The invention relates to a method for determining the color and/or composition of a material.
The invention further relates to an apparatus for determining color and/or composition of a material.
Color is a property of an object which depends on the object, conditions of illumination, and the observer. In general, the light reflected or transmitted by a non-self-luminous object depends on the nature of the light simultaneously incident on the object, and the geometrical relation of the light source and object. The perceived color of the reflected or transmitted light depends additionally on the visual receptivity of the observer, and the geometrical relation of the observer to said light.
The apparent reflectance of a non-self-luminous object in a particular geometrical relation to the light source and observer is defined to be the ratio of the spectral power in each wavelength band of the reflected light to the spectral power of the same wavelength band of the incident light: ##EQU1##
Similarly, the apparent transmittance of a non-self-luminous object in a particular relation to the light source and observer is defined to be the ratio of the spectral power in each wavelength band of the transmitted light to the spectral power of the same wavelength band of the incident light: ##EQU2##
Absorbance is often used instead of transmittance, being the ratio of spectral power in each wavelength band of the absorbed light to the spectral power of the same wavelength band of the incident light. Thus, it is the complement of transmittance: ##EQU3##
An alternative definition of absorbance is the logarithm of the absorbance as defined in (3). Absorbance and transmittance are interchangeable by trivial modification of any expression in which one or the other appears. In this specification, where either absorbance or transmittance is used, it is to be understood in each case that the equivalent formulation using the other is tacitly implied and within the scope of the specification. Similarly, while this specification expresses reflectance, transmittance, and other quantities as functions of wavelengths, equivalent expressions as functions of frequency or wave number are also in common use. These quantities can be easily converted between the different formulations. Thus, wherever a quantity is expressed as a function of wavelength, it is to be understood in each case that the equivalent formulations using functions of frequency or wave number are tacitly implied and within the scope of the specification.
Clearly, reflectance and transmittance as defined in (1) and (2) have meaning only for wavelength bands in which the incident light has sufficient power to be detectable. Accordingly, rich light sources, having significant amounts of energy at all humanly visible wavelengths, are normally used for measuring them.
Since the perceived color of an object depends on so many factors, standardization of definitions is most important for each of the variables. Standards authorities, such as the CIE (Commission Internationale d'Eclairage), have specified generally accepted standard illuminants having particular spectral power distributions, and color measurement devices usually contain means for approximating one or two such illuminants. Such means is often a rich physical light source with specific optical filters. The C, D55, D65, and D75 sources are frequently encountered, but others such as A, D60, F2, etc. may also be found in industrial applications.
Similarly, since human observers may match color samples differently depending on the size of the color samples, standard spectral observers have been defined for 2 degree and 10 degree fields of view.
Since human vision reduces many wavelength bands in a light spectrum into a three dimensional signal in the retina, color is conventionally expressed as colorimetric quantities having three values. Colorimetric systems in common use include for example CIE Tristimulus; CIE Chromaticity, Lightness; CIE L*a*b*; Hunter L,a,b; Hue Angle, Saturation Value and Dominant wavelength, Excitation purity, Lightness.
Under given conditions of illumination and geometry, CIE tristimulus values may be calculated for the standard spectral observers using formulae which are defined by the CIE. These tristimulus values provide a base from which the other colorimetric quantities can be calculated using formulae defined by the pertinent standards authorities. Such formulae are occasionally revised, as the state of the art is improved. Some auxiliary colorimetric quantities are also of importance in appearance specifications. These are also derived from the tristimulus values, with definitions provided by the CIE and other standards authorities. They include for example tint; whiteness index; yellowness index and blue reflectance.
The tristimulus values are calculated from the apparent reflectance or transmittance of an object, using the spectral power distribution of the illuminant for which the object's color appearance is to be evaluated. Conventionally, tristimulus values are defined as integrals but are normally evaluated as finite approximations: ##EQU4##
where k is a normalization factor, S is the spectral power distribution of the target illuminant, and x, y, z, are the standard observer functions, tabulated at uniform wavelength intervals. In the case that the reflectance data is abridged or truncated, or measured at non-standard wavelength intervals, there are various recommended techniques for interpolation, extrapolation or resampling. Similar equations to (4a-4c) and corresponding methods are used in calculating tristimulus from transmittance spectra. Note that the spectral power distribution of the illuminant used in evaluations (4a-4c) need not be the same as the spectral power distribution of the source used to illuminate the sample during measurement of reflectance or transmittance. It is assumed that the reflectance and transmittance do not depend on the light source.
