## Determination of optimal converting point of color temperature conversion complied with ANSI C78. 377 for indoor solid-state lighting and display applications |

Optics Express, Vol. 20, Issue 18, pp. 20059-20070 (2012)

http://dx.doi.org/10.1364/OE.20.020059

Acrobat PDF (1042 KB)

### Abstract

In recent years, displays and lighting require color temperature (CT) conversion function because observers have different preferences. This paper proposes effective methods to determine the optimal converting point of CT conversion for display and lighting application. For display application, the concepts of center of gravity and isotemperature line are applied to determine the optimal converting point. The maximal enhancement of luminance between the optimal and average is 18%. For lighting application, this paper proposes two methods to determine the optimal converting point in the CT quadrangle which complies with ANSI C78. 377. The enhancement of luminance in two CT modes (5700K and 6500K) are 14.2% and 23.6%, respectively.

© 2012 OSA

## 1. Introduction

9. M. Ou-Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express **15**(20), 13388–13403 (2007). [CrossRef] [PubMed]

10. S. Wen, “Design of relative primary luminances for four-primary displays,” Displays **26**(4–5), 171–176 (2005). [CrossRef]

11. L. Honam, C. Hyungjin, L. Bonggeun, P. Sewoong, and K. Bongsoon, “One-dimensional conversion of color temperature in perceived illumination,” IEEE Trans. Consum. Electron. **47**(3), 340–346 (2001). [CrossRef]

13. S. K. Kim, D. S. Park, W. H. Choi, and S. D. Lee, “Color temperature conversion for video on TV or PC reflecting human's display preference tendency,” in *Proceedings of IEEE Conferenc*e *on Convergence Information Technology* (Institute of Electrical and Electronics Engineers, Gyeongju, 2007), pp. 861–867.

*x,y*and

*u’,v’*). The standard defines the range of CCT as a quadrangle (7-steps from Planckain locus). The chromaticity tolerance is based on MacAdam ellipses to define the perceptible color difference. The appendix of the standard includes table for the chromaticity coordinates of the center points and the four corners of each quadrangle. Because the CIE 1976

*u’v’*chromaticity diagram is more uniform than the CIE 1931

*xy*chromaticity diagram and the CCT is defined on the CIE 1960 (

*u’,2/3v’)*chromacitity diagram, this paper derives the proposed algorithms based on the CIE 1976

*u’v’*chromaticity diagram.

15. M. Ou-Yang and S. W. Huang, “Design considerations between color gamut and brightness for multi-primary color displays,” J. Display Technol. **3**(1), 71–82 (2007). [CrossRef]

## 2. Theory

### 2.1 The method for determining the optimal converting point of CT conversion for display application

9. M. Ou-Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express **15**(20), 13388–13403 (2007). [CrossRef] [PubMed]

9. M. Ou-Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express **15**(20), 13388–13403 (2007). [CrossRef] [PubMed]

_{1}and C

_{2}were additively mixed, the resulting color C

_{3}was located on the line jointing C

_{1}and C

_{2}in a position given by the Centre of Gravity Law of Color Mixture. The line jointing C

_{3}and reference white point was called line of center of gravity of C

_{1}C

_{2}. Figure 1 is used to explain the proposed method. The dotted lines represent the isotemperature line. The dashed line represents the Planckian locus. The point p on the Planckian locus is chosen to be the target CT for example. When the luminance of R, G, and B are full input, the color gamut area is shrunk to a single point (point W; reference white point). As the luminance decreases, the single point is expanded to the triangle cde along the lines of center of gravity (RG, GB, and RB). When the luminance decreases again, these three apexes (the points c, d, and e) of the triangle also move along the lines of the center of gravity (RG, GB, and RB) and the area of the triangle increases (the triangle changes from cde to c’d’e’). Hence, when the reference white point is converted to the isotemperature line of target CT, the c is the optimal converting point. Because the point c is first met by the expanded color gamut from reference white point, the area of triangle cde is smaller than other triangles which are constructed by point on isotemperature line and the points on the lines of center of gravity RB, GB (for example, the area of triangle c’d’e’ is bigger than triangle cde). Therefore, the optimal converting point is the intersection between the line of center of gravity and the isotemperatue line. In addition, the lower CT is on the right side of the reference white point (W). Hence, when the target CT is lower than the reference white point of display, the optimal converting point of target CT can be obtained from the intersection between the line of the center of gravity RG and the isotemperature line. When the target CT is higher than the reference white point of the display, the optimal converting point can be obtained from the intersection between the line of the center of gravity GB and the isotemperature line.

