affected by major river discharges, which alter the constituents of the marine waters. Chlorophyll-a algorithms, designed for use at global scales, are less accurate due to the variability of optically active in-water constituents. Hence, regionally parameterized empirical algorithms are necessary. The main objective of the present study was to develop a regional algorithm to retrieve chl-a in surface water using in situ R _rs, for a subsequent application to Medium Resolution Imaging Spectrometer (MERIS) satellite images. To address this objective, a platform was developed initially and a measurement procedure adapted for the field HR4000CG Spectrometer. Subsequently, the procedure was tested during a survey over the south-eastern Bay of Biscay (North-East Atlantic Ocean), to establish a MERIS chl-a algorithm for the area, by comparing different global remote sensing chl-a algorithms, with band ratios. Results validated with the jackknife resampling procedure show a satisfactory relationship between the R _rs(510)/R _{r s}(560) and chl-a (R ² _jac?=?0.681). This ratio is better correlated to chl-a than those obtained with established chl-a remote sensing algorithms. High content in coloured dissolved organic matter (CDOM > 0.4 m^?1) and suspended particulate matter (SPM > 2.8 mg l^?1) influenced this relationship, with yellow substances having a stronger effect.     

A new approach for dynamic modelling of energy consumption in the grinding process using recurrent neural networks

Grinding is a critical machining process because it produces parts of high precision and high surface quality. Due to the semi-artisan production of the wheel, it is not possible to know in advance the performance of the wheel. One of the most useful parameters to characterize the grinding process is the specific grinding energy, which varies with the wear of the grinding wheel during its lifecycle. Thus, it would be useful to model the specific grinding energy in order to get information about the performance of the wheel before buying it. Unlike the typical applications of time series forecasting, in this work, a totally different issue is presented: the prediction of new and complete time series bounded in time without initial or historic values. In this context, an analysis of the effect of the time characteristics and the number of points of the time series on the prediction capabilities of the ANN is presented. The results of the analysis show that 200 points are enough to predict a complete time series up to 2000 mm³/mm of specific volume of material removed. Actually, it is shown that modelling the evolution of the grinding specific energy up to 2000 mm³/mm is possible. The net shows good capability to generalize to new grinding conditions, with errors below 23.65 %, and to new wheel characteristics, with errors below 20.01 %, which are satisfactory from the grinding process perspective.     

Mapping aerosol optical thickness and water-leaving signals using an improved NIR/SWIR switching atmospheric correction model: A case study in the Bohai Sea

In this study, the performance of the near-infrared & short wave infrared switching atmospheric correction (NSSAC) model in estimating remote sensing reflectance (R_rs(λ)) and aerosol optical thickness at 869 nm (τ_a(869)) were assessed by field measurements taken in the Bohai Sea. It was found that the NSSAC model had approximately 30% uncertainty for retrievals of R_rs(λ) in the green regions but provided approximately 50% uncertainty for estimations of τ_a(869) and R_rs(λ) at all other moderate resolution imaging spectroradiometer (MODIS) visible wavelengths. Therefore, an optimised method is proposed for optimizing the retrieval results of the NSSAC model; it was validated using the field measurements collected from the Oujiang River estuary. The results show that the performance of the NSSAC model for τ_a(869) and R_rs(λ) at the blue, red, and near-infrared bands was greatly improved by using the optimised NSSAC model. Moreover, the study also finds that the τ_a(869) shows a large variation in the Bohai Sea, decreasing from coastal to offshore regions. The monthly average τ_a(869) has a maximum at February and August. Due to the imperfect atmospheric correction procedure, the NSSAC model-derived R_rs(λ) is always larger than those of the field measurements. Future work is needed to minimise the detected water-leaving signals in the short wave infrared (SWIR) images.     

Platform tolerant dual‐band UHF‐RFID tag antenna with enhanced read range using artificial magnetic conductor structures

In this work, a platform tolerant novel dual band tag antenna is proposed for UHF‐RFID bands used in Europe (855‐867 MHz ) and Japan (950‐955 MHz). Asymmetrical shunt stub feed network is employed to effectively match its impedance to the microchip (Alien Higgs‐4). The antenna miniaturization is achieved by embedding inverted L‐shaped slit on left side of the patch. Also, asymmetrical stepped rectangular slot is embedded to further achieve the optimized dual band response at the desired resonant frequencies (f₁ = 866 MHz and f₂ = 953 MHz). To further enhance its radiation performance on conductive objects like metallic surfaces, the proposed tag is integrated with artificial magnetic conductor (AMC) structure. Also, antenna parameters such as main lobe gain, directivity, front‐to‐back ratio parameters are examined for the integrated tag in free space and on metallic sheet. The proposed integrated tag exhibits directional radiation pattern making it insensitive to underlying object and thus platform tolerant. Further, the proposed integrated tag exhibits steady gain response inside the resonating bands on different sized metallic sheets. The proposed integrated tag is compact (2635 mm³) covering European band with a read range of 7.3 m and Japanese band with a read range of 10.8 m.     