Each industry tends to have a preferred colorimetric system, although there may be regional differences in such preference. For example, Hunter L,a,b is used widely in the papermaking industry in the U.S.A., but rarely elsewhere, as CIE L*a*b is preferred in the papermaking industry in most other regions, and is also used in the U.S.A. The CIE L*a*b values are defined (1976) for photopic conditions as follows: ##EQU5##
where X.sub.n, Y.sub.n, and Z.sub.n are the tristimulus values for the illuminant. Photopic conditions exist when the ratios X/X.sub.n, Y/Y.sub.n, and Z/Z.sub.n all exceed 0.008856; otherwise either mesopic or scotopic conditions exist, and the equations used differ from (5a), (5b) and (5c), as described in ASTM test method E308-90, for example. These and other issues of colorimetry are well known per se, and are not further discussed. Measurement of color and evaluation of colorimetric quantities in photopic, mesopic, and scotopic conditions are contemplated by, and within the scope of the present invention.
Auxiliary non-colorimetric quantities are of importance in some industries. For example, indices of brightness may be derived from the reflectance spectrum, whereas indices of opacity and transparency may be derived from the transmittance spectrum. Definitions of these and other non-standardized quantities are often industry-specific. However, in their respective fields of application, they are of equal importance to the standardized colorimetric quantities.
The foregoing discussion pertains to describing the measured color of a sample. However, in the case that the sample is not opaque, it may be necessary to calculate the color which would be measured from a stack of samples which is thick enough to be effectively opaque. The transmittance of such a stack is obviously zero, so we are concerned only with its reflectance.
Often, a sufficient number of substantially identical samples can be stacked, and the measurement made directly thereon. However, in other cases this may not be practical--for instance, if the measurement is made on a moving sheet during manufacture. There are several multi-flux models which allow calculation of the infinite stack reflectance from measurements of sample reflectance and transmittance, and some knowledge of the relative absorbing and scattering power of the sample. One which is in widespread use in sheet forming industries is the Kubelka-Munk two-flux model, for diffuse light fluxes in both directions. Another is the four-flux model, which incorporates directional light fluxes in addition to the diffuse light fluxes.
If the quality specification for a translucent material is given in terms of the color of an infinite (or opaque) stack of samples, it is also necessary to perform the inverse calculations to derive a single-layer color from an infinite stack color. Similarly, these techniques can be used to calculate the color which would be measured from a sample of different thickness to the measured sample. In this case, the thickness need not be a multiple of the sample thickness, and may be less than or greater than the sample thickness. Since, in the general case, such calculation need not be for an opaque thickness, both reflectance and transmittance may be so calculated.
The equations and methods of multi-flux models, including the four-flux and Kubelka-Munk two-flux models may be found in Volz, H. G., "Industrial Color Testing", VCH, Weinheim Germany, 1995, among others. These models do not incorporate fluorescence or other spectral transformations; they only model absorption and scattering phenomena.
The difference in color between two samples, or between a sample and a color specification, can be evaluated on the basis of the available measurements. Customarily, a numerical expression of such a color difference is used to determine acceptability of manufactured items, by comparing that numerical value to the allowable maximum value. Depending on the number and type of color variables measured or specified, more than one method of evaluating color difference may be thus employed.
As an example, a commonly used expression for color difference in a colorimetric system is the distance between the co-ordinates of the compared measurements. The CIE L*a*b* color difference is defined (1976) as: EQU .DELTA.E*=[(.DELTA.L*).sup.2 +(.DELTA.a*).sup.2 +(.DELTA.b*).sup.2 ] (6)
A refinement of (6) was promulgated in 1994, but is not yet in widespread use in industry. Analogous definitions exist for other colorimetric systems, and specialized methods for evaluating color difference exist in specific industries.
It is possible for two different reflectance or transmittance curves to produce identical tristimulus or other colorimetric quantities under specific conditions of the illuminant and observation. However, if the illuminant or observer is changed, the colorimetric quantities will no longer match. This phenomenon is known as metamerism.
