WO2009013718A2

WO2009013718A2 - Methods and apparatus for tristimulus colorimetry

Info

Publication number: WO2009013718A2
Application number: PCT/IB2008/052963
Authority: WO
Inventors: Ian Ashdown
Original assignee: Koninklijke Philips Electronics N.V.
Priority date: 2007-07-23
Filing date: 2008-07-23
Publication date: 2009-01-29
Also published as: WO2009013718A3

Abstract

Tristimulus colorimeter apparatus and methods of tristimulus colorimetry are described. The tristimulus colorimeter apparatus can be used for determining color of light by specifying a first, a second and a third tristimulus value for the light. The colorimeter apparatus may detect signals according to color matching functions having spectral responsivities matched by detectors of the colorimeters. The detected signals may be processed by one or more computations, such as matrix operations, to provide the tristimulus values of the color.

Description

METHODS AND APPARATUS FOR TRISTIMULUS COLORIMETRY

FIELD OF THE INVENTION

[0001] The present invention relates generally to colorimetry and more particularly to methods and apparatus for determining and specifying the color of light.

BACKGROUND

[0002] It is often useful to be able to quantify and/or characterize light. Light can vary in many different ways, such as in its intensity, its spectral content, and, therefore, its color, among others. Accurate determination or identification of the color of light can facilitate accurate production, reproduction, or analysis of a particular color. Thus, accurate identification of color can be useful in lighting displays, illumination settings, printing, scanning, photography, and many other settings involving colored light and color.

[0003] Colorimetry is the defined, reproducible quantification and determination of the color of light, and is an important aspect when considering the utility of light emitted by, reflected from, or transmitted through objects or light sources. A number of professional organizations and institutes, including the Commission Internationale de l'Eclairage (CIE) and the Illuminating Engineering Society of North America, have been instrumental in defining standards and technologies for quantifying color, specifically for measuring color as it is perceived by the human visual system. For this purpose, a number of methods and definitions for measuring the characteristics of light in terms of luminous flux and chromaticity have been developed, and various widely used and recognized observation conditions have been defined.

[0004] One manner of characterizing color is using three tristimulus values X, Y, and Z, as defined by the CIE. The XYZ tristimulus values are intended to correspond to human perception of colors (i.e., after the eye has detected the color and the brain has processed the signals provided to it by the eye), and can be calculated from the so-called ^~x,y, ^~z color-matching functions illustrated in FIG. 1. Every color of light can be uniquely defined by its three tristimulus values. [0005] FIG. 2 illustrates a conventional tristimulus colorimeter for determining the XYZ tristimulus values of a color. As shown, the apparatus 200 includes a source 210 from which radiation 220 is emitted. The source may be a light source that generates light, or a color sample from which light is reflected. A detection system 230 receives the radiation 220 and provides an output signal 240. The detection system 230 includes one or more filters and sensors designed to have spectral responsivity characteristics that match as closely as possible the spectral characteristics of the x,y, and z color matching functions illustrated in FIG. 1. Therefore, the output signal 240 roughly approximates the XYZ tristimulus values, with little or no postprocessing of the output signal 240 needed.

[0006] The conventional detection system 230 is complex and typically expensive. As shown in FIG. 1, the x,y,z color matching functions include complexity, exemplified by the multiple peaks of the x matching function, which is particularly difficult to match in practice. Tristimulus colorimeters for measuring CIE 1931 XYZ chromaticity values, such as detection system 230, therefore require at a minimum three optical filters with spectral transmissivities or reflectivities that in combination with the sensitivities of suitable sensors provide combined responsivities that adequately accurately match the corresponding CIE x,y,z color matching functions as defined in CIE 15:2004, Colorimetry, Third Edition. In fact, known tristimulus colorimeters employ at least four filter-sensor units with spectral responsivities that approximately match the four peaks of the CIE x,y,z color matching functions. Conventional detection systems 230 often also include additional components such as mirrors, spectrometers, and other complex measurement devices.

[0007] While other color matching functions have been determined (other than the x,y, z color matching functions), they all involve complexities with respect to their spectral characteristics which are difficult to match with filters and/or sensors. Therefore, conventional attempts to determine XYZ tristimulus values of a color have been difficult and expensive.

SUMMARY OF THE INVENTION

[0008] In view of the foregoing described drawbacks associated with conventional methods and apparatus for determining tristimulus values of a color, Applicant has appreciated that new, simpler methods and apparatus for determining tristimulus values may be beneficial. Applicant has further appreciated that simple and reliable methods and apparatus for determining tristimulus values may be realized by deviating from the conventional approach to measuring tristimulus values.

[0009] For example, rather than attempting to directly detect/measure the desired tristimulus values using detectors that have complex spectral responsivities intended to approximately match the x,y,z color matching functions, or other complex color matching functions, in various inventive embodiments discussed herein, detectors (e.g., filter-sensor combinations) having spectral responsivities matching new color matching functions are used. Each of the new color matching functions may be simple, having one sign (i.e., positive or negative) across a relevant range of wavelengths (e.g., the visible spectrum), and only one peak across the relevant range. The new color matching functions may be converted to the x,y,z color matching functions using one or more linear transformations, or any other suitable mathematical processing. Thus, the quantities detected by apparatus according to various inventive embodiments described herein may be processed using one or more linear transformations, or any other suitable mathematical processing, to produce the desired tristimulus values (i.e., the end result corresponding to human perception after the brain has processed signals received from the eye).

