Further information relating to examination of SPD Curves

This web-page is designed to display example spectral distribution curves for tested light sources. For more information relating to the graphing library used in this page see the dygraphs website. For more information about the project in general contact Joseph Padfield.


Calculating the TM-30 Rf & Rg values along with the CCT and Duv values from the SPD curve of: Test Lamp: LED


TM-30 Calculations

TM-30 - Calculation Summary

The TM-30-15 standard metric is a two-measure system describing colour fidelity (Rf) and colour gamut (Rg), which are calculated based the state-of-the-art uniform colour space CAM02-UCS (CIECAM02), using a set of 99 real, color evaluation samples (CES) with colour space uniformity and spectral uniformity.

  • Starting with the test SPD curve, find the chromaticity xy co-ordinates of the test source from its calculated CIE 1931 color space XYZ values, using the 2° colour matching functions.
  • Determine the correlated color temperature (CCT) of the test source and select the appropriate black body reference source. This is done using a new linear combination of blackbody and daylight spectra for CCTs in the range 4500–5500 K.
  • All subsequent calculations are carried out using the 1964 10° color-matching functions.
  • For the colour fidelity (Rf) metric, the CAM02-UCS colour coordinates of the CES under the reference and test illuminants are calculated, along with the resulting colour error for each CES. The arithmetic mean of the errors is determined to obtain an average error ΔE for the SPD and an intermediate fidelity score using: Rf' = 100 − k * ΔE.
  • This value is then scaled between 0 an 100 using: Rf = 10 * ln exp ( Rf'/10 ) + 1
  • For the colour gamut (Rg) metric, the (J', a', b') color coordinates of the test samples under the reference illuminant and test source are computed, using the same test SPD curve and reference illuminant, and grouped into 16 hue bins of equal width.
  • In each bin we compute the average values of a' and b', resulting in 16-point polygons in the (a', b') plane for the reference and test samples.
  • The relative gamut is then: Rg = 100 * Atest/Aref, where Atest and Aref are the areas of the test and reference polygons.
  • This very brief description was taken from: A. David, P. Fini, K. Houser, Y. Ohno, M. Royer, K. Smet, M. Wei, and L. Whitehead, "Development of the IES method for evaluating the color rendition of light sources," Opt. Express 23, 15888-15906 (2015).

