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Color Measurement - Introduction, Historical Perspective, Definitions and Terminology, Components of a Spectrophotometer, Light Source, Detector, Dispersing Element

sample instrument incident specular

DAVID R. WYBLE
Rochester Institute of Technology

Introduction

At the most basic level, the perception of color exists as a three-part system: a light source, an object, and an observer. Color measurement involves the careful determination of the physical properties of all three parts of that system. The psychological nature of color cannot be understated: Because color only exists as a perception, when color is measured, and the observer is replaced by a detector, the perception aspect is lost. Therefore a large amount of effort has gone into the correlation of instrument output—"measured color"—with perceived color.

In general, there are two main applications of color measurement. The first is to correlate measured color with perceived color. This might seem obvious: Suppose a manufacturer desires to make widgets that are all identical in color to the standard widget. To improve consistency and reduce cost, an instrument is used to make quality control judgments instead of a human. The comparison of a standard color to a sample is referred to as color difference.

The second important application is to correlate measured color with some physical property of a material. Often, a material is a mixture of several substances, which contribute to its eventual color. Consider the procedure involved in matching paint to a fabric sample. Yes, the overall goal is to minimize the color difference between the paint and fabric, but to get there, measurements of the paint are used to adjust the quantities of the constituent pigments. This task is often referred to as formulation.

The applications of color difference and formulation rely on similar instrumentation. After exploring some historical background, we will describe the components of a spectropho-tometer, followed by the instrument configurations and the applications.

Historical Perspective

Given that neither of the above two applications of color measurement are particularly new, it is useful to follow the path that developed since the first enabling steps were made early in the 20th century. In the 1920s, as today, the international organization most concerned with color measurement was the Commission Internationale de l’Eclairage (CIE). Today we always use the acronym CIE, but in the 1920s the English title International Commission on Illumination; was used. Older works refer to it as the ICI. In 1924, the CIE established the Standard Photopic Observer. This spectral curve, V (?), can be used to predict the lightness of a material for a typical observer. By creating a detector with a spectral response of V (?), a device can predict lightness instrumentally. The CIE 1931 Standard Observer Functions extended this to full color. The three curves, x¯, y¯, and z¯, when combined with the input stimulus and integrated, generate three signals that relate closely to perceived color. These signals, called tristimulus values, and denoted as X, Y, and Z, form the basis of most popular and useful color spaces and color differences models.

There are two forms of color measurement devices: those that measure spectral reflectance (spectrophotometers) and those that measure only tristimulus values (colorimeters). The technical details of these instruments will be explored below, but the main difference is that spectrophotometers measure a physical property (spectral reflectance) from which tristim-ulus values are calculated. Colorimeters typically pass the light through specially designed filters allowing tristimulus values to be calculated directly from detector output levels. Initially, of course, these devices were entirely analog. In the case of spec-trophotometers, the reflectance was often recorded directly onto paper via a chart recorder. Workers then transcribed the data and computed the multiple and sum for tristimulus values by hand. Later, electrical integration schemes were developed to sum tristimulus values during the reflectance measurement.

Modern systems benefit from several innovations in controls, miniaturization, and computing power to greatly increase the ease of use, improve operator efficiency, and provide more reliable measurements. Measurement times are reduced from five or more minutes for a single measurement to a few seconds or less per measurement.

Definitions and Terminology

Spectrophotometry is the measurement of the reflectance, transmittance, or absorptance of a material as a function of the wavelength of the incident light. More specifically these properties are spectral reflectance, spectral transmittance, and spectral absorptance. Reflectance and transmittance will be fully explored below; absorptance can be calculated from these, and will not be mentioned further. A spectrophotometer is a device that measures the ratio of two quantities, one of which is always an actual or theoretical standard. For spectral reflectance, the ratio is the flux reflected by the sample divided by the flux reflected by a perfect white surface. The perfect white surface, called the perfect reflecting diffuser, is a theoretical construct. Therefore the ratio is accomplished by calibration, not by the use of an actual perfect white surface. For spectral transmittance, the ratio is the flux transmitted by the sample divided by the flux transmitted by a perfectly clear standard. For the wavelengths of interest in color measurement and over the very short path lengths within the instrumentation, air is sufficiently clear for use as a calibration standard.

