High-speed transport-of-intensity phase microscopy with an electrically tunable lens

Abstract

We present a high-speed transport-of-intensity equation (TIE) quantitative phase microscopy technique, named TL-TIE, by combining an electrically tunable lens with a conventional transmission microscope. This permits the specimen at different focus position to be imaged in rapid succession, with constant magnification and no physically moving parts. The simplified image stack collection significantly reduces the acquisition time, allows for the diffraction-limited through-focus intensity stack collection at 15 frames per second, making dynamic TIE phase imaging possible. The technique is demonstrated by profiling of microlens array using optimal frequency selection scheme, and time-lapse imaging of live breast cancer cells by inversion the defocused phase optical transfer function to correct the phase blurring in traditional TIE. Experimental results illustrate its outstanding capability of the technique for quantitative phase imaging, through a simple, non-interferometric, high-speed, high-resolution, and unwrapping-free approach with prosperous applications in micro-optics, life sciences and bio-photonics.

Rapid quantitative phase imaging for partially coherent light microscopy

“…This approximation of the ETL is justified in the Appendix and has also been assumed in other ETL-based setups, see for example [10,25]. For a realistic initial estimate of the input beam a circle function circ(2 |r| /D) (in our case with diameter D = 5 mm) can be considered, thus it yields g 1 (…”

“…Alternatively, non-interferometric techniques based on the measurement few diffraction patterns have also been successfully applied for quantitative phase imaging. They comprise iterative phase retrieval algorithms [6][7][8], or non-iterative methods that solve the so-called transport of intensity equation (TIE) [9,10]. All these computational imaging techniques allow for marker-free live cell analysis, which is highly demanded in biomedical sciences [10][11][12].…”

“…In addition, they are made from low dispersion and polarization preserving materials. Such ETLs have been used for high-speed volumetric imaging [25] and phase retrieval of coherent beams [10].…”

Phase space representation of transport of intensity phase retrieval for partially coherent fields

“…x ), the system then becomes linear and can be described in terms of weak object optical transfer function [4,8]. Thus the defocus phase transfer function can be applied to retrieve the phase or correct the phase blurring caused by the imaging PSF.…”

“…However, as we know no currently physically realizable sources are intrinsically perfectly coherent, and one must consider the effect of partial coherence on phase retrieval. The fact that TIE is not restricted to the purely coherent regime but works also with a partially coherent source seems to be very well known, and a wide range of applications in x-ray diffraction [2], electron-beam microscopy [3], and quantitative optical phase microscopy [4,5] have been reported. However, partially coherent field does not have a well-defined phase since the field experiences statistical fluctuations over time, which brings up an important question about what "phase" is being measured in such scenarios.…”