[0010] According to one aspect of the present invention, a method for determining X, Y, and Z tristimulus values is provided. The method comprises detecting at least three quantities of incident radiation, each quantity of incident radiation corresponding to a different Stockman Cone Fundamental, producing at least three output signals (512a, 512b, 512c in FIG. 5), each output signal of the at least three output signals corresponding to one of the at least three quantities, and processing the at least three output signals to produce the X, Y, and Z tristimulus values specifying a color of the incident radiation.

[0011] According to another aspect of the present invention, a method for determining tristimulus values is provided. The method comprises detecting, with a first detector (502) having a first spectral responsivity, a first quantity of incident radiation and producing a first output signal (512a) indicative of the first quantity. The method further comprises detecting, with a second detector (504) having a second spectral responsivity, a second quantity of the incident radiation and producing a second output signal (512b) indicative of the second quantity. The method further comprises detecting, with a third detector (506) having a third spectral responsivity, a third quantity of the incident radiation and producing a third output signal (512c) indicative of the third quantity. The method further comprises processing the first, second, and third output signals using at least one matrix operation to produce three tristimulus values indicative of a color of the incident radiation. Each of the first, second, and third spectral responsivities has a same sign, positive or negative, and only one peak over a first range of wavelengths from approximately 380nm to 780nm.

[0012] According to yet another aspect, an apparatus for determining tristimulus values of a color is provided. The apparatus comprises a detection system configured to receive incident radiation comprising colored light and to produce at least one output signal (512a, 512b, 512c) indicative of at least three quantities of the incident radiation. The detection system comprises a first detector (502) having a first spectral responsivity, a second detector (504) having a second spectral responsivity, and a third detector (506) having a third spectral responsivity. Each of the first, second, and third spectral responsivities has a same sign, positive or negative, and only one peak over a first range of wavelengths from approximately 380nm to 780nm. The apparatus further comprises a processing system (540) having an input coupled to receive the at least one output signal (512a, 512b, 512c), and being configured to process the at least output signal and provide at least one of an X, Y, and Z tristimulus value.

[0013] It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. It should also be appreciated that terminology explicitly employed herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein.

BRIEF DESCRIPTION OF THE FIGURES

[0014] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawings. In the drawings:

[0015] FIG. 1 illustrates the CIE x,y,z color matching functions known in the Prior Art;

[0016] FIG. 2 illustrates a Prior Art colorimeter for determining the XYZ tristimulus values;

[0017] FIG. 3 illustrates the Stockman cone fundamentals, also called I ,m,s^~ color matching functions;

[0018] FIG. 4 illustrates the r, g, b color matching functions as defined by CIE;

[0019] FIG. 5 is a block diagram of an apparatus for tristimulus colorimetry according to one embodiment of the present invention;

[0020] FIG. 6 is a graph of the spectral absorption characteristics of an interference filter that can be used in the apparatus of FIG. 5, according to one embodiment of the present invention; and

[0021] FIG. 7 is a detector implementing a diffuser, according to one embodiment of the present invention.

DETAILED DESCRIPTION

Definitions

[0022] The term "light-emitting element" (LEE) is used to define a device that emits radiation in a region or combination of regions of the electromagnetic spectrum, for example, the visible region, infrared and/or ultraviolet region, when activated by applying a potential difference across it or passing a current through it. Therefore, a light-emitting element can have monochromatic, quasi-monochromatic, polychromatic or broadband spectral emission characteristics. Examples of light-emitting elements include, but are not limited to, semiconductor, organic, or polymer/polymeric light-emitting diodes, blue or UV pumped phosphor coated light-emitting diodes, optically pumped nanocrystal light-emitting diodes or other similar devices as would be readily understood by a worker skilled in the art. Furthermore, the term light-emitting element is used to define the specific device that emits the radiation, for example a LED die, and can equally be used to define a combination of the specific device that emits the radiation together with a housing or package within which the specific device or devices are placed.

[0023] The term "optical sensor" is used to define an optical device having a measurable sensor parameter in response to a characteristic of incident light, such as its luminous flux or radiant flux.

[0024] The term "broadband optical sensor" is used to define an optical sensor that is responsive to light within a wide range of wavelengths, such as the visible spectrum for example.

[0025] The term "narrowband optical sensor" is used to define an optical sensor that is responsive to light within a narrow range of wavelengths, such as the red region of the visible spectrum, for example.

[0026] The term "chromaticity" is used to define the perceived color impression of light according to standards of the Illuminating Engineering Society of North America.

[0027] The term "luminous flux" is used to define the instantaneous quantity of visible light emitted by a light source according to standards of the Illuminating Engineering Society of North America.

