ANALYST, AUGUST 1991, VOL. 116 781 Compensation for Particle Size Effects in Near Infrared Reflectance Christine R. Bull Silsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK The interpretation of near infrared (NIR) reflectance in terms of material composition is complicated by particle size variation. An investigation is reported into the relationship between NIR reflectance and particle size using data from ground wheat samples. It is shown that the sensitivity of reflectance to particle size is dependent on the absorption properties of the material at the sampling wavelength. A theory relating a function of reflectance, known as the Kubelka-Munk function, to particle size suggests that the effects due to changing wheat composition can be isolated from the particle size effects using normalized Kubelka-Munk functions.Analysis of the spectral data from the ground wheat samples supports this theory. The ratio of Ku belka-Munk functions at appropriate absorption and reference wavelengths is subsequently manipulated to yield single term calibration equationsfor the protein and water in the wheat samples. Comments are made on the implication of the reported findings for various calibration techniques. Keywords: Near infrared reflection; particle size; Kubelka-Munk function In order to use near infrared (NIR) reflectance as an analytical tool it is necessary to relate the function of the sample reflectance at a given wavelength to the concentration of a sample constituent via a known calibration equation. For convenience this equation is usually chosen to be linear.Kubelka and Munkl developed a function, F(R), of the reflectance, R , which is linearly related to the absorption (and hence the concentration) of the sample. Their function is as follows: (1 - R)2 K F(R) = ~ -- 2R S - where K is the absorption coefficient and S is the scatter coefficient. However, most calibrations use the simpler log (1/R) signal treatment which is approximately proportional to the concen- tration of the absorbing material. For either mathematical treatment, the function value will depend not only on the concentration of the constituent to be measured but also on the physical properties of the sample. Consequently it is necessary to compensate for the interfering effects by measur- ing the reflectance at a number of absorption and reference wavelengths.In general, the calibration is then obtained from a linear combination of these terms. In some instances, the appropriate sampling wavelengths can be selected by looking at a series of reflectance scans from samples in which the component of interest is varied. The wavelength at which there is maximum variation is then identifiable as an absorp- tion wavelength whereas a wavelength at which there is minimal variation can be used as a reference. However, this simple selection procedure is often impossible because of interfering factors, such as particle size. This is illustrated in Fig. 1 which shows the Kubelka-Munk function at a water absorption band of 1944 nm as a function of the water content of ground wheat samples of varying particle size.When the wavelengths cannot be visually selected they are determined numerically using multiple linear regression. This 'black box' approach is not entirely satisfactory because the selection is not based on the absorption features and hence composition of the sample material. A technique that is used to emphasize the absorption features of a spectral scan is to look at the first and second differential of the log (1/R) plot. This will be sensitive to the change in shape of spectral scans taken from a series of samples. There are two disadvantages with this calibration technique. Firstly, one has to determine the reflectance of the sample over a segment of the spectrum. This makes the method inappropriate for simple analytical devices which determine the sample reflectance at a discrete number of fixed wavelengths.Secondly, the differences in the derivative scans are difficult to interpret. Norris and Williams2 compared these calibration techniques for samples of ground wheat with particular reference to the effects of varying particle size. They concluded that the most satisfactory mathematical treatment was to take second derivatives of the log (1/R) functions, although there was little difference in the performance of mathematical treatments provided equivalent numbers of wavelengths were used. Cowe and McNicoP used principal components analysis (PCA) to analyse log (UR) reflection scans of wheat flour samples. The principle of this analysis technique is that each of the multiple wavelength scans can be specified as a single point in the multi-dimensional space defined by the log (l/Ri) axes where i is the number of sampling wavelengths.The first component is a vector drawn through this space which accounts for the majority of the variation in the scans and will take the form where the coefficients C l j are the weights or loadings of the first component. The second component is the axis orthogonal to the first, along which there is maximum residual variation. Subsequent components are defined as the axes at right angles to all preceding principal components, which in turn exhibit the greatest amount of unexplained variation in the data. There are several advantages in using the PCA approach to analyse NIR data. Firstly, the spectra are reduced to a small number of computed values which can be easily used in regression modelling.Secondly, the relative loadings of each 0.9 E l + .