V(lambda) curve

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djozz
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V(lambda) curve

When thinking about light output and in discussions I regularly feel the need to refer to this V(lambda) luminosity curve, that describes the relative sensitivity of the human eye for the different colours of light, as a fraction of the sensitivity to 555nm for which the eye is most sensitive. The V(lambda) function is also integral to the lumen unit, which takes the different sensitivities for different wavelengths into account.

For example, recently when I tested the output (in lumen) of a 660nm led (to be posted still), I wanted to know the sensitivity of the human eye for 660nm (deep red) compared to a common 625nm (red) led. The curve tells me that the eye is 5 times as sensitive to 625nm, so for 660nm you need 5 times the optical power to perceive the same brightness (and measure the same lumen) as 625nm.

Because on the internet you can only find low-res luminosity curves that are not easily readable, I made one myself, using the data for the CIE (1924) standard V(lambda) function, which is by my knowledge still the most used photopic luminosity function for measuring candela (and lux and lumen). Since then a few improvements were proposed because it became clear the curve was not entirely correct for the blue and red region, but still the old V(lambda)function is mostly used.

Photopic (black) and scotopic (green) luminosity functions.[c 1] The photopic includes the CIE 1931 standard[c 2] (solid), the Judd–Vos 1978 modified data[c 3] (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data[c 4] (dotted). The horizontal axis is wavelength in nm.

(image and explanation from Wikipedia, link)

The dataset gives a coefficient per 1nm which is not practical for this curve, so I only used part of the dataset, per 5nm.

Here is the curve, mostly for my own reference, but maybe useful for others.

Edited by: djozz on 08/18/2019 - 15:37
djozz
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Here is the dataset behind the curve (source):

wavelength (nm) luminous coefficient
360 0,000003917
365 0,000006965
370 0,00001239
375 0,00002202
380 0,000039
385 0,000064
390 0,00012
395 0,000217
400 0,000396
405 0,00064
410 0,00121
415 0,00218
420 0,004
425 0,0073
430 0,0116
435 0,01684
440 0,023
445 0,0298
450 0,038
455 0,048
460 0,06
465 0,0739
470 0,09098
475 0,1126
480 0,13902
485 0,1693
490 0,20802
495 0,2586
500 0,323
505 0,4073
510 0,503
515 0,6082
520 0,71
525 0,7932
530 0,862
535 0,9148501
540 0,954
545 0,9803
550 0,9949501
555 1
560 0,995
565 0,9786
570 0,952
575 0,9154
580 0,87
585 0,8163
590 0,757
595 0,6949
600 0,631
605 0,5668
610 0,503
615 0,4412
620 0,381
625 0,321
630 0,265
635 0,217
640 0,175
645 0,1382
650 0,107
655 0,0816
660 0,061
665 0,04458
670 0,032
675 0,0232
680 0,017
685 0,01192
690 0,00821
695 0,005723
700 0,004102
705 0,002929
710 0,002091
715 0,001484
720 0,001047
725 0,00074
730 0,00052
735 0,0003611
740 0,0002492
745 0,0001719
750 0,00012
755 0,0000848
760 0,00006
765 0,0000424
770 0,00003
775 0,0000212
780 0,00001499
785 0,0000106
790 7,4657E-06
795 5,2578E-06
800 3,7029E-06
805 2,6078E-06
810 1,8366E-06
815 1,2934E-06
820 9,1093E-07
825 6,4153E-07
830 4,5181E-07
Yokiamy
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Fun fact
The story goes, that the original Subaru Impreza WRX 555 (the one which Colin McRae got world champion in in 1995 ) version is called 555 due to the wavelength and the corresponding luminous coefficient 1

Henk4U2
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Yokiamy wrote:
Fun fact The story goes, that the original Subaru Impreza WRX 555 (the one which Colin McRae got world champion in in 1995 ) version is called 555 due to the wavelength and the corresponding luminous coefficient 1

I thought the colors on that car were somehow related to their sponsor.

The way the Lancia Stratos was sponsored by Marlboro.
Until tobacco sponsoring was banned.

You are a flashaholic if you are forced to come out of the closet, to make room for more flashlights.

Yokiamy
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Henk4U2 wrote:
Yokiamy wrote:
Fun fact The story goes, that the original Subaru Impreza WRX 555 (the one which Colin McRae got world champion in in 1995 ) version is called 555 due to the wavelength and the corresponding luminous coefficient 1

I thought the colors on that car were somehow related to their sponsor.

The way the Lancia Stratos was sponsored by Marlboro.
Until tobacco sponsoring was banned.

Wim

That’s what i read as well, but i think it is just a nice fun fact, which could or could not be true