[0028] The term "spectral radiant flux" is used to define the instantaneous quantity of electromagnetic power emitted by a light source at a specified wavelength according to standards of the Illuminating Engineering Society of North America.

[0029] The term "spectral radiant power distribution" is used to define the distribution of spectral radiant flux emitted by a light source over a range of wavelengths, such as the visible spectrum, for example.

[0030] The term "radiant flux" is used to define the sum of spectral radiant flux emitted by a light source over a specified range of wavelengths. [0031] As used herein, the term "about" refers to a +/-10% variation from the nominal value. It is to be understood that such a variation is always included in any given value provided herein, whether or not it is specifically referred to.

[0032] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0033] Aspects of the invention arise from the realization that tristimulus colorimeters based on detector units (e.g., combinations of filters and sensors) whose spectral responsivities match the CIE x,y, z color matching functions at substantially all required wavelengths have been difficult to design and implement and have consequently been expensive. As mentioned, Applicants have appreciated that tristimulus values may be calculated from new color matching functions, which may have spectral characteristics that can be (easily and accurately) matched or approximated by available detection systems. Each of the new color matching functions may be defined or chosen to have a same sign (i.e., positive or negative) and only a single peak over a relevant range of wavelengths, and may also be defined or chose to be capable of conversion to the x, y, z color matching functions by suitable mathematical processing, such as one or more matrix operations, which may be linear or non-linear in some embodiments.

[0034] Thus, Applicants have appreciated that detection systems having spectral responsivities matching, or approximately matching, new color matching functions with simple spectral characteristics may be used to detect incident light, and the detected signals from the detection systems may be suitably processed to provide the XYZ tristimulus values (e.g. , by one or more matrix operations representing a linear transformation, or otherwise). Selecting color matching functions having simple spectral characteristics may allow for use of detection systems having simple spectral responsivities, and may thus reduce error, complexity, and cost in the detection apparatus and process compared to conventional schemes. Moreover, Applicants' appreciation offers flexibility in that any suitable color matching functions may be used as the basis for calculating the XYZ tristimulus values, and for designing or selecting apparatus (e.g., detection systems) having spectral responsivities matching the spectral characteristics of the color matching function(s). [0035] Thus, some aspects of the invention capitalize on the fact that the x,y,z color matching functions, which do not lend themselves to simple physical detection, may be transformed into other coordinate spaces using a typically linear and invertible transformation to yield new color matching functions that may be more easily matched with three, or any other suitable number, filter-sensor combinations that may be cost-effectively obtained. For example, the new color matching functions may comprise only three peaks, as compared to the four (or more) peaks associated with the conventional x,y, z color matching functions. While the transformation to other coordinate spaces may typically be defined to be linear to save computational effort when processing the respective sensor signals, non-linear transformations may be used, if required, to desirably improve resolution and dynamic range of the obtainable tristimulus values. The transformation may be selected to be invertible to facilitate a determination of luminous flux and chromaticity which require inversion of the corresponding transformation matrix, but need not be invertible in all embodiments.

[0036] According to one non-limiting embodiment, the Stockman Cone Fundamentals are used as new color matching functions, providing for easily detectable quantities which may be subsequently processed by suitable matrix operations to provide the XYZ tristimulus values. The Stockman Cone Fundamentals, illustrated in FIG. 3, are functions which express the spectral responsivities of the L-, M-, and S-cones in the human retina, i.e., correspond to the detection capabilities of the human eye. The L-, M-, and S-cones in the human retina are responsible for color vision.

[0037] Applicant has recognized and appreciated that optical filters and sensors may be chosen or designed to match the spectral responsivity of the ϊ , m, and J functions with high accuracy and minimal complexity. Applicants have further appreciated that the three functions, J,m, and / corresponding to the S, M, and L cones of the Stockman Cone Fundamentals may be converted to the x,y,z color matching functions by suitable computation involving multiple linear matrix operations. The CIE x,y,z color matching functions can be derived as linear combinations of the CIE r, g, b color matching functions. The CIE r, g, b color matching functions are illustrated in FIG. 4 and are defined for certain standardized observation conditions. The transformation from f, g^~ ,b to x,y,z space can be accomplished using a linear transformation as follows: 'x^Λ '2.76888 1.75175 1.13016^v jΛ 1.00000 4.59070 0.06010 O)

K²J V 0.00000 0.05651 5.59427 J\^h J

[0038] As this transformation is linear and the actual tristimulus values X, Y, and Z are weighted averages of the wavelength-integrated spectral radiant power distribution l(λ), the wavelength averaging can be defined as follows:

The corresponding tristimulus values transform in the same way as the color matching functions except for a scaling constant C , and can be defined as follows:

(3)

J

in which x, y, and z are the normalized values of X, Y, and Z, and r, g, and b are the normalized values of R, G, and B.

