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When I white balance my DSLR to a given color temperature that temperature shows as "white" on the LED screen, and on a computer monitor.
What color is the LED screen or computer monitor displaying as "white"? For most photos wouldn't we want the camera to be white balanced to the output of the screens that the pictures are being viewed on?
"white" is subjective to humans.
LED displays, CRT displays, and LCD(flourescent tube lit/LED lit) displays all have variances in what it considers to be "white". Only when that variance is greater than what our eyes will compensate for, do we detect it as being "off".
The exactly output color for "white" depends on your hardware. Calibrating your camera to the white from an LED lit monitor/display will probably result in everything being recorded and displayed as "warm" since the LED white tends towards the blueish side. Same with flourescents, some LED bulbs, and your average hot shoe flash. They are all on the "cool" side.
White balance calibration of your camera is a "per environment + lighting condition" activity. What is "white" for a room lit with incandescent bulbs will not be "white" in another room lit by noon time sunlight.
Even with two monitors of the same model/build/make/etc. from the same store, will probably be off by a bit. You can calibrate the monitor to a white value or to one another, so that they are similar in white balance.
Basically:
Sorry for the long winded answer. :) But in general, "white" on a monitor isn't actually white. Or rather, it is a particular color temperature range we generally call white.
Technically speaking, white on an LCD monitor or screen is the color displayed when the Red, Green, and Blue value of a given pixel are all the same and at or near saturation. With a 24 bit color space like the vast majority of computer monitors use, this would mean a value of 255, 255, 255 (8 bits per color; 2^8 = 256 different intensities = 0-255 inclusive). A value of 128, 128, 128 would render neutral gray. A value of 0, 0, 0 would result in black. If a monitor is calibrated and profiled properly, it will render the appropriate shade of white, gray, or black for these values. Pure red at 100% saturation would have a value of 255, 0, 0. Pure saturated green would be 0, 255, 0. Likewise, pure saturated blue would be 0, 0, 255. All properly adjusted monitors should display the same photo with the same white point and color tones.
The problem is not that all monitors have their own white point. They can (and should) all be profiled to correct for variations. The problem is that not all light sources have the same white point. When we set the white balance on our camera we are telling it what color temperature the light is so that when that light is reflected by a white surface the camera and monitor can display the white objects in the scene correctly.
Let's assume for a moment you are saving your photos as RAW files. In this case the only effect the WB you set in camera has is on the JPEG thumbnail generated by the camera. This is because the data in the main file from each pixel well on the sensor has not yet been interpolated and adjusted for the varying sensitivities of the human eye to Red, Green, and Blue. When you open a RAW file using the appropriate software, the white balance setting in the program might be set by the program itself or the camera's setting when the picture was taken may be read from the file's metadata and applied. In either case you are free to select another. The effect of different WB settings is in how the 10, 12, or 14 bits per color in a RAW file are translated to the 8 bits per color needed to display on your screen.
I'm looking at a RAW file I shot recently under mixed tungsten and fluorescent lighting. A friend in the photo was wearing a gray shirt. By placing the mouse pointer over the shirt, the value of the pixel is displayed at the bottom of the screen. A spot with a value translated at 204, 162, 114 (orange-grey) when the WB is set at 5200K is translated to 163, 174, 185 (blueish-grey) when the WB is set to 3200K. At a setting of 3500K the grey item is correctly translated to 183, 183, 183. Assuming the grey shirt my friend is wearing is neutral grey, I just found my WB point.
So what happens if you are shooting JPEG? The camera assigns the WB you have chosen. If Auto WB is selected the camera assigns a WB of its own choosing based on the value of the brightest parts of the scene. It then translates the data coming off the sensor into 8 bits per color and discards the rest of the information before saving the file to your memory card.
You want the image from the camera to be balanced in relation to a specific color profile, for example AdobeRGB. That way you know exactly what a color code in the image means. Calibrating the image directly for the output would not be practically possible, because for example a monitor and a printer has completely different color spaces.
When you display an image on a monitor, it's the color profile of that monitor that determines how each color is converted from the color profile in the image so that the monitor displays the color right.
It would be nice if all monitors were calibrated, so that they have a color profile, but most isn't. When the computer has to display an image on a monitor with unknown properties, it will use something like the generic sRGB profile that is supposed to be the approximage color space of an average uncalibrated monitor. The "supposed", "approximage" and "average" in that sentence should tell you that there is quite some variations between montors, so you simply can't expect a consistent result between uncalibrated monitors.
There is no set standard for "white" color temperature or intensity on a computer screen (both of which matter). The adjustments on the screen itself and the ICC profile being used both will impact the final color temperature of a white (255,255,255) output.
Even with a properly calibrated display, you choose the color temperature you wish to calibrate to and may periodically change the calibration to reflect a different color temperature for a different purpose. If everything is working properly, an ICC profile for a calibrated monitor should know the color temperature of the display and adjust correctly for the actual colors represented within the color space of the image.
If you also have calibrated printers, what you get for print output should closely represent what you see on the screen regardless of the color temperature you calibrate to. The main difference would be the range of colors within an off-temperature gamut that the monitor is able to produce. If an image is displaying at a 5200K whitepoint on a 3600K whitepoint display, the image processing simply won't use 255,255,255 for white, but rather alter the value to have it display correctly, but this obviously results in a lack of available colors since the "max" for one of the colors will be less than 255.
