However, these low-coherence QPI approaches usually require spatially coherent illumination to ensure accurate and halo-free phase measurements 17, 18, so the maximum achievable imaging resolution is still restricted to the coherent diffraction limit. The combination of broadband illumination with the common-path geometries significantly alleviates the coherent noise problem and enhances the stability to mechanical vibrations and air fluctuations that typically affect any interferometric systems. This limitation was overcome by the low-coherence QPI approaches, such as spatial light interference microscopy (SLIM) 13, white-light diffraction phase microcopy (wDPM) 14, quadriwave lateral shearing interferometry (QWLSI) 15, τ interferometry 16, etc. 6, 10, 11, 12 Nevertheless, due to the laser illumination sources typically used, coherent QPI methods suffered from speckle noise arising from stray interferences from imperfections in the optical system.

8, 9 By introducing the principles of interferometry and holography into microscopy, both amplitude and phase information of microscopic specimens can be simultaneously demodulated from the recorded interference patterns. Especially in cases where conventional preparation techniques, such as fixation, staining, or fluorescent tagging, may affect cellular functions and limit biological insight, QPI offers an important alternative. Quantitative phase profiles of cells allow determination of cellular structure and biophysical parameters with minimal sample manipulation. Besides, the photobleaching and phototoxicity of the fluorescent agents prevent live cells imaging over extended periods of time 4.ĭuring recent years, quantitative phase imaging (QPI) 5, 6, 7 has emerged as an invaluable optical tool for biomedical research thanks to its unique capabilities to image optical thickness variation of living cells and tissues without the need for specific staining or exogenous contrast agents ( e. However, such sub-diffraction imaging techniques require fluorescent dyes and fluorescent proteins as biomarkers, and are thus ill-suited for samples that are non-fluorescent or cannot be easily fluorescently tagged. Such a need has driven the development of many unique sub-diffraction imaging techniques that have made great impacts on biological fluorescence imaging, allowing visualization of sample features well beyond the diffraction limit by either single-molecule localization, such as in stochastic optical reconstruction microscopy (STORM) and photo activated localization microscopy (PALM) 1 or spatially modulated excitation, such as in stimulated emission depletion (STED) 2 and structured illumination microscopy (SIM) 3.

In the field of optical microscopy, there has been a continued need towards increasing imaging resolution for visualizing subcellular features of the biological samples. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution.

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit.

Absorption and light intensity equation