Recently, the research group of Prof. Qian Chen and Prof. Chao Zuo from the School of Electronic and Optical Engineering, Nanjing University of Science and Technology (NJUST) has published a research paper entitled “Accurate quantitative phase imaging by differential phase contrast with partially coherent illumination: beyond weak object approximation” in Photonics Research (IF= 7.254). The work, selected as the cover paper, has been reported by the public issue of China Laser Press. Doctoral student Yao Fan is the first author of the paper, Prof. Chen Qian and Prof. Zuo Chao are the co-corresponding authors of the paper, and NJUST is the first completing and corresponding institution.
Article Link: https://opg.optica.org/prj/fulltext.cfm?uri=prj-11-3-442&id=527100
In optical imaging, “phase” is one of the most important components of the light field (strictly speaking, monochromatic coherent light field). Especially in the field of optical microscopy, where most objects are weakly absorbing phase objects, the phase of transmitted light contains important information about the sample, such as three-dimensional (3D) morphology and refractive index distribution. Therefore, the acquisition of phase information is particularly important, which has driven the emergence of “phase measurement” technology. Nowadays, “phase measurement” has become a major research direction in the field of optical microscopic imaging and been widely used in biological cytology, pathology and drug discovery.
The classical phase measurement technique, based on the principle of interferometric imaging, combines algorithms such as fringe analysis, numerical propagation and phase unwrapping to demodulate the quantitative phase information of the sample, providing a reliable optical metrology method for accurate measurement of the phase of the sample. However, interferometric phase measurement has not been widely used because it requires a highly coherent illumination source and a precisely calibrated interferometric optical path, while it is highly susceptible to scattering noise.
QPI under partially coherent illumination (differential phase contrast, transport of intensity equation) opens up new prospects for higher quality “non-interferometric” phase measurements. It has the following advantages: 1) its imaging system configuration is simple and easier to implement; 2) its imaging algorithm doesn’t need phase unwrapping; 3) its imaging results has higher lateral/axial resolution. However, unlike the linear relationship between object distribution and complex amplitude in interferometric imaging, the intensity and object transmission in partially coherent imaging are “bilinear” in nature. This complex relationship makes it impossible to establish the intensity-phase solution mechanism directly. Usually, QPI techniques under partially coherent imaging require the introduction of a weak object approximation model to linearize its intensity distribution and thus establish an explicit expression of the acquired intensity and object phase to derive the phase inversion algorithm.
However, the introduction of weak-object approximation models also makes such techniques inherently flawed in two ways: 1) weak-object approximation models are described as qualitative, vague definitions of “objects with small phases”, lacking a clear physical or mathematical definition; 2) the accuracy of the phase reconstruction is limited by how well the real object matches the approximation model. These two limitations would make QPI lose its proudest “quantitative” properties and no longer provide accurate and reliable data for subsequent analyses such as cell morphology and cell stem mass measurements.
To address the above issues, the research group of Prof. Qian Chen and Prof. Chao Zuo of NJUST carried out an exploratory work on QPI based on partially coherent imaging and gave the first strict mathematical definition of weak object approximation through theoretical analysis and numerical simulation. Specifically, the weak phase approximation model requires the object phase to be no larger than 0.5 rad, when the one-step deconvolution algorithm can achieve accurate quantitative phase reconstruction for arbitrary object distribution and illumination aperture. When the object phase is larger than 0.5 rad, the weak phase approximation is not satisfied, and the reconstruction result is no longer consistent with the ground-truth value of the object. This conclusion provides a theoretical basis for measuring the accuracy of phase reconstruction by illustrating the conditions that need to be met for the “quantitative” nature of QPI.
Fig. 1. Numerical simulation results with variable phase to determine the definition of the strict weak object approximation. (a) Illumination apertures and their corresponding WPTFs. (b), (c) RMSE curves for the reconstructed phase of a microlens array and a sharply varying step with increasing phase values under different illumination apertures. (d), (e) Reconstructed phase and its profile for different phase values of a microlens array and a sharply varying step under half-annular illumination of 0.01 width.
To break the limitations that QPI techniques under weak object approximation are difficult to achieve the accurate reconstruction of large-phase objects, the research group further introduces the pseudo-weak object approximation model in electron microscopy to represent large-phase objects under partially coherent imaging as a superposition of multiple layers of weak-phase structures. On this basis, they considered phase inversion as an optimization problem and proposed an iterative deconvolution algorithm for phase reconstruction (Figure 2). The algorithm achieves accurate quantitative phase reconstruction of large-phase objects without additional acquisition data, thus extending the QPI algorithm of partially coherent to large-phase objects.
Fig. 2. Algorithm flow chart of the iterative deconvolution reconstruction.
The research group verified the accurate QPI capability of the iterative deconvolution algorithm through an experiment on MCF-7 human breast cancer cells, and the results are shown in Figure 3. Compared with the conventional one-step deconvolution algorithm (blue curve) that provides too small cell morphological features for mitotic cells, the iterative deconvolution accurately recovers the quantitative features of the samples (red curve), demonstrating their accurate 3D morphological data. The results show that this method provides more accurate 3D morphological data of cells, which is expected to provide an effective technical solution for early cancer confirmatory treatment.
复审 | 左超
终审 | 徐峰