IlluminantBlack Body
X1098.572497.416
Y10100100
Z1085.264684.4696

λ (nm)Test SPDRef SPD
3800.00080.3965
3810.00040.4011
3820.00050.4057
38300.4103
3840.00030.4148
3850.00110.4194
38600.4239
3870.00050.4285
3880.00110.433
3890.00030.4375
3900.00020.4421
3910.00250.4542
39200.4663
3930.00010.4784
3940.00090.4905
3950.00040.5026
3960.00210.5147
3970.00060.5268
3980.0010.5388
39900.5509
40000.5629
4010.00030.5683
40200.5737
40300.5791
40400.5844
4050.00030.5898
4060.00150.5951
4070.00230.6005
4080.00360.6058
4090.00370.6111
4100.00490.6164
4110.00930.6197
4120.00870.623
4130.01140.6263
4140.01390.6296
4150.01850.6329
4160.02310.6361
4170.02860.6394
4180.0330.6426
4190.04250.6458
4200.04910.6491
4210.05890.6492
4220.07010.6493
4230.08260.6494
4240.09840.6495
4250.11530.6496
4260.13380.6497
4270.1560.6498
4280.17990.6498
4290.20680.6499
4300.2360.6499
4310.26970.6602
4320.30510.6705
4330.34390.6808
4340.38660.6911
4350.43410.7014
4360.48510.7116
4370.54060.7219
4380.60410.7321
4390.67190.7423
4400.74640.7526
4410.82640.7603
4420.91450.768
4431.00930.7757
4441.1080.7834
4451.20940.7911
4461.31080.7988
4471.40680.8065
4481.49310.8142
4491.56670.8218
4501.6220.8295
4511.65550.8323
4521.66330.8351
4531.65010.8378
4541.6110.8406
4551.55380.8434
4561.48360.8461
4571.40350.8488
4581.31860.8516
4591.23610.8543
4601.15810.857
4611.08770.8583
4621.02640.8596
4630.97320.8608
4640.92570.8621
4650.8870.8633
4660.85430.8646
4670.82160.8658
4680.79120.867
4690.76250.8683
4700.73290.8695
4710.70740.8722
4720.68310.875
4730.66010.8778
4740.63750.8805
4750.61820.8833
4760.60470.886
4770.59180.8888
4780.58530.8915
4790.58230.8942
4800.57870.8969
4810.58110.8959
4820.58490.8949
4830.59040.8939
4840.59710.8929
4850.60470.8919
4860.61460.8908
4870.62510.8898
4880.63590.8887
4890.64630.8876
4900.65730.8866
4910.66920.8892
4920.68210.8917
4930.69540.8943
4940.70890.8969
4950.72190.8994
4960.73520.9019
4970.74860.9045
4980.76060.907
4990.77340.9095
5000.78620.912
5010.79770.913
5020.8080.914
5030.81970.9149
5040.82910.9159
5050.83830.9169
5060.84650.9178
5070.8540.9187
5080.86150.9197
5090.86820.9206
5100.87490.9215
5110.88120.9222
5120.88540.9228
5130.89040.9235
5140.8950.9242
5150.89930.9248
5160.90310.9254
5170.90780.9261
5180.91090.9267
5190.91390.9273
5200.91850.9279
5210.92150.9309
5220.9250.9338
5230.92960.9368
5240.93250.9397
5250.93640.9427
5260.93990.9456
5270.94420.9485
5280.94750.9514
5290.95110.9544
5300.95610.9573
5310.9610.9568
5320.96520.9563
5330.96970.9559
5340.97360.9554
5350.97780.9549
5360.98070.9544
5370.98370.9539
5380.98790.9534
5390.9910.9529
5400.9940.9524
5410.99750.9534
5421.00140.9544
5431.00330.9554
5441.00580.9564
5451.00850.9574
5461.01010.9584
5471.0120.9593
5481.01370.9603
5491.01460.9612
5501.01610.9622
5511.01710.9611
5521.01680.96
5531.01730.9588
5541.01670.9577
5551.01630.9566
5561.01510.9554
5571.01360.9543
5581.01170.9531
5591.00990.952
5601.00690.9508
5611.00470.9496
5621.00030.9485
5630.99740.9473
5640.9940.9462
5650.98980.945
5660.98630.9438
5670.98240.9426
5680.97820.9415
5690.97290.9403
5700.96820.9391
5710.96480.9397
5720.95960.9403
5730.95480.9408
5740.94990.9414
5750.94550.942
5760.94180.9426
5770.93740.9431
5780.93240.9437
5790.92840.9443
5800.9250.9448
5810.92060.9418
5820.91770.9389
5830.91480.9359
5840.91130.9329
5850.90840.9299
5860.90640.9269
5870.90430.9239
5880.90360.9209
5890.90210.9179
5900.90060.9149
5910.89950.9169
