Abstract: The color difference and/or chromaticness difference between target objects and background objects can be enhanced. Different colors with different color attributes mean different objects. In some cases, different chromaticness, such as saturation and hue, mean different two- or three-band ratio. The light from the surface of objects is filtered by optical system integrated with two- and three-band mixing method so that only the light in the wavelength range of the pass bands can reach optical sensors for opto-electronic sensing devices. With this kind of opto-electronic sensing devices, two- and/or three-band ratio criteria widely used in remote sensing and machine vision applications can be calculated in terms of color attributes. Multi-spectral imaging system can be replaced by this kind of sensing devices. This kind of two- or three-band mixing illumination can be used to identify, classify, and detect objects for human visual application, remote sensing, and machine vision application.

Abstract: A laser irradiation process includes: scanning a substrate with laser having a predetermined lasing frequency at different irradiation intensities to form a plurality of first irradiation areas corresponding to the irradiation intensities; illuminating the first irradiation areas to reflected light receive from the fist irradiation areas; determining microcrystallization intensity based on the received reflected light; and determining irradiation intensity based on the thus determined microcrystallization intensity. The laser irradiation process uses the irradiation intensity for irradiating a polycrystalline film in a product semiconductor device.

Abstract: A fault detection and classification method is disclosed that uses raw back-focal-plane image data of radiation from a substrate surface, detected by a scatterometer detector, to determine a variation in the raw data and correlate the variation in the raw data with a possible fault in a lithographic apparatus or a process that patterned the substrate surface. The correlation is carried out by comparing the variation in the raw data with known metrology data. Once a fault has been determined, a user may be notified of the fault.

Abstract: A method of producing an image of an object residing inside a transparent container of a first color includes: illuminating the container and the object with light of a second color, the second color being substantially the inverse of the first color; and producing an image of the object through the container. An image produced by this method can exhibit substantially the same color as the object itself, even when the image is taken through a colored transparent wall.

Abstract: A fabric whiteness guide comprising at least one visual scale of whiteness.

Abstract: A method of producing a finish for a paper substrate, wherein the finish provides the paper substrate with a color that matches the color of a target object. In accordance with the method, calculations are performed to determine the quantities of at least one group of colorants required to produce a semitransparent wood stain from a vehicle, wherein when the semitransparent wood stain is applied to the paper substrate, the paper substrate will have a color that matches the target object. The calculations are performed using reflectance measurements of the target object obtained using a spectrophotometer and previously obtained spectral data of the colorants as applied to a paper substrate. The colorants used to form the transparent or semitransparent wood stain do not include a white colorant or black-and-white masstone.

Abstract: A color measurement system includes a hand held color measurement instrument, which may be provided with a wireless interface to a computer. The color measurement system includes a scanning guide for holding the hand held color measurement instrument in proper alignment with a color target. The scanning guide includes a calibration reference to allow convenient calibration of the hand-held color measurement instrument. The hand-held color instrument includes an illumination ring to provide visual feedback to the user. The color of the illumination ring changes in order to display a color similar to that being read by the hand-held color measurement instrument. Color management profiling of the hand held color measurement instrument illumination ring improves the color rendition capability of the illumination ring.

Abstract: A miniaturized spectrometer/spectrophotometer system and methods are disclosed. A probe tip including one or more light sources and a plurality of light receivers is provided. A first spectrometer system receives light from a first set of the plurality of light receivers. A second spectrometer system receives light from a second set of the plurality of light receivers. A processor, wherein the processor receives data generated by the first spectrometer system and the second spectrometer system, wherein an optical measurement of a sample under test is produced based on the data generated by the first and second spectrometer systems. Improved shade matching/prediction results are obtained through the use of volumes/regions, preferably polygons, around shades in a shade system.

Abstract: Method for approximating the spectrum of a plurality of color samples, the method including the procedures of measuring the color of a reference color sample in a color space, determining a reference sample estimated spectrum from the measured color, measuring the actual spectrum of the reference color sample, determining a spectral delta from the difference between the reference sample estimated spectrum and the actual spectrum, measuring the color of each of the color samples, for each of the color samples, determining a sample estimated spectrum from the measured color, and for each of the color samples, determining a sample approximated spectrum by adding the spectral delta to the respective sample estimated spectrum.

