A Ccd-Based Tristimulus Colorimeter for Fast and Improved Measurement of Chromaticity

A CCD-BASED TRISTIMULUS COLORIMETER FOR FAST AND IMPROVED MEASUREMENT OF CHROMATICITY COORDINATES OF DISPLAYS BY MATRIX CORRECTION METHODS

D. TOMTSIS, K. SAPALIDIS

TEI of West Macedonia, KOILA, KOZANI, GR-50100, GREECE ,

Abstract: Color and luminance uniformity testing of displays is often limited to a few measurement points on the display surface due to the length of time necessary to make a single point measurement. A CCD-based tristimulus colorimeter has been developed which is capable of measuring chromaticity coordinates over thousand spatial locations in several seconds. A new calibration technique has been developed for improving the accuracy of chromaticity values obtained from the proposed CCD-based colorimeter. Matrix manipulations similar to ASTM standard practice E 1455 are applied with a goal of minimizing the errors in the measurement of the chromatic coordinates x and y, rather than those of the tristimulus values X, Y, Z, which are independent of luminance Y. Correction matrices are determined from CRT colors. A number of different colors from a CRTs gamut are measured with the proposed system using such matrices. The matrix computed from CRT colors reduced measurement errors in x and y, when compared to the current standard for display measurements.

Keywords: chromatic modulation, chromaticity, CCD, colorimeter, CRT displays.

1. Introduction combinations, the spectral responsivities of which are Tristimulus colorimeters are used extensively in approximated to the CIE color matching functions. manufacturing and testing of cathode ray tubes In such broad-band measurements, due to the (CRTs), as in-process and performance verification imperfect realization of the filter-detector tools [1]. Tristimulus colorimeters are often preferred responsivities, measurement errors are inevitable when to spectroradiometers because of their lower cost and the spectral power distribution of a test source is ease of use, though they are usually less accurate. Such dissimilar to that of the calibration source. Tristimulus colorimeters employ a single detector and are therefore colorimeters and luminance meters are often calibrated classified as ‘spot colorimeters’, which take many with CIE Illuminant A (2856 K Planckian source), and separate spot measurements of a display device thus, inaccuracies can occur in color CRT sequentially, having to move the spot detector for each measurements. measurement point over the image area. This is a time Matrix techniques have been known for over 20 years consuming method and usually very few points of the to improve the accuracy of tristimulus colorimeters for imaging area are measured. Many of the difficulties CRT measurements, utilizing the fact that colored light inherent in the spot-colorimeter method may be produced by a CRT is a linear superposition of the overcome using a CCD-based colorimeter spectral power distributions of three primaries [2]. measurement system. Such systems are able to image ASTM (American Society for Testing and Materials) the entire display onto many detectors at once thereby E1455 [3, 4] recommends a method to derive a capturing many thousands of points in several seconds. correction matrix (R’ matrix) that transforms measured In addition to the substantial savings in time for Xm,Ym,Zm values into better agreement with the measuring multiple test points on a display, the CCD reference values X, Y, Z. The matrix is made such that colorimeter offers the capability of measuring more the root-mean-square difference between transformed data points than would otherwise be possible in a Xm,Ym, Zm and X, Y, Z for several different colors of a reasonable amount of time during the engineering and display is minimized. quality assurance phase of display system design and Because these conventional methods are based on production. tristimulus values, the errors in luminance affect the The output of a typical tristimulus colorimeter is in the accuracy of the corrected results of chromaticity as form of three parameters, namely the chromatic well as luminance. The variation of luminance coordinates x, y and luminance Y. Tristimulus measurements can occur due to instability of the colorimeters employ broad-band filter-detector display, flicker effect on the detectors, interreflections between the display surface and the instrument, etc., while the measurement of (x, y) is normally more V stable and reproducible since it is a relative n un  (0) V measurement, and the error factors mentioned above n T tend to be cancelled out if the three channels are sampled at the same time. where chromaticity maps may be formed in terms of A new technique for the matrix method has been the chromaticity coordinates u1, u2, … u(n-1). The case of developed, which is based on the (x, y) values only, n=3 leads to a two-dimensional chromaticity map and is independent of Y value. Thus, in principle, it (u1:u2) on which changes in optical signals may be traced. The special case when R (λ), R (λ), R (λ) eliminates errors arising due to luminance 1 2 3 correspond to the responsivities of the human eye measurement variations. The correction matrix is leads to the chromaticity map reducing to the CIE obtained from the (x, y) values of the three primary diagram of color science [6]. The color model colors plus white from the display measured by a representing this mathematical formalism is called LXY target and a reference instrument. and provides the relative magnitudes of the tristimulus To evaluate the new technique, experiments have been values (i.e. X=u ; Y=u ; Z=u ). performed with the proposed CCD-based colorimeter 1 2 3 and a reference spectroradiometer measuring colors on a CRT. Correction matrices are computed that 3. Matrix Correction Method minimize differences only in x and y rather than the The primary colors (red, green, and blue) and a white tristimulus values, for sets of sample colors. color of a display are measured by the proposed CCD- based colorimeter (the target instrument) and a 2. Chromaticity Measurement reference instrument (a reference spectroradiometer). From the chromaticity coordinates (xm,R , ym,R), (xm,G , The essence of chromatic measurement - an integrated y ), and (x , y ) of red, green, and blue measured form of spectral measurement - is the utilization of m,G m,B m,B by the target instrument, the relative tristimulus values polychromatic light for sensing spectral changes by of the primary colors from the target instrument are monitoring the total profile of an optical signal within defined by: a spectral power distribution. Chromatic changes can be measured by a number (n) of detectors with xm,R xm,G xm,B  km,R 0 0  overlapping spectral responses. The output of each     detector may then be expressed as M RGB  ym,R ym,G ym,B   0 km,G 0  (0)     zm,R zm,G zm,B   0 0 km,B  Vn =  P()Rn()d (0) where where P() is the spectral power distribution in the optical signal and Rn() is the wavelength responsivity km,R  km,G  km,B 1 (0) of the nth detector and λ is the wavelength [5]. km,R , km,G and km,B are the relative factors for measured luminance of each display color, and are now unknown variables. z with any subscript L is obtained

