Colorimetric Characterization Model for Plasma ...

Journal of Imaging Science and Technology® 51(4): 337–347, 2007. © Society for Imaging Science and Technology 2007

Colorimetric Characterization Model for Plasma Display Panel Seo Young Choi, Ming Ronnier Luo䉱 and Peter Andrew Rhodes Department of Color & Polymer Chemistry, University of Leeds, Leeds, United Kingdom LS2 9JT E-mail: [email protected]

Eun Gi Heo and Im Su Choi PDP Division, Samsung SDI, 508 Sungsung-Dong, Chonan City, Chungchongnam-Do 330–300, South Korea

Abstract. This paper describes a new device characterization model applicable to plasma display panels (PDP). PDPs are inherently dissimilar to cathode ray tube and liquid crystal display devices, and so new techniques are needed to model their color characteristics. The intrinsic properties and distinct colorimetric characteristics are first introduced followed by model development. It was found that there was a large deviation in colorimetric additivity and a variation in color due to differences in the number of pixels in a color patch (pattern size). Three colorimetric characterization models, which define the relationship between the number of sustain pulses and CIE XYZ values, were successfully derived for full pattern size: A three-dimensional lookup table (3D-LUT) model, a single-step polynomial model and a two-step polynomial model including three 1D LUTs with a transformation matrix. The single-step and two-step polynomial models having more than 8 terms and the 3D LUT model produced the most accurate results. However, the single-step polynomial model was selected and extended to other pattern sizes because of its simplicity and good performance. Finally, a comprehensive model was proposed which can predict CIE XYZ at sizes different to that used for the training set. It was found that one combined training set formed using two different pattern sizes could give better results than a single-size training set. © 2007 Society for Imaging Science and Technology. 关DOI: 10.2352/J.ImagingSci.Technol.共2007兲51:4共337兲兴

INTRODUCTION Large size displays such as plasma display panel (PDP), liquid crystal display (LCD), and digital light processing (DLP) TV are promising candidates for replacing the cathode ray tube (CRT) displays that are currently in widespread use. Plasma display technology has the following characteristics: it is thin and light, has superior video image performance and uses a large screen size from 42 to 100 inches. These enable PDPs to be used inside stores for product promotion and, increasingly, for home theater. One of the desirable properties for large displays is to achieve a “lifelike” appearance under a range of practical viewing conditions as judged in terms of color and image quality. It is therefore important to investigate its colorimetric behavior and to make a characterization model based on the intrinsic physical properties of a PDP. Already, much research has been conducted to

investigate the use of LCD and CRT technology, however relatively little work has been performed for plasma displays.1–5 Only one paper deals with PDP characterization based on the gain-offset-gamma (GOG) model; (previously developed for CRT) at one pattern size, however the physical properties of PDPs and the pattern-size effect were not considered in this model.6 In other words, the model could not be successfully extended to different pattern sizes. The International Electrotechnical Commission (IEC) has issued a standard IEC 61966-5 which includes methods and parameters for investigating the use of PDPs to display colored images in multimedia applications.7 It does include the pattern size effect as a display area ratio characteristic, but changes in other characteristics such as color gamut due to pattern size were not considered. It assumes that a PDP’s RGB channels are independent. Unfortunately, PDPs typically exhibit significant additivity failure when compared to other display technologies. It is therefore essential that this additivity failure should be taken into account during the development of any device characterization model. The simplified structure of a PDP RGB cell is shown in Figure 1. A PDP is composed of two glass plates having a 100 ␮m gap and filled with a rare gas mixture which can

䉱

IS&T member.

Received Jul. 27, 2006; accepted for publication Mar. 1, 2007. 1062-3701/2007/51共4兲/337/11/$20.00.

Figure 1. The structure of a PDP’s RGB cells. 337

Choi et al.: Colorimetric characterization model for plasma display panel

and resultant CIE XYZ values at one particular pattern size. In addition, one of these models was extended to take into account other pattern sizes.

Figure 2. A 16.7 ms frame includes 8 subfields. The black boxes are the durations of the sustain periods proportional to 1,2,4,…,128.

include a 500 torr, Xe–Ne or Xe–Ne–He mixture which, when excited, results in the Xe atoms emitting vacuum ultraviolet (vuv) radiation at 147 and 173 nm, respectively. This vuv radiation then excites the red, green, and blue phosphors located on the rear glass plate. The discharge also emits red-orange visible light due to neon, which causes a subsequent reduction in color purity (see the Colorimetric characteristics of a PDP section). Each pixel has three individual 共RGB兲 microdischarge cells. An alternating current (ac) is generated by dielectric barrier discharge operating in a glow regime to generate plasma in each cell. The ac voltage is approximately rectangular with a frequency in the order of 100 kHz and a rise time of about 200– 300 ns.8 Different intensity levels are obtained via the modulation of the number of ac pulses (sustain pulses) in a discharge cell. For CRT and LCD, intensity levels are controlled differently from a PDP, i.e., according to voltage level. In addition, the luminance output of a PDP is dependent on the pattern size displayed, even when the RGB input values remain the same. The average level of input video signal—a product of RGB input values and pattern size—increases in proportion to the increase in pattern size. This is also accompanied by an increase in power consumption. As a result, there is a need to regulate the power consumed for large area patterns by means of the automatic power control (APC) function. Specifically, this regulates power consumption to within a certain upper limit. Moreover, luminance output is affected by the APC function and generates different values dependent on pattern size. This paper describes an investigation into the colorimetric characteristics of a PDP and the development of three device characterization models which describe the relationship between the number of sustain pulses of RGB input