Abstract: Based on area and color analyses, a cost-effective bi-directional people counter dedicated to the pedestrian flow passing through a gate or a door is proposed. Firstly, the passing people are roughly counted with the area of people projected on an image captured by a zenithal video camera. The moving direction of the pedestrian can be recognized by tracking each people-pattern with an analysis of its HSI histogram. To improve the accuracy of counting, the color vector extracted from the quantized histograms of intensity or hue is introduced to refine the early counting. Besides, the inherent problems of both people touching together and merge/split phenomenon can be overcome.

Abstract: Disclosed herein are systems and methods for measuring color and contrast in specular reflective devices such as interferometric modulators. To make color and contrast determinations, light reflected from a specular reflective device may be measured in-line with illumination of the device. The measurements may include measuring the spectra of light reflected from the device being tested as well as from specular bright and dark standards. The spectra may be used to determine a reflectance spectrum and color parameters for the specular reflective device.

Abstract: The invention relates to a computer readable medium comprising one or more programs for carrying out a method for determining a patient's tooth shade. The method generally includes the steps of generating an image of a patient's tooth wherein the image includes color information representative of the patient's tooth shade; storing color information representative of a plurality of tooth shades; and comparing the color information of the image with the stored tooth shade color information to identify one or more tooth shades having a combined color that corresponds to the patient's tooth shade, and the color information that is obtained may be displayed to identify one or more tooth shades having a combined color corresponding to the determined tooth color.

Abstract: Disclosed is an apparatus and method for a compact, rugged, and inexpensive spectrometer that will make possible a range of new applications for optical spectroscopy including point-of-care medical devices, personal monitors, and ubiquitous environmental sensing. Embodiments of the disclosure include silicon photodetectors where incident light passes through a layer of an inexpensive, absorbing thin film. In one embodiment, one or more photodetectors may be used where a series of absorbing thin film layers are passed over the photodetectors. In another embodiment, an absorbing thin film layer is placed over one or more photodetectors where the absorptivity of the thin film layer is different for each photodetector.

Abstract: Systems and method provide compensation for temperature induced peak wavelength shift of LEDs is color parameter measuring systems that use a model to reconstruct target color parameter values from the reflectance values measured when the target is illuminated by LEDs. Several models may be constructed, with each model being trained at a unique temperature, resulting in a set of models that span the temperature range of interest. In real-time, the LED based color parameter measuring system measures the temperature and interpolates between the models to estimate the appropriate model to use at the temperature of interest. The estimated model is then used to perform the color parameter value estimation.

Abstract: A liquid testing system includes a first well for receiving a sample to be tested, a first light, having a first wavelength, for illuminating the first well, and a second light, having a second wavelength, for illuminating the first well. The liquid testing system further includes a light control, coupled to the first light and the second light, for selecting one of the first light or the second light to illuminate the first well, a light detector receiving light passing into the first well, and a processor, coupled to the light control and the light detector, for determining a light characteristic of the sample over time.

Abstract: A process for color matching a metallic paint by taking a color measurement reading at a single angle using a regular spectrophotometer or colorimeter is provided. The preferred type of metallic pigment to be utilized in preparing the matching color can be selected by microscopic evaluation of the metallic pigment in the target metallic paint to identify its size, shape and probable composition.

Abstract: A method of producing a finish for a selected wood substrate, wherein the finish provides the selected wood substrate with a color that matches the color of a target object. In accordance with the method, calculations are performed to determine the quantities of at least one group of colorants required to produce a semitransparent wood stain from a vehicle, wherein when the semitransparent wood stain is applied to the selected wood substrate, the selected wood substrate will have a color that matches the target object. The calculations are performed using reflectance measurements of the target object obtained using a spectrophotometer and previously obtained spectral data of the colorants as applied to at least one type of wood. The colorants used to form the semitransparent wood stain do not include a white colorant.

Abstract: An instrument and related process for measuring color, shade, gloss, shape and/or translucence of a tooth. First, the instrument uses searchlight illumination to illuminate a tooth with constant irradiance. Second, the instrument uses calorimetric imaging to collect time-separated frames of different wavelengths of light reflected from a tooth and to combine those frames into a color image. Third, the instrument includes a sanitary shield to establish a reference color and a predetermined distance to a target tooth. Fourth, the instrument provides line-of-sight viewing so an operator may simultaneously view a display of the image on the instrument and the object being measured. Fifth, the instrument is impervious to pollutants because it incorporates a sealed measurement window. Sixth, optical measurements of a tooth taken by a dentist are compared to optical measurements of a prosthetic restoration for that tooth to confirm satisfactory matching of optical characteristics of the tooth and restoration.