from xL and yL by:

zL 1 xL  yL (0)

From the chromaticity coordinates (xr,R , yr,R), (xr,G ,

yr,G), and (xr,B , yr,B) of red, green, and blue measured by the reference instrument, the relative tristimulus values of the primary colors from the reference instrument are defined by:

xr,R xr,G xr,B  kr,R 0 0      N RGB yr,R yr,G yr,B   0 kr,G 0  (0)     zr,R zr,G zr,B   0 0 kr,B  Figure 1. The CIE 1931 Diagram where

The color model representing this mathematical kr,R  kr,G  kr,B 1 (0) formalism is generally called RGB and it is widely used in self-luminous display technologies. Each kr,R , kr,G and kr,B are the relative factors for luminance of detector output may also be intensity normalized each display color. according to: Based on the additivity of tristimulus values, and with the CCD array. This particular system utilized a

(xm,W , ym,W) and (xr,W , yr,W) being the chromaticity 512x512 pixel CCD and a 2-stage Peltier cooling coordinates of the display for the white color measured system using two back-to-back thermo-electric coolers by the target instrument and the reference instrument (TECs) to control the temperature of the CCD array. respectively, the following relationships hold: The cooling of the CCD allows us to operate the CCD at 16-bits analog to digital conversion with xm,W  xm,R xm,G xm,B km,R  approximately 2 bits of noise (i.e. 4 grayscale units of      noise out of a possible 65,536 maximum dynamic ym,W   ym,R ym,G ym,B km,G  (0) range). z  z z z k   m,W   m,R m,G m,B  m,B 

xr,W  xr,R xr,G xr,B kr,R       yr,W   yr,R yr,G yr,B kr,G  (0)      zr,W  zr,R zr,G zr,B kr,B  The white color of the display can be of any intensity combination of the three primary colors. The values

(km,R , km,G , km,B) and (kr,R , kr,G , kr,B) are now obtained by solving Eq.(8) and Eq. (9) as:

1 km,R  xm,R xm,G xm,B  xm,W  Figure 2 . The spectral response of the CCD-Based Colorimeter       approximates the spectral response of the CIE 1931 2 degree (0) km,G   ym,R ym,G ym,B  ym,W  observer color matching functions shown in this figure.       km,B  zm,R zm,G zm,B  zm,W  There are three filters contained within the computer-