PHYSICAL PROPERTIES OF A PDP Overall Transfer Process of the Input Video Signal As mentioned earlier, one unique feature of PDP is that, for a fixed RGB input, its luminance output varies according to the pattern size displayed. The average level of an input video signal increases not only in proportion to the RGB input but also to the increase in pattern size. Furthermore, power demand also grows, because a larger input video signal leads to a bigger discharge current in the PDP. To protect the electronic components from damage, it is necessary to impose a limit on power consumption. This is accomplished by controlling the discharge current. There are two methods for controlling this: adjusting the number of RGB sustain pulses and modifying the input level of the video signal. The PDP used in this study adopts the first method. The number of RGB sustain pulses is adjusted through the APC function, which is determined by the average intensity level of the input video signal. To explain the role of the APC function here, it is assumed that each discharge cell can display 256 gray levels. Unlike a CRT, each cell is only capable of being turned on or off (binary). Each gray level is obtained by modulating the number of sustain pulses during one frame (16.7 ms, 60 frames per second= 60 Hz). A frame is divided into eight subfields, having weight ratios of 1, 2, 4…,128 (Figure 2). The function of a subfield is to modulate light output over time. This is accomplished by dividing each video frame into shorter time periods where each cell is either turned on or off. Each subfield has a sustain period (see black box in Fig. 2) whose duration is proportional to weight ratios, and an address period (see white box in Fig. 2) whose duration is the same for 8 subfields. The address period is used to switch on or off a given cell. An 8-bit binary coding is used to obtain 256 gray levels since there are 256 possible levels that can be achieved by assigning on/off to any combination of the eight subfields. In practice, the number of sustain pulses is determined by the sum of the product of the sustain pulse limit and the “weight ratios” which correspond to the proportion of subfields turned on. This calculation is shown in Table I. The sustain pulse limit, as mentioned previously, safeguards the display’s electronics. It

Table I. One example of subfield configuration and the calculation process for the number of sustain pulses used for a color patch with input value of 5. Subfield

1

2

3

4

5

6

7

8

Weight ratios

0.004 共1 / 255兲

0.008

0.016

0.031

0.063

0.125

0.251

0.502 共128/ 255兲

Weight ratios’ sum= 1

Configurationa

1

0

1

0

0

0

0

0

共8 bits兲

The sustain pulse limit, 2600, is given in the APC table defined by the manufacturer Calculation

共2600⫻ 0.004兲 + 共2600⫻ 0.016兲 = 52 the practical number of sustain pulses assigned to RGB cells

a

Binary coding: 0 is off and 1 is on. This configuration corresponds to input value 5.

338

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Figure 4. Plot of CIE X values versus the number of red sustain pulses at 4 pattern sizes. Points 共1兲, 共2兲, and 共3兲 correspond to the maximum number of sustain pulses at 100%, 60%, and 30% pattern size, respectively. Figure 3. Flowchart explaining the transformation of input video signal to the emission of light in a PDP. Table II. Maximum CIE XYZ for RGB and the range of the number of sustain pulses at 4, 30, 60, and 100% pattern size. Color

CIE XYZ

4%

30%

60%

100%

Red

Max X

498.1

454.5

330.5

230.4

Green

Max Y

593.9

546.2

395.7

284.7

Blue

Max Z

Sustain pulse range

1311.6

1175.6

809.9

551.7

0–2594

0–2594

0–1826

0–1260

is determined from a manufacturer-defined APC table according to the average input video signal. Eight subfield combinations yield 256 gray levels corresponding to the supplied input values; however, the actual number of sustain pulses (and hence the brightness of each level) is controlled by the sustain pulse limit. The overall transfer process of input video signal to output stimulus can be expressed in terms of the steps shown in Figure 3, which includes an example for a full white pattern. RGB input values for the video signal are transformed into the number of RGB sustain pulses via the PDP’s logic board. These are calculated from the sub-field configuration corresponding to the RGB input value and the sustain pulse limit assigned by the APC table. The number of sustain pulses are the same as the number of plasma discharges occurring in each cell. A succession of discharge pulses occurs between two sustain electrodes inside the front plate of the RGB cells according to the number of RGB sustain pulses assigned. The rare gas mixture (Xe–Ne or Xe–Ne–He) emits vacuum ultraviolet (vuv) photons at 147 and 173 nm during discharge in RGB cells and those intensities are governed by the number of RGB sustain pulses. Xenon is used as a vuv emitter and neon acts as a buffer gas which lowers the breakdown voltage, i.e., the minimum voltage to initiate plasma. The vuv photons are converted into visible photons by the phosphor materials deposited on the inner walls of RGB discharge cells. Based on an understanding of this process, the final characterization model was developed between CIE XYZ values and the number of RGB sustain pulses (rather than simply RGB input values).


