Fixed-illumination grating peak change with slit width ($I_m\propto N^2{w}^2{\mathrm{sinc}}^2(\pi mw/p)$)

For a uniformly illuminated grating of $N$ identical slits, width $w$ and pitch $p$, the amplitude is a single-slit diffraction factor times the coherent array sum. At integer order $m$, the array amplitude is $N$, giving the displayed peak intensity at fixed incoming intensity. Changing $w$ can increase the central intensity while suppressing a higher order through its envelope. Renormalizing both patterns to unit central intensity removes the information needed for that comparison.