Species Richness in Fluctuating Environments
Electronic tristimulus chromatic Measurement systems
D. TOMTSIS, K. sapalidis, c. katsanos*TEI of West Macedonia, / * PATRAS UNIVERSITY,
MACEDONIA RESEARCH CENTRE, / DEPT. Of Elect. Eng. And Computer Tech.,
KOILA, KOZANI, / PATRA,
GR-50100, GREECE , / gr-26441, greece,
Abstract: Three practical electronic systems were designed to measure colour or chromaticity. The development of all systems was based on tristimulus detection, which offers both dominant wavelength and saturation information. Such colour or chromatic measurement systems are generally used in colour vision systems or robotic vision applications and in manufacturing and testing of CRT displays as a performance verification tool. In general, the chromatic approach provides a powerful and flexible measurement method with attractive advantages over intensity and two wavelength modulation techniques.
Keywords: chromatic modulation, chromaticity.
1. Introduction
There are many situations in which the optical measurement of a physical parameter would be of benefit to industry. For example, optical systems can be used safely in hazardous environments and also in areas where high magnetic or electrical fields make electronic systems inadequate. However, the uptake by industry of optical technology has been slow either because of a lack of confidence in the technology or because optical monitoring tends to be specialized, expensive and insufficiently robust to withstand the industrial environment.
Of the methods available for modulating light (e.g. amplitude, phase, polarization changes) intensity modulation offers the advantages of inherent simplicity. However, conventional methods involving absolute intensity have associated problems. The most basic intensity monitoring systems use only a single photodiode to produce an output but these systems tend to be sensitive to spurious changes in intensity resulting from variations in the light source or other components within the system. Removing these spurious effects is difficult and leads to complicated and expensive systems.
Wavelength monitors attempt to deduce the state of a system by taking the ratio of intensities at two different wavelengths. In principle, the two wavelengths should be chosen tο be close enough together to ensure that spurious signals affect both wavelengths equally. However, the modulator needs tο affect only one of the wavelengths so leading to conflicting demands. Such wavelength modulated systems may be constructed using spectrometers or by using two narrow-band optical filters in conjunction with two photo-detectors. Systems which make use of a spectrometer are expensive, optically inefficient and, require excessive data processing. Systems using filters and photo-detectors are less expensive, but are wasteful of optical power. Such systems may also be used for wavelength encoding detection but the spectrometer approach leads to improved resolution only at the expense of optical power whilst the narrow-band filtered photodiodes only have a limited range of operation.
Many of the difficulties inherent in the spectral or two wavelength monitoring methods may be overcome using a chromatic measurement system. A number of sensors based upon this approach have been developed [1, 2] and shown to possess attractive advantages. Such systems measure changes in the spectral signatures of polychromatic light using carefully configured combinations of broad band detectors. The technology evolves from the study of colour vision [3]. The chromatic approach provides a powerful and flexible measurement method whose full potential is still being explored.
This contribution seeks to describe some of the fundamental aspects of chromatic measurement systems, which are relevant for optical sensing applications. These are based upon the understanding that although the considerations derive from the concepts of colour science [4, 5, 6, 7], e.g. chromaticity diagrams, dominant wavelength etc, they need to be adapted in fundamental1y different ways for their advantages to be ful1y exploited. The work presented in this paper, which is based on tristimulus chromatic modulation, is an extension of our previous work [8] on distimulus chromatic modulation.
1.1. Optical Spectrophotometry
Spectrophotometry is a technique for determining the spectral energy of an electromagnetic wave. This distribution is represented as a record of intensity against wavelength. To achieve this, comparison of intensities is performed using narrow-band, non-overlapping filters or detectors centered on wavelengths situated at regular intervals throughout the spectrum. At each wavelength, a comparison is made between the incident light and a working standard. There are a large number of designs for spectral photometry, which provide varying degrees of resolution and accuracy. However, they all require a light source, a method of dispersing light into a spectrum, and a means of detecting and comparing the intensities from the sample and the standard beams.
