Photon count spectral luminosity ($L_{\epsilon }^N=dN/(dtd\epsilon )=L_{\nu }/(h\epsilon )$)

For photon energy $\epsilon =h\nu$, equating radiated energy in corresponding spectral intervals gives $L_{\nu }d\nu =\epsilon L_{\epsilon }^{N}d\epsilon$. Thus $L_{\epsilon }^N=L_{\nu }/(h\epsilon )$. A quoted rate per joule must be multiplied by the number of joules per electronvolt or per $\mathrm{keV}$ to express it in that spectral unit. For homogeneous optically thin emission, $L_{\nu }=4\pi V{j}_{\nu }$ if $j_{\nu }$ is defined per solid angle.