- Y O.* t + + 11 12 13 14 15 Water content (%I Kubelka-Munk function at a water absorption band (1944 Fig. 1 nm) as a function of the water content of ground wheat samples782 ANALYST, AUGUST 1991, VOL. 116 of the principal components give some indication of the location and strength of the absorption bands and hence chemical composition of the samples. This paper shows how PCA can be developed to isolate the changes in reflectance due to compositional change from those due to particle size effects. The influence of particle size on reflectance is discussed and it is shown that the displacement in the log 1/R spectra due to particle size is greater at absorption bands.A theory relating the Kubelka-Munk function to particle size is introduced and is used to show how the variations in normalized Kubelka-Munk functions can be used to highlight areas in which changes in sample composi- tion give rise to variation in reflectance. This is then used to determine suitable absorption and reference wavelengths for use in a calibration based on the ratio of two Kubelka-Munk functions. A discussion on the influence of particle size variations on various calibration techniques is given in the final section. Experimental Thirty-nine samples of wheat flour were scanned at the Flour Milling and Baking Research Association (FMBRA), Chor- leywood, Hertfordshire, UK, with a Neotec 6350 analyser.Spectra were recorded as log (UR) at 2 nm intervals from 1100 to 2500 nm. In order to reduce the effect of electrical noise, the spectrum for each sample was calculated as the average of 50 scans and was smoothed with the use of a five point moving average algorithm. To eliminate edge effects, data points below 1120 and above 2480 nm were discarded. For the purpose of this paper a reduced data set of 171 data points, evenly spaced between 1120 and 2472 nm, which were taken from the original data, was used. Reference analytical values for protein and moisture were also supplied by FMBRA. These samples have previously been used by Osborne4 in investigations into the use of NIR as a tool for assessing potential for bread making and by Cowe and McNicoP in the PCA described earlier.The data presented by Norris and Williams2 have also been used in the present analysis. Results Effect of Particle Size on Near Infrared Reflectance The analysis of the wheat data by PCA (Cowe and McNicol) showed that 98.6% of the variation in the log (1/R) spectral scans could be accounted for by the first component. The loadings Cli [eqn. (2)] for each of the wavelengths of the first component are illustrated in Fig. 2. This profile closely resembles the original log 1/R spectra. The weights show a general trend to increase with increasing wavelength but are peaked at wavelengths usually associated with the water 1000 1500 2000 2500 Wavelengthhm Fig. 2 Loadings of the first component from the principal component analysis of the reciprocal log reflectance spectra for ground wheat samples absorption bands (approximately 1200, 1450 and 1944 nm).However, the analysis showed that there was little correlation (0.16) between the water content of the wheat and the first component, which led Cowe and McNicol to conclude that there was bound water in the sample. In practice, as will be shown below, the increased variation at the absorption bands is consistent with the particle size effects. The total reflection for a particulate material consists of reflections of the incident light at each of the refractive index discontinuities, particularly at the air-particle interfaces. In addition, there will be some absorption of the radiation within each particle which will reduce the radiation penetrating the sample and hence reduce the back-reflection from subsequent interfaces. Consequently, for two samples of the same composition ground to different particle sizes, there is more back-reflection from the finer particles because the radiation encounters more discontinuities per unit length of the sample material traversed.This effect becomes more pronounced when the light is absorbed more strongly. Consequently, there is a stronger relationship between back-reflection and particle size for wavelengths that are more strongly absorbed than those that are only weakly absorbed. If the majority of the variation in the wheat samples is due to particle size differences, the loadings of the first principal component, illustrated in Fig. 2, will be strongly correlated with the sensitivity of the log (UR) measurements to particle size.A recent paper5 related the reflectance from an infinitely thick powdered sample to the reflectance and absorption of the average particulate. By expressing the average properties of the individual particle in terms of the mean particle size it was shown that the relationship between the Kubelka-Munk function, F(Rk), and the mean particle size, x , is (3) X F(R1) = - 2dkrx where dk, the l/e penetration depth, is the depth at which the radiation into a ‘solid block’ of the material has reduced by a factor l/e (e = 2.718) and rk is the reflectance