[0039] As illustrated in FIG. 4, the CIE r, g,b color matching functions contain positive as well as negative weighting factors depending on wavelength, which means that they cannot be embodied by three simple filter-sensor units with physically realizable spectral responsivities. Yet, as shown by A. Stockman et al. in "Isolation of the Middle and Long- Wavelength Sensitive Cones in Normal Trichromats" (J. Optical Society of America A, Vol. 10, pp. 2491-2521), the CIE r,g,b color matching functions can be linearly transformed into the Stockman Cone Fundamentals as follows:

[0040] It is noted that the transformation matrix defined in Equation (4) is determined subject to certain constraints given desired physiological interpretations of the Stockman Cone Fundamental functions. The constraints are imposed because the spectral responsivity of the S- cones to red light has been defined to be zero, and so the matrix element in the first column of the third row is zero. Furthermore, it has been defined that a certain linear combination of the L- cone and M-cone spectral responsivities must yield the luminous efficiency function.

[0041] Thus, sufficiently accurate x,y,z values may be obtained from l,m,s values as defined by the matrix operation shown in Equation (5) below. Equation (5) can be obtained by eliminating r,g,b, from a combination of Equations (3) and (4) by replacing r,g,b in Equation (3) with r, g^~,b from Equation (4). r,g,b can be obtained from Equation (4) by inverse transformation.

^A2.76888 1.75175 1.13016 0.214808 0.751035 0.045156VY/^Λ 1.00000 4.59070 0.06010 0.022882 0.940534 0.076827 m (5)

V 0.00000 0.05651 5.59427 0.000000 0.016500 0.999989 K ⁵ J

[0042] Therefore, Applicant has appreciated that detecting the 1, m, and s quantities of incident radiation (i.e., the quantities of incident radiation corresponding to the / , m, and J functions), described in further detail below, can lead to the X,Y,Z tristimulus values by using the matrix operation defined in Eq. 5 and the relationships defined in Eq. 2, or by any other suitable processing.

[0043] It should be appreciated that using the Stockman Cone Fundamentals as color matching functions defining physically detectable quantities provides one non- limiting example. Other color matching functions may be defined having spectral responsitivities favorable to detection, such as having one sign {i.e., all positive values or all negative values) over a range of relevant wavelengths (e.g., 400nm to 700nm or any other suitable range of wavelengths) and having only a single peak over the range. Apparatus according to various embodiments described herein may be used in various fields, such as illumination, printing or photography. Depending on the use, the practically relevant range of wavelengths may, for example, range from about 380nm to about 780nm. In addition, for a particular field or application in a field, the range of wavelengths for a desired level of functionality may be different, with different lower or upper limits or different lower and upper limits, and thus different transformations may be applicable for different wavelength ranges. For example, a transformation suitable for a narrow range of wavelengths may not be suitable for a broad wavelength range.

[0044] Depending on the color matching functions to which the spectral responsivitiies of a detection apparatus may be matched, the processing performed on the output(s) of the detection systems (i.e., the detected quantities of incident radiation) to achieve the tristimulus values may differ. For example, the output signals of detectors having spectral responsitivities matching new color matching functions having the characteristics described above may be processed to produce the X,Y,Z tristimulus values by performing a linear transformation directly between the new color matching function and the x, y, and z color matching functions, performing a transformation between the new color matching function and the f,g,b color matching functions and then to the x,y, z color matching functions, or performing any suitable computation to arrive at the XYZ tristimulus values.

[0045] According to some embodiments, transformation functions or matrices for defining new color matching functions do not need to be subject to constraints other than that the transformation functions should be configured in order to implement the new color matching functions with simple filter-sensor combinations. In addition, the new color matching functions are not required to be interpreted to model a specific physiological effect. Hence, the new color matching functions can be selected to define three peaks (or any other suitable number of peaks) that can be relatively easily matched using only three filter-sensor combinations that require a desired small level of computational effort for processing of sensed signals to arrive at the XYZ tristimulus values. In other embodiments of the present invention different linear or nonlinear optimization and regression techniques may be used to obtain new color matching functions. A number of different regression and optimization techniques are known in the art. Apparatus

[0046] According to an aspect of the invention, a tristimulus colorimeter apparatus is provided comprising a detection portion and a processing portion. The detection portion may receive incident radiation, for example from a color light source, a color sample, or any other suitable source of incident radiation, and detect at least a portion of the incident radiation. The detection portion may include at least one sensor, and in some instances may include additional components such as filters and/or diffusers. The combination of the sensor and any additional components {e.g., filters, diffusers, etc.) may have a spectral responsivity substantially matching that of a desired color matching function {e.g., a Stockman Cone Fundamental or any other suitable color matching function(s)). The sensors may provide output signals indicative of the detected incident radiation, which may be provided to the processing portion. The processing portion may perform any suitable processing on the output signals from the detection portion to produce the X, Y, and Z tristimulus values, such as performing one or more linear matrix operations such as that shown in Eq. 5, or any other suitable processing. The processing portion may be implemented in hardware, software, or some combination thereof, and may take any suitable form, as the various aspects of the invention are not limited in this respect.

[0047] FIG. 5 is a block diagram of a non-limiting example of an apparatus 1000 for tristimulus colorimetry according to one embodiment of the invention. The apparatus 1000 comprises three detectors 502, 504, and 506, each configured to receive incident light 500. It should be appreciated that any suitable number of detectors could be included, and that three is only one non-limiting example. In addition, while the detectors 502, 504, and 506 are illustrated as distinct, it should be appreciated that they could alternatively be part of a single detection system. The incident light 500 may be colored light, and may fall on the detectors 502, 504, and 506 evenly or in different amounts, as the various aspects of the invention are not limited in this respect.

