  Photoinjectors are the main high brightness electron sources for X-ray free
electron lasers (XFEL). Photoinjector emittance reduction is one of the key
knobs for improving XFEL lasing, so precise emittance measurement is critical.
It's well known that rms emittance is very sensitive to low intensity tails of
particle distributions in the phase space, whose measurement depend on the
signal to noise ratio (SNR) and image processing procedures. Such sensitivities
make the interpretations of beam transverse brightness challenging, leading to
different emittance definitions to reduce the impact of tail particles. In this
paper, transverse phase space is analyzed in action and phase coordinates for
both analytical models and experiments, which give a more intuitive way to
calculate the beam core brightness.