To avoid source metamerism and field metamerism, the color specification for an object may be supplied in spectral form, as reflectance and/or transmittance curves. In the absence of fluorescence, reflectance curves are invariant with changes to the illuminant. Thus, if the reflectance and transmittance curves match for two samples under one illuminant, they will have matching tristimulus and other colorimetric values under all illuminants and observers.
Instrument metamerism is the phenomenon whereby one color measurement device may indicate that a pair of samples match in color, while another color measurement device indicates a color mismatch. Instrument metamerism arises in spectrophotometric devices through differences in source spectrum, polychromator characteristics, number and wavelength of photodetector elements, and internal standards, among others.
The color of a non-self-luminous opaque sample is commonly measured by means of spectrophotometers in which a sample is illuminated with a particular rich light source (one having significant energy at all visible wavelengths), usually filtered to approximate a standard illuminant, and the reflected light is measured at several wavelengths in the visible band. The sample may be continuously illuminated, using a constant light source, or intermittently, using a flashing source.
In the case of a non-self-luminous translucent sample, the transmitted light may be measured additionally or alternatively to the reflected light by means of a detector on the opposite side of the sample to the illuminant. In other prior art apparatuses, the transmitted light can be reflected back through the sample by a suitable reflector opposite the illuminant such that the detector for transmitted light is on the same side as the illuminant and the detector for reflected light. By suitable means for alternating a reflective white backing with a non-reflective black backing, a device may use a single detector to measure reflected light and reflected light with doubly transmitted light alternately. Estimates of the single layer transmittance and of the infinite stack reflectance may then be derived by suitable calculations. For example, if the black backing is completely non-reflective, then the following Kubelka-Munk equation (given in Wendtland, W. W. and Hecht, H. G., "Reflectance Spectroscopy", Wiley, New York USA, 1966) may be used to estimate the infinite stack reflectance: ##EQU6##
where R.sub.white is the reflectance with white backing, R.sub.black is the reflectance with black backing, and R.sub.backing is the reflectance of the white backing.
In practice, the reflectance is rarely calculated using (1). Instead, the reflected light is compared to the reflected light obtained when a reference sample of known reflectance is placed in the sample location and illuminated with the same source: ##EQU7##
In all these cases of prior art, neither true reflectance nor true transmittance is measured. Rather, the measuring device measures the apparent reflectance and/or the apparent transmittance. This is a consequence of measuring all wavelength bands of the reflected or transmitted light while illuminating with a rich light source.
The apparent reflectance of an infinite stack is often calculated from the apparent reflectance of a single layer, and inverse calculations are often performed for apparent reflectance targets, as disclosed by U.S. Pat. No. 5,082,529. This adjustment typically uses methods based on the Kubelka-Munk two-flux model, even in cases where it is inappropriate (e.g. when the instrumental illumination contains a directional radiance, and is not purely diffuse).
Whereas the true reflectance and transmittance at each wavelength is at most unity, the apparent reflectance and apparent transmittance may exceed unity due to fluorescence. The process of fluorescence involves absorption of light in a range of wavelengths termed the absorption band, and the emission of part of that absorbed energy as light in an emission band, containing longer wavelengths than the absorption band, but which may partly overlap the absorption band. The efficiency of absorption may vary at different wavelengths in the absorption band. Each wavelength in the absorption band can have a different efficiency of emission at each of the wavelengths in the emission band. If the incident light contains sufficient power in the absorption band of a fluorescent object, the light consequently emitted in its emission band, when combined with light reflected or transmitted in the emission band, can yield an apparent reflectance or transmittance in the emission band which is greater than unity. If there is little or no incident light in the emission band, the apparent reflectance or transmittance in that band may be much greater than unity. Note that, regardless of whether the light absorbed in a fluorescent relation is directional or diffuse, the emitted light will generally be diffuse.
In this specification, we shall continue to use the terms "reflected" and "transmitted" to describe respectively the light excident from a sample on the same side as the illumination and on the opposite side, including the effects of fluorescent emission. Note that while the above mentioned multi-flux models incorporate absorption and scattering, they do not incorporate spectral transformations of the kind under discussion here.