Estimation of chlorophyll-a concentration in coastal waters with HJ-1A HSI data using a three-band bio-optical model and validation

Accurate assessment of phytoplankton chlorophyll-a (chl-a) concentration in turbid waters by means of remote sensing is challenging because of the optical complexity of case 2 waters. We applied a bio-optical model of the form [R^–1(λ₁) – R^–1(λ₂)](λ₃), where R(λ_i) is the remote-sensing reflectance at wavelength λ_i, to estimate chl-a concentration in coastal waters. The objectives of this article are (1) to validate the three-band bio-optical model using a data set collected in coastal waters, (2) to evaluate the extent to which the three-band bio-optical model could be applied to the spectral radiometer (SR) ISI921VF-512T data and the hyperspectral imager (HSI) data on board the Chinese HJ-1A satellite, (3) to evaluate the application prospects of HJ-1A HSI data in case 2 waters chl-a concentration mapping. The three-band model was calibrated using three SR spectral bands (λ₁ = 664.9 nm, λ₂ = 706.54 nm, and λ₃ = 737.33 nm) and three HJ-1A HSI spectral bands (λ₁ = 637.725 nm, λ₂ = 711.495 nm, and λ₃ = 753.750 nm). We assessed the accuracy of chl-a prediction with 21 in situ sample plots. Chl-a predicted by SR data was strongly correlated with observed chl-a (R² = 0.93, root mean square error (RMSE) = 0.48 mg m^–3, coefficient of variation (CV) (RMSE/mean(chl-a_mea)) = 3.72%). Chl-a predicted by HJ-1A HSI data was also closely correlated with observed chl-a (R² = 0.78, RMSE = 0.45 mg m^–3, CV (RMSE/mean(chl-a_mea)) = 7.51%). These findings demonstrate that the HJ-1A HSI data are promising for quantitative monitoring of chl-a in coastal case-2 waters.     

Effect of optically active substances and atmospheric correction schemes on remote-sensing reflectance at a coastal site off Kochi

The present study focused on understanding the variability of optically active substances (OASs) and their effect on spectral remote-sensing reflectance (R_rs). Furthermore, the effect of atmospheric correction schemes on the retrieval of chlorophyll-a (chl-a) from satellite data was also analysed. The OASs considered here are chl-a, coloured dissolved organic matter (CDOM), and total suspended matter (TSM). Satellite data from the Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite was used for this study. The two atmospheric correction schemes considered were: multi-scattering with two-band model selection NIR correction (hereon referred as ‘A1’) and Management Unit of the North Sea Mathematical Models (MUMM) correction and MUMM NIR calculation (hereafter referred as ‘A2’). The default MODIS bio-optical algorithm (OC3M) was used for the retrieval of chl-a. Analysis of OASs showed that chl-a was the major light-absorbing component, with highly variable distribution (0.006–25.85 mg m^–3). Absorption due to CDOM at 440 nm (a_CDOM440) varied from 0.002 to 0.31 m^–1 whereas TSM varied from 0.005 to 33.44 mg l^–1. The highest concentration of chl-a was observed from August to November (i.e. end of the southwest monsoon and beginning of the northeast monsoon), which was attributed to coastal upwelling. The average value of a_CDOM440 was found to be lower than the global mean. A significant negative relationship between a_CDOM440 and salinity during the southwest monsoon indicated that much of the CDOM during this season was derived from river discharge. Spectral R_rs was found to be strongly linked to the variability in chl-a concentration, indicating that chl-a was the major light-absorbing component. Satellite-derived spectral R_rs was in good agreement with that in situ when chl-a concentration was lower than 5 mg m^–3. The validation of chl-a, derived from in situ R_rs, showed moderate performance (correlation coefficient, R² = 0.64; log₁₀(RMSE) = 0.434; absolute percentage difference (APD) = 43.6% and relative percentage difference (RPD) = 42.33%). However the accuracy of the algorithm was still within acceptable limits. The statistical analysis for atmospheric correction schemes showed improved mean ratio of measured to estimated chl-a (‘r’ = 1.6), log₁₀(RMSE) (0.49), APD (25.46%), and RPD (17.57%) in the case of A1 as compared with A2, whereas in the case of A2, R² (0.56), slope (0.26), and intercept (0.27) were better as compared with A1. The two atmospheric correction schemes did not show any significant statistical difference. However the default atmospheric correction scheme (A1) was found to be performing comparatively better probably due to the fact that the concentration of TSM and CDOM was much lower to overcome the impact of chl-a.