For these ratio quantities, the range of values is nearly always between zero and one, although exceptions are discussed below. The values are sometimes expressed as a percentage, but the fractional values are more useful for computation. So a very white material reflecting an equal amount of flux as the perfect reflecting diffuser is assigned a reflectance of 1.0.

Spectroradiometry is the measurement of light in narrow bands across the spectrum. Spectroradiometers are devices that make this measurement. Spectroradiometers do not measure ratios, but output an absolute amount of light measures. There-fore, the range of output values is not zero to one, but in theory has no upper bound except as determined by the instrument’s own limitations. The most common quantities measured are luminance (flux emitted by a surface per unit area and solid angle) and illuminance (flux incident on a surface per unit area). There are numerous units for these quantities, but the values are typically expressed as candelas per unit area (cd/m 2 ) and lumens per unit area (lm/m 2 ) for luminance and illuminance, respectively.

In summary, spectrophotometers measure ratio quantities of the properties of materials, and spectroradiometers measure absolute quantities of flux from a light source. Hence, spectrophotometry is used to quantify the reflectance or trans-mittance of paints, filters, papers, etc., and spectroradiometry is used to measure the luminance or illuminance of surfaces such as computer monitors, light booths, or studio lights.

Components of a Spectrophotometer

The various spectrophotometer designs all share a set of common systems that are analogous to the vision system’s perception of color; namely, there will be a light source, an object to be measured, and a detector. Since multiple quantities need to be measured (i.e., the wavelength bands), the dispersing element separates the light into components, and these components are individually measured.

Light Source

The important properties of the light source are stability, spectral content, and brightness. For consistent measurements, the light output should be stable over time. Instruments may have secondary detectors that provide feedback for brightness control, but inexpensive instruments may simply rely on the constant output over time. Good light sources should have sufficient quantity of flux at all the wavelengths of interest. Considering the ratio measurement described above, the denominator of the ratio will be the amount of flux reflecting from the perfect white. If, in certain wavelength regions, this value is low, then the amount reflecting from the sample can only be lower. The ratio of two very small numbers tends to amplify the noise, so a high quantity across the spectrum is ideal.

If an instrument is to be used for measuring fluorescent samples, the spectral content of the light source becomes more important. There must be sufficient content in the areas of excitation for the fluorescent samples of interest.

Detector

In most modern instruments, the detector is in fact a linear array of detectors. The wavelengths of light are dispersed and imaged onto the array. A measurement of the entire spectrum becomes a single sampling of the array, which is typically very fast. The two important aspects of the detector are its dark current output and photometric linearity. Dark current is the small level of output that every detector produces even in the absence of any incident light. The calibration procedure of most spectrophotometers records the dark current once, and assumes it is constant thereafter. For quality measurements, a detector should have low, uniform dark current. The photometric scale of a detector is the relationship between incident light and the detector output. This relationship must be linear for the calibration assumptions to be valid. More details on calibration are below.

Dispersing Element

The dispersing element separates the reflected or transmitted light into its constituent wavelengths. Schematically shown as the familiar prism, these are more typically a diffraction grating. Modern instruments disperse the reflected light and image it onto an array detector to capture the amount of light present at all wavelengths simultaneously. For example, an instrument might use a 1024 element linear CCD array, and measure the wavelength range of 380 to 730 nm. Each element of the CCD array corresponds to a particular wavelength band of reflected light. The quality of the dispersion is evaluated by how efficient the system rejects undesirable wavelengths and to what degree the dispersed light is distributed around the wavelength of interest. A particular wavelength of reflected light, e.g., 450nm, should pass through the dispersing element and be imaged onto the 450-nm region of the detector array. Rejecting undesirable wavelengths means that the reflected 450-nm light is imaged on the appropriate detector element and further, no light of any other wavelength is imaged onto that element. The degree to which the dispersed light is distributed around the desired wavelength is called bandpass. Theoretically, the measurement should be made of monochromatic light at the detector, i.e., the light of precisely one wavelength and no other. In practice a single wavelength of light is insufficiently bright. Therefore detectors are not configured to detect single wavelength, instead narrow sections of the spectrum centered around the wavelength of interest are detected.