Abstract: A method of verifying the color and tinting strength of a manufactured batch of a semi-transparent wood stain. In accordance with the method, a standard batch of the wood stain is formed and then mixed with a specified amount of a white colorant to form a standard measurement batch. A test sample of the manufactured batch is obtained and is also mixed with a specified amount of the white colorant to form a test measurement sample. Layers of the standard measurement batch and the test measurement sample are formed on the substrates and complete hide obtained. Reflectance measurements of the layers are made using a spectrophotometer. The reflectance measurements are used to determine if the color and the tinting strength of the manufactured batch is within an acceptable deviation range of the color and tinting strength of the standard batch.

Abstract: The invention relates to a computer readable medium comprising one or more programs for carrying out a method for determining a patient's tooth shade. The method generally includes the steps of generating an image of a patient's tooth wherein the image includes color information representative of the patient's tooth shade; storing color information representative of a plurality of tooth shades; and comparing the color information of the image with the stored tooth shade color information to identify one or more tooth shades having a combined color that corresponds to the patient's tooth shade, and the color information that is obtained may be displayed to identify one or more tooth shades having a combined color corresponding to the determined tooth color.

Abstract: A wavemeter for determining a wavelength of an incoming optical beam. The wavemeter comprises a coarse-measuring unit determining in a first wavelength range a first wavelength value as representing the wavelength of the incoming optical beam, and a fine-measuring unit providing a wavelength determination for the incoming optical beam that is ambiguous within the first wavelength range but unambiguous in each of a plurality of unambiguous wavelength ranges, so that a plurality of different wavelength values correspond to a measuring value as measured by the fine-measuring unit for the incoming optical beam. The wavemeter further comprises an evaluation unit for determining a second wavelength range as the one of the plurality of unambiguous wavelength ranges that covers the first wavelength value, and for determining a second wavelength value as the one of the plurality of different wavelength values that corresponds to the measuring value in the second wavelength range.

Abstract: The surface contribution to appearance of an object is characterized using a plurality of viewing and illumination angles. The color determining and surface contribution are determined to aid in the predicting of the appearance of an object as well as matching an object to another object.

Abstract: A computer color matching method of paint for measuring a proper formulation of colorants for obtaining a target color or color and luster, or a proper formulation of colorants and luster color materials, directly in a liquid state of paint, without preparing painted panels from adjusted paint, and calculating the adjusted blending ratio easily and accurately, and a paint manufacturing method by using this method.

Abstract: A neutral paint colorant has a composition comprising approximately 7.0% Color Index Pigment Yellow 42, 2.4% Color Index Pigment Red 101, and 4.0% Color Index Pigment Black 7. A pre-blended mixture of the neutral colorant and a paint base can be blended with a first paint to form a second paint having substantially the same hue and value (lightness) as the first paint, but a lower chroma (brightness).

Abstract: The invention relates to a method for restoration of a patient's tooth. An electronic image of a patient's tooth or tooth preparation is generated in a dentist's office by the dentist. The image includes color information of the tooth preparation or of the patient's tooth shade. The electronic image is forwarded to a dental laboratory by direct computer link or e-mail. A technician at the laboratory evaluates the image and suggests restorative options to the dentist, including whether further tooth preparation is required. The technician also selects the appropriate restoration tooth shade(s) so that the dental prosthesis matches the color of the patient's tooth. The laboratory then manufactures the prosthesis utilizing a plurality of porcelain coatings. If desired, an image of the prosthesis can be generated in the laboratory and forwarded to the dentist for verification of color and/or fit prior to finalizing manufacture of the prosthesis.

Abstract: A method for determining a patient's tooth shade, by generating an electronic image of a patient's tooth wherein the image includes color information representative of the patient's tooth shade; storing color information representative of a plurality of tooth shades; and comparing the color information of the image with the stored tooth shade color information to identify one or more tooth shades having a combined color that corresponds to the patient's tooth shade. the image of the patient's tooth and the stored tooth shade color information are electronically displayed in color to enable a viewer to comparatively determine the color of the patient's tooth shade.

