Quantitative Phase Microscopy is a simple imaging methodology for resolving internal morphology of unstained living specimens. It computes the 2D phase images of a specimen from a combination of bright field images. However, when used in conjunction with polarised light can lead to the simultaneous mapping of the phase and the retardation of an optically anisotropic specimen. Experimentally the procedure is implemented without the need of expensive compensators used in traditional methods.
Optical Phase Imaging: Qualitative vs. Quantitative Aspects
Quantifying the optical properties living cells in both two and three dimensions (D) without modifying the observed specimen is a problem of ongoing interest in many research disciplines. This is particularly applicable to imaging of living cells that are frequently transparent and whose morphometric features have often being inferred by using exogenous contrast agents or expensive cromophores. Observed under a microscope, a live cell produces little or no information about changes in amplitude (i.e. it does not strongly absorb or reflect the incident light) but produces significant changes in the wavefront of an incident light due to variations in either the refractive index or the thickness of the sample that is generally considered a pure phase object. That is why, an alternative imaging method based on phase information, pioneered by the Dutch physicist Fritz Zernike in 1935 was developed to create the necessary contrast for viewing live unstained/undyed cells . Other techniques based on phase delay, including Nomarski Differential Interference Contrast (DIC) or Hoffman Modulation Contrast have subsequently become commonly employed for mostly qualitative studies of living cells . Although efforts have been made to enable quantitative phase measurements from these existing imaging modalities [2-4], conveying information regarding both phase and amplitude has been achieved only by few [5, 6]. It is worth noting that traditionally, quantitative information regarding phase is obtained from various interferometric techniques. Due to the intermingling of amplitude and phase information in living cells, partially coherent illumination is required for an optimal spatial resolution in microscopic imaging.
This is inconsistent with conventional interferometric methods which require the use of coherent light.
Quantitative Phase Microscopy: A Non-Interferometric Approach
Quantitative phase microscopy (QPM)  is a recently developed imaging technology, based on a non-interferometric approach, for high spatial resolution phase imaging. This non-invasive method for imaging transparent structures has been demonstrated for both thick  and thin ; biological  and inorganic  specimens. It can be used with partially coherent light in a conventional bright field microscope to uniquely determine the phase shift introduced into an optical wavefield by a transparent specimen. It represents a powerful alternative to other phase imaging techniques since it is able to provide simultaneous but separate quantitative information about both the absorption of the specimen and the phase .
Specifically, QPM entails acquiring a series of three transverse bright-field images: one at the in-focus plane and two at positive and negative differential defocus relative to it. As it is well known the plane of in-focus, for transparent specimens is easy to find as it is commonly the plane with least contrast in bright field imaging. Commercial software (QPm V2.1 IATIA, http://www.iatia.com.au) is then used to generate a 2D phase map of the specimen under study (fig.2 + 3). The phase values are determined within a diffraction-limited transverse spatial resolution by the magnitude of the phase shift induced in light traversing the specimen.
Anisotropic Specimens: A Perspective
Frequently the cellular material is not only transparent or translucent but is also optically anisotropic. Simply said this means that its optical properties are not the same in all directions. Often this is due to the cellular material and is responsible for the local structural order existent at very small scales including at the level of atomic bonds and molecular shapes in the specimens' structure. Birefringence is a term used to characterise the differential speed of light propagation between two states of polarisation orthogonal to each other, which is the direct consequence of the existence of more than one index of refraction. Furthermore, this means that the two orthogonal light components that are in phase before entering the specimen exit the specimen out of phase. This phase difference, termed retardation, can be used to determine the birefringence, i. e. retardation divided by sample thickness.
A number of imaging procedures, based on either polarisation or interferometric imaging are capable of identifying birefringence changes only, have led to a plethora of multidisciplinary research endeavour in the scientific and technical community. The method illustrated in the following demonstrates that information on both the specimen's phase and retardation are possible using non-interferometric imaging based on QPM combined with polarised light.
Quantitative Polarised Phase Microscopy
Quantitative Polarised Phase Microscopy (QPPM) combines the measurement principle of QPM with polarised light. In the case of a birefringent specimen, QPPM can be used to determine the 2D spatial variation of the retardation simultaneously with phase and absorption information. If the principal axis of the specimen is known one can obtain two different phase images: one where the light incident on the specimen is polarised along one principal axis and another where the light is polarised along the orthogonal direction (fig. 3). The retardation is then simply the difference between these two phase images. Experimentally this is achievable using only one polariser without the need for other compensators or analysers.
Application of QPPM
The capacity of QPPM as a practical tool in the investigation of the 2D birefringence of a transparent anisotropic specimen without the use of additional compensators is demonstrated by imaging isolated cardiac cells. In its simplest model, the birefringence of a cardiac muscle cell, simply termed a cardiomyocyte, can be explained considering that it has the same characteristics as an uniaxial crystal whose optic axis is usually considered to be parallel to the long axis of the cell. One can thus obtain phase images of the cell with the vibration transmission axis of a polariser either parallel or perpendicular to the long axis of the muscle cell. Retardation is obtained by simply subtracting these two images.
A typical bright field image of an unstained ventricular cardiomyocyte isolated from the heart of an adult rat by an enzymatic procedure is presented in fig.1.
Viewed between crossed polarisers, (fig.2), the cell appears, as expected, with bright areas against a dark background displaying distinct birefringent characteristics. The image illustrates that the refractive index for a plane polarised light traveling through the cell with its direction of polarisation along the long axis of the cell is different from the refractive index for light polarised in a transverse plane. It shows that the alignment of the repeating sarcomeric structures of contractile myofilaments is distinguishable as periodic striations.
Transverse phase images (fig.3) of the cell are computed from a series of bright field images using QPPM. Distinguishable are the characteristic sarcomeric structures of con-tractile filaments illustrating subtle phase changes. A two-dimensional retardation map (fig.4) is determined by subtracting these two phase images. The retardation values obtained agree well with the expected values existent in the literature.
Quantitative 2D representation of the retardation of a living cell was demonstrated using a simple procedure based on quantitative polarised phase measurement. The method is complementary to other ways of measuring the retardation of an anisotropic specimen in that it enables simultaneous access to the phase and the retardation. One main advantage of this method is that it makes use of a single linear polariser introduced into the optical pathway without the need of any other additional compensators, quarter-wave plates or analysers. Currently research is focusing on protocols able to use QPPM for the simultaneous determination of the orientation of the principal axes and the principal indices of a linear birefringent material. We expect that this novel method to be an effective analytical tool in studying the cardiac muscle contraction without the need for staining agents.
This research was supported by the Australian Research Council's Discovery Projects Scheme. The authors thank Dr Claire Curl for preparation of the cardiac cells.
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