at a single air-particle discontinuity. The assumptions made in the derivation of this equation are: that the dimensions of the particle size are greater than half the coherence length of the radiation within the sample; that the absorption within each particle is small; and that the ratio between particle, absorp- tion and reflectance is not large.It has been shown5 that these approximations are applicable to milled grain. Manipulation of eqns. (3) and (1) enables us to explore the relationship between the log (1/R) function and the particle size (in units of dirk). This is illustrated for a series of samples of varying concentration in Fig. 3. Over a small range of Kubelka-Munk values there is a near linear relationship between log (UR) and mean particle size. This was observed by Norris and Wil- hams2 They presented data for spectral scans of ground wheat 0.5 0.334 s c 0) -I 0.167 1 I I 0 0.25 0.50 0.75 Kubelka-Munk function (particle size in units of 2dhrh) Fig.3 Theoretical relationship between the reciprocal log reflec- tance, log 1/R, and particle size for samples with different exponential penetration depths, dANALYST, AUGUST 1991, VOL. 116 Table 1 Theoretically derived values of reciprocal log reflectances (log l/R), at a number of wavelengths, for grain particles of various milled sizes; the gradient of the log 1/R versus mean particle size (MPS) response graph, and the loadings of the first principal component of the log 1/R data set 783 Log 1/R for various MPS Gradient of Loading of CLm 150 pm 200 pm 250 pm 300 pm MPS/10-4 pm-l component Wavelength/ log 1/R versus first principal 5 - 4 - 3 - 2 - 1.200 1.300 1.400 1 so0 1.600 1.700 1.800 1.950 2.000 2.100 2.200 2.300 2.400 01.2 '1.3 1 - 0.0606 0.0519 0.0866 0.1265 0.1132 0.1085 0.1065 0.1870 0.1540 0.1904 0.1598 0.1971 0.1998 0.0699 0.0600 0.0999 0.1459 0.1306 0.1252 0.1229 0.2154 0.1775 0.2193 0.1842 0.2269 0.2300 0.0782 0.0670 0.1116 0.1629 0.1458 0.1399 0.1373 0.2402 0.1981 0.2446 0.2056 0.2350 0.2564 0.0856 0.0734 0.1222 0.1783 0.1596 0.1531 0.1503 0.2620 0.2167 0.2672 0.2248 0.2764 0.2801 1.666 1.430 2.370 3.448 3.088 2.970 2.916 4.996 4.174 5.114 4.328 5.280 5.346 0.01841 0.0 1253 0.03809 0.06569 0.05259 0.05239 0.05240 0.11544 0.09664 0.09825 0.09265 0.10808 0.11095 61 1 01.5 1.8 01.4 2.3 2-4 0 2.1 1% 2.2 a0 2.0 I I I I I I I 0.02 0.04 0.06 0.08 0.10 0.12 Loadings of first principal component Fig.4 Plot of the gradient of the reciprocal log reflectance, log 1/R, versus mean particle size (MPS) relationship plotted against the first component from the principal component analysis of the log 1/R spectra for ground wheat samples.The sampling wavelength in micrometres is indicated beside each point samples with mean particle size varying from 150 to 335 pm. The reflectance of the sample with the smallest mean particle size has been ascertained at a number of sampling wavelengths, taken at 100 nm intervals from 1.2 to 2.4 pm. The reflectance value at 1.9 pm was unclear from their data so a closely adjacent value at 1.95 pm has been taken. These reflectance values were substituted into eqn. (1) to calculate the Kubelka-Munk functions, which were then placed into eqn. (3) in order to obtain values for the dkrh product at each of the sampling wavelengths.Once the dhrh product is known it is possible to calculate the Kubelka-Munk and log (l/R) functions for a range of particle sizes from 150 to 300pm (Table 1). This approach has been used previously5 on ground wheat samples and it has been shown that the theoretically predicted sensitivity of the reflectance to particle size is in close agreement with the experimentally determined values (Norris and Williams) at a number of wavelengths. Table 1 shows that there is a tendency for the reflectance from a sample to be more sensitive to particle size effects at longer wavelengths. However, the increase is not uniform but is peaked at wavelengths at which there is high sample absorp- tion. For example, the gradient of the response at 1950 nm is greater than that at 2200 nm.Fig. 4 shows the calculated gradients of the log (l/R) versus particle size graphs plotted against the appropriate loadings Cli of the first principal component. The correlation is good (0.986) bearing in mind that the wheat samples used to determine the sensitivity of the log (URJ function to particle size are unrelated to those used to determine the loadings. This linearity indicates that most of the structure shown in the first principal component loadings, and hence most of the variation in the spectra of the 39 samples, is due to differences in the sensitivity of each wavelength to particle size variations. The importance of this observation is that spectral scans of two powdered samples which are markedly different from each other, especially at the absorption bands, may have the same chemical composi- tion with the differences arising solely from particle size effects.This explains why the first principal component from the analysis of the log (l/R) spectra shows little correlation (0.16) with water (Cowe and McNicol3) despite peaks in the loadings at the water absorption bands. The ability of eqn. (3) to explain most of the spectral variations of the 39 samples in terms of particle size effects is a strong indication of the validity of