Fig. 2: Focusing and imaging properties of our objective chip.

a Simulated and experimental widths of belts at the different regions of our objective chip. Inset: SEM images of the different regions by addressing the corresponding zone numbers. b The etched depth around the center region of the objective chip is measured experimentally by using a profilometer. c Optical field near the focal plane of the objective chip. Cross sections of the measured intensity profiles are shown in the left panel, while the right panel shows a comparison between the simulated and experimental on-axis line-scanning intensity profiles. d Simulated and experimental line-scanning intensity profiles at the focal plane of the objective chip. Their 2-dimensional intensity profiles in the region of 1.2 μm × 1.2 μm are provided in the insert. e Lateral FWHMs of the measured spot near the focal plane. RC: Rayleigh criterion (0.51 λ/NA); SOC: Superoscillation criterion (0.358 λ/NA). f Simulated and experimental efficiency when the phase difference \(\Delta \varphi\) between two neighboring etched and unetched parts changes from 0 to 2 π. g Sketch for wide-field imaging by using our objective chip. The object and image distances are 1.2 f and 6 f (the focal length \({f}=1{{{{{\rm{mm}}}}}}\)) respectively, yielding a magnification of 5×. Such a magnification is chosen to avoid optical aberration, while it is enough to demonstrate the capability of collecting light with high spatial frequencies. Inserts: the knife-edge object (left, captured by using a reflective microscope that generates bright chromium film and dark quartz substrate) and its image (right) taken by using our objective chip. h Experimental edge spread function (ESF, which is calculated by using the average intensity along the long side of the red box in the insert of (g)). To evaluate its resolving power, the spatial coordinate y is scaled down by its magnification of 5. The experimental ESF is fitted by an error function, the deviation of which outputs the line spread function (LSF). i Retrieved modulation transfer function (MTF, solid-circle curve) of the objective chip by using the Fourier transform of the achieved LSF in (h). The diffraction limit is also provided for a better comparison.