Cells are the basic units of biomass, and their morphological structures are often associated with the functional state of biomass. Therefore, the morphology of a cell is an important research topic in life science and a critical factor in clinical medical diagnosis. Quantitative phase imaging technology, as a powerful nondestructive and label-free imaging tool, provides various biological and physical properties for the quantitative evaluation of cells. Although the phase diagram of the sample provided by this technology contains information about its internal structure, the thickness and refractive index of the sample is coupled with the phase data. Decoupling the phase data is required to reconstruct a three-dimensional (3D) morphology of the sample. Dual-wavelength imaging technology is effective for single medium samples. However, this method does not work for multimedia phase objects. In response to this shortage, this study proposes a new reconstruction method based on orthogonal dual-wavelength measurements.

The 3D reconstruction method is based on three phase images from two orthogonal directions. Two of these phase images are obtained with two different wavelengths. The first step is to separate the phase shift due to different substructures. Given that the environmental liquid is a highly dispersive material relative to the cell sample, the refractive index (RI) of the environmental liquid correspondingly changes under different incident light, whereas the RI of the sample remains constant. Thus, by subtracting the two images at two different wavelengths, the physical thickness of the media adjacent to the environment (such as cytoplasm) can be determined. Next, the average RI of the cytoplasm can be extracted using the associated phase value distribution, while phase shifts due to cytoplasm and nucleus are also separated immediately. Following that, the thickness information of the nucleus for the incidence along the two directions can be obtained using a phase diagram from the orthogonal direction. Thus, the RI of the nucleus can be calculated from the nuclear phase value. The relative position of the cytoplasm and nucleus can also be determined using two orthogonal phase diagrams. The 3D morphology of the multimedia phase object is obtained by combining the physical thickness distributions of the cytoplasm and nucleus.

The reconstructions of models with different structural characteristics are explored, including a cell with a single spherical nucleus (Fig. 2), a cell with a single saddle shape nucleus [Fig. 5(a)], and a binuclear cell with a double spherical nucleus [Fig. 6(a)]. The results of these samples [Figs. 9, 11(c), and 12(e)] are consistent with the initial model. Especially, the analytic method provides a sharp reconstruction result of the physical thickness of the cytoplasm and the entire reconstruction process takes a short time (Tables 1, 2, and 3). This study suggests the feasibility of this reconstruction method, but the actual application effect depends on many factors, such as image noise, heterogeneity of RI distribution, and calculation error in edge detection. An emphasis of the following study is to explore an efficient reconstruction algorithm suitable for experiments.

This study proposes a 3D morphological reconstruction method for nucleated cells based on orthogonal dual-wavelength phase images. This method requires three phase images from two orthogonal directions and is divided into two steps. First, using the high dispersion characteristics of environmental liquid and edge detection, the phases of the cytoplasm and nucleus are separated based on the independence and superposition of phase data, and the thickness of the cytoplasm is decoupled simultaneously. Then, the 3D morphology of the sample is reconstructed using another orthogonal phase diagram, RI and thickness information of the coupling nucleus, and the relative position relationship of the substructure expressed by two mutually orthogonal phase diagrams. This method collects sample information from two directions simultaneously. A small amount of data means convenient data acquisition and fast data processing. The simulation results show that the algorithm, which may provide a reference for real-time imaging of biological cells, is effective.