Transport-of-intensity approach to differential interference contrast (TI-DIC) microscopy for quantitative phase imaging

Abstract

Differential interference contrast (DIC) microscopy is an inherently qualitative phase-imaging technique. What is obtained is an image with mixed phase-gradient and amplitude information rather than a true linear mapping of actual optical path length (OPL) differences. Here we investigate an approach that combines the transport-of-intensity equation (TIE) with DIC microscopy, thus improving direct visual observation. There is little hardware modification and the computation is noniterative. Numerically solving for the propagation of light in a series of through-focus DIC images allows linear phase information in a single slice to be completely determined and restored from DIC intensity values.

Variational Phase Imaging Using the Transport-of-Intensity Equation

“…Following the lead of Kou et al [15], we choose to apply our TIE formalism to differential interference contrast (DIC) images. These authors have investigated the DIC image formation model (under the thin phase-only object assumption) and have demonstrated the applicability of (11) for this modality (see [15] for further details). Practically observing the implications of (20), we thus acquire DIC images using an A-Plan 10×0.25 NA with a DIC analyser II.…”

“…In this paper, we consider a low-cost label-free phase imaging approach that uses the transport-of-intensity equation (TIE) [13]. This method has significant advantages: it is a computational method that can be used with either bright-field [14] or DIC [15] microscopes; the resulting phase dispenses with the unwrapping task required by interferometric methods such as DHM [16]. As we shall see later, TIE puts forward a linear mathematical formalism that relates the spatial phase map of the sample to the derivative of its intensity map along the propagation direction.…”

Characterization of spatially varying aberrations for wide field-of-view microscopy

“…Phase diversity may be introduced either with additional optical elements or by simply inducing system defocus. Various methods for phase retrieval using defocus diversity have been reported in literature, including transport-of-intensity equation (TIE) based methods [25][26][27][28], iterative algorithms [29] and other non-iterative methods [30,31].…”

Analysis of Absorption and Phase Difference Images from Differential Interference Contrast Microscopy

“…The images generally contain both phase and absorption information about the sample. To extract the phase and amplitude information from the images, various methods have been proposed to acquire phase and absorption information, such as the phase shifting method [1], the TIE method [2], the retardation-modulated DIC [3], and the iterative alternating minimization method [4], which require either four images, a phase modulation plate, or complicated iterative calculations. Here we present a simple, straightforward, non-iterative method capable of extracting the absorption and the phase difference images from two images collected at different phase shifts of the birefringent prisms (a Normaski or a modified Wollaston prism) in a DIC microscopy-a method less sensitive to mechanical instabilities of the optical system.…”

“…The feasibility of our method is confirmed by experimental results of imaging liquid paraffin drops using a commercial DIC microscope. Compared with the available methods and previous research [1][2][3][4], our approach simplifies the procedures to extract the absorption and phase difference images without weak absorption limit. …”