Polychromatic versus Monochromatic

Illumination The dispersing element can be placed in two locations in the optical path. Most modern instruments position it after the sample, so the path is light source, sample, dispersion, detector. This configuration is called polychromatic illumination, because the sample is illuminated with the entire spectrum of the light source. Alternatively, the incident light can be dispersed prior to the sample. In this case, called monochromatic illumination, a single narrow band in the spectrum is incident on the sample, and the visible spectrum is scanned, one band at a time. Therefore the detector can only measure one single wavelength band at a time. Since the polychromatic case allows for a single measurement, and is therefore much faster, it is the choice for most modern instruments.

The case can be made for either mono- or polychromatic illumination. For non-fluorescent samples, they should result in identical results; hence the leaning toward polychromatic illumination for the speed with which measurements can be made. For more discussion on illumination, see below under the section Design of Spectrofluorimeters.

Calibration Procedure

Instrument manufacturers typically recommend a calibration procedure daily, at the start of each shift, or more frequently should the operator feel it is necessary. The instructions for calibration should be provided by software either on an attached computer or on the instrument itself. Spectral reflectance calibration first involves the measurement of a light trap (a nearly fully absorbing sample) to determine the dark current of the detector. That measurement is followed by a standard of known reflectance, typically a white tile. From these two measurements and the known data for the standard tile, the software builds an equation used to calculate spectral reflectance of measured samples.

The calibration for transmittance is similar, except that the standard is usually replaced by an open measurement of air. The dark current should still be measured first, and can be accomplished by blocking the beam of light by placing an opaque card in front of the detector.

Measuring Light: Spectroradiometers

A spectroradiometer has some components in common with a spectrophotometer. Because it is designed to measure sources of light, an internal light source is not required. A dispersing element and detector are still needed. Additionally, more specialized input optics are required. The considerations of the dispersing element and detector are the same as those described above. To evaluate the input optics, the primary questions are at what distances the device can focus and what is the angular size of the detector. Spectroradiom-eters are often sold with a variety of lens designs and detector port sizes, so they can be customized to the requirements of the application.

Other Devices

Devices sampling wider spectral bands than 20nm are often called abridged spectrophotometers or colorimeters. A colorimeter has three or four filters that attempt to simulate the color-matching functions, or a linear transform thereof. These devices output tristimulus values, not spectra, and therefore are limited to a fixed illuminant and standard observer combination. This might prove too limiting for many users, but some industries have long settled on the color measurement conditions, and the use of a colorimeter might not be unreasonable. Colorimetry can, of course, be calculated from spectral reflectance or transmittance data, so the use of a spectrophotometer can serve to replace a colorimeter.

Some industries rely on densitometry and densitometers. A densitometer measures optical density. After determining the relationship between a specific colorant (e.g., cyan, magenta, or yellow ink) and the optical density, a densitometer can be used to estimate the amount of that colorant present. The measurement of color mixtures and the measurement of arbitrary colorants will not yield a useful color measurement. Again, a spectrophotometer can be used in place of a densitometer in most situations.

Gloss meters provide information about the surface characteristics of a material. In general, there is no color information, although gloss is an important attribute of color. Like spectrophotometers, these devices shine light on a sample and measure light reflecting off the sample. The geometry of a gloss meter is quite different: The incident and measured light beams are always at equal and opposite angles. That is, gloss meters measure only the specular and near-specular angles of reflected light. The specific designs of spectrophotometers are described below. For now, understand that spectrophotometers generally strive to eliminate the light at the specular angles. Gloss meters come in a variety of configurations, such as 20°, 60°, etc. The number of degrees indicates the angle of the incident and detected light.

Spectrofluorimeters are a special type of spectrophotometer designed to measure fluorescence. To adequately characterize the fluorescence of a sample, the illumination and detection must be monochromatic. In this case, the optical path is light source, dispersion, sample, dispersion, detector. A spectrofluorimeter does not output a single array of spectral reflectance data, but rather an array of data for each incident wavelength. This results in an M × N matrix of data, where there are M incident wavelengths and N detected wavelengths. M is typically larger than N because the incident wavelengths should include the ultraviolet where fluorescence is most often active.

Phenomenology and Design

There are two standardized spectrophotometer configurations: bidirectional and hemispherical. These will be described along with appropriate applications for each. The difference between configuration relates to the methods of illuminating the sample and detecting the reflected light. The CIE notation used to designate a configuration is i:v where i and v are the illuminating and viewing conditions, respectively.

Bidirectional Spectrophotometers

Geometric Definition

The CIE standard bidirectional configurations are 45:0 and 0:45. These are shown schematically below.