Spectrophotometry is the most precise method of describing the spectral profile and thus the measurement of color of the incident light. However, the interpretation of this spectral data is complex, and together with the high cost of spectrophotometers, makes it an unattractive technique for general color measurement.
In this case, it is necessary to reduce this amount of data to only a few parameters which are able to provide spectral profile information and also a perceptual correlation between the color of light detected and the observer, a method which is commonly known as color matching.
1.2. Color Matching
Color matching is important both for commercial and scientific purposes. Its importance lies in the reproduction of perceived color, for example, in photography and television. The standard method of color matching is by using a human observer presented with a color sample together with three controllable color sources matched to the human eye responses. The observer adjusts the intensities of the sources and forms the basic color components of the sample. Color vision is basically a function of the responses of three different spectral weighting functions. Hence, it is expected that color can be extracted from the spectral data using similar functions. The advent of cheap electronic detector systems that have spectral responses similar to the human eye have made this approach to color matching a preferred technique for colorimetry.
2. Chromatic Modulation Theory
The essence of chromatic modulation is the utilisation of polychromatic light for sensing spectral changes by monitoring the total profile of an optical signal within a spectral power distribution. Chromatic changes can be monitored by a number (n) of detectors with overlapping spectral responses. The output of each detector may then be expressed as [9]
/ (1)where P(l) is the spectral power distribution in the optical signal and Rn(l) is the wavelength responsivity of the nth detector and λ is the wavelength. Each detector output may also be intensity normalised according to:
/ (2)where
u1 + u2 + … + u(n-1) + un = 1 / (3)In such a way, chromaticity maps may be formed in terms of the coordinates u1, u2, … u(n-1).
System simplification and implementation economy is therefore possible by reducing the amount of information acquired and which may be achieved through the use of two rather than n detectors. The case of n=2 leads to a distimulus chromaticity map on which either chromaticity coordinate (u1 or u2) may be used to completely describe changes in optical signals. Any two detectors with different but overlapping spectral responsivities may be used to form a distimulus measurement system. The chromatic model representing this mathematical formalism is called LXY and provides the relative magnitudes of the distimulus values (i.e. X=u1; Y=u2).
Fig. 1. Chromaticity diagram for distimulus detection.
The two-dimensional nature of the chromaticity diagram, shown in fig. 1, implies that in general, the status of the measurand is over-specified in being defined by two coordinates, u1, u2.
Since the ratio υ1 / υ2 provides normalization with respect to signal intensity the distimulus method preserves the intensity-independent nature of chromatic monitoring. Also, since the signals υ1 and u2 are derived from overlapping detector responsivities there is a degree of inbuilt immunity to extraneous spectral noise in the output υ1 / υ2.
The determination of color using three detectors is called tristimulus detection [10]. The human eye and many computer vision systems are examples of tristimulus chromatic detection systems. Tristimulus detection is not reliant on the detection of a complete spectral power distribution. It is sufficient to measure three attributes of the spectral power distribution. The three detector (tri-stimulus) system can, therefore, be used to measure those spectral signature changes, which lead to a change in dominant wavelength and saturation.
3. Electronic Tristimulus color measurement systems
The practical measurement of the tristimu1us values Χ, Υ and Ζ, and their subsequent processing to obtain the co1our coordinates x and y, is discussed in this section. Three electronic color measurement systems are presented. The first uses a computer to calculate the color coordinates from a measured spectral signature. The second system combines direct optical measurements of the tristimulus variables Χ, Υ and X+Y+Ζ. The final system measures the tristimulus variables individually, and uses a computer to calculate the color coordinates, although in this case the detectors do not have the same spectral responsivities (x, y and z) as the standard CIE observer.
3.1. Obtaining color coordinates from a spectral signature
This section describes the operation of the developed colorimetric measurement system, which was designed to measure the color properties of visible light sources and optical filters.
