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Thread: The perfect white balance - feedback requested

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    Default The perfect white balance - feedback requested

    As some of you might know I've been reading up on color science for a while. Now I feel it's time to present my findings in a form that hopefully will be easily accessible and usable for all users here. It seems to be a frequent thread subject here.

    So where do I start? Since the subject is white balance I should perhaps start by defining what I mean by white. Without delving too deep in the theory, I have chosen the CIE Standard illuminant D65 as my white point. It "corresponds roughly to a mid-day sun in Western Europe / Northern Europe" and has color coordinates (x,y: 0.31, 0.33) that are close to that of an equal energy spectrum (x,y: 0.33, 0.33).

    Knowing what color is desired I need to specify the means by which to reach it. We're dealing with lasers here, so monochromatic light sources. While it is possible to get white light using any number of lasers the most common configuration is a simple three laser RGB system using solid state lasers. These limitations are simply to make the following calculations easier to perform and present. Especially so because the only commonly available green is 532nm.

    Results:
    Click image for larger version. 

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    How to read, understand and use the table?

    The leftmost column contains the wavelengths of the blue laser source and the red wavelengths can be found on the horizontal axis. The space spanned by them contains the relative (radiative) laser powers required to get white light. The table is actually only 4x4, but since each combination of wavelengths requires two powers to be specified there are two values in each cell. The upper value is the relative power of the blue laser and below it is the power of the red laser.

    To use it first pick two wavelengths, for example 445 and 640 nm. Looking in the table you will find that the relative radiative powers required are 0.8 and 1.56 respectively. Given that you have a 2W 532nm laser you will need 0.8*2W = 1.6W of 445nm and 1.56*2W = 3.12W of 640nm (after losses in transmission and reflection) to match it.

    Now, you might have noticed the blue powers are pretty much the same regardless of the red wavelength, so it is possible to simplify the table (this time with less gay colors):

    Click image for larger version. 

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    I think you can figure out how to use it. It is also possible to further reduce the table, though it's less obvious how to make the next step.

    Feedback
    I need feedback from real world situations! Are these tables accurate? Compare to your setup and tell me how well you think they correlate to your RGB laser. I need to know the power of your lasers (optimally after all optics) and how you perceive your white. I don't have a blue laser or a laser power meter so I can't test it myself.

    Currently I am using the Judd-Vos color matching functions which should give more accurate results in the violet region (compared to CIE 1931). It should be pointed out however that these values are for light reflected off a perfectly white surface. I don't know how well it applies to light scattered by air/haze/fog yet. Possibly a scattering correction needs to be added, but using the normal scattering angle-wavelength relation severely increases the amount of red required and reduces the amount of blue.

    Here is the matlab code I wrote to solve the problem for those (select few) of you who might be interested (it is solved using fminsearch for each set of wavelengths):

    Code:
    function d=d2wp(P)
    %D2WP   Distance to whitepoint
    % d = d2wp(P) returns the square of the distance to the whitepoint given 
    % an RB SPD vector P relative to 532nm.
    
    global WLV WP; %WLV = wavelength vector, WP = whitepoint coordinates
    
    % choose the color matching function
    [wl,x_bar,y_bar,z_bar] = colorMatchFcn('judd_vos');
     
    % zero the tristimulus values
    X = 0;
    Y = X; Z = X;
    
    % add 532nm (last) to the SPD
    P = [P,1];
    
    % calculate tristimulus values
    for i = 1:3
        wli  = find(wl == WLV(i)); %look for the index of the current wl
        X = X + P(i)*x_bar(wli);
        Y = Y + P(i)*y_bar(wli);
        Z = Z + P(i)*z_bar(wli);
    end
    
    % normalize
    x=X/(X+Y+Z);
    y=Y/(X+Y+Z);
    
    % calculate distance to whitepoint
    d = (WP(1)-x)^2 + (WP(2)-y)^2;
    Any comments or questions are most welcome!
    Last edited by tocket; 09-15-2010 at 00:15.