[0048] The detectors 502, 504, and 506 are configured to detect the light 500 falling thereon and produce an output signal indicative of the quantity of light detected by each. In the non- limiting example of FIG. 5, the detectors 502, 504, and 506 comprise respective photosensors 510, 520, and 530 and associated color filter 515, 525, and 535. The combination of each photosensor and color filter may exhibit a spectral responsivity substantially matching a desired color matching function, such as one of the Stockman Cone Fundamental, or any other suitable color matching function.

[0049] The detectors 502, 504, and 506 are connected to a processing system 540 to receive the output signals 512a, 512b, and 512c of photosensors 510, 520, and 530, respectively. The processing system 540 may be an analog or digital processing system, and is not limited in this respect. According to one non-limiting embodiment, the processing system may perform a linear transformation on the received output signals to produce the normalized tristimulus values x, y, and z, as follows:

where s_r,s_g ,s_b represent the output signals of the photosensors according to the new color matching functions (e.g., the Stockman Cone Fundamentals or any other suitable color matching function(s)). The elements

e {l,2,3},y e {l,2,3}j of the transformation matrix can be determined in accordance with one of the previously described methods and relationships (e.g., Eq. (5)). According to another embodiment, the processing system may output the tristimulus values X, Y, and Z (i.e., not the normalized values), for example by calculating x, y, and z as shown in Eq. (6) and then using the relationships shown in Eq. (2), or by any other suitable method.

[0050] Alternatively, or in addition, the processing system 540 can be configured to process the output signals of photosensors 510, 520 and 530 in other ways, for example, non-linear ways. The processing system 540 may provide the output x,y,z values in a number of different ways.

The output may be analog or digital and respectively analog or digitally encoded. The x,y,z values may be encoded in separate serial or parallel signals. The x,y,z values may also be encoded in a single time multiplexed serial or parallel signal (not illustrated).

[0051] In some embodiments, such as the example of FIG. 5, the outputs of a processing system (e.g., x, y, and z, or alternatively X, Y, and Z) may be sent to a memory 514, which may store the outputs. The memory may be, for example, part of a computer, disk drive, or take any suitable form. It should be appreciated that the memory 514 is optional, and in some embodiments the outputs of the processing system may be used directly to determine or identify a color, or for any other reason, as the various aspects of the invention are not limited in this respect.

[0052] As has been mentioned, the XYZ tristimulus values can be used to define color, and therefore the values output by the processing system may be used directly, or read out of a memory, such as memory 514, for use in any application involving determination or analysis of color. For example, in some embodiments, the determined XYZ values may be used to control a color of light emitted from a light emitting element, for example to provide a desired color. Other uses of the determined XYZ tristimulus values are also possible.

Detectors

[0053] As shown in FIG. 5, a colorimeter apparatus 1000 according to an embodiment of the invention may comprise one or more detectors, shown in that non-limiting example as detectors 502, 504, and 506. The detector(s) may take any suitable form for detecting a desired quantity of incident light. Therefore, the detectors may exhibit spectral responsivities which match that of a function {e.g., a Stockman Cone Fundamental) defining the quantity to be detected. There are various manners in which a detector may be designed and configured to exhibit such spectral responsivities, and the various aspects of the invention are not limited to any particular design or configuration.

[0054] For example, according to one embodiment, a detector may include only a sensor {e.g., a photodiode, or any other suitable type of sensor) having the desired spectral responsivity matching that of the function defining the quantity to be detected. Alternatively, a detector {e.g., detector 502) may include both a sensor and a filter, as illustrated in FIG. 5. A sensor can be combined with a filter so that the spectral characteristics, for example, the transmissivity or the reflectivity, of the filter together with the spectral sensitivity of the sensor provide a filter-sensor combination with a spectral responsivity that adequately matches one of the desired color matching functions, e.g., one of the Stockman Cone Fundamentals. Generally, at each wavelength within a range of wavelengths, the responsivity of the filter-sensor combination corresponds to the product of the transmissivity of the filter and the sensitivity of the sensor or alternatively to the product of the reflectivity of the filter and the sensitivity of the sensor. It is noted that embodiments of the present invention may also utilize filter-sensor combinations that are integrally formed and which may be fabricated from suitable materials.

[0055] Thus, according to one embodiment of the invention, a set of one or more photosensors with three optical filters whose spectral responsivities approximate the Stockman cone fundamentals as illustrated in FIG. 3 can be employed. A least squares nonlinear regression as described for example by Hu et al. in "Algebraic Expressions of the CIE Standard Observers and Stockman Cone Fundamentals" (Leukos Vol. 1, No. 4, pp. 81-90), hereby incorporated by reference in its entirety, may be applied to determine an optimal linear transformation between the spectral responsivities and the CIE x, y, z color matching functions.