the theory applied to ground wheat. The deviations from linearity of the points in Fig. 4 is due either to limitation in the theory or to interference effects resulting from changes in the sample composition. However, variations in sample composition will only affect the loading of the first component if they are positively correlated with changes in the particle size, otherwise these variations will appear in the loadings of the higher order (and orthogonal) principal components.To isolate the changes in the loading of the first principal component that are not due to particle size variation we can look at the variation in the spectra given by the logarithm to the base ten of the Kubelka-Munk function, log F(Rh), at each wavelength A. Eqn. (3) states that this wavelength dependent function is equally sensitive to changes in the sample particle size at all wavelengths. Consequently, if the major variation in the sample reflectance is due to particle size effects and these effects are not correlated to any other sample variable, one would expect the loadings of the first principal component, which essentially show the sensitivity of each wavelength to particle size, to be uniform over the whole wavelength range.If, however, the protein content is correlated to particle size, features of the protein absorption bands would be super- imposed on the flat topped particle size response. The loadings of the first principal component of the log F(R1) scans are shown in Fig. 5. Overall, the response is much flatter than that obtained for the log (UR) data but there are features corresponding to protein at 1200, 1500, 1700, 2200 and 2370 nm (Mohsenin6) which implies that the protein content of the samples is correlated to the particle size. This supposition is supported by the relatively strong correlation between the first principal component and the protein content of the wheat samples (0.71) (Cowe and McNicol). This observation high- lights a limitation of the PCA technique, i.e., if the sample set is not defined relative to an appropriate set of axes then the effects of one source of sample variation may mask another in the loadings of the principal axes.Having shown that approximately 98.0% of the variability in the spectral scans of the wheat samples (the variance accounted for by the first principal component) is due to784 ANALYST, AUGUST 1991, VOL. 116 E E 0.10 00 h +, 0.05 r? b- I I 1 1000 1500 2000 2500 Wavelengthlnm Fig. 5 Loadings of the first component from the principal component analysis of log Kubelka-Munk spectra for ground wheat samples 1000 1500 2000 2500 Wavelengthlnm Fig.6 Loadings of the first component from the principal component analysis of the normalized Kubelka-Munk spectra for ground wheat samples particle size it is clear that in order to use NIR as an analytical tool, it is imperative to compensate effectively for particle size effects. Compensation for Particle Size Effects In order to compensate effectively for particle size effects, one needs to determine some function of the sample reflectance at one or more wavelengths, which is correlated to the analyte to be measured but which is independent of the physical properties of the sample. Eqn. (3) states that the Kubelka- Munk function is directly proportional to the particle size, x . Consequently, the ratio of two Kubelka-Munk functions should be independent of particle size. Furthermore, if the Kubelka-Munk functions are taken at appropriate absorp- tion, F(RA) and reference F(RR), wavelengths, it should be possible to obtain a calibration, F , given by (4) which is particularly sensitive to a given constituent, where RA and RR are the reflection of the sample at the absorption and reference wavelengths, respectively.The problem now lies in the selection of the appropriate wavelengths because the correlation between the Kubelka- Munk function at an absorption band and the concentration of the absorbing constituent is masked by particle size effects (Fig. 1). This difficulty can be overcome by looking at the normalized Kubelka-Munk functions. The mean particle size of a sample affects the Kubelka-Munk functions at each of the sampling wavelengths by the same multiplicative factor [eqn.(3)] so the normalized Kubelka-Munk function, defined by + * 0.011 1 1 12 13 14 15 Water content (%) Fig. 7 Normalized Kubelka-Munk function at a water absorption band (1944 nm) as a function of the water content of ground wheat samples is independent of particle size where h is one of the sampling wavelengths. Furthermore, this normalized function will only vary strongly at wavelengths corresponding to the absorption bands of the varying constituents. The identification of the wavelength at which the variation is maximum can be achieved by looking at the loadings of the first principal component of the normalized Kubelka-Munk data set.These loadings will be peaked at wavelengths which are particularly sensitive to compositional changes. The loadings of the first principal component for the grain data set are shown in Fig. 6. Identifying which of these peaks is sensitive to a particular varying constituent is not a trivial matter and absorption bands associated with various constituents will often overlap. However, the peaks in Fig. 6 at 1450 and 1944 nm have been