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    Nice write up! I wish I had a power meter, I would check my set up. I find it interesting about the blue values; seems to be a wierd curve there that is not expected.
    Love, peace, and grease,

    allthat... aka: aaron@pangolin

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    Does anyone have a colour meter as I'd be interested to know what most regard as the colour temperature for the best white and this might even give a way of working backwards to it in terms of laser powers and wavelengths.

    To this extent, this version of the standard colour diagram with temperature overlaid is of interest:



    Now the interesting thing in all this is there are literally millions of shades of white from a common lightbulb (quite yellowy) at around 3000K to a standard Halogen Bulb at around 3800K to a white halogen bulb at around 4100K to true daylight at around 5500K to bluey white at around 6000K etc.

    Most people seem to like the crisp white produced by HID lighting on cars so this would seem a good starting point for a nice clean white. This varies according to the bulbs used but is usually between 4300K for OEM lighting, to 5000K for aftermarket to 6000K for slightly bluey white. I think I have 6000K in mine and it does look crisp albeit apparently headlights not designed for HID seem to be slightly more yellowy (something to do with the reflector) so a higher colour temp is needed. Therefore for a laser, probably 5000-5500K is nearer the mark. I changed my lights over with a kit back when I was working.



    This is an over the dash picture of 6000k bulbs in non HID reflectors (my car).

    Interestingly the Wiki, appears to give some formulas for back calculating RGB wavelengths from colour temperature. I couldn't be bothered at this time of night to read in detail so I'm going to leave to someone else!

    http://en.wikipedia.org/wiki/Color_temperature

    Gives another interesting approach to finding white though.

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    [QUOTE=RGBLaserFan;

    slightly bluey white. I think I have 6000K in mine and it does look crisp albeit apparently headlights not designed for HID seem to be slightly more yellowy (something to do with the reflector) so a higher colour temp is needed. Therefore for a laser, probably 5000-5500K is nearer the mark. I changed my lights over with a kit back when I was working.
    end quote-------------------------------------------------

    Tocket's D65 is a 6500K white, so if you use Tocket's table you can get your 6000K and anything below it by setting your max levels lower.

    A few years ago a company I was working with on LED flashlights, bought, at my suggestion, a Minolta ColorMeter II color meter, used on ebay, for about 200$. That was about the minimum they went for. The Minolta bottomed out at around 1600 K.


    Steve

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    Great post Tocket!

    Nice to see how our previous discussion on the 445nm blue versus 473nm blue is summarized by the figures.
    I'm a laser-graphics oriented person. So white balance is my concern. I have more relative blue power wrt red so my whites are cold looking (but hot in terms of K) but I prefer that before tuning down the blue and have less light on the screen

    A lot of people here are beams oriented people. Then white balance is nice but what they want is equal visibility of the beams. Using the result from the other thread the laser powers can be computed using relative brightness of the green and red wavelength directly but for the blue side of the spectrum an area of 'desired blue color' needs to be defined in the CIE diagram.
    This 'desired blue' then dictates the blue-green mixing ratio (in case of 445nm especially). In turn the relative brightness of the mix needs to equal that of green and red at full power.

    So the question: what is a nice blue hue for beams shows. Buffo mentioned he likes the 473nm hue, other say it is too close to cyan. My opinion is that 743 is a bit too close to cyan for graphics but for beams it may be fine, maybe it can be boosted even a bit more with green. Any thoughts?

    Of course laser software systems will have to provide the primary color mixing functionality.

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    Note that actual values for a laser will be different when compared with wider bandwidth monochromatic sources because of the effects of Ralleigh scattering (when the beam hits a surface) and forward scattering (when the beam is coming toward you in mid-air)...

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    Quote Originally Posted by allthatwhichis View Post
    Nice write up! I wish I had a power meter, I would check my set up. I find it interesting about the blue values; seems to be a wierd curve there that is not expected.
    Thank you. Yes, intuitively one might expect a brighter blue color like the icy 473nm blue to require less of it to be added. However, this high wavelength stimulates M-cones (responsible for green vision) significantly, effectively adding more green to the system.

    For those interested in the specific form of this curve I have plotted it at 1nm intervals.


