Minimizing scattering-induced phase errors in
differential interference contrast microscopy
Wataru Takano ,a,b Shuhei Shibata,c Nathan Hagen ,a,b Masaru Matsuda,dand Yukitoshi Otania,b,*aUtsunomiya University, Department of Optical Engineering, Tochigi, Japan
Utsunomiya University, Center for Optical Research and Education, Tochigi, Japanc
Utsunomiya University, Center for Industry-University Innovation Support, Tochigi, Japand
Utsunomiya University, Center for Bioscience Research and Education, Tochigi, Japanb

Abstract
Significance: Differential interference contrast (DIC) microscopes allow noninvasive in vivo
observation of transparent microstructures in tissue without the use of fluorescent dyes or genetic
modification. We show how to modify a DIC microscope to measure the sample phase distribution accurately and in real-time even deep inside sample tissue.
Aim: Our aim is to improve the DIC microscope’s phase measurement to remove the phase biasthat occurs in the presence of strong scattering.
Approach: A quarter-wave plate was added in front of the polarization camera, allowing amodified phase calculation to incorporate all four polarization orientation angles (0 deg, 45 deg,
90 deg, and 135 deg) captured simultaneously by the polarization camera, followed bydeconvolution.
Results: We confirm that the proposed method reduces phase measurement error in the presenceof scattering and demonstrate the method using in vivo imaging of a beating heart inside a
medaka egg and the whole-body blood circulation in a young medaka fish.
Conclusions: Modifying a polarization-camera DIC microscope with a quarter-wave plateallows users to image deep inside samples without phase bias due to scattering effects.
© The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License.
Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.JBO.25.12.123703]

Keywords: differential interference contrast microscope; polarization camera; quarter-wave
plate; real-time phase measurement.
Paper 200280SSRR received Aug. 31, 2020; accepted for publication Oct. 26, 2020; published
online Dec. 14, 2020.

1 Introduction
Noninvasive in vivo observation of transparent microstructures such as cells is important forbiology and medicine. Differential interference contrast (DIC) microscopes make it possible
to observe a transparent sample without fluorescent dyes or genetic modification by converting
sample phase gradients into intensity variations through shearing interferometry.1 Although thisrenders phase gradients visible, quantifying the sample’s phase distribution requires collecting
multiple images. Many researchers have proposed methods for quantitative phase measurement
using transmission DIC microscopy2,3 and surface profile measurement using reflection DIC
microscopy.4–8 These methods are difficult to use for living samples because they require taking
multiple images while rotating the polarization analyzer to multiple angles. For in vivo measurement, researchers have developed techniques where the input and output of the Nomarski
set up can be electronically modulated, demonstrating speeds of 1 frame in 12 s, although higher
speeds are likely possible.9*Address all correspondence to Yukitoshi Otani, otani@cc.utsunomiya-u.ac.jp

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In addition to DIC microscopy, other phase imaging techniques exist and have been adaptedfor video detection. Zernike phase contrast microscopy (PCM) has been adapted with color multiplexing to collect video-rate phase images.10 Although PCM has a simpler hardware set up than
DIC and is not subject to error from object birefringence, it typically provides lower axial
resolution (optical sectioning) and produces haloes around phase objects.11,12 Ptychography anddigital holographic microscopy are more recent methods that can also provide video-rate phaseimaging.13,14
In our previous paper,15 we quantified the phase distribution in real time for a DIC microscope using a polarization camera—a camera for which a micropolarizer array has been attachedto the detector array.16–18 A polarization camera can detect the intensity at four polarization orientation angles (0 deg, 45 deg, 90 deg, and 135 deg) in a snapshot, so that detection speeds arelimited only by the frame rate of the detector. We previously used only two intensities detectedusing the pixels oriented at 45 deg and 135 deg of the micropolarizer array. That is we used only
half the light intensity detected by the detector. In such a set up, the intensities detected using the
pixels oriented at 0 deg and 90 deg do not produce interference because these axes are aligned tothe shearing direction. We show below that using only two of the four micropolarizer orientations decreases the quantitative accuracy of phase measurement with this method in the presenceof scattering. We show that adding a quarter-wave plate in front of the polarization camera andusing the full light intensity at all four polarization orientation angles (0 deg, 45 deg, 90 deg, and
135 deg) improves the phase measurement accuracy, especially in the presence of scattering.