identified in the literature as water absorption bands (Soc- rates’) and those at 2200 and 2370 nm are associated with protein (Mohsenin6). Clearly, this approach is more successful for isolating the effects of the various chemical absorbers of a material than using PCA on log (1/R) data as the majority of the particle size effects have been removed. The normalized Kubelka-Munk function at 1944 nm is shown plotted against the moisture content of the samples in Fig.7. The correlation coefficient of the graph is 0.972 which corresponds to a standard error in calibration of 0.22%. In comparison with Fig. 1, the normalization procedure has largely corrected for particle size effects. This again gives support to the assumption [eqn. (3)J that the Kubelka-Munk function is proportional to the mean particle size of the sample. Basing a calibration on a normalized Kubelka-Munk function of this sort limits the technique to instruments that can determine the reflectance over a scan of wavelengths. This renders the method inappropriate for instruments that measure the reflectance at a number of fixed wavelengths.In this instance, it is necessary to use a Kubelka-Munk ratio of the form given in eqn. (4). Fig. 7 shows that 1944 nm is a suitable wavelength value in the numerator function F(RA). A suitable reference function, F(R,), can be determined by maximizing the correlation between the ratio F(RA)/F(RR) and the moisture content for the reference wavelength. This was found to be at 2064 nm which corresponds to a wavelength value that is comparatively insensitive to compositional changes in the sample (Fig. 6) although its selection will also have been optimized to compensate for the influence of other variable constituents on the 1944 nm absorption peak. The calibration ratio is shown plotted against the moisture content of the wheat samples in Fig.8. The correlation coefficient of this graph is 0.989 which corresponds to a standard error of 0.12%. The same approach can be used for protein. From Fig. 6 and the literature6 it is assumed that the Kubelka-Munk function which is most sensitive to protein variation is at 2200 nm. This function has therefore to be used as the numerator in a ratio ofANALYST, AUGUST 1991, VOL. 116 785 1.5 i 1 c 0 C .- +- 0 a 1.2 1 I I I I 11 12 13 14 15 Ratio of the Kubelka-Munk functions at 1944 and 2064 nm as Water content (%) Fig. 8 a function of the water content of ground wheat samples 0.81 r I .- 0.80 1 .- 0.75 1 U 0.74 L . . 6 8 10 12 14 Protein content (%) Fig. 9 a function of the protein content of ground wheat samples Ratio of the Kubelka-Munk functions at 2200 and 2120 nm as the form given in eqn.(4). The best denominator function F(RR) determined as before has been found to be at 2120 nm. The relationship between the ratio of these two Kubelka- Munk functions and the protein content is shown in Fig. 9. The correlation coefficient of this graph is 0.971 which corresponds to a standard error in calibration of 0.42%. Clearly, as one would expect from the theory, the ratio of two Kubelka-Munk functions compensates for most particle size effects and it is possible to obtain a reasonably accurate single term calibration for the water and protein content of the samples. Unfortunately, however, the accuracy and stability of such a calibration depends not only on the effective compensation for particle size effects but also on the optimum selection of the sampling wavelengths.Absorption features of various constituents often overlap which means that a particular absorption peak cannot be uniquely identified with one absorber and it is necessary to compensate for the effects of interfering constituents. This often requires more than two sampling wavelengths. However, the basic principle of using a number of terms based on the division of Kubelka-Munk functions (or appropriate summations of Kubelka-Munk functions) to compensate for particle size effects is still valid. The ability of the theory to relate the majority of the variation in the 39 wheat spectra to the sensitivity of each wavelength to particle size effects and to compensate effectively for particle size effects using the normalized Kubelka-Munk function and Kubelka-Munk ratio gives some confidence in the validity of eqn.(3). This understanding of the relationship between reflectance and particle size has some implications on the applicability of various calibration algorithms which are discussed in the following section. Influence of Particle Size Variations on Various Calibration Techniques The simplest procedure that corrects for some of the physical variability in the samples is to take the ratio of reflectance at an absorption and reference wavelength. This ratio can then be linearly related to absorber concentration (Stafford et ~ 1 . 