Transient chromatic adaptation produced by an abrupt change of background color permits an easier and closer approach to cone isolation than does steady-state adaptation. Using this technique, we measured middle-wave-sensitive (M-) cone spectral sensitivities in 11 normals and 2 protanopes and long-wavelength-sensitive (L-) cone spectral sensitivities in 12 normals and 4 deuteranopes. Although there is great individual variation in the adapting intensity required for effective isolation, there is little variation in the shape of the M- and L-cone spectral-sensitivity functions across subjects. At middle and long wavelengths, our mean spectral sensitivities agree extremely well with dichromatic spectral sensitivities and with the M- and L-cone fundamentals of Smith and Pokorny [
Vision Res. 15,
161 (
1975)] and of Vos and Walraven [
Vision Res. 11,
799 (
1971)], both of which are based on the CIE (Judd-revised) 2° color-matching functions (CMF’s). But the agreement with the M-cone fundamentals of Estévez [
Ph.D. dissertation,
Amsterdam University (
1979)] and of Vos et al. [
Vision Res. 30,
936 (
1990)], which are based on the Stiles–Burch 2° CMF’s, is poor. Using our spectral-sensitivity data, tritanopic color-matching data, and Stiles’s π_{3}, we derive new sets of cone fundamentals. The consistency of the proposed fundamentals based on either the Stiles–Burch 2° CMF’s or the CIE 10° large-field CMF’s with each other, with protanopic and deuteranopic spectral sensitivities, with tritanopic color-matching data, and with short-wavelength-sensitive (S-) cone spectral-sensitivity data suggests that they are to be perferred over fundamentals based on the CIE 2° CMF’s.

John Krauskopf J. Opt. Soc. Am. A 17(3) 510-516 (2000)

References

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The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{x}+{b}_{M}\overline{y}+{c}_{M}\overline{z};{L}_{\lambda}={a}_{L}\overline{x}+{b}_{L}\overline{y}+{c}_{L}\overline{z}$, where
$\overline{x},\overline{y}$, and
$\overline{z}$ are the Judd39 and Vos40 modified CIE 2° CMF’s and M_{λ} and L_{λ} are the cone sensitivities.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 3

Linear Combinations of the Stiles–Burch_{1955}$\overline{r},\overline{g}$, and
$\overline{b}$ 2° CMF’s Best Fitting Our Data^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{r}+{b}_{M}\overline{g}+{c}_{M}\overline{b};{L}_{\lambda}={a}_{L}\overline{r}+{b}_{L}\overline{g}+{c}_{L}\overline{b}$, where
$\overline{r},\overline{g}$, and
$\overline{b}$ are the Stiles–Burch 2° CMF’s.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 4

Linear Combinations of the CIE_{Judd}$\overline{x},\overline{y}$, and
$\overline{z}$ 2° CMF’s That Best Fit the Proposed Stiles–Burch_{1955}-Based Estimates of the M- and L-Cone Sensitivities (Appendix A)^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{x}+{b}_{M}\overline{y}+{c}_{M}\overline{z};{L}_{\lambda}={a}_{L}\overline{x}+{b}_{L}\overline{y}+{c}_{L}\overline{z}$, where
$\overline{x},\overline{y}$, and
$\overline{z}$ are the Judd39 and Vos40 modified CIE 2° CMF’s and M_{λ} and L_{λ} are the linear combinations yielding the best fits to the Stiles–Burch_{1955}-based cone fundamentals proposed in Appendix A.
Reduction of 0.115 in peak macular density and 0.017 in lens density at 400 nm applied to the CIE_{Judd} 2° CMF’s.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 5