1 controlled filter wheel. The spectral transmittance of kr,R  xr,R xr,G xr,B  xr,W  these filters was specifically designed to match the       k  y y y y (0) spectral transmission characteristics of the imaging  r,G   r,R r,G r,B   r,W  lens and CCD of the system so that the combined lens-       kr,B  zr,R zr,G zr,B  zr,W  filter-CCD spectral response would be as close as possible to the CIE 1931 2 degree observer color The correction matrix R is then given by: matching functions, which are shown in Figure 2. The 1 computer-controlled camera records three images of a R  N RGB . M RGB (0) display under test using the three filters sequentially. If the relative tristimulus values M for any colors Once the system has been properly calibrated, the measured by the target instrument are given by: luminance value and CIE 1931 chromaticity coordinates may then be determined from each pixel X x  m   m  within the image using the computer software. M   Y   k y   m   m  (0) 5. Experiment Z m  zm  The reference instrument used in this work was a where k is an arbitrary factor, then the relative spectroradiometer comprised of a scanning type, tristimulus values M from the target instrument are double-grating monochromator in subtractive mode, corrected to M  by using the correction matrix R as: that was equipped with imaging optics (with a viewfinder) which provided an acceptance angle of M   R . M (0) approximately 3°. Its three slits were adjusted to The corrected chromaticity coordinate (x, y) is provide a triangular bandshape with 5 nm half-width. computed from M  . The relative spectral responsivity of the spectroradiometer was calibrated immediately before 4. The System and after the measurements against two standard lamps The CCD based color measurement system consists of traceable to the NIST spectral irradiance scale [7]. The a 16-bit CCD camera and windows-based software for spectroradiometer measurements on the standard camera control and data analysis. In this system, light lamps reproduced to ± 0.0002 in x and y. The from a display device under test enters the imaging luminance of each sample color was also measured lens, passes through a lens aperture, through a color with a reference luminance meter of known spectral filter in a computer-controlled filter wheel, and responsivity. The reference luminance values (Y) were through a mechanical shutter before being imaged onto obtained from the luminance meter values, which were corrected for the spectral mismatch of the instrument Table 2. Comparison of readings between the CCD-based using the relative spectral power distribution of each tristimulus colorimeter and the reference spectroradiometer. sample color obtained by the spectroradiometer. The Y Difference (Target-Reference) values obtained in this manner were more stable and CRT x y Y (%) reproducible than the Y values obtained from the 1 (White) - - - spectroradiometer itself which employed a 2 (Red) 0.0116 -0.0112 -1.2 photomultiplier. 3 (Green) -0.0103 0.0124 2.0 A broadcast-quality color CRT was used in 4 (Blue) -0.0008 -0.0083 -13.7 combination with a video signal generator. The CRT 5 (Yellow) -0.0010 0.0026 1.1 was selected for spatial uniformity and stability. The 6 (Cyan) -0.0045 0.0036 -0.2 monitor was allowed to stabilize for more than 2 7 (Magenta) 0.0059 -0.0079 -4.5 minutes after changing to a new color. 8 (Royal blue) -0.0010 -0.0052 -4.6 Measurements took place with each instrument 9 0.0102 -0.0090 -1.3 sequentially. The spectroradiometer scan required 10 -0.0083 0.0102 1.4 more than 10 minutes to complete while the CCD- 11 0.0004 0.0007 0.8 based tristimulus colorimeter produced results in a 12 0.0002 -0.0005 0.6 time duration of less than 1 minute. The luminance for 13 -0.0026 0.0016 1.1 each color was recorded before and after the two 14 0.0056 -0.0052 -2.2 measurements. The measurements were repeated when 15 -0.0004 0.0023 1.4 the two luminance values varied by more than 0.2%. Table 3 shows the measurements produced when the 6. Results R’ correction matrix was computed following the procedure given in ASTM Standard E 1455-92. The Table 1 presents the chromatic coordinates (x, y) and same CRT color set was used as the input data. the luminance Y measurements produced by the reference spectroradiometer for a sample set of fifteen Table 3. Results produced by the application of the correction CRT colors (first column) that fell inside the color matrix based on ASTM Standard E 1455-92. gamut of a tested CRT display. ASTM R' Matrix Results Table 1. Chromaticity (x, y) and luminance Y measurements CRT x y produced by the reference spectroradiometer 1 (White) -0.0003 0.0004 2 (Red) 0.0021 0.0005 Reference Spectroradiometer 3 (Green) -0.0004 -0.0027 CRT x y Y (cd/m2) 4 (Blue) -0.0001 -0.0001 1 (White) 0.3148 0.3173 129.22 5 (Yellow) -0.0009 -0.0005 2 (Red) 0.6322 0.3362 65.25 6 (Cyan) 0.0005 0.0009 3 (Green) 0.3078 0.5930 183.45 7 (Magenta) -0.0003 -0.0003 4 (Blue) 0.1500 0.0623 22.46 8 (Royal blue) 0.0003 0.0005 5 (Yellow) 0.4315 0.4965 149.90 9 0.0008 0.0002 6 (Cyan) 0.2244 0.3107 142.32 10 -0.0006 -0.0019 7 (Magenta) 0.3200 0.1592 58.70 11 0.0003 0.0010 8 (Royal blue) 0.1741 0.1238 50.87 12 -0.0002 -0.0001 9 0.5319 0.2936 67.53 13 0.0008 -0.0003 10 0.3251 0.5599 175.02 14 0.0013 0.0004 11 0.3082 0.3138 8.05 15 -0.0003 -0.0002 12 0.3146 0.3170 128.64 13 0.2490 0.3155 32.51 Table 4 shows the results obtained by the application 14 0.3101 0.2014 17.11 of the new minimization technique. The correction 15 0.3911 0.4436 36.90 matrix was computed using the same sample set of CRT colors. Table 2 compares the readings of the CCD-based tristimulus colorimeter to the reference Table 4. Results obtained when the CCD-based colorimeter was spectroradiometer before applying any matrix used in combination with the new minimization technique. corrections for the same set of test colors. The New minimization technique colorimeter readings are based on a calibration using CRT x y the first CRT color (white). The chromaticity 1 (White) -0.0003 0.0001 differences for some colors exceed 0.010, and the 2 (Red) 0.0004 -0.0004 luminance differences range over several percent. 3 (Green) 0.0001 -0.0002 4 (Blue) 0.0000 -0.0004 [6] Hunt R.W., Measuring Colour, J. Wiley and Sons, 5 (Yellow) -0.0004 0.0001 New York, 1987. 6 (Cyan) 0.0005 0.0008 [7] Steven W. Brown and Yoshi Ohno, “NIST 7 (Magenta) -0.0006 -0.0007 Colorimetric Calibration Facility for Displays”, 8 (Royal blue) 0.0003 0.0001 National Institute of Standards and Technology, 9 -0.0002 -0.0005 Gaithersburg, MD USA. 10 -0.0001 0.0000 11 0.0003 0.0008 12 -0.0002 -0.0004 13 0.0008 -0.0004 14 0.0011 -0.0001 15 0.0000 0.0002