[0056] According to another embodiment of the invention, a predetermined model of three filter-sensor combinations may be used comprising a set of adequate parameters. The model can be designed to be able to sufficiently accurately predict the spectral characteristics of corresponding real filter-sensor combinations in accordance with variations of the model parameters over predetermined wavelength ranges. The model parameters can be used to describe certain properties of the real filter-sensor combinations that can be controlled, either via design, or through operating conditions such as material or geometrical parameters of the filters or the sensors, for example. A number of different regression and optimization techniques can be applied to determine a certain transformation matrix, or, in general, certain parameters of a predetermined transformation function, along with certain values for the parameters of the filter- sensor combinations.

[0057] The regression or optimization can minimize deviations between the accurate tristimulus values and those that can be inferred by using the model. The model can additionally provide corresponding required values for the parameters of the filter-sensor combination models. Subsequently, real filter-sensor combinations with spectral responsivities that are sufficiently accurately modeled by the corresponding filter-sensor combination models can be used in embodiments of the present invention.

[0058] Alternatively, according to one embodiment, a detector may include a sensor, a filter, and a diffuser. The sensor-filter combination may operate substantially as described above, and the diffuser may reduce the effect on the detected signal of the angle of incidence of the light falling on the detector. The diffuser may be any suitable type of diffuser, and may take any suitable positioning relative to the filter and/or sensor.

Sensors

[0059] As mentioned, the sensors employed in a detector according to various aspects of the invention may be any suitable type of sensors. For example, the sensors 510, 520 and 530 in the non-limiting example of FIG. 5 may be narrowband or broadband optical sensors. The sensors 510, 520 and 530 can include photoresistors, photovoltaic elements, photodiodes, photomultipliers, phototransistors, charge-coupled devices or CMOS detectors, for example. Also, as mentioned, it is possible to design photosensors with spectral sensitivities that are proximate or substantially equal to certain desired weighting functions even without additionally optically filtering light with optical filters.

[0060] According to some aspects of the invention, each sensor is required to provide an adequate signal that is integral over a predetermined wavelength range in response to sensed light. Other types of sensors that provide spectrally resolved sensor signals may be used, but are optional.

Filters

[0061] As mentioned, according to some embodiments of the invention, a detector for use in a colorimeter apparatus comprises both a sensor and an associated filter. The spectral filter characteristics (transmissivity or reflectivity) provided by each filter in combination with the spectral sensitivity provided by an associated sensor, provide an overall spectral responsivity for the filter-sensor combination that may adequately and accurately match the desired weighting function, or, in other words, the desired color matching function over the desired range of wavelengths.

[0062] Optical filters for purposes of the present invention are devices which selectively transmit or reflect light with different strengths at different wavelengths and so can affect the spectral composition of the transmitted or reflected light via the spectral filter characteristics. Optical filters can be classified into a number of different types including absorptive, reflective, or interference optical filters, for example. Suitable filters for use in an apparatus according to an aspect of the invention, such as that shown in FIG. 5, can be selected by choosing a filter having spectral characteristics approximately matching those of the desired weighting function. For example, according to one embodiment, the filters implemented as part of a colorimeter apparatus are selected to have spectral characteristics matching the Stockman Cone Fundamentals illustrated in FIG. 3. Such filters are available from commercial vendors, for example Rosco Laboratories, Inc. of Stamford, CT.

[0063] Absorptive filters can be made from glass to which dyes of various inorganic or organic compounds may have been added. The dyes as well as the glass can absorb light of different wavelengths at different rates while correspondingly transmitting light of other wavelengths. Dyes can also be added to other transparent materials, for example, polycarbonate or acrylic, to produce gel filters, which are typically lighter and may be cheaper than glass-based filters.

[0064] As is known in the art, the spectral bandwidth of absorptive optical filters can vary with the thickness of the filter in accordance with Beer's law which can be defined as follows:

¹M) _ _l0-aic _m

Φ^{) ' ( )} where I₀ {λ) is the incident light spectral intensity at wavelength λ, I_t{λ) is the transmitted light spectral intensity, a is the absorption coefficient of the filter material, / is the filter thickness, and c is the optical concentration of the absorbing dye. Changing the thickness of the filter or the optical concentration of the absorbing dye will modify the transmissivity of the filter and can consequently be used to achieve a desired spectral responsivity of a filter-sensor combination and so enable a better approximation of the desired CIE color matching functions.

[0065] Reflective optical filters, sometimes also referred to as dichroic filters, can be made by coating, for example, a glass substrate with a suitable optical coating. Reflective filters can reflect a portion of the light while transmitting the remainder. In accordance with the present invention, either light which is transmitted by an adequate filter or reflected by an adequate filter may be used in combination with suitable sensors. Reflective optical filters may require careful control of the incidence angle of the to-be-filtered light relative to the filter surface as well as consideration of polarization and dichroism of the reflected or transmitted light. Interference filters may utilize more complex geometries and sequences of coatings and may also be used in embodiments according to the present invention.