Linear Combinations of the CIE_{1931}$\overline{x},\overline{y}$, and
$\overline{z}$ 2° CMF’s That Best Fit the Proposed Stiles–Burch_{1955} 2°-Based Estimates of the M- and L-Cone Sensitivities (Appendix A)^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{x}+{b}_{M}\overline{y}+{c}_{M}\overline{z};{L}_{\lambda}={a}_{L}\overline{x}+{b}_{L}\overline{y}+{c}_{L}\overline{z}$, where
$\overline{x},\overline{y}$, and
$\overline{z}$ are the CIE_{1931} 2° CMF’s and M_{λ} and L_{λ} are the linear combinations yielding the best fits to the Stiles–Burch_{1955}-based cone fundamentals proposed in Appendix A.
Reduction of 0.020 in peak macular density and 0.57 in lens density at 400 nm applied to the CIE_{1931} 2° CMF’s.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 6

Linear Combinations of the CIE_{1964}${\overline{x}}_{10},{\overline{y}}_{10}$, and
${\overline{z}}_{10}$ 10° CMF’s That Best Fit the Proposed Stiles–Burch_{1955} 2°-Based Estimates of the M- and L-Cone Sensitivities (Appendix A)^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}{\overline{x}}_{10}+{b}_{M}{\overline{y}}_{10}+{c}_{M}{\overline{z}}_{10};{L}_{\lambda}={a}_{L}{\overline{x}}_{10}+{b}_{L}{\overline{y}}_{10}+{c}_{L}{\overline{z}}_{10}$, where
${\overline{x}}_{10},{\overline{y}}_{10}$, and
${\overline{z}}_{10}$ are the 10° CMF’s and M_{λ} and L_{λ} are the linear combinations yielding best fits to the Stiles–Burch_{1955}-based cone fundamentals proposed in Appendix A.
Increase of 0.195 peak macular density and reduction of 0.168 lens density at 400 nm applied to the CIE_{1964} CMF’s.
Best-fitting photopigment density adjustment from an assumed photopigment density of 0.40 in the 2° observer to 0.30 in the 10° observer and best-fitting macular and lens density adjustments (an increase of 0.210 peak macular density and a reduction of 0.185 lens density at 400 nm applied to the CIE_{1964} 10° CMF’s).
Sensitivities best fitting column (C) with the constraint that their weighted sum be
${\overline{y}}_{10}$ (see text for details).
Root-mean-square fitting errors in log_{10} sensitivity.

Table 7

Proposed Lens Pigment Densities for a Standard Observer with a Completely Open Pupil^{a}

Wavelength (nm)

Density

390

2.069

395

1.711

400

1.397

405

1.127

410

0.905

415

0.724

420

0.582

425

0.480

430

0.403

435

0.338

440

0.289

445

0.250

450

0.224

455

0.207

460

0.194

For a small pupil, multiply the densities by 1.16; for densities at λ > 460 nm, use Table II(2.4.6) of Ref. 48. The tabulated densities are based on Adjustment B to the van Norren–Vos lens pigment template shape.44

Table 8

Proposed 2° Cone Fundamentals Based on the Stiles–Burch_{1955} 2° CMF’s or on the CIE_{1964} 10° CMF’s

Wavelength (nm)

