Wavelength-scanning-based lensless Fourier ptychographic diffraction tomography microscopy method

A wavelength-scanning-based lensless Fourier ptychographic diffraction tomography method, comprising:

• step 1:
• sequentially illuminating a sample placed on a surface of a CMOS image sensor using a wavelength-scanning illumination source at a fixed position, and triggering the CMOS image sensor to collect a holographic intensity image sequence at a plurality of wavelengths to capture diffraction information of the sample, wherein the wavelength-scanning illumination source comprises a supercontinuum laser and an acousto-optic tunable filter (AOTF), the step 1 comprising emitting a broadband beam from the supercontinuum laser, filtering the broadband beam with the AOTF to provide a specific wavelength, and vertically irradiating the sample with the filtered beam;;
• step 2:
• constructing, by a processor, a high-resolution three-dimensional (3D) refractive index space for the sample, wherein a pixel size of the 3D refractive index space is set to exceed a discrete sampling limit of the CMOS image sensor to achieve pixel super-resolution;
• step 3:
• updating the 3D refractive index space at a corresponding wavelength by:
• (a) calculating a scattering potential of the sample based on a refractive index distribution of the sample and a refractive index of a background medium;
• (b) performing a 3D Fourier transform on the scattering potential to obtain a 3D Fourier spectrum, and projecting a 3D sub-spectrum along a direction to obtain a 2D sub-spectrum;
• (c) performing an inverse Fourier transform on the 2D sub-spectrum to obtain a normalized first-order scattering field complex amplitude on a focal plane, and utilizing a Rytov approximation to obtain a complex amplitude on the focal plane;
• (d) propagating the complex amplitude from the focal plane to a sensor plane using an angular spectrum method, updating an amplitude of the propagated complex amplitude using a square root of an intensity from the holographic intensity image sequence, and propagating the updated complex amplitude back to the focal plane;
• (e) performing a logarithmic operation on the updated complex amplitude on the focal plane to obtain an updated normalized first-order scattering field, and performing a Fourier transform to obtain an updated 2D spectrum;
• and
• (f) filling the 3D Fourier spectrum by remapping the updated 2D spectrum into an Ewald shell and inserting it into a corresponding position of the 3D Fourier spectrum to obtain an updated refractive index distribution via 3D inverse Fourier transform;
• and
• step 4:
• repeating step 3 for each wavelength in the holographic intensity image sequence until the refractive index distribution converges, to produce a pixel super-resolved 3D tomographic image with uniform resolution across the entire field of view of the CMOS image sensor, wherein the 3D tomographic image comprises a rendered 3D refractive index distribution and a series of 2D refractive index distribution maps at different z-axis depths.