Pattern Size Effect As mentioned in the Overall Transfer Process of the Input Video Signal section brightness varies according to pattern size. Figure 4 depicts CIE X values plotted against the normalized number of R sustain pulses. In the figure, there are four sets of data points corresponding to pattern sizes of 4%, 30%, 60%, and 100% respectively. Each set includes 26 equal steps of the red channel. The decrease of maximum X value with increasing size shown in Fig. 4 can be explained due to an increased power demand by larger pattern sizes. To limit the total power consumption of a PDP, the number of sustain pulses must be lowered for larger color patches by the APC function. This results in the decrease in maximum X value with increasing size shown in Fig. 4. Table II illustrates also the size effect on color patches at 4% and 30% of the total screen area. It can be seen that they have a higher maximum range of the number of sustain pulses which result in larger CIE XYZ values than those for the 60% and 100% pattern sizes. The highest number of sustain pulses for the R primary color at 100% pattern size is 1260 while the 4% pattern size is 2594, even though the input RGB values are the same (0,255,0). Hence, the resultant maximum Y value for the 4% pattern size is higher than for the 100% pattern size. This implies that the number of sustain pulses should be used as an input color specification, contrary to conventional approaches to display characterization which only consider the input digital RGB values. EXPERIMENTAL METHODS The colorimetric characterization of a 42-inch Samsung high-definition PDP (model PPM42H3) was evaluated. Its 339


Table III. 共a兲 Color patches for three characterization models at 100% pattern size. 共b兲 Color patches used for developing single-step polynomial models at other pattern sizes. 共a兲 Models at 100% pattern Training sets Testing set

3D LUT

Single-step polynomial model

6level 3D LUT

6-, 5-, 4& 3-level 3D LUT

Two-step polynomial model Three 1D LUT

Transformation matrix

52 steps of RGB

6-, 5-, 4& 3-level 3D LUT

115-color test set 共b兲

Pattern size

4%, 30%, and 60%

Training sets

5-, 4-, and 3-level 3D LUT at each pattern size

Test sets

Three 27-color test sets at three pattern sizes

pixel resolution is 1024⫻ 768 with an aspect ratio of 16:9 and it is capable of addressing 512 intensity levels per channel, although only 256 were used here. Its pixel pitch is 0.912 mm 共H兲 ⫻ 0.693 mm 共V兲 so that the total display area is 933.89⫻ 532.22 mm2. Color patches were displayed in the middle of the screen and generated by a computercontrolled graphic card equipped with digital visual interface (DVI) output. This allows the PDP’s logic board to receive a digital signal directly from the computer. Contrary to typical display characterization, the number of sustain pulses was used as input color specification in this study, as explained previously in the Pattern Size Effect section. Color measurements were taken using a Minolta CS-1000 tele-spectroradiometer (TSR) in a dark room. The repeatability of both the TSR and PDP was evaluated using 15 colors measured twice over a two-month period. The * were 0.38 and 1.18 during this median and maximum ⌬Eab time. This performance is considered satisfactory. Measurement patches consisted of rectangles which were 100%, 80%, 60%, 45%, 30%, or 4% of the display area. The background was set to black (except for the 100% case). Three characterization models were first developed for the 100% pattern size. Table III(a) describes the data set generated for the three types of characterization models: 3D LUT, single-step polynomial, and two-step polynomial model. For the 3D LUT model, 6 levels were used. For the other two models, 6-, 5-, 4-, and 3-level 3D LUTs were compared in order to determine which training set gave the optimum performance with the fewest number of measurements. The 6-level 3D LUT was first generated using 1, 15, 43, 66, 105, and 255 digital input values for each of the RGB channels. These values were empirically determined to have approximately uniform coverage of the CIE XYZ destination color space. The distribution of the 6-level training set is 340

Figure 5. Plot of 216 colors of the 6-level 3D LUT in 共a兲 XY, 共b兲 YZ, and 共c兲 a*b* plane, respectively.

shown as an XY and YZ projection in Figures 5(a) and 5(b), respectively. In addition, an a*b* diagram depicting the whole of the 6-level training set can be seen in Fig. 5(c). Among the 6 digital input values, 1, 15, 43, 105, and 255 were used to make the 5-level 3D LUT; 1, 15, 66, and 255 J. Imaging Sci. Technol. 51共4兲/Jul.-Aug. 2007


