Making sure I'm interpreting this right: $\bar{x}$, $\bar{y}$, and $\bar{z}$ can be negative but $k$ will never be negative.
EDIT: This is not correct, see below.
kayvonf
$k$ is just a normalization constant. You could think of it as being buried in $\bar{x}$, $\bar{y}$, and $\bar{z}$ if you wish. I kept it in the figure to be consistent with CIE convention, but the big point here is that we're integrating a spectrum against these specifically chosen response functions. The functions are chosen so that we have the convenient property that the response for any observable monochromatic light (light of one wavelength) is positive.
ak-47
Okay. Does that mean that if $\Phi(z)$ is a $\delta$ function (AKA monochromatic light), X, Y, and Z are positive?
kayvonf
Yes. That is the property that that XYZ primaries are specifically designed to preserve.
ak-47
Why aren't $\bar{x},\ \bar{y}$, and $\bar{z}$ physically realizable? It seems like I could approximate the $\bar{z}$ with an array of lasers from 380 nm to 540 nm.
kayvonf
What I didn't show a picture of in this lecture is the spectrum for the primaries $\bar{x}(lambda)$, $\bar{y}(\lambda)$, and $\bar{z}(\lambda)$. If I did, you'd see the spectrum would be negative for some wavelengths, which obviously isn't possible. (You can't have a light that emits negative energy in certain wavelengths. If so, it would be an awesome air conditioner.)
The plot on this side is not the spectrum for these primaries. Rather, it's the same plot as that shown for the RGB primaries shown on slide 29. The plot shows the amount of X source, Y source, and Z source you need to match monochromatic light of the given wavelength. In other words, if X, Y and Z were realizable light sources (and remember they are not), then these curves tell you how much you'd have to crank the intensity dial for each of these sources for the resulting output to match monochromatic light of the specified wavelength $\lambda$.
Making sure I'm interpreting this right: $\bar{x}$, $\bar{y}$, and $\bar{z}$ can be negative but $k$ will never be negative. EDIT: This is not correct, see below.
$k$ is just a normalization constant. You could think of it as being buried in $\bar{x}$, $\bar{y}$, and $\bar{z}$ if you wish. I kept it in the figure to be consistent with CIE convention, but the big point here is that we're integrating a spectrum against these specifically chosen response functions. The functions are chosen so that we have the convenient property that the response for any observable monochromatic light (light of one wavelength) is positive.
Okay. Does that mean that if $\Phi(z)$ is a $\delta$ function (AKA monochromatic light), X, Y, and Z are positive?
Yes. That is the property that that XYZ primaries are specifically designed to preserve.
Why aren't $\bar{x},\ \bar{y}$, and $\bar{z}$ physically realizable? It seems like I could approximate the $\bar{z}$ with an array of lasers from 380 nm to 540 nm.
What I didn't show a picture of in this lecture is the spectrum for the primaries $\bar{x}(lambda)$, $\bar{y}(\lambda)$, and $\bar{z}(\lambda)$. If I did, you'd see the spectrum would be negative for some wavelengths, which obviously isn't possible. (You can't have a light that emits negative energy in certain wavelengths. If so, it would be an awesome air conditioner.)
The plot on this side is not the spectrum for these primaries. Rather, it's the same plot as that shown for the RGB primaries shown on slide 29. The plot shows the amount of X source, Y source, and Z source you need to match monochromatic light of the given wavelength. In other words, if X, Y and Z were realizable light sources (and remember they are not), then these curves tell you how much you'd have to crank the intensity dial for each of these sources for the resulting output to match monochromatic light of the specified wavelength $\lambda$.