#### 2.1.1 The chromaticity coordinate of the optimal converting point of CT conversion

*u’*,

_{i}*v’*), (

_{i}*u’*,

_{j}*v’*), and (

_{j}*u’*,

_{k}*v’*) are respectively the chromaticity coordinate of the primary color

_{k}*i*,

*j*and

*k*. Moreover,

*m*,

_{i}= Y_{i,MAX}/v’_{i}*m*,

_{j}= Y_{j,MAX}/v’_{j}*m*. When

_{k}= Y_{k,MAX}/v’_{k}*i*,

*j,*and

*k*represent R, G, and B, respectively, Eq. (1) is the equation for the line of the center of gravity of RG. When

*i*,

*j,*and

*k*represent G, B, and R, respectively, Eq. (1) is the equation for the line of the center of gravity of GB. When

*i, j,*and

*k*represent B, R, and G, respectively, Eq. (1) is the equation for the line of the center of gravity of RB.

*u’, 2/3v’*) chromaticity diagram. In 1992, McCamy [8

8. C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. **17**(2), 142–144 (1992). [CrossRef]

*T*represents the CT. Substitute the CT into Eq. (2) yields

*N*, which has three values - two complex numbers and one real number. Only the real number is of interest, and the value is between 1and −1. McCamy [10

10. S. Wen, “Design of relative primary luminances for four-primary displays,” Displays **26**(4–5), 171–176 (2005). [CrossRef]

*N*as

*(x-0.332)/(0.185-y)*. This paper transforms CIE 1931

*xy*coordinates to CIE 1976

*u’v’*coordinates because chromaticity of the space is more uniform than the CIE 1931

*xy*.where

*u’*and

*v’*represent chromaticity coordinates. The Eq. (3) is the equation of the isotemperature line.

### 2.2 Obtainment of the maximal luminance

15. M. Ou-Yang and S. W. Huang, “Design considerations between color gamut and brightness for multi-primary color displays,” J. Display Technol. **3**(1), 71–82 (2007). [CrossRef]

*Y*equals

_{R}*Y*(the luminance of R is full input) in the combination of luminance of tri-primaries, the CT conversion is associated with maximal luminance. In this case, the maximal luminance (

_{R,MAX}*Y*) equals to

_{total}*Y*+

_{R,MAX}*Y*+

_{G}*Y*., where

_{B}*Y*and

_{G}*Y*are variables which can be obtained from Eqs. (4) and (5)

_{B}*u’*,

_{W}*v’*) is the chromaticity coordinate of reference white point (P(R,G,B)),

_{W}*u’*and

_{W}= (m_{R}u’_{R}+ m_{G}u’_{G}+ m_{B}u’_{B})/(m_{R}+ m_{G}+ m_{B})*v’*= (

_{W}*m*+

_{R}v’_{R}*m*+

_{G}v’_{G}*m*)/(

_{B}v’_{B}*m*+

_{R}*m*+

_{G}*m*), where

_{B}*m*=

_{R}*Y*/

_{R,MAX}*v’*,

_{R}*m*=

_{G}*Y*/

_{G,MAX}*v’*, and

_{G}*m*=

_{B}*Y*/

_{B,MAX}*v’*. (

_{B}*u’*,

_{R}*v’*), (

_{R}*u’*,

_{G}*v’*), and (

_{G}*u’*,

_{B}*v’*) are the chromaticity coordinates of tri-primaries. This rule also can apply to the color point of target CT in zones 2 and 3. When

_{B}*Y*or

_{G}*Y*equals

_{B}*Y*or

_{G,MAX}*Y*, respectively, in the combination of the luminance of tri-primaries, the CT conversion is associated with maximal luminance. Clearly, only two variables are remained in the combination of the luminance of tri-primaries. The general form can be derived as Eqs. (6) and (7)

_{B,MAX}*l*is equal to B. When the color point of target CT is located on zone 3, the

*l*is equal to G.

