Optical film, backlight, and display

An optical film comprising an optically diffusive single layer having an average thickness of between about 0.5 and about 5 microns and comprising:

• opposing first and second major surfaces;
• a plurality of nanoparticles dispersed between and across the first and second major surfaces, the nanoparticles comprising silica, the plurality of nanoparticles having a nanoparticle size distribution comprising at least two distinct first and second peaks at respective nanoparticle sizes d1 and d2, 1.5≤d2/d1≤10, wherein the nanoparticles in the plurality of nanoparticles within a full width at half maximum (FWHM) of the first peak and within a FWHM of the second peak form respective W1 and W2 percent by weight of the plurality of nanoparticles, 1.1≤W1/W2≤2;
• and
• a polymeric material bonding the nanoparticles to each other to form a plurality of nanoparticle aggregates defining a plurality of voids therebetween,
• wherein, for a substantially collimated substantially normally incident light and a visible wavelength range from about 420 nanometers (nm) to about 680 nm and an infrared wavelength range from about 900 nm to about 1000 nm, the optical film has:
• in the visible wavelength range, an average specular transmittance VTs and an average total transmittance VTt;
• and
• in the infrared wavelength range, an average total transmittance ITt and an average specular transmittance ITs, 0.3≤VTs/VTt≤0.7, VTs/ITs≤0.25, ITs/ITt≥0.7.