[0066] According to some embodiments, the filters (e.g., filters 515, 525, and 535 in FIG. 5) may include dyed glass or plastic color filters. According to other embodiments, the filters may be interference filters, such as thin film interference filters. For example, as mentioned, according to one embodiment a colorimeter apparatus includes one or more detectors for detecting quantities corresponding to the Stockman Cone Fundamentals. The Stockman Cone Fundamentals can each be approximated by a sum of four Gaussian functions:

Stockman's. Cone Fiaxlanientals

0.0 1014 exp

1 _/A -- 569^ 1 / λ - 570.4 *

1.312 «φ 2 I 30,91 .1 + 2.26 ! expj

2 I. 37, 14 >

-O.08376 exp

. f A - 535.3 * Ir I /h. - 559.7\ ²

+ 0.4944 expj - ^ ( ^■ 37.5 4- 0.645 <?-φ

2 \ 40.7 I

1 A - 433.3^1 /K 456.5^-^'

S = 0,8884 exp 10.65 4- t.09 i. exp 2 K

^' 3 ,^• λ - 648.8 \ ^2~

0.5747 iiKp ^~ 2 I 2S.0B ) + 5.74 X 10^"r>exp 2 \ 22.01 /

[0067] The Stockman cone functions may also be approximated with one, two, or three Gaussian functions that are appropriately weighted, as determined by the least square minimization method disclosed by Hu et al, which is incorporated herein by reference in its entirety (Hu et al, "Algebraic Expressions of the CIE Standard Observers and Stockman Cone Fundamentals," (Leukos Vol. 1, No. 4, pp. 81-90)).

[0068] Thin film interference filters may exhibit approximately Gaussian spectral absorption characteristics, thus making them suitable choices for filters in colorimeters according to aspects of the invention. In other words, the Stockman cone functions may be realized with appropriately designed thin film interference filters. FIG. 6 illustrates the spectral absorption characteristics for a thin film interference filter, showing wavelength (nm) on the x-axis and optical density on the y-axis. The spectral absorption characteristics are shown for various cavities, i.e., pairs of layers of the thin film interference filter.

Diffusers

[0069] According to some embodiments, a detector may include a diffuser in combination with a filter. For example, the bandpass characteristics of thin film interference filters are dependent on the angle of incidence of incoming radiation. Thus, in the embodiments in which a thin film interference filter is included with a detector, or in any other suitable embodiment, a diffuser may also be included to minimize or eliminate the effect of the incidence angle on the operation of the thin film interference filter. FIG. 7 illustrates an example of the detector 502 according to one embodiment.

[0070] As shown, the detector 502 comprises the sensor 510, the filter 515, which in the non- limiting example of FIG. 7 is an interference filter, and a diffuser 702. Incident radiation 500 impinges on the diffuser 702 prior to impacting the interference filter 515. Thus, the diffuser may reduce any effect of the incidence angle of the radiation 500 on the function of the interference filter 515.

[0071] The diffuser 702 may be any suitable type of diffuser. For example, the diffuser 702 may be a bulk diffuser, and may be formed of ground glass, acrylic, holographic material, or any other suitable material.

Processing system

[0072] As mentioned, according to an aspect of the invention a colorimeter apparatus for determining the X, Y, and Z tristimulus values includes a processor, such as the processing system 540 shown in FIG. 5. The processor may be a digital or analog processor, and may comprise a programmable central processing unit (CPU), for example, a microcontroller, and optional peripheral input/output devices, for example, analog-to-digital converters. Peripheral input/output devices may be used for monitoring parameters from the filter-sensor combinations, for example. The input/output devices may also be used to communicate signals or instructions to, and thereby control, the filter-sensor combinations, for example. The processing system can optionally include memory such as one or more storage media. The memory can be volatile and non-volatile computer memory such as RAM, PROM, EPROM, and EEPROM, floppy disks, compact disks, optical disks, magnetic tape, or the like, wherein data and control programs for example software, microcode, or firmware, for monitoring or controlling the devices coupled to the digital processing system can be stored. The digital processing system can be interfaced with a user interface for configuration or to receive user-specified commands. The user-interface can comprise a keyboard, for example. Furthermore, the digital processing system can be capable of being operatively coupled with other systems.

[0073] Thus, various methods and apparatus have been described herein for tristimulus colorimetry. These methods and apparatus may be useful in fields such as illumination, printing, scanning and photography, for example. Specifically in the field of illumination it can be used to determine chromaticity and optionally the luminous flux of light emitted by a combination of light-emitting elements. For example, a colorimeter, such as that shown in FIG. 5, may be placed next to, within, or formed as part of, a lighting fixture having one or more light-emitting elements. The light-emitting elements may be used to provide light for space illumination, for example. Implementations of the present invention may be particularly useful, for example, when the chromaticity of the light emitted by the light-emitting elements may need to be carefully maintained at a desired level. Maintaining light at desired perceptible color characteristics can be achieved by controlling the operating conditions of a number of possibly multi-color light-emitting elements. The operating conditions of the light-emitting elements may be controlled using a number of different techniques including feed forward as well as feedback control schemes. The method and apparatus for tristimulus colorimetry according to aspects of the invention can be favorably employed in chromaticity feedback control systems, for example.