Abstract: A fiber optic system includes an optical fiber carrying an optical signal having a wavelength peak, an optical detector coupled to the optical fiber for detecting a current optical level (e.g. a photon power level), and a tunable optical filter coupled to the optical fiber upstream from the optical detector. The system further includes a controller connected to the optical detector and the tunable optical filter, for stepping the tunable optical filter over a sequence of wavelengths while analyzing respective optical levels, and for reversing the stepping direction of the tunable optical filter, based upon the current optical level being less than a prior optical level, to locate the wavelength peak of the at least one optical signal. A sample rate is reduced when the wavelength peak of the optical signal is located, to thereby reduce a power consumption of the controller.

Abstract: The invention provides methods and apparatus for correcting spectral measurements, such as are obtained by a spectrophotometer for measuring color. A single matrix is used that operates on a raw measurement vector (spectrum) to obtain a corrected spectrum. The matrix may embody a transform that minimizes the difference between the corrected spectra and a set of reference spectra. The difference may be characterized by a set of basis function weighting vectors which are then used to build the correction matrix. Correction of high resolution spectra (very long measurement vectors) is thereby allowed, without the large number of measurements that would normally be required. The reference spectra can be calibration data, or measurements made by another instrument which is desired to be simulated.

Abstract: A method of obtaining a range of colors includes the following steps:

Abstract: A multichannel fluorosensor includes an optical module and an electronic module combined in a watertight housing with an underwater connector. The fluorosensor has an integral calibrator for periodical sensitivity validation of the fluorosensor. The optical module has one or several excitation channels and one or several emission channels that use a mutual focusing system. To increase efficiency, the excitation and emission channels each have a micro-collimator made with one or more ball lenses. Each excitation channel has a light emitting diode and an optical filter. Each emission channel has a photodiode with a preamplifier and an optical filter. The electronic module connects directly to the optical module and includes a lock-in amplifier, a power supply and a controller with an A/D converter and a connector. The calibrator provides a response proportional to the excitation intensity, and matches with spectral parameter of fluorescence for the analyzed fluorescent substance.

Abstract: A cassette reader for detecting the status of stained samples is provided. The colorimeter includes one or more high power emitting diodes as the source of illuminating the sample. An elliptical mirror, with a central aperture to permit the light to penetrate on to the sample, directs the scattered light on to its focal point at a detector. The colorimeter includes a microprocessor which compares an output signal for the percent ratio value of the detected values of a sample and a standard sample. The colorimeter housing provides position sensors which allow the identification of the well being examined. Finally, the system is modified to measure cell motility by determining the ratio of motile sperms to total cell concentration.

Abstract: The present invention is directed to a process for addition of amines to carbon-carbon double bonds in a substrate, comprising: reacting an amine with a compound containing at least one carbon-carbon double bond in the presence a transition metal catalyst under reaction conditions effective to form a product having a covalent bond between the amine and a carbon atom of the former carbon-carbon double bond. The transition metal catalyst comprises a Group 8 metal and a ligand containing one or more 2-electron donor atoms. The present invention is also directed to enantioselective reactions of amine compounds with compounds containing carbon-carbon double bonds, and a calorimetric assay to evaluate potential catalysts in these reactions.

Abstract: A method of determining the formulating ratio of metallic or pearlescent pigments to colorants for matching the color of a metallic or pearlescent coating to an target color wherein, the spectral reflectances of a plurality of samples varied in the formulation of colorants and metallic or pearlescent pigments are measured with a goniospectrophotometer and stored in a computer memory beforehand and, in performing a CCM using the stored data, reproduction spectral reflectances are calculated by reflecting the changes in spectral reflectance due to changes in the amount of the metallic or pearlescent pigments.

Abstract: The invention relates to a method for determining a patient's tooth shade, by generating an electronic image of a patient's tooth wherein the image includes color information representative of the patient's tooth shade; electronically storing color information representative of a plurality of tooth shades; and comparing the color information of the image with the stored tooth shade color information to identify one or more tooth shades having a combined color that corresponds to the patient's tooth shade.

Abstract: The present invention suggests an apparatus for simulating the ambient color and translucence conditions present in the oral cavity of a patient for the purpose of checking the color stimulus specification of dentures prior to their implanting into the oral cavity of a patient. The apparatus comprises an artificial jaw portion including a dimensionally stable, elastic artificial gum body portion simulating at least the vestibulary gum of a patient in which the teeth are inserted. The artificial gum body portion is made of a translucent material. The teeth can be individually replaced by dentures. The color stimulus specification of a denture inserted into the apparatus is checked by means of a color stimulus specification measuring apparatus and compared to the values obtained from a measurement taken in the oral cavity of a patient.