2 Quantification Method of Phase Distribution
A DIC microscope modifies a microscope’s optical layout by adding polarization optics to boththe illumination and imaging sides as shown in Fig. 1. The resulting system utilizes lateral shearing interference between the two orthogonally polarized beams produced by a pair of Nomarski
prisms and passing through slightly shifted paths (shifted by the shear distance Δx) through thesample. The two beams are then combined by a second pair of Nomarski prisms that cancel theshear. The resulting interferogram observed at the imaging plane encodes the spatial gradient of
the object phase along the shear direction.
The two orthogonal beams are expressed as




 
 
1
1
U1 ðxÞ ¼ α1 exp iθ x þ Δx − iωt e^ x ; U 2 ðxÞ ¼ α2 exp iθ x − Δx − iωt e^ y ; (1)2
2
EQ-TARGET;temp:intralink-;e001;116;357

(a)

(b)

Fig. 1 (a) The optical system of the DIC microscope using a polarization camera, with a quarterwave plate added after the second Nomarski prism pair. (b) The change of the wavefront as lightpasses through the system.
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where x is the one-dimensional spatial coordinate, Δx is the shear distance, α1 and α2 are theamplitudes of the two beams, θðxÞ is the phase of the beams, ω is the angular frequency, t is thetime, and e^ x and e^ y are the unit vectors along the x and y axes.
When these two beams pass through a polarizer oriented at angle φ, they are forced to interfere, and the resulting time-average intensity is obtained as
Iðx; φÞ ¼ ½α21 cos2 φ þ α22 sin2 φ þ 2α1 α2 cos φ sin φ cosðΔθ þ 2βÞ^eφ ;EQ-TARGET;temp:intralink-;e002;116;675(2)

where Δθ ≈ θðx þ 12 ΔxÞ − θðx − 12 ΔxÞ, β is the bias phase, and e^ φ is a unit orientation vector,
pointing along the transmission axis of the polarizer. For the two beams sheared by the Nomarski
prismsΔθ θ x þ 12 Δx − θ x − 12 Δx
¼
Δx
Δx


1
1
dθ
θðxÞ þ 2 Δx · dθddx − θðxÞ − 2 Δx · dx
≈
θðxÞ;
(3)
¼
dx
Δx
EQ-TARGET;temp:intralink-;e003;116;604

so that the phase gradient dθ∕dx detected by the DIC microscope is given by Δθ, the phasedifference induced by the sample between the two sheared beams, and Δx is the shear distance.
We adjust the DIC microscope by sliding the second pair of Nomarski prisms so that the retardation along the shear direction (i.e., the bias phase) becomes 2β ¼ π∕2. In this configuration,
small changes in the phase gradient cause the largest variation in intensity, so that the system has
maximum phase sensitivity.
Figure 1 shows our proposed optical layout of a DIC microscope using a polarization camera
in which we have added a quarter-wave plate oriented at 45 deg between the second pair of
Nomarski prisms and the detector array. With this layout, the two orthogonally polarized beams
produced by the Nomarski prisms are converted to left and right circular polarization by the
waveplate. The polarization camera then detects the light intensity at each polarizer azimuthal
angle (0 deg, 45 deg, 90 deg, and 135 deg). Although the intensities detected using the pixels
oriented at 0 deg and 90 deg of the micropolarizer array do not produce interference in theconventional method, all four orientation angles sense the interference in our proposed method.
The four-phase-shift method is an algorithm for calculating the relative phase of a fringe
pattern from four images taken at phase shifts 0 deg, 45 deg, 90 deg, and 135 deg. This relative
phase corresponds to the spatial phase difference Δθ across the sample, as given by2,19,20
ΔθðxÞ ¼ tan−1

EQ-TARGET;temp:intralink-;e004;116;329

Iðx; 135 degÞ − Iðx; 45 degÞ;Iðx; 0 degÞ − Iðx; 90 degÞ(4)

where Iðx; φÞ is the intensity detected by a pixel behind a micropolarizer oriented at angle φ.
Equation (4) holds true for all nonpolarizing samples, so that the imaged sample need not be apure phase object (i.e., it can have nonzero extinction). The phase difference can be measured
even for an attenuating medium in the four-phase-shift method because the effect of amplitude
does not remain in the calculation result. The spatial phase gradient dθ∕dx detected by the DIC
microscope is the phase difference Δθ induced by the sample divided by the shear distance Δx
EQ-TARGET;temp:intralink-;e005;116;212

d
ΔθðxÞ
1
Iðx; 135 degÞ − Iðx; 45 degÞθðxÞ ≈
¼
tan−1
:
dx
Δx
Δx
Iðx; 0 degÞ − Iðx; 90 degÞ(5)

