i think youll need a device that can calibrate TV screens as they run a different colour profile to regular monitors.
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arad85 knows. i'll tag him here and he can explain hopefully.
It will run under whatever profile is created by the calibrator, as it's software profiling... the profile is applied to the graphics card's LUT, not the TVs. Technically, on most monitors and TVs, you're calibrating your video card's output to display properly on the screen, not the screen itself. Only high end stuff allows you to actually calibrate the screen's LUT. Strangely, the Dell U2413 does as well though... but only with the i1 Display Pro colorimeter.
Neil has a point though... a lot of TVs apply a great deal of colour processing, and contrast control that will be fighting against the calibrator. If dynamic contrast can not be disabled on your TV for instance, it will constantly be trying to adjust this as the gamma curve is manipulated by the calibrator's software. They may be fighting one another. Turn ALL processing or presets off on your TV... all of it.
It depends on what you are trying to calibrate. Display systems use different technologies - but essentially any LCD screen is the the same basic technology as any other - there's a light behind some pixels that can vary their brightness to give you the user an impression of colour. The problem for calibration comes with what is lighting the screen. Fundamentally, you can only display a colour that is available in the light that is backlighting (for an LCD) so what is important for calibrating an LCD is what is actually creating the backlight. There's two main choices: CCFL (fluorescent light) and LED backlight. They each have different characteristics and what you need to ensure is that your chosen calibrator is capable of covering the colourspace the panel can display.
It's a TV....and as it's a 24", probably not a high end TV: it's gamut will be quite narrow. Spyder4, i1 Display Pro, Colormunki... all the usual suspects will calibrate to and beyond Adobe RGB, so a TV is well within their capabilities. Even if it uses cold cathode lighting, it will still be easily within the scope of any of those three. There's provision in the software for the colormunki and i1 to profile TVs and projectors. In fact, in the i1 software, it doesn't even differentiate between TVs or monitors. It just asks whether it's a wide gamut LCD screen or not.
For the money, my choice is X-rite Colormunki. Simple, effective software, and works well, and good price. Just remember to turn OFF the setting to adjust the screen to ambient light conditions.
I have to say at this juncture though.... most TVs are pretty rough in comparison with a decent monitor. They're designed for maximum contrast (often at the expense of subtle and accurate colour rendition), and have all manner of processing to deliver smooth movement etc... things that, in short, are not really important to a decent display designed for photographic work. Go in your TV's menus and turn off all processing... sharpness, dynamic contrast, colour presets.. anything you can find before you try to calibrate it. If the TV is adding all this crap, it's just giving the calibrator and software more work to do as they will be trying to lower contrast, and fight against colour processing... as you're at 8bit level here, the less the colour, gamma and luminance needs to be adjusted the cleaner the output. Heavy adjustments at 8bit GPU level (which you'll be at) will result in banding in subtle colour gradients.