Abstract: The invention relates to a method for determining a patient's tooth shade, by generating an electronic image of a patient's tooth wherein the image includes color information representative of the patient's tooth shade; electronically storing color information representative of a plurality of tooth shades; and comparing the color information of the image with the stored tooth shade color information to identify one or more tooth shades having a combined color that corresponds to the patient's tooth shade.

Abstract: In a shade determination apparatus for teeth and dental restorations, a set of reference templates for comparing to a patient's tooth is provided, whereby based on the coloration of the reference template the shade of a tooth or of a restoration to be employed can be determined. The reference templates are produced in a layer arrangement, taking into consideration layer thickness and/or material selection, that corresponds to the tooth or the dental restoration to be employed. A storage apparatus stores the coloration of the reference templates, and the layering of the tooth or of the dental restoration can be matched and determined based on partial images from an image of the patient's tooth.

Abstract: A produce data collector with minimal spectral distortion. The produce data collector includes a light pipe having entrance and exit ends through which a portion of light reflected from a produce item travels, and a spectrometer adjacent the exit end of the light pipe which splits the portion of light into a plurality of wavelengths and which produces signals associated with the wavelengths for identifying the produce item.

Abstract: The invention relates to a method and apparatus for determining the color and/or composition of a material. A sample of the material is illuminated with at least three separate illumination bands singly or in combination, said illumination bands collectively substantially spanning at least the visible range. The light reflected or transmitted by the sample is measured with at least four light detector elements responsive to light in wavelength bands which substantially span the visible range when the sample is illuminated. The width of the illumination bands differs in such a manner that the illumination bands are narrowest near the expected fluorescence absorption bands.

Abstract: A digital camera connects to a tooth shade analyzer subsystem, e.g., a digital video processor, and a color display monitor for the electronic determination of the color of patient's teeth. Preliminarily, the camera captures series of digital color images of tooth shades corresponding to reference shade guides, and electronically compares the reference shades to an image of the patient's tooth. In a preferred embodiment the comparison is done over a set of pseudo-pixels, each corresponding to a group of pixels in an high-resolution camera. Once a match is found, it is communicated to a user of the system. In a specific embodiment the camera is equipped with a sleeve and illumination subsystems that help reduce the variations in the color of digital images due to external factors.

Abstract: A digital camera connects to a tooth shade analyzer subsystem, e.g., a digital video processor, and a color display monitor for the electronic determination of the color of patient's teeth. Preliminarily, the camera captures series of digital color images of tooth shades corresponding to reference shade guides, and electronically compares the reference shades to an image of the patient's tooth. In a preferred embodiment the comparison is done over a set of pseudo-pixels, each corresponding to a group of pixels in an high-resolution camera. Once a match is found, it is communicated to a user of the system. In a specific embodiment the camera is equipped with a sleeve and illumination subsystems that help reduce the variations in the color of digital images due to external factors.

Abstract: A reference beam detector according to the invention can be used to accurately and efficiently perform a level shifting operation by means of a reference beam and effectively eliminate the use of markers and other devices that are structurally simple but entail cumbersome operations and also the use of a level shifter. The beam detector comprises a detector main body having a beam receiving section for detecting an emitted laser beam, a display section for displaying the position of receiving the emitted beam relative to the reference position of the beam receiving section and a slidable index section having an index for indicating the position relative to the reference position.

Abstract: A laser irradiation system according to the present invention comprises a laser light emitter for emitting a laser beam, a rotator for irradiating the laser beam emitted from said laser light emitter by rotary irradiation and for forming a laser plane, a tilt setting unit for tilting said rotator and said laser plane, a photodetection unit integrated with said tilt setting unit for receiving a reflection laser beam reflected from a target which reflects the laser beam from said rotator as a reflection laser beam, wherein said photodetection unit comprises a photodetection element being long in a scanning direction of the laser beam.

Abstract: A tooth shade analyzing system and method of use. The system includes a digital camera which connects to a shade analyzer subsystem, e.g., a digital video processor, and a color display monitor. The camera captures a digital color image of the patient's tooth and the subsystem compares that image to a stored plurality of tooth shades. Each tooth shade is represented in a block of data, including color image data, a tooth shade digital word, and a manufacturer type. The patient's tooth image includes an RGB chromaticity representation that is scanned and compared with the several tooth shades stored in memory, and a match is determined and communicated to a user of the system. The method of use includes the specification of fractional tooth shades, if needed, corresponding to a plurality of porcelain films for manufacturing a reconstructed tooth.

