Video-rate quantitative phase analysis by a DIC microscope using a polarization camera

: This paper describes how to take advantage of the replacement of an intensity camera with a polarization camera in a standard differential interference contrast (DIC) microscope. Using a polarization camera enables snapshot quantitative phase analysis so that real-time imaging of living transparent tissues become possible. Using our method, we quantify the phase measurement accuracy using a phantom consisting of glass beads embedded in lacquer. In order to demonstrate these advantages, we image the pumping heart and blood flow in a living medaka egg.


Introduction
Differential interference contrast (DIC) microscopy [1] is a widely used method for observing tissues or cells in vivo without the need for applying florescent dyes. DIC microscopy allows analysis of detailed structures, high sensitivity in detecting phase information, and has a strong capability for optical sectioning [2]. Many researchers have proposed methods for the quantitative phase measurement of volumes using transmission DIC microscopy [3,4], and surface profile measurement using reflection DIC microscopy [5][6][7]. Ishiwata et al. proposed a retardation-modulated DIC (RM-DIC) microscope for quantitative measurement of planar microstructure at a given focal depth [8,9], and to measure 3D phase volume by optical sectioning [2]. However, these quantitative reconstruction methods [2][3][4][5][6][7][8][9] can require significant computation for each phase image because of the need to acquire multiple images for use with the phase shift technique.
We show below that it is possible to obtain a quantitative phase image from a single raw frame, so that real-time video is possible for a DIC microscope using a polarization cameraa camera for which a micropolarizer array has been attached to a detector array [10][11][12]. While Fabre et al. have previously shown how to make use of a photonic crystal polarization camera [11] with a DIC microscope, they used scanning to collect multiple raw images in order to obtain a single phase image [13]. Thus, they were unable to demonstrate video imaging of dynamic phase objects. We demonstrate that it is possible to capture measurements at the native frame rate of the polarization camera, and that through deconvolution with the DIC system's inverse MTF, we can convert the raw intensity data into quantitative phase images.
In Section 2 below, we introduce how to calculate a quantitative phase image from one image captured by a polarization camera. In Section 3, we evaluate the proposed method for getting accurate phase measurement using a sample of glass beads inside a lacquer medium. In order to demonstrate the advantages of our method, we also show a video-rate phase measurement of rapid motion in a living medaka egg.

Snapshot
We ) , are Jones mat and −45°, and case of a polar , ) ( ], we will as n atop a (poten oximated by its olarizer and th nes matrix of th a is rewritten u ) .
stribution nt of any (7) to Eq. scalar to a vector, we also need to convert the complex conjugate in Eq. (1) to an adjoint operator (i.e. conjugate transpose), producing Here . 2 The object phase gradient (the differential phase distribution) can be obtained by , el whose 90° pixel n order to g to (x, y). s S 0 (ζ, η), age I(x, y, S 2 (ζ, η)} ed images an inverse n (17) a's pixels a result, polarization e and aliasing e

Evaluatio
A DIC micros camera is sho nm bandpass of ~30 across pixels is 648 × In our ana wavelength, s 1/MTF(f x ) usi that the syste 0.6μm −1 , for t  determine how well the system can estimate quantitative phase using the proposed analysis. The diameter d of the glass beads is 2 μm. Figure 6 shows the measurement results of the differential phase on a region of our sample before the inverse Fourier transform (calculated by Eq. (11), shown on the left side of the figure) and the quantitative phase after inverse Fourier transform (calculated by Eq. (14), shown on the right side of the figure). The image shown in the figure is sampled at 0.25 μm / pixel We can see the well-known halo artifact indicated by negative phase values on both sides of the glass beads. The theoretical curve is calculated from the difference of refractive index (n 1 − n 2 = 0.02), the bead diameter (d = 2 μm), and the wavelength (650 nm).
The halo artifact visible in Fig. 6(f) is caused by insufficient spatial coherence of the illumination system. Nguyen et al. have shown that they were able to successfully remove the artifact by using an external interferometric unit [17], but our system currently does not have a similar hardware setup allowing for removal of the halo. We obtain an absolute maximum phase difference of 0.05 rad between our measurement curve and theoretical curve at the glass bead area without the halo artifact.

Video-rate quantitative analysis result
In biology, zebrafish and medaka are often used for investigating the tissue formation process and for the observation of abnormal and healthy cells. Therefore, in order to demonstrate video-rate quantitative phase measurement, we measure a living medaka egg (5~6 days after spawning) (see Fig. 7). Figure 8 shows a 20 Hz video measurement of a medaka heart's pumping and conventional take detailed measurement) valve between heart's pumpi

Conclusio
Adding a po measurement the DIC imag distribution fr depth-integrat microscopy w object that m measurement the structures

Acknowledg
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