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