were used for the 4-level 3D LUT; and 1, 43, and 255 for the 3-level 3D LUT. Another model is called the “two-step polynomial” model which includes three 1D-LUTs between the normalized RGB luminance values and the number of RGB sustain pulses. This is followed by a transformation from normalized RGB luminance values to XYZ values via transformation matrix. Three 1D-LUTs were created for each of the RGB channels including 52 equal steps in RGB space. Linear interpolation was then used to predict the normalized luminance values between the data points. Six transformation matrices were used. One of them was the primary matrix obtained by measurements of RGB primary colors. This matrix can be used for the ideal case where there is little interaction among RGB channels and little unwanted emission. Additionally, five transformation matrices for nonideal cases, were derived using polynomial regression between the measured XYZ values for 6-, 5-, 4-, and 3-level 3D LUTs and their corresponding normalized RGB luminance values. The cross terms RG, RB, GB, and RGB were included in the matrix to compensate for cross-channel interaction. The square terms R2, G2, and B2 were also included, although these terms have no particular physical meaning. These terms were chosen because they were included in some previous display characterization studies.1,9 The performance of the three models was evaluated using three test sets. The first set includes 4 ⫻ 4 ⫻ 4 bright color patches that were chosen to correspond to L* values of 45, 85, 95, and 99 for each of the RGB channels. Two additional sets, including 24 colors 共L* ⬍ 40兲 and 27 colors composed of three L* values (20, 60, and 90), were also added to verify model performance. The three sets were merged to form a combined test set of 115 colors. The color difference * 共⌬Eab 兲 between the predicted and measured values for these test colors was calculated to evaluate the accuracy of characterization models. All measured tristimulus values were corrected by subtracting those of the black level. A subsequent experiment was carried out to investigate model performance for different pattern sizes. Only the single-step polynomial model was further developed in this experiment. Three training sets at each pattern size were used to generate the 3D LUTs [see Table III(b)]. Performance was then evaluated by measuring 27 test colors consisting of combinations of three input levels producing L* values of 20, 60, and 90 for each channel. Table IV gives the terms used to develop the single-step model and the transformation matrices of the two-step model. The polynomial coefficients were computed from experimental data consisting of 216, 125, 64, or 27 colors measured from the 6-, 5-, 4-, and 3-level 3D LUTs, respectively. Each sample includes a set of RGB sustain numbers and their corresponding XYZ values. In the two-step model’s transformation matrix, a polynomial relationship was determined between the normalized RGB luminances and XYZ values. All calculations were executed using Matlab.


Table IV. Detailed description of the terms used in the single- and two-step polynomial models. The matrices consisting of various polynomial coefficients

Independent variables

3⫻3

R, G, B

3⫻4

R, G, B, 1

3⫻5

R, G, B, RGB, 1

3⫻8

R, G, B, RG, RB, GB, RGB, 1

3 ⫻ 11

R, G, B, R2, G2, B2, RG, RB, GB, RGB, 1

3 ⫻ 20

关3 ⫻ 11兴 plus R3, G3, B3, R2G, R2B, G2R, G2B, B2R, B2G

3 ⫻ 35

关3 ⫻ 20兴 plus R3G, R3B, G3R, G3B, B3R, B3G, R2GB, RG2B, RGB2, R4, G4, B4, R2G2, R2B2, G2B2

COLORIMETRIC CHARACTERISTICS OF A PDP Spectral Characteristics The spectral power distributions of the maximum intensity RGB primaries are shown in Figure 6(a). Two kinds of green phosphors were used for boosting luminance and stabilizing discharge: Zn2SiO4 : Mn with a broad band at 526 nm and YBO3 : Tb with a sharp peak at 544 nm, respectively. To improve red saturation, two types of red phosphors were mixed: 共Y , Gd兲BO3 : Eu with three main peaks at 593, 611, and 628 nm, together with Y共V , P兲O4 : Eu which has a sharp peak at 620 nm. The former red phosphor appears redorange due to its main 593 nm emission peak, and it also possesses the highest conversion efficiency of vuv radiation into red visible light. On the other hand, Y共V , P兲O4 : Eu, having a sharp main peak at 620 nm, offers good red color purity. BaMaAl10O17 : Eu was employed as the blue phosphor. It generates high luminance from a vuv excitation source but is weak under the harsh conditions of high energy vuv radiation. Consequently, it plays a key role in display longevity. For these reasons, the spectral properties of a PDP appear to be more complex than the other kinds of displays. Fig. 6(b) is an enlargement of Fig. 6(a) and illustrates the red-orange emission of Ne gas. The intensity of red-orange emission due to Ne gas was quite small compared with the other main peaks caused by phosphor materials. Hence the maximum radiance values used for Figs. 6(a) and 6(b) are different. The fluctuations cause decrease in color purity as mentioned earlier. The characteristic redorange Ne gas emission at 585.2 nm results from atomic electronic transitions from the higher energy 2p quantum state to the lower lying 1s energy level.10 Temporal Stability A PDP needs time to reach a steady state for accurate measurement. As a result, temporal stability was evaluated over 60 minutes using four pattern sizes, each consisting of a white color as shown in Figure 7. The white color at size 4% and having the highest number of sustain pulses shows the

341


Figure 6. 共a兲 Spectral power distributions of normalized RGB primaries. 共b兲 Visible emission of neon gas between 580 and 680 nm.

crease in luminance ratio is inversely proportional to pattern size due to the shorter time needed to reach a stable RGB cell temperature.

Figure 7. Plot of relative luminance values over time for white at 4, 30, 60, and 100% pattern size.

