The phase problem is encountered and required to be solved in many optical applications, such as optical metrology, adaptive optics, and biomedical imaging. This problem arises because optical detectors can only record the amplitudes of light beams, and the phases of light beams are missed. However, the transparent object, such as a living cell, does not affect the amplitude of a light beam passing through it, except for a phase shift, and phase imaging is the only way to acquire the structure information of transparent objects. Although the Zernike phase contrast microscope can convert a phase shift of the light beam passing through a transparent object, it is not quantitative and only effective for small phase shifts. Quantitative phase imaging (QPI), which is a label-free and powerful technique for providing quantitative information of transparent objects, attracts growing interest in biomedical applications. Up to now, the mainstream techniques for QPI are digital holography microscopy and phase retrieval. Digital holography microscopy, an interferometric technique, is highly accurate but extremely sensitive to the environment. Phase retrieval can recover the input phase from intensity-only measurements, but it has a stagnation problem and a limited dynamical range. These drawbacks have greatly limited the application of phase retrieval. In this study, a QPI technique based on both wavefront segmentation by a microlens array and multiplane phase retrieval is proposed for achieving QPI of phase objects with a large dynamic range. This technique has the characteristics of high accuracy, fast convergence speed, and large dynamic range, which can be a potential technique for QPI of phase objects in biomedical imaging.

The proposed method for QPI of a phase object is based on both wavefront segmentation by a microlens array and multiplane phase retrieval. In order to acquire QPI of a phase object with a large dynamic range, the proposed method imposes three constraints on the light field passing through the phase object. The first one is wavefront segmentation, which divides the input wavefront into small ones by a microlens array. The second one involves multiple intensity distributions recorded at different diffraction planes along the axial direction of the microlens array. Due to the abundant information provided by intensity maps at different diffraction distances, phase retrieval algorithms typically converge quickly. The third one is to employ multiple illuminations at different wavelengths. In order to acquire an unwrapped phase imaging of a phase object by the proposed approach, three steps need to be performed: firstly, recording multiple diffraction intensity distributions near the focal plane of the microlens array under different illumination wavelengths; secondly, retrieving the phase of the phase object using multi-plane phase retrieval at different wavelengths, respectively; finally, unwrapping the phase of the phase object using the retrieved phases at the synthetic wavelength. A series of numerical experiments are performed to evaluate the performance of the proposed method. Four different types of aberrations (the phase of a microlens array, complex random combination wavefronts, peak functions, and cell slices) are selected as the phase to be measured for exploring the versatility of the proposed method under the illumination wavelengths of 640 nm and 685 nm. Then, phase retrieval of wavefronts with different peak-to-valley (PV) values is performed to verify the large dynamic range of the proposed method. At last, the convergence of the proposed method is compared with that of the classical phase retrieval algorithm.

The numerical experiments for retrieving four different types of phases show that the proposed method can recover phases of phase objects quickly and accurately (Figs. 5, 6, 7, and 8), which indicates that the proposed method is an effective way for QPI of phase objects. Using the proposed method, phase retrieval of a wavefront with a PV value exceeding 3 μm is achieved under the illumination wavelengths of 640 nm and 685 nm, nearly 5 times one illumination wavelength, indicating that the method covers a large dynamic range (Fig. 9 and Table 1). Furthermore, the comparison of convergence speed shows that the convergence of the proposed method is always better than that of the classical phase retrieval algorithm (Fig. 10 and Table 2).

In this study, a QPI technique for phase objects based on both wavefront segmentation by a microlens array and multiplane phase retrieval is proposed. This technique requires the recording of the intensity distribution maps of different diffraction distances near the focal plane of the microlens array under two different illumination wavelengths. The recorded intensity distribution maps are used to recover the digital complex light field passing through the phase object by multi-plane phase retrieval algorithm. The retrieved digital complex light field phases at different wavelengths are used to calculate the phase image of the phase object at a synthetic wavelength. In the numerical simulation experiments, the QPI for different types of phase objects with different PV values is achieved. It shows that this technique is powerful and efficient for QPI and serves as a promising technique for QPI of phase objects.