Fig. 4: Experimental resolution and Slepian–Pollak coefficient retrieval accuracy.
a, Representative PSF of LSOM (FWHM ≈ λ/6) compared with that of ideal conventional coherent Fourier imaging with NA = 0.9. b, Resolution test using a nanoscale Siemens star (sample no. 5 in Fig. 3). The intensity along a circumference with the minimum diameter that satisfies the Rayleigh criterion on average reveals a resolvable centre-to-centre spacing of ~λ/7 between neighbouring spokes. θ denotes the polar angle of a point on the circumference (inset). Scale bar, 200 nm. c, Real (Re) and imaginary (Im) parts of the experimentally (Exp.) measured Slepian–Pollak coefficients for all of the objects (sample numbers 1–8) in Fig. 3 compared with those obtained from simulations (Sim.), showing good estimation accuracy for both strong and weak channels. Each coloured dot corresponds to a different channel; for all channels, the Pearson correlation coefficient, ρ, is ≥0.82. The continuous curve in each plot marks the 2σ ellipse of the covariance matrix. The labelling in the top left plot also applies to the other seven samples. Scale bars, 200 nm. d, Calculated |γi|2 as a function of the mode order i, quantifying the decrease in signal strength of Slepian–Pollak modes with increasing order.