[0074] While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure.

[0075] All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms.

[0076] The indefinite articles "a" and "an," as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean "at least one."

[0077] The phrase "and/or," as used herein in the specification and in the claims, should be understood to mean "either or both" of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with "and/or" should be construed in the same fashion, i.e., "one or more" of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the "and/or" clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to "A and/or B", when used in conjunction with open-ended language such as "comprising" can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

[0078] As used herein in the specification and in the claims, "or" should be understood to have the same meaning as "and/or" as defined above. For example, when separating items in a list, "or" or "and/or" shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as "only one of or "exactly one of," or, when used in the claims, "consisting of," will refer to the inclusion of exactly one element of a number or list of elements. In general, the term "or" as used herein shall only be interpreted as indicating exclusive alternatives (i.e. "one or the other but not both") when preceded by terms of exclusivity, such as "either," "one of," "only one of," or "exactly one of." "Consisting essentially of," when used in the claims, shall have its ordinary meaning as used in the field of patent law.

[0079] As used herein in the specification and in the claims, the phrase "at least one," in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase "at least one" refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B," or, equivalently "at least one of A and/or B") can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

[0080] It should also be understood that, unless clearly indicated to the contrary, in any methods claimed herein that include more than one step or act, the order of the steps or acts of the method is not necessarily limited to the order in which the steps or acts of the method are recited.

[0081] In the claims, as well as in the specification above, all transitional phrases such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," "composed of," and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases "consisting of and "consisting essentially of shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

WE CLAIM:

1. A method for determining X,Y, and Z tristimulus values, comprising: detecting at least three quantities of incident radiation, each quantity of incident radiation corresponding to a different Stockman Cone Fundamental; producing at least three output signals (512a, 512b, 512c), each output signal of the at least three output signals corresponding to one of the at least three quantities; and processing the at least three output signals to produce the X, Y, and Z tristimulus values specifying a color of the incident radiation.

2. The method of claim 1, wherein detecting at least three quantities of incident radiation comprises receiving incident radiation at a detection apparatus comprising at least three detectors, each detector of the at least three detectors configured to detect one of the at least three quantities.

3. The method of claim 2, wherein the at least three detectors includes only three detectors.

4. The method of claim 1 , wherein processing the at least three output signals to produce the tristimulus values comprises performing at least one matrix operation on the at least three output signals to produce the tristimulus values.

5. The method of claim 4, wherein the at least one matrix operation depends at least partially upon a transformation between xyz color space and rgb color space.

6. A method for determining tristimulus values, comprising: detecting, with a first detector (502) having a first spectral responsivity, a first quantity of incident radiation and producing a first output signal (512a) indicative of the first quantity; detecting, with a second detector (504) having a second spectral responsivity, a second quantity of the incident radiation and producing a second output signal (512b) indicative of the second quantity; detecting, with a third detector (506) having a third spectral responsivity, a third quantity of the incident radiation and producing a third output signal (512c) indicative of the third quantity; and processing the first, second, and third output signals using at least one matrix operation to produce three tristimulus values indicative of a color of the incident radiation; wherein each of the first, second, and third spectral responsivities has a same sign, positive or negative, and only one peak over a first range of wavelengths from approximately 380nm to 780nm.

7. The method of claim 6, wherein the first detector comprises a first filter having the first spectral responsivity, the second detector comprises a second filter having the second spectral responsivity, and the third detector comprises a third filter having the third spectral responsivity.

8. The method of claim 6, wherein the at least one matrix operation represents a linear transformation between the first, second, and third output signals and the three tristimulus values.

9. The method of claim 6, wherein processing the first, second, and third output signals comprises performing a non-linear computation with the first, second, and third output signals.

10. The method of claim 6, further comprising diffusing and filtering the incident radiation to produce the first quantity.

11. An apparatus for determining tristimulus values of a color, comprising: a detection system configured to receive incident radiation comprising colored light and to produce at least one output signal (512a, 512b, 512c) indicative of at least three quantities of the incident radiation, the detection system comprising: a first detector (502) having a first spectral responsivity; a second detector (504) having a second spectral responsivity; and a third detector (506) having a third spectral responsivity; wherein each of the first, second, and third spectral responsivities has a same sign, positive or negative, and only one peak over a first range of wavelengths from approximately 380nm to 780nm; and a processing system (540) having an input coupled to receive the at least one output signal (512a, 512b, 512c), and being configured to process the at least output signal and provide at least one of an X, Y, and Z tristimulus value.

12. The apparatus of claim 11, wherein the first detector comprises a sensor and a filter configured to filter the incident radiation before the incident radiation is received by the sensor, the filter characterized by an approximately Gaussian spectral responsivity over the first range of wavelengths.

13. The apparatus of claim 12, wherein the filter is a thin film interference filter.

14. The apparatus of claim 13, wherein the first detector further comprises a diffuser configured to receive the incident radiation, diffuse the incident radiation, and pass the incident radiation to the thin film interference filter.

15. The apparatus of claim 14, wherein the diffuser is formed of ground glass.