Hybrid brightfield and darkfield transport of intensity approach for high-throughput quantitative phase microscopy

Abstract. Transport of intensity equation (TIE) is a well-established non-interferometric phase retrieval approach that enables quantitative phase imaging (QPI) by simply measuring intensity images at multiple axially displaced planes. The advantage of a TIE-based QPI system is its compatibility with partially coherent illumination, which provides speckle-free imaging with resolution beyond the coherent diffraction limit. However, TIE is generally implemented with a brightfield (BF) configuration, and the maximum achievable imaging resolution is still limited to the incoherent diffraction limit (twice the coherent diffraction limit). It is desirable that TIE-related approaches can surpass this limit and achieve high-throughput [high-resolution and wide field of view (FOV)] QPI. We propose a hybrid BF and darkfield transport of intensity (HBDTI) approach for high-throughput quantitative phase microscopy. Two through-focus intensity stacks corresponding to BF and darkfield illuminations are acquired through a low-numerical-aperture (NA) objective lens. The high-resolution and large-FOV complex amplitude (both quantitative absorption and phase distributions) can then be synthesized based on an iterative phase retrieval algorithm taking the coherence model decomposition into account. The effectiveness of the proposed method is experimentally verified by the retrieval of the USAF resolution target and different types of biological cells. The experimental results demonstrate that the half-width imaging resolution can be improved from 1230 nm to 488 nm with 2.5  ×   expansion across a 4  ×   FOV of 7.19  mm2, corresponding to a 6.25  ×   increase in space-bandwidth product from ∼5 to ∼30.2  megapixels. In contrast to conventional TIE-based QPI methods where only BF illumination is used, the synthetic aperture process of HBDTI further incorporates darkfield illuminations to expand the accessible object frequency, thereby significantly extending the maximum available resolution from 2NA to ∼5NA with a ∼5  ×   promotion of the coherent diffraction limit. Given its capability for high-throughput QPI, the proposed HBDTI approach is expected to be adopted in biomedical fields, such as personalized genomics and cancer diagnostics.