Modulation of Point Spread Function for Super-Resolution Imaging

High image resolution is desired in wave-related areas such as ultrasound, acoustics, optics, and electromagnetics. However, the spatial resolution of an imaging system is limited by the spatial frequency of the point spread function (PSF) of the system due to diffraction. In this article, the PSF is modulated in amplitude, phase, or both to increase the spatial frequency to reconstruct super-resolution images of objects or wave sources/fields, where the modulator can be a focused shear wave produced remotely by, for example, a radiation force from a focused Bessel beam or X-wave, or can be a small particle manipulated remotely by a radiation-force (such as acoustic and optical tweezers) or electrical and magnetic forces. A theory of the PSF-modulation method was developed, and computer simulations and experiments were conducted. The result of an ultrasound experiment shows that a pulse-echo (two-way) image reconstructed has a super-resolution (0.65 mm) as compared to the diffraction limit (2.65 mm) using a 0.5-mm-diameter modulator at 1.483-mm wavelength, and the signal-to-noise ratio (SNR) of the image was about 31 dB. If the minimal SNR of a "visible" image is 3, the resolution can be further increased to about 0.19 mm by decreasing the size of the modulator. Another ultrasound experiment shows that a wave source was imaged (one-way) at about 30-dB SNR using the same modulator size and wavelength above. The image clearly separated two 0.5-mm spaced lines, which gives a 7.26-fold higher resolution than that of the diffraction limit (3.63 mm). Although, in theory, the method has no limit on the highest achievable image resolution, in practice, the resolution is limited by noises. Also, a PSF-weighted super-resolution imaging method based on the PSF-modulation method was developed. This method is easier to implement but may have some limitations. Finally, the methods above can be applied to imaging systems of an arbitrary PSF and can produce 4-D super-resolution images. With a proper choice of a modulator (e.g., a quantum dot) and imaging system, nanoscale (a few nanometers) imaging is possible.