The CIE provides very specific guidelines on the definition of bidirectional geometries. For the case of 45:0, the incident light is 45° to the sample normal and the detector is positioned at the sample normal. The illumination can be from a single source at 45° or from any number of sources as long as all are 45° from sample normal. A popular configuration is circumferential illumination with many individual incident beams. To eliminate the need to control several sources, circumferential illumination is often implemented using fiber optics from a single physical source. Circumferential illumination avoids the case of textured samples that might have orientation-specific reflectance. For example, consider a paint sample with parallel brush strokes. A bidirectional device with a single incident beam might measure differently depending on whether the light source is parallel or perpendicular to the strokes. If the sample is simultaneously illuminated from the entire circumference, this issue is largely avoided.

The alternative recommended bidirectional geometry, 0:45, amounts to optical reversal of the 45:0 case. The light source is now a single beam from the sample normal and detectors(s) are at one or more radial angles, always at 45° from the sample normal. The reversibility of optics implies that these two configurations should report identical measured data. For flat uniform surfaces this should be the case.

Applications

From the diagram of the 45:0 bidirectional geometry it can be seen that the surface gloss is reflected 45° to normal. This is sufficiently far from the detector to assume that the detector measures none of the gloss. This geometry works well for applications where the primary use of the color measurement correlates with visual observations. Consider measuring the color of a glossy photographic print. Without other instructions, observers evaluating the print color will typically position it for viewing so that the eye is viewing approximately normal to the print and no gloss is seen from the light source. This orientation is well-approximated by the 45:0 geometry.

Hemispherical Spectrophotometers

Geometric Definition

As the name implies, hemispherical spectrophotometers either illuminate or detect the light from the entire hemisphere above the sample. This is accomplished by the use of an integrating sphere, shown schematically below in Figure 83. As with the bidirectional case, there are two versions: 0:d and d:0. In these versions the “d” stands for diffuse, and hence at all angles. Also like the bidirectional case, the CIE provides very specific guidelines to which manufacturers should adhere if they are claiming that instruments are d:0 or 0:d. The left diagram shows the d:0 geometry. The light beam enters the sphere diffusely from the port at the right and is further diffused by many reflections off the white sphere walls. Some of this is eventually incident on the sample, and some of that incident light will be reflected in the direction of the detector, located at a near-normal angle.

The 0:d case is shown on the right of the figure. The light is incident upon the sample from a near normal angle. The light reflected from the sample is collected over the entire hemisphere by the integrating sphere. Some of the light will eventually bounce into the detector. Note the baffles in each configuration. These are to prevent the light source beam from being directly incident on the sample (d:0) or to prevent light reflected off the sample from directly entering the detector (0:d). Without the baffles, the diffuse assumption of either configuration could be violated.

Accounting for the Specular Component

Comparing the geometries, it is apparent that the hemispherical geometry does not eliminate the surface gloss. The nature of the integrating sphere is to keep all reflected light within the system. This may be seen as a shortfall, but integrating spheres are usually built with a port (an opening) to control the handling of the surface gloss. Shown as a black rectangle in the hemispherical diagram, this specular port is positioned at an angle equal and opposite to the detector (0:d) or the light source (d:0). If the specular port is covered with a light trap, surface gloss is absorbed and therefore removed from the measurement. If the specular port is covered with a diffuse white material, specular gloss is reflected back into the sphere, and remains in the measurement. Including the specular gloss is called specular component included (SCI) and excluding it is called specular component excluded (SCE). SCI is also referred to as specular component included (SPIN) or SIN in older texts. Likewise SCE is sometimes referred to as SPEX or SEX.

As samples become more glossy, more specular light is present at the specular port. Therefore the difference between SCE and SCI reflectance will increase with surface gloss.

Applications

The justification for the use of SCE follows a similar argument to that of the bidirectional geometries: Excluding the gloss component can better correlate to visual color assessment. However, the CIE recommendations for hemispherical geometry do not include specific details on the specular port configuration. The angular size of the specular port as viewed from the sample port determines the amount of gloss that is removed from the measurement. Different implementations have naturally varied, and without CIE guidelines the size of specular ports can be found to vary by more than 100%. There-fore it cannot be expected that two instruments of different design will necessarily predict the same SCE reflectance for glossy materials.