Abstract: An improved photocell configuration is provided to create a more accurate laser receiver that not only is very accurate and flexible in its operational capabilities, but also can greatly reduce the effect of rotational offset due to shading of the photocell. In one embodiment, a very long photocell is provided in which multiple split-cells are used to present a geometry that will tend to negate some of the effects of shading. The shading effects are minimized by having a different active photocell area along each vertical edge of the photocell. In another embodiment, a "segmented" photocell is used, in which the split-cell design of a long photocell is also divided into vertical segments. These segments can be re-configured so that alternating segments comprise a mirror image about the longitudinal of the long photocell. Such an arrangement tends to reduce the effect of rotational offset due to shading to an extremely small percentage of error.

Abstract: A visual control strip for imageable media such as a printing plate, a photographic film or a printable substrate is described wherein the visual control strip is to be applied to the imageable medium. The control strip includes a plurality of first control fields having differing grey tone values which are relatively insensitive to the processing variables which influence the size of the spots or dots produced on the imaged medium. The control strip also includes at least one second control field which is relatively sensitive to these process variables. The second control field is located immediately adjacent to the first insensitive control fields for ease of comparison. The second sensitive control field has a target grey tone value which may typically be 25%, 50% or 75%. To improve assessment of exposure parameters, the insensitive fields are completely surrounded by a sensitive field or vice versa.

Abstract: A laser survey instrument, which comprises at least a main unit for emitting a laser beam and an object reflector for reflecting the laser beam from the main unit toward the main unit, whereby said main unit comprises an emitter for emitting the laser beam, a rotating unit for rotating and scanning the laser beam, a tilting mechanism for tilting the laser beam at an arbitrary angle at least in one direction with respect to a horizontal plane, a rotating angle detector interlocked with the rotating unit and for detecting irradiating direction of the laser beam, a reflection light detector for detecting reflection light from the object reflector, and an alignment display unit for detecting a deviation of direction with respect to the object reflector and a deviation of tilt angle based on a signal from the reflection light detector and for obtaining information on the deviation of direction or the tilt angle, the laser beam emitted from the main unit is irradiated to scan, the center of the object reflector is

Abstract: An execution height setting system 100 includes laser device 102 for setting a horizontal reference plane by rotatably radiating a laser beam and a execution height display device 104. The execution height display device 104 has a light receiving section 112 for receiving the laser beam, an indexing section 118 for indicating a shift of the sensed laser beam relative to the reference position, and a data display section 108 for displaying the inputted grade or execution height. As the execution height display device 104 receives the laser beam, it senses the distance between the laser device 102 and the execution height display device 104 and then computes the desired execution height based on the set grade value. The computation result for the execution height is displayed on the execution height display portion 108c.

Abstract: A desktop color measurement system that includes an instrument capable of making color measurements. The system includes a host computer and a digital color sensor (DCS) in communication with the host computer. The DCS includes optical elements for making spectral measurements, and control electronics for controlling the optical elements. In a specific embodiment, the DCS is dedicated to the mechanics of acquiring the raw data. The host computer, which may be a personal computer, performs all the calculations needed to convert raw measurement values into spectral data and other color representations such as tristimulus values and density. This also allows the system to function as a calorimeter and a densitometer as well as a spectrophotometer. The DCS control circuitry includes non-volatile writable storage for information obtained during a factory calibration procedure, which information allows the user to recalibrate the DCS in the field.

Abstract: A method and apparatus for controlling the color of an article such as a paper web includes performing a comparison between target and measured reflectance values in numerous wavelength bands spanning the visible spectrum. The comparison quantifies correspondingly numerous errors that are modified by a non-linear operation, such as squaring, and then added together. The resulting sum is minimized by individually adjusting the application of a number of colorants to the article. The number of wavelength bands is greater than the number of colorants. This avoids metameric effects which are common in conventional systems that rely on three color space coordinates such as Hunter Laboratories L, a, b; C.I.E. L*, a*, b*; chromaticity x, y, z; and tristimulus X, Y, Z. Colorant response simulators enable the effects of changes in application of colorants to be tested while the actual application of colorants to the article is unchanged.