These processes can be expressed in the following way: ##EQU8##
where E(.lambda.,.zeta.) is the apparent emissivity of the sample, being the ratio of light apparently reflected at wavelength .lambda. to the light incident at wavelength .zeta., and U(.lambda.,.zeta.) is the apparent transmissivity of the sample, being the ratio of light apparently transmitted at wavelength .lambda. to the light incident at wavelength .zeta.. The lower limit of each integration, min, is a wavelength below the fluorescence absorption band of the sample; in practical cases, this wavelength is generally 200 nm or higher. Matrix representation of emissivity and transmissivity provide finite approximations: ##EQU9##
where E.sub.jk and U.sub.jk are respectively the apparent emissivity matrix and apparent transmissivity matrix, with elements defined for quantum relations between discrete wavelength bands, centered on specific sets of wavelengths .lambda..sub.j, .zeta..sub.k, and .DELTA..zeta..sub.k is the width of the wavelength band centered on .zeta..sub.k. For instance: ##EQU10##
Thus, the light apparently reflected from a sample depends on the apparent emissivity matrix of the sample as well as on the light incident on the sample. In the same way, the light transmitted through a translucent sample depends on the apparent transmissivity of the sample as well as on the light incident on the sample.
For non-fluorescent samples, the apparent emissivity E.sub.jk is nonzero only for elements where .lambda..sub.j =.zeta..sub.k, and these emissivity values are the reflectance values at those wavelengths. Similarly, the apparent transmissivity U.sub.jk of a non-fluorescent translucent sample is nonzero only for elements where .lambda..sub.j =.zeta..sub.k, and these transmissivity values are the transmittance values at those wavelengths. For fluorescent samples the emissivity and, if translucent, the transmissivity have nonzero values for some elements where .lambda..sub.j &gt;.zeta..sub.k.
It is clear from (9a) or (10a) combined with (1) or (8) that for a fluorescent sample, there can be a difference between its apparent reflectance curves measured under different conditions of illumination. The degree to which the apparent reflectance curves differ depends on the degree to which the illuminants differ in their spectral power distribution in the fluorescence absorption and emission bands. The apparent transmittance of a translucent fluorescent sample will depend in an analogous way on the spectral distribution of illuminants, as is obvious from combining (9b) or (10 b) with (2).
These phenomena give rise to fluorescent metamerism, in which samples which have identical apparent reflectance and apparent transmittance curves when measured with one rich illuminant can have non-identical apparent reflectance and apparent transmittance curves when measured with another rich illuminant.
It is important to note for the purposes of this invention that, although the apparent reflectance and apparent transmittance of a sample will vary with the illumination used in the measuring device, the apparent emissivity and apparent transmissivity are invariant. Similarly, although addition of a fluorescent colorant to a substrate will cause changes .DELTA.R(.lambda.) and .DELTA.T(.lambda.) in its apparent reflectance R(.lambda.) and transmittance T(.lambda.) which will vary with the illumination S(.lambda.) used in the measuring device, the changes .DELTA.E(.lambda.,.zeta.) and .DELTA.U(S.lambda.,.xi.) caused in its apparent emissivity E(.lambda..xi.) and transmissivity U(.lambda.,.xi.) are invariant with illumination.
When there are plural absorption-emission relations between different bands, it is possible for fluorescent cascades to exist. In this case, the emission band of a first fluorescent relation is partly or wholly in the absorption band of a second fluorescent relation. Thus, part of the light emitted as a result of absorption in the first absorption band may be emitted in the second emission band, even when there is no incident light in the second absorption band. Such cascades can involve more than two fluorescent relations, and be complex in nature.
Methods whereby source metamerism and observer metamerism can be avoided in non-fluorescent materials are well-known. Most of these involve specifying, measuring, and controlling the reflectance spectrum of the material, rather than merely a set of colorimetric quantities. For example, U.S. Pat. No. 4,439,038 uses a least-squares approximation of the reflectance spectrum, while Shakespeare, J. and Shakespeare, T., "An Optimizing Color Controller", proc. TAPPI 1997 PCE&l at Birmingham Ala., 127-135, TAPPI Press, Atlanta USA, 1997 use a reflectance model to optimize colorimetric quantities in addition to the reflectance. U.S. Pat. No. 4,565,444 discloses methods whereby measurements of color are made across the entire width of a sheet without scanning by means of light pipes, or by providing illumination and detection across the entire sheet. U.S. Pat. No. 4,801,809 discloses a similar idea to U.S. Pat. No. 4,565,444, but implements it differently. U.S. Pat. No. 5,082,529 also discloses measurement and control of reflectance, adding Kubelka-Munk-type adjustments for infinite stack calculations.
