Based on the characteristics of liquid lens sparse aperture imaging, a radiative multiplet array structure is proposed; a simplified model of sparse aperture imaging is given, and the analytical expression of the modulation transfer function is derived from the optical pupil function of the multiplet array structure; the specific distribution form of this multiplet array structure is given, and the structure parameters are approximated by the dimensionless method; the two types of radiative multiplet array structures are discussed, and the filling factor, redundancy, modulation transfer function and other characteristic parameters are calculated. The physical phenomena exhibited by the parametric scan are discussed, and the structural features and imaging characteristics of these two arrays are compared. The results show that the type-II structure with larger actual equivalent aperture and actual cutoff frequency and lower redundancy is selected when the average modulation transfer function and the IF characteristics of the modulation transfer function of the two structures are close to each other; the type-II structure has certain advantages in imaging; the conclusion is suitable for arbitrary enclosing circle size because the liquid lens-based multiplet array structure adopts dimensionless approximation parameters; compared with the composite toroidal structure, the radiative multiplet mirror structure has a larger actual cut-off frequency and actual equivalent aperture when the filling factor is the same.

The electro-magnetic (EM) waves transmitted through a thin object with fine structures are observed by a microsphere located above the thin object. The EM radiation transmitted through the object produces both evanescent waves, which include information on the fine structures of the object (smaller than a wavelength), and propagating waves, which include the large image of the object (with dimensions larger than a wavelength). The super-resolutions are calculated by using the Helmholtz equation. According to this equation, evanescent waves have an imaginary component of the wavevector in the z direction, leading the components of the wavevector in the transversal directions to become very large so that the fine structures of the object can be observed. Due to the decay of the evanescent waves, only a small region near the contact point between the thin object and the microsphere is effective for producing the super resolution effects. The image with super-resolution can be increased by a movement of the microsphere over the object or by using arrays of microspheres. Both propagating and evanescent waves arrive at the inner surface of the microsphere. A coupling between the transmitted EM waves and resonances produced in the dielectric sphere, possibly obtained by the Mie method, leads to a product of the EM distribution function with the transfer function. While this transfer function might be calculated by the Mie method, it is also possible to use it as an experimental function. By Fourier transform of the above product, we get convolution between the EM spatial modes and those of the transfer function arriving at the nano-jet, which leads the evanescent waves to become propagating waves with effective very small wavelengths and thus increase the resolution.