Figure 8. 共a兲 White color patch at 30% pattern size with a black background. 共b兲 White color patch at 30% pattern size with a white background.

largest gap between its initial state and a steady state. For the 4% and 30% color patches, the luminance decreases significantly at the beginning. Although the time to reach a steady state is similar for all four pattern sizes (around 40 min), the decrease in luminance is dependent on pattern size. A decrease in pattern size leads to an increase the number of RGB sustain pulses accompanied by an increase in temperature of the RGB cells. If a small color patch is displayed on a PDP, the initial temperature is higher than that for a larger sized patch; however this is mitigated by a greater rate of temperature change. As a result, the time to reach a steady state is not dependent on pattern size. Conversely, the de342

Spatial Independence The two color patches shown in Figures 8(a) and 8(b) have the same center square color and different backgrounds. Spatial independence defines by how much the central white color is affected by changes in background color.11 The central white colors of Figs. 8(a) and 8(b) have quite different CIE XYZ values (445, 444, 550) and (160, 166, 186), respectively, because the colorimetric characteristics of a PDP are dictated by the number of RGB sustain pulses as determined by the APC rather directly from the RGB input values. For example, in order to produce the same light output for the white in Figs. 8(a) and 8(b), there is a need to have different numbers of sustain pulses. Color Gamut The definition of color gamut is the range of colors that is achievable on a given color reproduction medium under a specified set of viewing conditions. Figure 9 shows the color gamut under dark viewing conditions defined by the primary and secondary colors of a PDP. The ranges of tristimulus values displayed differ according to pattern size (as explained in Pattern size effect section). The color gamuts of four pattern sizes are plotted in a CIELAB a*b* diagram [Fig. 9(a)]. In addition, color gamuts of four pattern sizes at a hue angle of 137° are compared using a CIELAB C*L* diagram [Fig. 9(b)]. The CIE L*a*b* color coordinates were calculated based on the peak white at 4% pattern size representing an L* of 100 共848.4 cd/ m2兲. Therefore, the C*L* coordinates of the white color patches for 30, 60, and 100% pattern sizes show lower values than those at the 4% pattern size. As pattern size decreases, the range of colors achievable on a PDP becomes larger. Tone Reproduction Curve The tone reproduction curve depicts the relationship between RGB input values and their resultant luminance valJ. Imaging Sci. Technol. 51共4兲/Jul.-Aug. 2007


Figure 9. 共a兲 Color gamuts for the 4, 30, 60, and 100% pattern sizes plotted in an a*b* diagram. 共b兲 Color gamuts at a hue angle of 137° for the 4, 30, 60, and 100% pattern sizes plotted in a C*L* diagram.

ues. The RGB luminances of a CRT are controlled by cathode voltages. For PDPs, on the other hand, the number of RGB sustain pulses controls luminance. Figures 10(a) and 10(b) illustrate the intrinsic properties of the PDP studied. Figures 10(a) and 10(b) contain plots of normalized Y values for the 4% size (white luminance is 1) against the normalized number of sustain pulses and input values, respectively. It can be clearly seen in Fig. 10(a) that an increase in the number of RGB sustain pulses leads to an increase in RGB luminance. Furthermore, a larger patch size has a smaller range of sustain pulse numbers. This is because a larger pattern size is constrained to a lower maximum number of sustain pulses in order avoid exceeding power consumption limitations. The points indicated by the arrows correspond to 95% relative luminance, with respect to the maximum white luminance value at each pattern size. The intrinsic TRC of a PDP [Figs. 10(a) and 10(b)] should be modified so that the slope of the low luminance range is much smaller than that at high luminances. Figure 10(c) shows the result after gamma is modified by adjusting the number of sustain pulses. The shape of the TRC after gamma modification is the same regardless of pattern size. The usable range of the number of sustain pulses, however, depends on pattern size. For example, to produce a white patch on this PDP using an input value of 255, either 466, 766, 1376, or 2594 RGB sustain pulses are assigned, respectively, for the 100%, 60%, 30%, and 4% pattern sizes. The number of sustain pulses available for white at 100% pattern size, 0 to 466, are quantized to 256 levels to make white luminance follow a power function of approximately 2.2 (the gamma value). Additivity The channel additivity was evaluated for white at four pattern sizes. The results are given in Table V in terms of percentage change in tristimulus values and color difference * 兲. The tristimulus values of the RGB patches having 共⌬Eab J. Imaging Sci. Technol. 51共4兲/Jul.-Aug. 2007