5920.89890.9189
5930.89870.921
5940.89910.923
5950.89860.925
5960.89920.927
5970.90.929
5980.90050.931
5990.90110.933
6000.9030.935
6010.90430.9356
6020.90470.9363
6030.90790.9369
6040.91080.9375
6050.91310.9381
6060.91510.9387
6070.91810.9393
6080.9210.9399
6090.9240.9405
6100.92740.9411
6110.93140.9407
6120.9360.9403
6130.93970.94
6140.94350.9396
6150.94720.9392
6160.9510.9388
6170.95490.9384
6180.95880.938
6190.96170.9376
6200.96470.9372
6210.96850.9352
6220.97160.9332
6230.97440.9311
6240.97720.9291
6250.97930.927
6260.98150.925
6270.98360.9229
6280.98480.9209
6290.98610.9188
6300.98580.9168
6310.98580.9181
6320.98810.9193
6330.98440.9206
6340.98490.9219
6350.98350.9232
6360.98240.9244
6370.98030.9257
6380.97770.927
6390.97610.9282
6400.9720.9295
6410.96810.9275
6420.96390.9254
6430.96130.9234
6440.9560.9213
6450.95040.9193
6460.94560.9173
6470.93980.9152
6480.93330.9132
6490.92750.9111
6500.9210.909
6510.91390.91
6520.9060.9109
6530.89770.9118
6540.89030.9127
6550.87990.9136
6560.87340.9144
6570.86450.9153
6580.85350.9162
6590.84270.9171
6600.83270.918
6610.8210.9201
6620.80840.9221
6630.79740.9242
6640.78420.9263
6650.770.9284
6660.75610.9304
6670.74240.9325
6680.72830.9346
6690.71390.9366
6700.70150.9387
6710.68690.9362
6720.67450.9337
6730.66180.9313
6740.64930.9288
6750.63830.9263
6760.62620.9238
6770.61670.9213
6780.60750.9189
6790.59740.9164
6800.58820.9139
6810.5790.9073
6820.57050.9008
6830.56270.8942
6840.55380.8877
6850.54530.8811
6860.53620.8746
6870.52810.868
6880.5180.8614
6890.50940.8549
6900.49990.8483
6910.49160.85
6920.48250.8517
6930.4730.8534
6940.46350.8551
6950.4550.8568
6960.44390.8585
6970.43480.8602
6980.42630.8619
6990.41720.8635
7000.40710.8652
7010.39840.8655
7020.38890.8657
7030.37910.866
7040.37050.8662
7050.36170.8665
7060.35230.8667
7070.34370.8669
7080.33630.8672
7090.32760.8674
7100.31940.8676
7110.31130.8588
7120.30360.8499
7130.2960.841
7140.28850.8321
7150.28010.8233
7160.27220.8144
7170.26380.8055
7180.25960.7966
7190.25420.7877
7200.24530.7789
7210.2390.7834
7220.23280.788
7230.22670.7925
7240.22090.7971
7250.21520.8016
7260.20890.8062
7270.20380.8107
7280.19640.8153
7290.19260.8198
7300.18730.8243
7310.18190.827
7320.17710.8297
7330.17190.8323
7340.16740.835
7350.16280.8376
7360.15810.8403
7370.15390.843
7380.14960.8456
7390.14430.8483
7400.1430.8509
7410.13840.8429
7420.13310.8348
7430.12750.8268
7440.12540.8188
7450.12150.8107
7460.11880.8027
7470.11640.7947
7480.11340.7866
7490.11050.7786
7500.10820.7706
7510.10480.7593
7520.09990.748
7530.1010.7367
7540.09740.7254
7550.09480.7141
7560.09050.7028
7570.08750.6915
7580.08560.6802
7590.08540.6689
7600.08190.6576
7610.08190.6702
7620.07840.6829
7630.0750.6955
7640.07540.7082
7650.07270.7208
7660.07010.7335
7670.06810.7461
7680.06650.7587
7690.06060.7714
7700.06670.784
7710.06190.7811
7720.05910.7781
7730.05590.7751
7740.05630.7721
7750.05390.7692
7760.05480.7662
7770.05180.7632
7780.05010.7603
7790.05230.7573
7800.05350.7543
Rf:91            CCT(K):5055
Rg:101 Duv:0.0002
u':0.2107
LER: 273 v': 0.4841
The Test SPD compared with the matching Reference SPD
Color Distortion Graphic
Graphic shifts (%)
Hue BinRfChroma
194-1%(Rg,h1)
297-1%(Rg,h2)
393-1%(Rg,h3)
492-1%(Rg,h4)
592-2%(Rg,h5)
6960%(Rg,h6)
795-2%(Rg,h7)
893-3%(Rg,h8)
990-3%(Rg,h9)
1084-1%(Rg,h10)
11823%(Rg,h11)
12932%(Rg,h12)
13945%(Rg,h13)
14933%(Rg,h14)
15849%(Rg,h15)
16941%(Rg,h16)