Table 1.
Spectral Performances of the Matched Spectra with
$\mathsf{p}$
and RMSE as the Objective Function, Respectively
 Objective Function:
$p$
 Objective Function: RMSE 
Target  GFC 
$\mathrm{RMSE}/(\times {10}^{4})$

$p$
 GFC 
$\mathrm{RMSE}/(\times {10}^{4})$

$p$

A_500 lx  0.9960  1.8275  0.0619  0.9971  1.5536  0.0597 
A_1000 lx  0.9968  3.2731  0.0603  0.9973  2.9711  0.0556 
D65_500 lx  0.9936  2.6747  0.0809  0.9930  2.3730  0.0768 
D65_1000 lx  0.9930  5.0735  0.0668  0.9950  4.6818  0.0803 
Table 2.
Colorimetric Performances of the Matched Spectra with
$\mathsf{p}$
and RMSE as the Objective Function, Respectively
 Objective Function:
$p$
 Objective Function: RMSE 
Target 
${\mathrm{\Delta}}_{Tc}/\%$

${\mathrm{\Delta}}_{{u}^{\prime},{v}^{\prime}}$

${\mathrm{\Delta}}_{E}/\%$

${R}_{a}$

${R}_{9}$

${R}_{f}$

${R}_{g}$

${\mathrm{\Delta}}_{Tc}/\%$

${\mathrm{\Delta}}_{{u}^{\prime},{v}^{\prime}}$

${\mathrm{\Delta}}_{E}/\%$

${R}_{a}$

${R}_{9}$

${R}_{f}$

${R}_{g}$

A_500 lx  9.38  0.0120  4.60  93  53  91  100  6.27  0.0078  4.40  93  53  92  98 
A_1000 lx  8.47  0.0105  2.70  92  52  92  99  7.28  0.0093  4.00  93  58  92  99 
D65_500 lx  2.14  0.0017  2.40  96  72  94  98  0.74  0.0059  3.00  94  58  92  96 
D65_1000 lx  0.77  0.0060  0.50  93  57  93  96  5.60  0.0063  3.30  94  64  92  97 
Table 3.
Spectral and Colorimetric Performances of the Matched Spectra of D65 with the Combination of
$\mathsf{p}$
and
${\mathsf{M}}_{\mathsf{v}}$
as the Objective Function
 Spectral Performance  Colorimetric Performance 
Target  GFC 
$\mathrm{RMSE}/(\times {10}^{4})$

$p$

${\mathrm{\Delta}}_{Tc}/\%$

${\mathrm{\Delta}}_{{u}^{\prime},{v}^{\prime}}$

${\mathrm{\Delta}}_{E}/\%$

${\mathrm{\Delta}}_{{u}^{\prime}10,{v}^{\prime}10}$

${M}_{v}$

${R}_{a}$

${R}_{9}$

${R}_{f}$

${R}_{g}$

D65  500 lx  0.9894  3.3425  0.0955  4.23  0.0036  0.60  0.0040  0.48  98  93  97  101 
1000 lx  0.9903  6.3616  0.0895  3.18  0.0026  0.30  0.0032  0.47  99  97  97  101 
Table 4.
Statistical Results of the Optimized
$\mathsf{p}$
among 25 Runs of SA, GA, ES, PSO, and the Proposed Method when Matching CIE Standard Illuminant A at 500 lx with the Parameter
$\mathsf{p}$
as the Objective Function
 Mean  Best  Poorest  St. Dev 
SA  0.1643  0.1069  0.2528  0.0344 
GA  0.1063  0.0671  0.1605  0.0220 
ES  0.0758  0.0643  0.1098  0.0110 
PSO  0.0648  0.0576  0.0904  0.0096 
Proposed  0.0603  0.0576  0.0658  0.0018 
Table 5.
Colorimetric Performances of the Optimal SPDs Corresponding to the Eight Target CCTs at 500 and 1000 lx
Target CCT/K  2800  3500  4000  4500  5000  5500  6000  6500 
500 lx 
${\mathrm{\Delta}}_{Tc}/\%$
 0.32  0.29  0.05  0.02  0.20  0.07  0.27  0.12 
${\mathrm{\Delta}}_{{u}^{\prime},{v}^{\prime}}/(\times {10}^{4})$
 6.49  4.71  5.48  5.04  4.80  2.01  12.48  12.68 
${\mathrm{\Delta}}_{E}/\%$
 0.60  0.80  0.40  1.20  0.80  1.40  0.20  1.20 
${R}_{a}$
 96  97  98  98  98  99  99  99 
${R}_{9}$
 74  72  83  91  86  97  97  97 
${R}_{f}$
 93  94  96  97  96  96  97  95 
${R}_{g}$
 102  101  101  100  100  100  100  99 
1000 lx 
${\mathrm{\Delta}}_{Tc}/\%$
 0.68  0.23  0.15  0.16  0.10  0.35  0.08  0.26 
${\mathrm{\Delta}}_{{u}^{\prime},{v}^{\prime}}/(\times {10}^{4})$
 7.16  8.91  8.34  7.85  13.93  9.77  12.64  10.99 
${\mathrm{\Delta}}_{E}/\%$
 1.10  0.90  0.80  0.70  0.80  0.50  0.50  0.70 
${R}_{a}$
 96  97  98  99  99  99  99  99 
${R}_{9}$
 73  80  90  93  96  93  99  93 
${R}_{f}$
 93  93  96  97  97  97  96  96 
${R}_{g}$
 102  101  100  100  100  100  99  100 
Table 6.
Statistical Results of the Optimal
${\mathsf{R}}_{\mathsf{a}}$
Among 25 Runs of CHDE, ALGA, HMPSO, and the Proposed Method at the Joint Target of 6500 K and 1000 lx
 Mean  Best  Poorest  St. Dev 
CHDE  84  96  57  9.71 
ALGA  80  95  63  9.10 
HMPSO  83  98  61  8.63 
Proposed  98  99  96  0.96 