the same number of sustain pulses as the peak white patch were measured to evaluate additivity for each pattern size. A substantial difference between the tristimulus values for white and the sum of the red, green and blue channels was found. The latter is larger than the former by about 15% * units. The availwhich corresponds to approximately 6 ⌬Eab able power to a cell drops as other cells become active, leading to a reduction in brightness. This means that, for example, in terms of luminance, 共R + G + B兲 ⬎ white. To counteract the problem of deviation from additivity, several matrix coefficients—including RGB channel cross terms (RG, RB, GB, and RGB)—were incorporated into the transformation matrices of the two-step model. In addition, a 3D LUT model was implemented in which many measured data points were included so as to compensate for the inherent additivity failure of a PDP. COLORIMETRIC CHARACTERIZATION MODEL FOR A PDP Testing the Models’ Performance at 100% Pattern Size As introduced in the third section, three types of characterization models were developed: 3D-LUT, single-step polynomial, and two-step polynomial. These were tested using the 115-test color set. All of the models developed here are based on a 100% pattern size. The results are summarized in Table * units. VI in terms of mean and 95th percentile ⌬Eab It can be seen that the 3D-LUT model using tetrahedral interpolation12 gave a reasonable prediction to the test data * units. with a mean and a 95th percentile of 1.3 and 2.5 ⌬Eab The two-step model using the primary matrix in which their coefficients were based on the measurement data gave quite poor performance with a mean difference of 4.3. Comparing different single-step polynomial models, there is a trend that the higher order polynomial models performed better than the lower ones. However, this is only true for the models developed using more training samples. 343


ing and testing data sets. It can be seen that the models predicted more accurately when the terms increase until reaching 3 ⫻ 11 and 3 ⫻ 20 polynomial models. For the 3 ⫻ 35 model, this fits the training data set best, however it performed poorly for the testing data set due to modeling the noise in the training data set. In real applications, both the forward and reverse characterization models are used, i.e., from device signal to XYZ and vice versa. However, not all models are analytically invertible and so reverse models were developed having the same structure as the forward model. The numerical reversibility of the single-step model was also tested. The testing procedure is shown in Figure 12 and does not require any color measurement. Here the 115-test color set, defined in terms of XYZ, was again used to first predict RGB sustain pluses using the reverse model and then further predict the corresponding XYZ via the forward model. Finally, the color difference was calculated between the target XYZ and predicted XYZ values. The results for each combination of forward and reverse polynomial model developed by the 4-level training data are given in Table VII. It can be seen that the 3 ⫻ 11 polynomial model can give acceptable performance * (its mean and 95th percentile are 0.3 and 0.8 ⌬Eab , respectively). This can be further improved by using the 3 ⫻ 20 model. Both models outperformed the other models studied.

Figure 10. 共a兲 The relationship between normalized number of sustain pulses and normalized white luminance for 4, 30, 60, and 100% pattern sizes before the modification of gamma. 共b兲 The relationship between normalized input values and normalized white luminance for four pattern sizes before the modification of gamma. 共c兲 The relationship between normalized input values and normalized white luminance for four pattern sizes after modifying gamma.

For those models developed using the 3-level and 4-level training samples, the higher term polynomial models did not exhibit more accurate prediction than the lower order models. This could be caused by over-fitting the measurement noise when using higher order polynomial models based on small number of training samples. Overall, the 3 ⫻ 11 polynomial model developed using the 4-level training data set (which included 64 colors) was found to be acceptable for industrial applications. Using the 3 ⫻ 20 model can lead to further improvements in the modeling performance. In comparing the single- and two-step models, the single-step model performed slightly better than the twostep model except for the 3 ⫻ 3 model. This implies that single-step polynomial models with a higher order already consider the cross-talk between different channels in PDPs. There is needless to include a 1D-LUT normalization. Figure 11 shows different polynomial performances for * using the traina single-step model in terms of mean ⌬Eab 344

Testing the Models’ Performance at Different Pattern Sizes Using the same approach as for the 100% pattern size (previous section), different single-step polynomial models developed using 3-, 4-, and 5-level 3D-LUT training data for each of the 4%, 30%, and 60% pattern sizes. Very similar performances were found and so only the results from the 30% pattern size are reported in Table VIII in terms of mean * and 95th percentile ⌬Eab values. The results showed that the 3 ⫻ 11 and 3 ⫻ 20 polynomial models using 4- or 5-level training data gave a reasonable prediction. These results are very similar to those found at 100% pattern size (see Table VI). Developing a Single Characterization Model As mentioned in the Pattern size effect section, light output is proportional to the number of sustain pulses and the range these are regulated by the APC according to pattern size. Hence the characterization models developed earlier are only applicable to a single pattern size. A new method is developed here which aims to predict the colors displayed at different pattern sizes. In order to make a single model which can predict CIE XYZ at pattern sizes other than that used for the training set, it is necessary to select an appropriate training set covering the whole range of sustain pulses used for the test set. For example, it needs to predict CIE XYZ values of several colors in 80% and 45% sizes. There are two approaches to the selection of a training set for this purpose. First, a set having smaller size than 45% can be used because this can cover a higher range of sustain pulses than those available for the 80% and 45% sizes. Second, two J. Imaging Sci. Technol. 51共4兲/Jul.-Aug. 2007

Choi et al.: Colorimetric characterization model for plasma display panel Table V. Tristimulus additivity failure and corresponding color difference for white at 4, 30, 60, and 100% pattern size. Pattern size

RGB IVs

Y 共cd/ m2兲

APC level

No. of sustain

X

Y

Z

* ⌬Eab

100%

255

166.1

255

466

15.1%

13.9%

16.4%

5.6

60%

255

263.2

219

766

16.7%

15.2%

19.2%

6.5

30%

255

443.6

146

1376

17.6%

17.8%

19.9%

6.6

4%

255

848.0

0

2594

16.7%

16.6%

21.1%

6.6

* Table VI. Testing the performance 共in terms of ⌬Eab 兲 of the characterization models using the 115-color test set. The models were developed based on 6-, 5-, 4- and 3-level training sets.