Stiles–Burch 2° L-Cone Fundamental

Stiles–Burch 2° M-Cone Fundamental

Stiles–Burch 2° S-Cone Fundamental

CIE_{1964} 10°-Based 2° L-Cone Fundamental

CIE_{1964} 10°-Based 2° M-Cone Fundamental

CIEI_{964} 10°-Based 2° S-Cone Fundamental

390

−3.2197

−3.2606

−1.9156

−3.5037

−3.5967

−2.1038

395

−2.7931

−2.8206

−1.5073

−3.0445

−3.1245

−1.6412

400

−2.4874

−2.5269

−1.2053

−2.6515

−2.7147

−1.2413

405

−2.1744

−2.1953

−0.8810

−2.3204

−2.3631

−0.8994

410

−1.9401

−1.9428

−0.6433

−2.0576

−2.0726

−0.6216

415

−1.7991

−1.7768

−0.4452

−1.8795

−1.8560

−0.4200

420

−1.6526

−1.5888

−0.2809

−1.7576

−1.6883

−0.2777

425

−1.5789

−1.4695

−0.1640

−1.6575

−1.5418

−0.1740

430

−1.5159

−1.3623

−0.0992

−1.5695

−1.4113

−0.0953

435

−1.4531

−1.2650

−0.0485

−1.4872

−1.2951

−0.0370

440

−1.3853

−1.1708

−0.0160

−1.4161

−1.1968

−0.0058

445

−1.3411

−1.1084

−0.0008

−1.3620

−1.1209

−0.0017

450

−1.3014

−1.0537

−0.0367

−1.3116

−1.0561

−0.0222

455

−1.2452

−0.9877

−0.0832

−1.2585

−0.9962

−0.0535

460

−1.1669

−0.9035

−0.1042

−1.1860

−0.9220

−0.0902

465

−1.0791

−0.8188

−0.1745

−1.1045

−0.8404

−0.1272

470

−0.9857

−0.7332

−0.2122

−1.0138

−0.7533

−0.1863

475

−0.9029

−0.6599

−0.3084

−0.9238

−0.6733

−0.2767

480

−0.8362

−0.6047

−0.4366

−0.8613

−0.6239

−0.4042

485

−0.7770

−0.5562

−0.5671

−0.7910

−0.5674

−0.5402

490

−0.6994

−0.4916

−0.6959

−0.7267

−0.5170

−0.6791

495

−0.6048

−0.4137

−0.8125

−0.6342

−0.4405

−0.8046

500

−0.5087

−0.3345

−0.9371

−0.5277

−0.3488

−0.9243

505

−0.4114

−0.2515

−1.0627

−0.4272

−0.2633

−1.0485

510

−0.3262

−0.1819

−1.2088

−0.3380

−0.1892

−1.2068

515

−0.2504

−0.1205

−1.3755

−0.2622

−0.1284

−1.3635

520

−0.1852

−0.0684

−1.5477

−0.1976

−0.0793

−1.5313

525

−0.1354

−0.0336

−1.7360

−0.1484

−0.0459

−1.7112

530

−0.0974

−0.0112

−1.9224

−0.1101

−0.0239

−1.8918

535

−0.0722

−0.0015

−2.1058

−0.0773

−0.0069

−2.0710

540

−0.0560

−0.0011

−2.2859

−0.0542

−0.0002

−2.2510

545

−0.0385

−0.0001

−2.4626

−0.0382

−0.0022

−2.4277

550

−0.0233

−0.0034

−2.6361

−0.0261

−0.0099

−2.6012

555

−0.0152

−0.0174

−2.8065

−0.0142

−0.0205

−2.7716

560

−0.0143

−0.0414

−2.9738

−0.0054

−0.0369

−2.9389

565

−0.0101

−0.0652

−3.1382

−0.0008

−0.0617

−3.1033

570

−0.0013

−0.0872

−3.2997

−0.0005

−0.0952

−3.2648

575

−0.0023

−0.1262

−3.4584

−0.0057

−0.1389

−3.4235

580

−0.0108

−0.1792

−3.6143

−0.0140

−0.1906

−3.5794

585

−0.0189

−0.2321

−3.7676

−0.0219

−0.2469

−3.7327

590

−0.0307

−0.2933

−3.9183

−0.0337

−0.3120

−3.8834

595

−0.0495

−0.3708

−4.0665

−0.0525

−0.3882

−4.0316

600

−0.0744

−0.4582

−4.2122

−0.0777

−0.4748

−4.1773

605

−0.1055

−0.5529

−4.3554

−0.1092

−0.5711

−4.3205

610

−0.1443

−0.6598

−4.4964

−0.1478

−0.6771

−4.4615

615

−0.1914

−0.7792

−4.6350