In an attempt to quantify the effects of fluorescence, various modified spectrophotometers have been devised. In general, these employ additional rich light sources or optical filters to approximate each of plural specific illuminants, such as C, D65, F12 or intermittently removing some or all of the near ultraviolet from the approximation to an illuminant such as D65 or intermittently adding a rich ultraviolet illuminant to a specific illuminant such as C or D65.
Each of these techniques partly addresses the issue of measuring fluorescent metamerism, but none copes with it in a satisfactory way. Equally, none provides an adequate model for color control in the presence of fluorescent metamerism or for color control which will avoid or minimize the effects of fluorescent metamerism.
Removal of near-ultraviolet light from, and addition of near-ultraviolet light to an illuminant are equivalent in that they allow the apparent reflectance to be measured with different amounts of near-ultraviolet light in the illuminant. Thus, the sensitivity of apparent reflectance to near-ultraviolet light can be quantified. However, this technique completely fails to address fluorescence where both absorption and emission occur within the visible range. Similarly, it fails to address fluorescence where both absorption and emission occur within the near-ultraviolet range. Also, since rich near-ultraviolet sources are used, it does not distinguish between the different efficiencies in each quantum relation of a fluorescence from near-ultraviolet to visible. Thus, it cannot provide a model for addition or removal of near-ultraviolet light of different relative spectral distribution than that used in the measuring device. Another consequence is that it cannot provide a model for fluorescent cascades existing in any wavelength bands, whether near-ultraviolet or visible.
From colorimetric data alone, it is difficult or impossible to deduce the amounts of different colorants present in a sample, even when the nature of the substrate and colorants is known. However, if reflectance and/or transmittance spectral data are provided in the visible range of wavelengths, it becomes possible in some cases to estimate the amounts of known non-fluorescent colorants present, provided the spectral responses of all colorants are quantified and the reflectance and/or transmittance of the substrate is known. The estimation can be performed, for example, by modification of the control calculations disclosed in the above mentioned article "An Optimizing Color Controller", so that the difference in reflectance or transmittance between the substrate and the sample is optimally fitted by scaled combination of normalized spectral responses of the colorants, hence providing the amounts of colorants present as said scale factors. A different method is disclosed in U.S. Pat. No. 4,977,522 which omits consideration of the substrate, and hence applies only to opaque coatings such as paints. These estimation methods are unreliable if fluorescence is present to a significant degree either in the substrate or in the colorants even if the data covers the fluorescent absorption region as well as the fluorescent emission region, as a result of several of the issues discussed earlier.
The discussion thus far has concentrated mainly on the measurement of color and related issues, and colorimetry is concerned only with the range of wavelengths visible to humans. However, in relation to the properties of reflectance, transmittance, and fluorescence, and their effects, the issues raised are not limited to those wavelengths, but are valid over a much wider range.
Spectral reflectance and transmittance measurements both inside and outside the visible range are commonly used to determine the composition of samples. U.S. Pat. No. 5,250,811 discloses a method for analyzing the composition of a multilayer web by measuring spectral reflectance in the near infra-red region. This method employs polychromatic illumination, in a similar manner to the polychromatic illumination used in determining color by measurement of reflectance as discussed above, differing only in the wavelength range.
U.S. Pat. No. 5,155,546 discloses a method employing spectral reflectance measurements in the visible region for analyzing the composition of rock samples. Also, U.S. Pat. No. 4,602,160 discloses an apparatus for measuring diffuse spectral reflectance and spectral transmittance in the infra-red region, and for analyzing those measurements to estimate the content of specific substances in a material. In these latter two disclosures, the sample to be analyzed is illuminated with monochromatic or nearly monochromatic light at each of several wavelengths bands one at a time, but the measurement of the reflected or transmitted light does not employ a monochromator, although it may employ a filter to exclude wavelengths outside the range to be measured which is substantially the same as the whole gamut of illumination bands. Thus, the reflected or transmitted light measured when the sample is illuminated at wavelength .xi. with a detector uniformly sensitive to wavelengths from .lambda..sub.min to .lambda..sub.max is given by: ##EQU11##
A simple modification of these equations is required if the detector is differently sensitive to different wavelengths between .lambda..sub.min and .lambda..sub.max. For non-fluorescent samples, (101a) and (101b) give results substantially identical to (9a) and (9b), and for such samples, it is largely irrelevant whether the single monochromator is used in the illuminator or in the detector. The apparent reflectance and transmittance calculated using (1), (2) or (8) from measurements described by (101a) and (101b) are given by: ##EQU12##
For non-fluorescent samples, the apparent reflectance measured in this way is clearly the true reflectance, R(.zeta.)=E(.zeta.,.zeta.), and the apparent transmittance is clearly the true transmittance, T(.zeta.)=U(.zeta.,.zeta.).
