Extended Data Fig. 1: Standing-wave modelling and light coherence.

a, Reflecting light within the thin film interferes to form standing waves. As the thickness of the film increases, the minimum intensity remains close to zero while the maximum intensity of the standing wave oscillates within the film, as shown by finite difference time domain simulations of polystyrene on silicon. b, Profiles of standing waves in films of different thickness. The colour shows the light intensity relative to the maximum light intensity that can be achieved in this system (the colour scale shows relative light intensity, unitless). At any thickness, for example those indicated by A and B in a, standing-wave interference occurs, although the anti-node intensity can vary by a factor of up to 0.6 in this polystyrene system. Fluctuations in thickness of the thin films therefore do not prevent crosslinking from occurring as long as the applied dose is high enough. The table below outlines the coherence length of the LED light sources used. Approximating Gaussian light sources, the coherence length is \({l}_{{\rm{c}}}=\sqrt{\frac{2ln\left(2\right)}{{\rm{\pi }}}}\frac{{\lambda }_{0}^{2}}{n{\rm{\Delta }}{\lambda }_{0}}\) where λ₀ is the free space wavelength of the light source, Δλ₀ is the spectral width (full-width at half-maximum, FWHM), and n is the refractive index of the medium³⁹. The polymer films in this study had thicknesses of less than 1 μm so that coherent interference could be achieved with light sources that have coherence lengths on the micrometre scale.