    And a zoom in around the most relevant values...

    ...Shows the most efficient blue is at 439nm.

    Quote Originally Posted by RGBLaserFan
    Now the interesting thing in all this is there are literally millions of shades of white from a common lightbulb (quite yellowy) at around 3000K to a standard Halogen Bulb at around 3800K to a white halogen bulb at around 4100K to true daylight at around 5500K to bluey white at around 6000K etc.
    Well, there are, but we can't distinguish between that many whites. Especially if we don't have them side by side. Daylight is 6500K though, at least for most of us (it depends on where you live).

    Quote Originally Posted by RGBLaserFan
    Interestingly the Wiki, appears to give some formulas for back calculating RGB wavelengths from colour temperature. I couldn't be bothered at this time of night to read in detail so I'm going to leave to someone else!
    One problem with this is that what color is displayed will depend on your monitor. The standard white point for computer graphics seems to be D65, which would give it the RGB values (1,1,1). This means that the white you see on your computer screen should be D65! For this kind of work it would be highly useful to have a calibrated professional display device.

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    Quote Originally Posted by Zoof View Post
    So the question: what is a nice blue hue for beams shows. Buffo mentioned he likes the 473nm hue, other say it is too close to cyan. My opinion is that 743 is a bit too close to cyan for graphics but for beams it may be fine, maybe it can be boosted even a bit more with green. Any thoughts?

    Of course laser software systems will have to provide the primary color mixing functionality.
    This is the big dilemma with the shorter wavelength blue lasers as I see it. It's a wonderful deep blue color, but it's also fairly weak. Adding a little green to it can give you the 473nm icy blue, albeit with some loss of saturation. I think it's a really nice possibility, but it's also a shame to use only this blue if you have a 445nm laser. You are significantly reducing the gamut. It isn't really visible in the CIE 1931 diagram, but if one instead looks at for example the CIE 1978 UCS diagram it becomes obvious. Again, computer displays don't do this one justice. Every point inside of the "horseshoe" represents a unique color.



    I think the solution to this problem is to have different "palettes". One where the blue is a simulated (shortwave blue + green) ~470nm for high visibility, and another one that retains the original blue color. This is why software is the answer to it, but is there any software out there cabaple of it? Bill?

    Quote Originally Posted by Pangolin
    Note that actual values for a laser will be different when compared with wider bandwidth monochromatic sources because of the effects of Ralleigh scattering (when the beam hits a surface) and forward scattering (when the beam is coming toward you in mid-air)...
    Scattering is tricky. I doubt Rayleigh scattering will have much effect though, unless over very large distances. Scattering due to particles in the air is a different story though, which I'm not sure how to account for. Any help here would be highly valuable.

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    Quote Originally Posted by tocket View Post
    Well, there are, but we can't distinguish between that many whites.
    I would have to disagree there. Get a paint swatch card and then tell me your eye can't distinguish between the different shades of white. Paint manufacturers make over 500 different shades and you can see the difference albeit most would need to be side by side. However, some whites are whiter and cleaner than others which is why our eyes can see the difference between eg a halogen floodlight and the icy white of a HID headlight.

    Looking at Hugo's Shows, when you see the white he's achieved, can you really say this is the same as the white from your projector? Yes he's running more watts, but I've yet to see any amateur projector achieve this white:



    To my mind, it would be very interesting to achieve white, using the swatch and colour temp overlay for wavelength guidance, then use a colour temperature meter to help make power adjustments to try achieve the perfect icy white shade.

    Also potentially once discovered, a table of wavelengths vs powers could be drawn up for various different shades so as to give a reference table for achieveing white.
    Last edited by White-Light; 11-05-2008 at 00:58.

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    Quote Originally Posted by RGBLaserFan View Post
    Looking at Hugo's Shows, when you see the white he's achieved, can you really say this is the same as the white from your projector? Yes he's running more watts, but I've yet to see any amateur projector achieve this white:

    That white is from the Jenlas whitelight-laser. The "new" white is made by combining yellow/blue OPS lasers (even nicer).

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