### 2.3 Determination of the optimal converting point of CT conversion for SSL complied with ANSI C78. 377

## 3. Simulations and discussion

### 3.1 Simulation of display application

2. K. L. Kelley, “Lines of constant correlated color temperature based on MacAdam’s (u,v) uniform chromaticity transformation of the CIE diagram,” J. Opt. Soc. Am. **53**(8), 999–1002 (1963). [CrossRef]

*Δu’v’*= ± 0.04 between endpoint of isotemperature line and Planckian locus. The parameters of simulation were measured from the 30 inch LCD (Panasonic, TC-30MTF). The

*u’v’*chromaticity coordinates of the tri-primaries, R, G, and B were respectively (0.4490, 0.5241), (0.1139, 0.5556), and (0.1627, 0.1688). The luminance of the tri-primaries, R, G, and B were respectively 108.4 cd/m

^{2}, 347.08 cd/m

^{2}, and 56.41 cd/m

^{2}. The reference white point of the display was 10500K. Figure 4(a) shows the variation of luminance and chromaticity coordinates of simulated points of target CTs from 6000K to 13000K. The optimal converting points (solid circles) of each target CT were located on the intersection between line of center of gravity and isotemperature line. The worst points (hollow circles) were located on the endpoint of each isotemperature line. This was because when the color gamut expanded from the reference white point to the endpoint of isotempature line, the area of color gamut was bigger than it expanding to others point on the isotemperature line. For example, when the reference white point was converted to the color point on the 9500K isotemperature line, the luminance of black solid circle was more than hollow circle. Moreover, when the target CT was lower than the 10500K (reference white point), the optimal converting point of target CT was the intersection between line of center of gravity RG and the isotemperature line of target CT. When the target CT was higher than the 10500K, the optimal converting point was the intersection between line of center of gravity GB and the isotemperature line of target CT. The results were in accordance with the proposed method of this paper. Figure 4(b) shows the luminance of optimal converting points, worst points, and average value of all target CTs. The enhancement of the luminance was defined as “(optimal-average)/average”, where the optimal represented the optimal converting point and the average represented the average luminance value of 31 simulated color points of each CT. The maximal enhancement of luminance was on 6000K with 18%. The minimal enhancement of luminance was on 10500K with 6%. Hence, when the target CT was close to the reference white point (10500K) of the display, the enhancement of the luminance was limited. This was because the luminance of target CT was already close to the luminance of the reference white point of the display. Figure 4(c) shows the luminance of 31 simulated points of three CT modes (6500K, 8000K and 9500K) usually using by the display. Table 1 lists the results of these three useful CT modes. From the results, when people used the proposed method to implement the CT conversion of these three CT modes, the enhancement of luminance was 14%, 10%, and 7.5%, respectively.

### 3.2 Simulation of SSL application

*Y*= 42.3 cd/m

_{R}^{2},

*Y*= 428.8 cd/m

_{G}^{2}and

*Y*= 5.1 cd/m

_{B}^{2}. The

*u’v’*chromaticity coordinates of the tri-primaries, R, G, and B were respectively (0.5509, 0.5168), (0.1420, 0.5741), and (0.2002, 0.0339). These parameters were based on the LED product specification (RED POWER CO., LTD., u42RGBC2B-016). The ANSI C78. 377 gauged eight CTs for application. Figure 5(a) shows the simulated results of these eight CTs. As shown in Fig. 5(a), only the 6500K CT quadrangle intersected with the line of center of gravity. Hence, the simulation used the 5700K and 6500K to be the examples. We individual took 10000 points in these two CT quadrangles for simulation. The chromaticity coordinate of four corners of 5700K and 6500K quadrangles were according to the gauge of ANSI C78. 377. As shown in Fig. 5(b), when the color points were located away from the reference white point, the luminance of the color points must be decreased. This was because when the expanded color gamut from reference white point met the distant color point, the area of expanded color gamut was bigger than it meeting others color points. Therefore, the optimal converting point was located on the leftmost point of the quadrangle with the luminance of 226.4316 cd/m