Training set


Two-step polynomial model

3D LUT

3⫻5

3⫻8

3 ⫻ 11

3 ⫻ 20

3 ⫻ 35

1.5

1.2

1.2

6-level

Mean

1.3

3.8

3.1

95th

2.5

9.4

11.7

3.8

2.7

2.8

5-level

Mean

3.5

2.8

1.4

1.2

1.1

95th

8.3

9.4

3.3

2.7

2.3

4-level

Mean

3.4

2.5

1.5

1.2

3.9

95th

7.8

7.8

3.7

2.8

11.7

3-level

a

Primary matrix

4.3 6.9

3⫻3

3⫻4

3⫻8

3 ⫻ 11

3 ⫻ 20

3 ⫻ 35

3.2

3.5

1.7

1.5

1.3

1.4

8.3

8.3

4.5

3.4

2.9

3.0

3.1

3.2

1.6

1.5

1.3

1.3

7.4

7.4

4.1

3.2

2.7

2.5

3.0

3.0

1.6

1.5

1.3

3.8

6.6

6.8

3.6

3.4

3.0

10.3

Mean

3.2

2.3

1.6

7.0

69.5

3.0

3.1

1.5

1.6

3.6

17.9

95th

8.0

7.2

3.5

22.9

305.5

6.8

6.7

3.7

3.6

11.5

55.2

a

The primary matrix was obtained from RGB primary colors.

Table VII. Reversibility result of polynomials for the 4-level training set in terms of * . ⌬Eab

* Figure 11. A comparison of average ⌬Eab values against the terms used in the single-step polynomial model for the test and training set.

training sets—one set having smaller pattern size than 45% and another having 100% size—can be combined to make a new training set. The reasoning behind the second method is to improve model accuracy. If two color patches at different pattern sizes but with same RGB sustain pulses are measured, a subtle difference in their XYZ values could be found. One practical example is that the luminance values for 30%, 60% and 100% pattern sizes using the same number of sustain pulses (408), are 111, 107, and 104, respectively. This is due to the available power to a cell being slightly different because of the different number of activated cells at different pattern sizes. Although the first training set may be sufficient, the polynomial coefficients computed by the second training set can be expected to take into account this small color difference due to pattern size. In real applications, the number of sustain pulses used to display comJ. Imaging Sci. Technol. 51共4兲/Jul.-Aug. 2007

3⫻5

3⫻8

3 ⫻ 11

3 ⫻ 20

3 ⫻ 35

Mean

2.3

1.6

0.3

0.2

1.7

95th

5.9

4.9

0.8

0.5

4.8

plex images typically corresponds to those associated with 40–50 % pattern sizes. Therefore, we generated the first training set as 4-level 3D LUT for the 30% pattern size. In addition, a second training set was produced by combining two 4-level 3D LUTs of 100% and 30% pattern sizes. These two 4-level 3D LUTs were composed of different combinations of RGB sustain pulses. The test data included three 27-color test sets at 80%, 60%, and 45% sizes. Tables IX(a) and IX(b) summarize the results from the first and second training sets. The results from the second training set show that the polynomials with 11, 20, and 35 terms performed well and gave similar predictive accuracy for the three pattern sizes in Table IX(b). Table IX(a) summarizes the results for the models developed using only the 30% pattern size. The results in Table IX(b) are worse than those in Table IX(b) in all cases. This demonstrates that it is better to use the combined training set of 100% and 30% sizes for predicting midsized test colors. CONCLUSIONS The physical properties of a PDP which affect colorimetric characterization were examined. Also, colorimetric characteristics unique to PDP displays were investigated. Among those, a pattern-size influence and a substantial additivity 345


Figure 12. The process for testing reversibility. * Table VIII. A comparison of the performances 共in terms of ⌬Eab 兲 using the 27-color test set and 5-, 4-, and 3-level training sets at 30% pattern size.


Training set

3⫻5

3⫻8

3 ⫻ 11

3 ⫻ 20

3 ⫻ 35

5-level

Mean

3.8

3.3

1.1

1.3

1.5

95th

8.8

9.1

2.2

3.0

3.4

4-level

Mean

3.7

3.0

1.4

1.5

3.2

95th

7.6

6.6

2.4

2.6

8.8

Mean

3.9

3.2

2.2

8.6

26.9

95th

7.7

6.8

4.2

18.2

52.0

3-level

* Table IX. 共a兲 Comparing models’ performance 共⌬Eab 兲 using each 27-color test set at 80%, 60%, and 45% pattern size. Each model was developed * using the 4-level training set at 30% pattern size. 共b兲 Comparing models’ performance 共⌬Eab 兲 using each 27-color test set at 80%, 60%, and 45% pattern size. Each model was developed using two 4-level training sets at 30% and 100% pattern sizes.

