Angle-scan optical diffraction tomomgraphy (ODT) relies on measuring 2-D optical phase delay maps (due to 3D refractive index distribution) in multiple directions. This can be achieved by either keeping the illumination angle fixed and rotating the sample OR by changing the illumination angle while keeping the sample undisturbed. The later is particularly advantageous for substrate-attached cells. The following briefly describes angle-scan based ODT systems developed at the LBRC.
Angle-scan based ODT was first optical tomography system developed at the LBRC [1]. Figure 1(a) shows the heterodyne Mach-Zehnder interferometer based tomographic phase microscopy setup. A helium-neon laser beam (λ = 633 nm) is split into sample and reference arms. A galvo mirror is used to vary the angle of illumination on the sample, placed between oil-immersion condenser and objective lenses. Maximum illumination angles are limited to θ < 60o. The reference beam passes through two acousto-optic modulators, which shift the frequency of the laser beam by 1,250 Hz. A second beamsplitter recombines the sample and reference beams for interference at the image plane. A high-speed CMOS camera (Photron 1024PCI) is used to record 4 images at 5,000 frames/sec, such that the sample-reference phase shift between consecutive frames is π /2. Quantitative phase images are then calculated by applying phase-shifting interferometry algorithm.
Reconstruction of 3D refractive index tomogram from the measured angle-dependent phase images is achieved by using filtered back-projection method. A discrete inverse Radon transform is applied to every x-θ slice in the beam rotation direction. In addition, iterative method with positivity constraint is used to reduce the effects of the missing cone. Imaging of a 3D refractive index tomogram for a single HeLa cell presented in Fig. 1(b). Further improvement in tomographic reconstruction was achieved by solving Maxwell's equation using Rytov approximation. In this way, the effect of diffraction is taken into account in the reconstruction process and diffraction-free high-resolution 3D images are obtained throughout the entire sample volume [2]. Figures 1(c) shows the transfer function in (kx, ky, kz = 0) and (kx, ky = 0, kz) planes, respectively, after mapping all the angular E-field images for a 6 µm polystyrene bead. Ring patterns are clearly visible after mapping various angular images, which is expected for the spherical shape of the sample. A comparison of refractive index construction using filtered back-projection algorithm and Rytov approximation based diffraction tomography is shown Fig. 1(d). More specifically, the images show slice images of tomograms at the objective focus in the middle of the 6 µm diameter bead for the two reconstruction approaches. Clearly, Rytov approximation based optical diffraction tomography provides more accurate refractive index values as well as improved spatial resolution.