After what $$shutter time$,$ or rather integration time, $$t$,$ do the pixels in your camera become saturated?

Projector$$s LED source visible band radiance: $1\mathrm{.}00$x$105$W$/$m$2$Sr

LED lamp emitting area, $24$ mm x $24$ mm

Distance from the projector to screen: $4$ m

Illuminated scene on the screen: $3\mathrm{.}5$ m x $5$ m

Reflection of the Lambertian screen: $=0\mathrm{.}75$

Distance from the screen to your camera: $3$ m

Camera Lens: F$/2\mathrm{.}1,$ T$=0\mathrm{.}75,$ EPD$=2\mathrm{.}5$ mm

FPA:$$xp$=2\mathrm{.}5$ m$,$ Nw$=1,500$ m$-2,$ Responsivity $=0\mathrm{.}62$ A$/$W

Use a wavelength of $0\mathrm{.}555$ m