8 ) . It was shown above that this is a fairly crude correction because the relationship between particle size and reflectance is wavelength dependent.However, if the reference and absorption wavelengths are chosen to be suitably close together, their sensitivity to particle size will be sufficiently similar to derive a reasonable calibration (Bull9). A calibration in which the measured constituent is related to a linear combination of the reflectance or log (UR) functions at paired wavelengths is well established and, over a small range of mean particle sizes, it can compensate for particle size effects as well as (and sometimes better than) the Kubelka- Munk ratio (Norris and Williams*). The success of these calibrations can be explained by making reference to Fig. 3 which shows how the log (1/R) function at the reference and absorption wavelength will vary as a function of particle size. Over a small particle size range, the relationship between log (1/R) and particle size is approximately linear.Consequently, if the log (1/R) functions at the absorption and reference wavelengths are multiplied by appropriate calibration con- stants they will have similar sensitivity to particle size over a range of absorber concentrations. Similar reasoning can be applied to the calibration based on a linear combination of the reflectance at two wavelengths because, over a small range, the reflectance will vary approximately linearly with particle size. The difference between the functions will therefore be largely independent of particle size. However, the gradient and intercept of the log (1/R) versus particle size response graph, at the reference and absorption wavelength, will depend on the range of particle sizes covered (Fig.3). Consequently, one would expect a calibration based on the linear combination of log (l/R) or reflection functions to be dependent on the range of mean particle sizes in the calibration set and for the calibration accuracy to deteriorate when used on a sample set with dissimilar particle size distributions. This was observed by Norris and Williams2 who showed that the standard error of prediction of protein, in ground wheat samples, for a calibration using three log (1/R) terms, varied between 0.2 and 0.4% with a variation in mean particle size of 50 ym in the test data sets. This shows the importance of ensuring that the test samples are milled in the same way as the calibration set. It will also be noted that, for wheat samples, it is necessary for the calibration set to have similar protein contents as the test set because of the correlation between particle size and protein content.A further disadvantage of these calibration techniques is that the measured quantities do not give a feel for the relative absorber concentrations in the samples prior to calibration. It is anticipated, from the theory presented above, that a calibration based on the ratio of paired Kubelka-Munk functions will be independent of the mean particle sizes of the test and calibration set because the particle size dependence of the Kubelka-Munk functions cancel each other out. This function will therefore be the basis of a calibration which is more robust with respect to changes in the average particle size of the sample sets.Conclusions A theory which relates the effects of particle size to the reflectance of ground wheat flour has been used to show that the majority of the variation in the spectra from the ground wheat samples is due to particle size effects. The effects of particle size changes are particularly pronounced at the absorption bands of the sample which masks the effects of changing sample composition. A technique which highlights the changes in NIR reflectance due to compositional changes is presented. This paper shows that the normalized Kubelka-Munk function and the ratio of two Kubelka-Munk functions is786 ANALYST, AUGUST 1991, VOL. 116 largely independent of particle size. Consequently, by careful selection of the denominator and numerator functions, it is possible to obtain a function that is linearly related to the abundance of a given sample constituent. A linear calibration based on a Kubelka-Munk ratio has been determined for water and protein. A discussion on the influence of particle size variations on various calibration techniques draws a number of conclusions. Firstly, the ratio of reflectance at two wavelengths will always be particle size dependent because the relationship between particle size and reflectance is wavelength dependent. Secondly, a calibration based on a linear combination of reflectance functions will only be able to compensate for particle size effects over a limited range of particle sizes. It is argued that a calibration based on a combination of Kubelka- Munk ratios will be insensitive to changes in the mean particle size of the test and calibration set. The author thanks Dr. B. Osborne of the FMBRA for providing the reflectance scans and analytical values for the samples, and Dr. J. McNicol of the Scottish Agricultural Statistics Service for his helpful advice. References 1 Kubelka, P., and Munk, F., 2. Tech. Phys., 1931,12, 593. 2 Norris, K. H., and Williams, P. C., Cereal Chem. , 1984,61,159. 3 Cowe, I. A., and McNicol, J. W., Appl. Spectrosc., 1985, 39, 257. 4 Osborne, B. G., J. Sci. Food Agric., 1984,35, 106. 5 Bull, C. R., J. Mod. Opt., 1990, 37, 1955. 6 Mohsenin, N. N. , Electromagnetic Radiation Properties of Food and Agricultural Products, Gorden and Breach, London, 1984, 7 Socrates, G. , Infrared Characteristic Group Frequencies, Wiley, Chichester, 1980, p. 137. 8 Stafford, J. V., Weaving, G. S., and Bull, C. R., J. Agric. Eng. Res., 1989, 43, 57. 9 Bull, C. R., J . Agric. Eng. Res., 1991, 49, 113. p. 300. Paper 1100941 I Received February 2nd, 1991 Accepted April 18th, I991