−0.1946

−0.7924

−4.6001

620

−0.2472

−0.9050

−4.7714

−0.2491

−0.9139

−4.7365

625

−0.3123

−1.0370

−4.9056

−0.3101

−1.0334

−4.8707

630

−0.3877

−1.1789

−5.0377

−0.3815

−1.1594

−5.0028

635

−0.4723

−1.3295

−5.1677

−0.4688

−1.3073

−5.1328

640

−0.5641

−1.4825

−5.2957

−0.5663

−1.4670

−5.2608

645

−0.6645

−1.6355

−5.4217

−0.6690

−1.6345

−5.3868

650

−0.7761

−1.7917

−5.5458

−0.7795

−1.8047

−5.5109

655

−0.8990

−1.9512

−5.6679

−0.8992

−1.9615

−5.6330

660

−1.0304

−2.1141

−5.7882

−1.0267

−2.1137

−5.7533

665

−1.1681

−2.2785

−5.9067

−1.1609

−2.2722

−5.8718

670

−1.3099

−2.4412

−6.0235

−1.3016

−2.4327

−5.9886

675

−1.4536

−2.5996

−6.1385

−1.4490

−2.5949

−6.1036

680

−1.5994

−2.7550

−6.2518

−1.6010

−2.7574

−6.2169

685

−1.7486

−2.9125

−6.3635

−1.7556

−2.9185

−6.3285

690

−1.9024

−3.0719

−6.4735

−1.9126

−3.0793

−6.4386

695

−2.0647

−3.2353

−6.5819

−2.0712

−3.2415

−6.5470

700

−2.2334

−3.4003

−6.6889

−2.2312

−3.4031

−6.6539

705

−2.4006

−3.5629

−6.7942

−2.3925

−3.5636

−6.7593

710

−2.5580

−3.7191

−6.8982

−2.5540

−3.7226

−6.8632

715

−2.7084

−3.8690

−7.0006

−2.7145

−3.8796

−6.9657

720

−2.8674

−4.0206

−7.1016

−2.8744

−4.0350

−7.0667

725

−3.0243

−4.1705

−7.2013

−3.0338

−4.1890

−7.1664

730

−3.1791

−4.3186

−7.2995

−3.1922

−4.3414

−7.2646

Tables (8)

Table 1

Means and Standard Deviations of the M- and L-Cone Spectral Sensitivities Obtained with the Exchange Procedure

M-Cone (n = 13)

L-Cone (n = 16)

Wavelength (nm)

Log Sensitivity

Standard Deviation

Log Sensitivity

Standard Deviation

442

−0.985

0.175

−1.262

0.177

470

−0.641

0.155

−0.963

0.178

500

−0.262

0.101

−0.519

0.113

516

−0.098

0.067

−0.169

0.072

545

0.000

0.019

−0.003

0.042

576

−0.128

0.070

0.000

0.036

600

−0.552

0.046

−0.095

0.044

617

−0.938

0.042

−0.255

0.051

638

−1.498

0.036

−0.587

0.040

668

−2.463

0.035

−1.330

0.053

Table 2

Linear Combinations of the CIE_{Judd}$\overline{x},\overline{y}$, and
$\overline{z}$ 2° CMF’s Best Fitting Our Data^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{x}+{b}_{M}\overline{y}+{c}_{M}\overline{z};{L}_{\lambda}={a}_{L}\overline{x}+{b}_{L}\overline{y}+{c}_{L}\overline{z}$, where
$\overline{x},\overline{y}$, and
$\overline{z}$ are the Judd39 and Vos40 modified CIE 2° CMF’s and M_{λ} and L_{λ} are the cone sensitivities.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 3

Linear Combinations of the Stiles–Burch_{1955}$\overline{r},\overline{g}$, and
$\overline{b}$ 2° CMF’s Best Fitting Our Data^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{r}+{b}_{M}\overline{g}+{c}_{M}\overline{b};{L}_{\lambda}={a}_{L}\overline{r}+{b}_{L}\overline{g}+{c}_{L}\overline{b}$, where
$\overline{r},\overline{g}$, and
$\overline{b}$ are the Stiles–Burch 2° CMF’s.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 4