When comparing instruments, the use of SCI will be more useful, since the significant variable of specular port size is removed. Other design aspects might still differ (e.g., the sizes of the detector and sample ports), but reflectance variations due to these differences should be mostly eliminated by proper calibration.

Analysis of Design and Applications

In many industries, the use of color measurement is well established, and the definition of measurement geometry has been long decided. In cases such as these, the user who wishes to continue interacting with such an industry should use the defined geometry. When communicating color, it is always important and proper to use the most similar geometries as the hardware allows. For the best correlations, identical models of instruments should be used. This avoids the small implementation variations that might be important depending on the specific instruments and sample properties. For example, as discussed above, glossy samples have a large specular component, and therefore will be more susceptible to variations in specular port design.

Design of Spectrofluorimeters

Spectrofluorimeter design can include bidirectional or hemispherical geometry. There are issues related to the implementation of either choice that need to be addressed by the instrument manufacturer. The use of hemispherical geometry is particularly challenging because the sphere will capture the fluorescently emitted light and some of this light will be incident upon the sample. Should this incident light excite more fluorescent emissions, the calibration equation of the instrument is no longer valid, since the detector has no way to know whether the emitted light was excited by the light source or by re-excitation as described above. The effect will seem as though the light source were not stable.

Implications for Color Measurement Instrumentation

Instrument Evaluation

Spectrophotometers are evaluated in three primary ways: repeatability, reproducibility, and accuracy. Repeatability is the ability of an instrument to make consistent measurements. Accuracy is the ability of an instrument to make measurements that closely match known values. These aspects are evaluated with different methods.

Repeatability

The evaluation of repeatability takes several forms, relating to the time interval between measurements. Short-term repeatability is the comparison of measurements taken as fast as the instrument can measure. Medium-term repeatability compares measurements taken over a work shift or single day. Long-term repeatability compares measurements taken over several weeks, months, or even years.

The comparison made is the difference between the initial and subsequent measurements. The statistical analysis is beyond the scope of this work, but methods vary from simple color difference to complex multivariate analyses. Most instrument manufacturers will quote an average DE*ab for a set of replicate measurements of a white tile. For a good instrument this average will be small, perhaps 0.1 DE*ab or less. As the time span increases, the repeatability can be expected to worsen somewhat. It is difficult to cite a specific performance that should be expected. The needs of applications will vary and, perhaps more important, manufacturers rarely specify medium- or long-term repeatability performance.

Reproducibility

When one or more measurement conditions have changed, the evaluation is termed reproducibility. These conditions may be a different operator, instrument, or procedures. Reproduc-ibility is reported with similar metrics as repeatability, and is basically the color difference that can be attributed to the condition change.

Accuracy

The above methods evaluate an instrument’s performance to itself, evaluating the consistency of the device. Accuracy compares an instrument’s measurements to known values provided by a national standards laboratory or other high-accuracy organization. Note that “known” values should not be confused with “truth.” Even national standards laboratories have uncertainty in their measurements and never claim truth.

Accuracy evaluation is performed separately on the subsystems described above under the section Components of a Spectrophotometer. The detector is evaluated for photometric linearity and the dispersing element/detector combination is evaluated for wavelength accuracy.

Other Evaluation Methods

Also of interest are the inter-instrument agreement and inter-model agreement. Inter-instrument agreement compares instruments of identical design. Inter-model agreement compares instruments of different design. Proper analysis of either of these methods requires sophisticated multivariate techniques. However, both methods are often reported using measurement and analysis techniques similar to repeatability.

Instrument Selection

There are several considerations when selecting an instrument for a given measurement task.

Type of measurement data. Does the application require spectral data, or can a less expensive colorimeter suffice?

Instrument geometry. Is there an existing convention for the measurement application? Can a specific type of sample be identified as representative?

Precision and accuracy. What is required? Is a more expensive instrument worth it?

Bandpass and wavelength sampling interval. Are the spectral data very smooth or sharply changing? Smooth data can be adequately measured with fewer wavelengths.

Light source. This is very important if fluorescence is an issue.

Functionality

Time of measurement. Faster instruments require less operator time.

Software interface. A useful interface delivers the relevant data quickly and operates on the platforms that are currently in use.

Service and support. A large, reputable company should be able to provide good service.

Robustness. Is the instrument for the laboratory or the factory floor? What is the level of training the operators will receive?

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