Given Chromaticity Values $x, y$ , How Do We Reconstitute the Tristimulus Values

Essay

Given chromaticity values $x, y$ , how do we reconstitute the tristimulus values $X, Y, Z$ ? Actually, this is an impossible question, since chromaticities remove the brightness from colors; therefore a proper question might be: given a target luminance value $Y$ (often taken to be 1), what is the relationship between $x, y, Y$ and $X, Y, Z$ ?