The results show that the computed R’ matrix provides a significant improvement in the operation of the CCD-based tristimulus colorimeter. The new minimization technique is seen to yield better results than the ASTM formula. Additional analysis shows that much of this improvement with the minimization in (x, y) space arises due to common mode noise in the (X, Y, Z) values of a single measurement (e.g., from display flicker).

7. Conclusion The results show that a matrix transformation based on an (x, y) difference metric may improve the calibration accuracy of a tristimulus colorimeter when measuring the chromatic coordinates, as compared to the current standard for display measurements. More experiments are necessary using different colorimeters, displays, and other colored samples. It would be interesting to experiment with other difference metrics, such as those based on a uniform color space or standard color difference equations.

References: [1] D. Tomtsis, K. Sapalidis, C. Katsanos, “Electronic Tristimulus Measurement Systems”, 3rd WSEAS International Conference on Electronics, Control and Signal Processing (ICECS 04), Rethymno, Crete Island, Greece 24-26 October 2004. [2] CIE / ISO 10527 Standard Colorimetric Observers (1991). [3] ASTM E 1455-92 “Standard Practice for Obtaining Colorimetric Data from a Visual Display Unit Using Tristimulus Colorimeters”, ASTM Standards on Color Appearance Measurement, 4th Ed., 1992. [4] ASTM E 1455-96 “Standard Practice for Obtaining Colorimetric Data from a Visual Display Unit Using Tristimulus Colorimeters”, ASTM Standards on Color Appearance Measurement, 1996. [5] D. Tomtsis, V. Kodogiannis, P. Chountas, “Distimulus Chromatic Measurement Systems”, WSEAS Transactions on Circuits and Systems, Vol. 3., No. 2, April 2004, pp. 211-214, ISBN: 11092734.