^{2}. The worst point was located on the rightmost point of the quadrangle with the luminance of 188.0372 cd/m

^{2}. As shown in Fig. 5(c), the optimal converting point was the first intersection between line of center of gravity and edge line of 6500K CT quadrangle. The luminance of optimal converting point was 395.2242 cd/m

^{2}. The worst point was located on the rightmost point of the quadrangle with the luminance of 296.9473 cd/m

^{2}. The enhancement of luminance was defined as “(optimal-average)/average”, where the average was the average luminance value of 10000 points and optimal was the luminance of optimal converting point. The enhancement of luminance of 5700K and 6500K was 14.2% and 23.6%, respectively. Therefore, when the line of center of gravity intersected with the edge line of the CT quadrangle, the optimal converting point was the first intersection on the edge line of CT quadrangle. When the CT quadrangle did not intersect with the line of center of gravity, the corner point of CT quadrangle which was closest to the reference white point was the optimal converting pint. The results were in accordance with the proposed method of the article.

## 4. Experiment and discussion

*Δu’v’*= ± 0.04 between the endpoint of isotemperature line and the Planckian locus. In order to make the 21 measured points had the same chromaticity coordinates as the simulations, the experiment tuned luminance of the tri-primaries (R, G and B) of the display. Figure 6(b) shows the results of 1050 simulated points and 21 measured points. The values were listed on Table 2 . The 13th measured point on the 6500K isotemperature line was the optimal converting point with luminous flux of 5.889 lx. The point was also the optimal converting point of the simulation. The 21th measured point was the worst point with luminous flux of 4.737 lx. The point was also worst point of simulation. The average luminous flux of the 21 points was 5.162 lx. The enhancement of luminous flux was about 14.08%. The optimal and worst points were the same in the simulation and experiment. Since the target CT was close to the reference white point (6100K) of the 17” LCD, the enhancement of luminous flux was only about 14.08%. The color difference between the simulated points and measured points did not exceed 0.003. Hence, the experimental results were credible. The color difference between the simulated and measured points was caused by the luminance of quantization effects. Moreover, the leakage of light from displays also caused a tiny error.

## 5. Conclusions

## Acknowledgments

## References and links

1. | A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl. |

2. | K. L. Kelley, “Lines of constant correlated color temperature based on MacAdam’s (u,v) uniform chromaticity transformation of the CIE diagram,” J. Opt. Soc. Am. |

3. | A. R. Robertson, “Computation of correlated color temperature and distribution temperature,” J. Opt. Soc. Am. |

4. | D. B. Judd, “Estimation of chromaticity differences and nearest color temperature on the standard 1931 ICI colorimetric coordinate system,” J. Opt. Soc. Am. |

5. | J. Schanda and M. Danyi, “Correlated color-temperature calculations in the CIE 1976 chromaticity diagram,” Color Res. Appl. |

6. | M. Krystek, “An algorithm to calculate correlated colour temperature,” Color Res. Appl. |

7. | Q. Xingzhong, “Formulas for computing correlated color temperature,” Color Res. Appl. |

8. | C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. |

9. | M. Ou-Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express |

10. | S. Wen, “Design of relative primary luminances for four-primary displays,” Displays |

11. | L. Honam, C. Hyungjin, L. Bonggeun, P. Sewoong, and K. Bongsoon, “One-dimensional conversion of color temperature in perceived illumination,” IEEE Trans. Consum. Electron. |

12. | D. S. Park, S. K. Kim, C. Y. Kim, W. H. Choi, S. D. Lee, and Y. S. Seo, “User-preferred color temperature conversion for video on TV or PC,” Proc. SPIE |