For fluorescent samples, the reflectance or transmittance calculated from measurements of this type does not exceed unity, but it fails to distinguish between luminescent and non-luminescent contributions to the measurement. This deficiency reduces the amount of information which can be used to determine composition or other properties of the sample from the spectral measurements, and a significant fluorescent emission leads to an error in the calculated reflectance or transmittance. This error leads to an overestimation of the reflectance or transmittance in the fluorescent absorption band rather than in the fluorescent emission band, as would happen in the case of a device employing a detector monochromator with a rich light source. This systematic problem obviously introduces further sources of error in estimating properties or composition of the measured material when fluorescent substances are present.
U.S. Pat. No. 3,904,876 discloses a method for determining the amount of ash in paper by measuring the absorption of one or more monochromatic X-ray beams. U.S. Pat. No. 4,845,730 discloses a method which combines infra-red absorption measurements at several wavelengths with an absorption measurement for a monochromatic X-ray beam and measurements of beta ray absorption in estimating the amounts of a base material and two or three other components present in a paper web. The measurements made according to these methods also are described by equations (101a) and (101b), except that a different essentially monochrome detector may be used for each monochrome illumination wavelength.
U.S. Pat. No. 5,778,041 discloses a method which employs two polychromatic X-ray beams whose spectral power distribution differ in a particular way, and by measuring the amount of each beam absorbed in passing through a paper web, estimate the amounts of specific substances in that web. A different detector may be employed for each beam, but, monochromators are not employed either on the illuminator or on the detectors. However, filters may be used in controlling the spectral power distributions of the two illuminator beams.
Prior art methods also exist for estimation of composition and other properties from reflectance and transmittance spectral measurements by reference to sets of calibration data measured on samples of known properties. These methods are used for reflectance, transmittance, and absorbance spectral measurements, obtained either with a monochromator on the illuminator or on the detector. U.S. Pat. No. 4,800,279 discloses a method using infra-red absorbance spectra of calibration samples of known physical properties to determine those infra-red wavelengths at which the absorbance correlates with a physical property to be quantified, and then estimate that property for a sample from its infra-red absorbance spectrum. U.S. Pat. No. 5,121,337 discloses a method for estimating unmeasured properties such as composition from spectral measurements on a sample, using a model fitted by least-squares fitting, principal components regression, or partial least-squares regression to spectral measurements and measurements of the desired property or composition for a set of calibration samples. U.S. Pat. No. 5,446,681 discloses a method which employs rule-based critera in addition to statistical procedures in the estimation of property or composition from spectral measurements on a sample and spectral measurements on a calibration set of known properties or composition.
The above methods for analyzing spectral measurements to estimate composition or other physical properties, and for use of calibration data sets in such methods have a number of common features: i) the spectral data or a simple variant thereof such as its derivative is fitted as a combination of particular component spectral factors which are suitably scaled, (ii) the particular component spectral factors or known combinations thereof are associated with the physical properties or composition variables, (iii) the physical properties or composition variables are calculated using coefficients in a specific relation from the fitting parameters of the associated component spectral factors, and (iv) the particular component spectral factors and coefficients for relations are either known a priori or are derived from calibration data. The reliability of this class of analysis method depends on the extent to which the requisite component spectral factors can be discerned in the measurement, and the extent to which those patterns are invariant both within the calibration data set and between the calibration data and the measurements to be analyzed. The presence of significant amounts of fluorescence, and especially variation in that fluorescence can severely comprise the accuracy and reliability of such analyses based on spectrophotometric or spectroscopic measurements.