Linear Combinations of the CIE_{Judd}$\overline{x},\overline{y}$, and
$\overline{z}$ 2° CMF’s That Best Fit the Proposed Stiles–Burch_{1955}-Based Estimates of the M- and L-Cone Sensitivities (Appendix A)^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{x}+{b}_{M}\overline{y}+{c}_{M}\overline{z};{L}_{\lambda}={a}_{L}\overline{x}+{b}_{L}\overline{y}+{c}_{L}\overline{z}$, where
$\overline{x},\overline{y}$, and
$\overline{z}$ are the Judd39 and Vos40 modified CIE 2° CMF’s and M_{λ} and L_{λ} are the linear combinations yielding the best fits to the Stiles–Burch_{1955}-based cone fundamentals proposed in Appendix A.
Reduction of 0.115 in peak macular density and 0.017 in lens density at 400 nm applied to the CIE_{Judd} 2° CMF’s.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 5

Linear Combinations of the CIE_{1931}$\overline{x},\overline{y}$, and
$\overline{z}$ 2° CMF’s That Best Fit the Proposed Stiles–Burch_{1955} 2°-Based Estimates of the M- and L-Cone Sensitivities (Appendix A)^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}\overline{x}+{b}_{M}\overline{y}+{c}_{M}\overline{z};{L}_{\lambda}={a}_{L}\overline{x}+{b}_{L}\overline{y}+{c}_{L}\overline{z}$, where
$\overline{x},\overline{y}$, and
$\overline{z}$ are the CIE_{1931} 2° CMF’s and M_{λ} and L_{λ} are the linear combinations yielding the best fits to the Stiles–Burch_{1955}-based cone fundamentals proposed in Appendix A.
Reduction of 0.020 in peak macular density and 0.57 in lens density at 400 nm applied to the CIE_{1931} 2° CMF’s.
Root-mean-square fitting errors in log_{10} sensitivity.

Table 6

Linear Combinations of the CIE_{1964}${\overline{x}}_{10},{\overline{y}}_{10}$, and
${\overline{z}}_{10}$ 10° CMF’s That Best Fit the Proposed Stiles–Burch_{1955} 2°-Based Estimates of the M- and L-Cone Sensitivities (Appendix A)^{a}

The coefficients a_{M} through c_{L} refer to
${M}_{\lambda}={a}_{M}{\overline{x}}_{10}+{b}_{M}{\overline{y}}_{10}+{c}_{M}{\overline{z}}_{10};{L}_{\lambda}={a}_{L}{\overline{x}}_{10}+{b}_{L}{\overline{y}}_{10}+{c}_{L}{\overline{z}}_{10}$, where
${\overline{x}}_{10},{\overline{y}}_{10}$, and
${\overline{z}}_{10}$ are the 10° CMF’s and M_{λ} and L_{λ} are the linear combinations yielding best fits to the Stiles–Burch_{1955}-based cone fundamentals proposed in Appendix A.
Increase of 0.195 peak macular density and reduction of 0.168 lens density at 400 nm applied to the CIE_{1964} CMF’s.
Best-fitting photopigment density adjustment from an assumed photopigment density of 0.40 in the 2° observer to 0.30 in the 10° observer and best-fitting macular and lens density adjustments (an increase of 0.210 peak macular density and a reduction of 0.185 lens density at 400 nm applied to the CIE_{1964} 10° CMF’s).
Sensitivities best fitting column (C) with the constraint that their weighted sum be
${\overline{y}}_{10}$ (see text for details).
Root-mean-square fitting errors in log_{10} sensitivity.

Table 7

Proposed Lens Pigment Densities for a Standard Observer with a Completely Open Pupil^{a}

Wavelength (nm)

Density

390

2.069

395

1.711

400

1.397

405

1.127

410

0.905

415

0.724

420

0.582

425

0.480

430

0.403

435

0.338

440

0.289

445

0.250

450

0.224

455

0.207

460

0.194

For a small pupil, multiply the densities by 1.16; for densities at λ > 460 nm, use Table II(2.4.6) of Ref. 48. The tabulated densities are based on Adjustment B to the van Norren–Vos lens pigment template shape.44

Table 8

Proposed 2° Cone Fundamentals Based on the Stiles–Burch_{1955} 2° CMF’s or on the CIE_{1964} 10° CMF’s