The system uses a monochromator, with wavelength selection controlled by a microcomputer. The optical intensity at each selected wavelength is measured using a photomultiplier tube, the output of which is interfaced to the microcomputer. The microcomputer is programmed to scan the whole optical spectrum, and to store the outputs from the photomultiplier tube. In this mode of operation, the microcomputer controlled monochromator system behaves as a spectrum analyzer, and hence the stored photomultiplier responses give the spectral signature of light incident on the monochromator. The measured spectral signatures are processed in order to compensate for the spectral gain characteristics of the monochromator and photomultiplier, hence producing the true spectral signature of the incident light. The microcomputer calculates the tristimulus values Χ, Υ and Ζ from the stored spectral signature. This is achieved by multiplying the CIE standard observer responsivities by the captured spectral signature on a wavelength by wave1ength basis in a numerical approximation to eq. 1 ie;
/ (4)/ (5)
/ (6)
Where S(λ) is the incident spectral intensity and x(λ), y(λ), z(λ) are the spectral responsivities of the detectors.
Finally the co1or coordinates, x and y are ca1cu1ated using eq. 2. This system is ab1e to produce very accurate co1or measurements (there is a 95% confidence that any measurement wi11 1ie within 0.0001 of the true va1ue). The main disadvantages of the system are that each spectral scan takes three minutes and that the system is quite cost1y to imp1ement.
3.2. Α direct reading chromaticity meter
Light is gathered into a fiber bund1e from a camera head, which is focused on a region where co1our is to be measured. The fiber bund1e is sp1it into three such that the 1ight is incident on three optica1 fi1ters, giving the tristimu1us va1ues Χ, Υ and Χ+Υ+Ζ. The fi1ter responsivities were matched to the CIE spectra1 responsivities, Χ, Y and Ζ, using a computer program which chose the best combinations of different fi1ter types and thicknesses from a database of readi1y obtained optica1 fi1ter spectra1 transmission characteristics.
Fig. 2. The Direct Reading Chromaticity Meter
The intensity of the 1ight passing through each of the fi1ters is converted to an e1ectrica1 signa1 by a sing1e photomu1tip1ier tube. The 1ight intensity measurements made with the photomu1tip1ier are taken at different time interva1s such that the Χ, then the Υ and fina11y the Χ+Υ+Ζ va1ues are measured, this being achieved by cutting ho1es in a rotating timing disk, shown in figure 3, such that the Χ and Υ fi1ters are individua11y uncovered and then the Χ, Υ and Ζ fi1ters are simu1taneous1y uncovered, as the disk rotates.
The output from the photomu1tip1ier tube is digitized using an ana1ogue to digita1 converter, and a digita1 processing system is used to convert the measured tristimu1us va1ues into co1or Coordinates.
The main advantage of this system is that the measurements may be acquired more rapidly than those taken with the system described in the previous section. The disadvantage of the system is the practical difficulty in obtaining filters with the exact responsivities of a CIE standard observer. Deviations in the filter responses lead to errors in the measured color coordinates, which may be particularly noticeable with some spectral sources. However, if it is sufficient to make chromaticity measurements not based on the CIE standard observer, the deviation of the filter responses from the CIE standard observer is not a problem. Α color space may be defined using three detectors of known optical responsivities a, b and c. The tristimulus values Α, Β and C could be directly obtained using standard filters.
Fig. 3. Front View of the Rotating Timing Disk
3.3. Α Continuous tristimulus measurement system
The system described in this section makes use of three photodiodes with different spectral responsivities as the basis of a tristimulus measurement system. The three photodiodes produce photocurrents with values depending on both the spectral signature, and the intensity of the incident light. The photocurrents are converted into voltages, using transresistance amplifiers, which are digitized using analogue to digital converters (ADC’s). Α microcomputer uses the ADC digitization results to calculate and continuously display the chromaticity coordinates. It should be noted that this system is not designed to measure colour, but chromaticity (i.e. the spectral responsivities of the three photodiodes were not the same as the CIE Χ, Υ and Ζ detectors). The circuit diagram of a photodiode with the associated transresistance amplifier is shown in figure 4.
Fig. 4. Photodiode and transresistance amplifier combination, where ip, Rf and Vp are the values of photocurrent, feedback resistor and output voltage respectively