13. | S. K. Kim, D. S. Park, W. H. Choi, and S. D. Lee, “Color temperature conversion for video on TV or PC reflecting human's display preference tendency,” in |

14. | ANSI_NEMA_ANSLG C78.377–2008. |

15. | M. Ou-Yang and S. W. Huang, “Design considerations between color gamut and brightness for multi-primary color displays,” J. Display Technol. |

16. | R. W. G. Hunt and M. R. Pointer, |

**OCIS Codes**

(120.2040) Instrumentation, measurement, and metrology : Displays

(150.2950) Machine vision : Illumination

(230.3670) Optical devices : Light-emitting diodes

(330.1690) Vision, color, and visual optics : Color

(330.1710) Vision, color, and visual optics : Color, measurement

**ToC Category:**

Vision, Color, and Visual Optics

**History**

Original Manuscript: April 24, 2012

Revised Manuscript: August 11, 2012

Manuscript Accepted: August 15, 2012

Published: August 17, 2012

**Virtual Issues**

Vol. 7, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Yao-Fang Hsieh, Mang Ou-Yang, Ting-Wei Huang, and Cheng-Chung Lee, "Determination of optimal converting point of color temperature conversion complied with ANSI C78. 377 for indoor solid-state lighting and display applications," Opt. Express **20**, 20059-20070 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-18-20059

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### References

- A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001). [CrossRef]
- K. L. Kelley, “Lines of constant correlated color temperature based on MacAdam’s (u,v) uniform chromaticity transformation of the CIE diagram,” J. Opt. Soc. Am.53(8), 999–1002 (1963). [CrossRef]
- A. R. Robertson, “Computation of correlated color temperature and distribution temperature,” J. Opt. Soc. Am.58(11), 1528–1535 (1968). [CrossRef]
- D. B. Judd, “Estimation of chromaticity differences and nearest color temperature on the standard 1931 ICI colorimetric coordinate system,” J. Opt. Soc. Am.26(11), 421–424 (1936). [CrossRef]
- J. Schanda and M. Danyi, “Correlated color-temperature calculations in the CIE 1976 chromaticity diagram,” Color Res. Appl.2(4), 161–163 (1977). [CrossRef]
- M. Krystek, “An algorithm to calculate correlated colour temperature,” Color Res. Appl.10(1), 38–40 (1985). [CrossRef]
- Q. Xingzhong, “Formulas for computing correlated color temperature,” Color Res. Appl.12(5), 285–287 (1987). [CrossRef]
- C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl.17(2), 142–144 (1992). [CrossRef]
- M. Ou-Yang and S. W. Huang, “Determination of gamut boundary description for multi-primary color displays,” Opt. Express15(20), 13388–13403 (2007). [CrossRef] [PubMed]
- S. Wen, “Design of relative primary luminances for four-primary displays,” Displays26(4–5), 171–176 (2005). [CrossRef]
- L. Honam, C. Hyungjin, L. Bonggeun, P. Sewoong, and K. Bongsoon, “One-dimensional conversion of color temperature in perceived illumination,” IEEE Trans. Consum. Electron.47(3), 340–346 (2001). [CrossRef]
- D. S. Park, S. K. Kim, C. Y. Kim, W. H. Choi, S. D. Lee, and Y. S. Seo, “User-preferred color temperature conversion for video on TV or PC,” Proc. SPIE5008, 285–293 (2003). [CrossRef]
- S. K. Kim, D. S. Park, W. H. Choi, and S. D. Lee, “Color temperature conversion for video on TV or PC reflecting human's display preference tendency,” in Proceedings of IEEE Conference on Convergence Information Technology (Institute of Electrical and Electronics Engineers, Gyeongju, 2007), pp. 861–867.
- ANSI_NEMA_ANSLG C78.377–2008.
- M. Ou-Yang and S. W. Huang, “Design considerations between color gamut and brightness for multi-primary color displays,” J. Display Technol.3(1), 71–82 (2007). [CrossRef]
- R. W. G. Hunt and M. R. Pointer, Measuring Colour (Willey, 2011).

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