Figure 5: Modelling to compare image formation with SLED illumination and bright-field illumination.

a) Schematics showing the sequence of optical elements in the imaging experiments. From left to right: SLED surface – phase object – 4f-imaging system, schematically represented by two lenses – image plane, where the camera is positioned. b) The angular spectrum ${\mathcal{J}}_{\mathrm{s}}\left(\mathrm{u},\mathrm{v}\right)$, where u,v are the spatial frequencies. The graphs on the top show ${\mathcal{J}}_{\mathrm{s}}$ for the SLED surface (left) and for bright-field illumination through a water objective with numerical aperture 1.0 (right); scale bar – 1/μm. The bottom graph displays normalized magnitudes of ${\mathcal{J}}_{\mathrm{s}}$ for the SLED surface (red) and bright-field illumination (black) acquired along the dashed lines in the top graphs. c) The complex degree of mutual spatial coherence j_s(x₂ − x₁,y₂ − y₁) for the SLED surface (left) and the bright-field illumination (right). The bottom graph displays normalized magnitudes of j_s(x₂ − x₁,0) for the SLED surface (red) and bright-field illumination (black) acquired along the dashed lines in the top graphs. d) Phase map of the complex amplitude transmission function A(x,y) of a transparent spherical particle with refractive index 1.37 for light of 630nm wavelength. The bottom yellow graph shows the phase profile along the dashed line in the top map. The black line represents the absolute value of the object’s amplitude transmission function. e) Amplitude spread function of the imaging system as a 2D map and a profile taken along the white dashed line in the map. f) SLED image and bright-field image of the phase object with corresponding profiles shown below. Scale bars in (c-f) – 1μm. g) Contrast ratio used as a metric to compare image contrast obtained with SLED light and with bright-field illumination as a function of refractive index difference Δn between phase object and surrounding medium. For Δn ≤ 0.3 SLED illumination provides better contrast then bright-field light (corresponding data points marked in red).