Digital holographic diffraction tomography combines digital holography with optical diffraction tomography. According to the Fourier diffraction theory, the spectrum information is unevenly distributed on a Ewald sphere, and most of these data cannot exactly locate on the 3D matrix points. To solve this problem, a single assignment based nearest neighbor interpolation method is proposed. Firstly, the points to be interpolated are chosen on the 3D matrix. For each angle, a search scope is confirmed by two spheres with a radius R (k<sub>0</sub>-0.5< R <k<sub>0</sub>+0.5), where k0 is the radius of Ewald sphere. Then, the point on the 3D matrix is assigned by the value of the nearest neighbor point within this scope. After the assignment of the frequency information for all the angles, the object function is obtained by 3D inverse Fourier transform. In order to verify the feasibility of this method, a digital holographic diffraction tomography system is built. The 3D refractive index (RI) distribution of a microsphere with known RI 1.4607 is measured. Comparing with the conventional nearest neighbor interpolation algorithm, the relative error is reduced from 0.51% to 0.36%. It is demonstrated that the proposed algorithm can improve the reconstruction accuracy for diffraction tomography.
Optical Diffraction Tomography (ODT), as a novel 3D imaging technique, can obtain a 3D refractive index (RI) distribution to reveal the important optical properties of transparent samples. According to the theory of ODT, an optical diffraction tomography setup is built based on the Mach-Zehnder interferometer. The propagation direction of object beam is controlled by a 2D translation stage, and 121 holograms based on different illumination angles are recorded by a Charge-coupled Device (CCD). In order to prove the validity and accuracy of the ODT, the 3D RI profile of microsphere with a known RI is firstly measured. An iterative constraint algorithm is employed to improve the imaging accuracy effectively. The 3D morphology and average RI of the microsphere are consistent with that of the actual situation, and the RI error is less than 0.0033. Then, an optical element fabricated by laser with a non-uniform RI is taken as the sample. Its 3D RI profile is obtained by the optical diffraction tomography system.