共a兲 Single-step polynomial model

Training set

Test set

* ⌬Eab

3⫻5

3⫻8

3 ⫻ 11

3 ⫻ 20

3 ⫻ 35

30% pattern size 共4-level兲

80%

Mean

5.1

5.3

2.1

2.5

2.9

95th

9.5

10.6

4.2

5.2

7.6

60%

Mean

4.8

4.9

1.9

2.2

2.4

95th

9.5

10.1

4.3

4.8

6.7

Mean

3.9

3.7

1.8

1.7

2.4

95th

7.7

7.6

3.2

3.1

6.3

3 ⫻ 20

3 ⫻ 35

45%

共b兲 Training set

Test set

* ⌬Eab

Mixture of 100% 共4-level兲 & 30% 共4-level兲 pattern size

80%

Mean

4.4

4.8

1.7

1.5

1.1

95th

9.0

11.0

3.5

3.3

2.5

60% 45%

Single-step polynomial model 3⫻5

3 ⫻ 11

Mean

4.2

4.4

1.7

1.5

1.3

95th

8.8

10.3

3.7

2.8

2.3

Mean

3.3

3.1

1.6

1.4

1.6

95th

6.8

6.9

2.7

2.0

3.2

failure were found. These must necessarily be considered when making an accurate colorimetric characterization model. Initially, three characterization methods were derived between the number of sustain pulses and CIE XYZ values at 100% pattern size in order to determine an appropriate model for a PDP. In the forward direction, single- and twostep polynomial models, which each have more than 8 terms, and a 3D LUT model showed the best results for the 346

3⫻8

6-, 5-, and 4-level training set. However, the single-step model was eventually selected because of its simplicity. The required number of training set samples needed to obtain good model performance and requiring the least measurement, was 64 for the 4-level 3D LUT. Also the reversibility of the single-step model was evaluated using a 4-level 3D LUT and this was shown to produce satisfactory results for 11and 20-term polynomials. Therefore, the single-step model was extended to various other pattern sizes. Their results J. Imaging Sci. Technol. 51共4兲/Jul.-Aug. 2007


validated that the polynomial regression method using the 4-level training set was a good characterization model for this PDP display. Finally, one comprehensive training set consisting of two 4-level 3D LUTs corresponding to 100% and 30% pattern sizes were produced to predict CIE XYZ at intermediate pattern sizes (i.e., sizes which were not present in the training set). These outcomes demonstrated that the single-step model could be successfully applied to estimate colors at different pattern sizes using just one combined training set. REFERENCES 1

N. Katoh, T. Deguchi, and R. S. Berns, “An Accurate Characterization of CRT Monitor (I) Verification of Past Studies and Clarification of Gamma”, Opt. Rev. 8, 305 (2001). 2 N. Katoh, T. Deguchi, and R. S. Berns, “An Accurate Characterization of CRT Monitor (II) Proposal for an Extension to CIE Method and its Verification”, Opt. Rev. 8, 397 (2001). 3 M. D. Fairchild and J. E. Gibson, “Colorimetric Characterization of Three Computer Displays (LCD and CRT)”, Munsell Color Science Laboratory Technical Report, http://www.cis.rit.edu/mcsl/research/PDFs/ GibsonFairchild.pdf (2000).


4

Y. S. Kwak and L. MacDonald, “Characterization of a Desktop LCD Projector”, Displays 21, 179 (2000). 5 D. R. Wyble and H. Zhang, “Colorimetric Characterization Model for DLP Projectors”, Proc. IS&T/SID 11th Color Imaging Conference (IS&T, Springfield, VA, 2003), pp. 346–350. 6 G. Kutas and P. Bodrogi, “Colorimetric Characterization of HD-PDP Device”, in IS&T’s 2nd European Conference on Color Graphics, Imaging and Vision, (IS&T, Springfield, VA, 2004,). pp. 65–69. 7 Multimedia Systems and Equipment—Color Measurement and Management, Part 5: Equipment using Plasma Display Panels, IEC 61966–5, 2001. 8 J. P. Boeuf, “Plasma Display Panels: Physics, Recent Developments and Key Issues”, J. Phys. D 36, R53 (2003). 9 P. Bodrogi and J. Schanda, “Testing a Calibration Method for Color CRT Monitors. A Method to Characterize the Extent of Spatial Interdependence and Channel Interdependence”, Displays 16(3), 123 (1995). 10 R. S. Van Dyck, C. E. Johnson, and H. A. Shugart, “Lifetime Lower Limits for the 3p0 and 3p2 Metastable States of Neon, Argon and Krypton”, Phys. Rev. A 5, 991 (1972). 11 P. Green and L. MacDonald, Color Engineering: Achieving Device Independent Color (John Wiley and Sons Ltd, West Sussex, UK, 2002), p. 158. 12 H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE Optical Engineering Press, Bellingham, WA, 1997), p. 64.

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