The shear distance must, therefore, be known in order to accurately quantify the phase gradient, but the shear distance is generally not disclosed by DIC microscope vendors. Our estimate
follows a technique described by Shribak21 in which the shear distance is estimated by firstmeasuring the shear angle, from which we use the known objective lens focal length and simple
trigonometry to compute the shear distance, giving Δx ∼ 650 μm for the Nomarski prism in oursystem. The shear angle was obtained by removing one pair of Nomarski prisms and transmitting
a laser through them, while observing the pair of beams produced at a screen far away andcalculating the splitting angle.
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Following the approach of Munster et al.,22 we can express any phase gradientΔθðxÞ θ x þ 12 Δx − θ x − 12 Δx¼
Δx
Δx
EQ-TARGET;temp:intralink-;e006;116;723(6)

as a convolutionΔθðxÞ gðxÞ ⊗ θðxÞ¼
Δx
Δx

EQ-TARGET;temp:intralink-;e007;116;668(7)of the sample phase function θðxÞ with the kernel




1
1
gðxÞ ¼ δ x þ Δx − δ x − Δx ;
2
2

(8)

EQ-TARGET;temp:intralink-;e008;116;614

where δðxÞ is the Dirac delta function. The spatial domain Fourier transform of Eq. (7) isexpressed as

EQ-TARGET;temp:intralink-;e009;116;545

ΔΘðuÞ GðuÞΘðuÞ
¼
;
Δx
Δx

(9)

where u is the spatial frequency, andEQ-TARGET;temp:intralink-;e010;116;490

GðuÞ ¼ −i sinð2πuΔxÞ:(10)

The obvious thing to try is ΘðuÞ ¼ G−1 ðuÞΔΘðuÞ, but G−1 ðuÞ is undefined where GðuÞ isnear zero. In order to regularize the inverse, we use a Wiener filter W 0 ðuÞ
W 0 ðuÞ ¼

EQ-TARGET;temp:intralink-;e011;116;434G ðuÞ
:jGðuÞj2 þ ½SNRðuÞ−1(11)

The sample phase estimate in the Fourier domain is given by

EQ-TARGET;temp:intralink-;e012;116;377

^
ΘðuÞ
ΔΘðuÞ
¼ WðuÞ ·
;
Δx
Δx

(12)

and SNRðuÞ is the spectral distribution of the signal-to-noise ratio. Munster et al. (1997) approximated the SNR as a Gaussian
−0.5u2SNRðuÞ ¼ s · exp
;
(13)
σ2
EQ-TARGET;temp:intralink-;e013;116;308

where s is the maximum SNRðuÞ.
Figure 2 shows the regularized inverse W 0 ðuÞ when s is 25, σ is 0.6, and GðuÞ ¼−i sinð1.17πuΔxÞ, producing a function that has two peaks near 0.05 and 1.1 ðμm−1 Þ. Thisfunction does not yet take into account the objective lens optical transfer function (OTF).
The regularized inverse system transfer function incorporating the objective lens OTF (alsoshown in Fig. 2) is

EQ-TARGET;temp:intralink-;e014;116;190

W1 ðuÞ ¼½GðuÞ · OTFðuÞ:jGðuÞ · OTFðuÞj2 þ ½SNRðuÞ−1(14)This function has two peaks near 0.08 and 0.80 ðμm−1 Þ and is zero for u > 1.25 ðμm−1 Þ at
maximum aperture and for u > 1.07 ðμm−1 Þ at half aperture.
The sample phase θðxÞ can be obtained by deconvolution using


ΔθðxÞ
−1
θðxÞ ¼ F W1 ðuÞF
;
(15)
Δx
EQ-TARGET;temp:intralink-;e015;116;108

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Fig. 2 (Blue dotted curve) The regularized inverse W 0 ðuÞ of DIC microscope without incorporating
the objective lens’ OTF according to Munster et al.’s approach.22 (Red dashed curve.) The regularized inverse W 1 ðuÞ of the our DIC microscope with 20× objective lens; (black curve) W 1 ðuÞ forthe same conditions at maximum aperture.

where Ff g and F−1 ½  are the Fourier and inverse Fourier transform, W 1 ðuÞ is the Wiener-filtered
inverse transfer function of the DIC microscope system, and Δx is the shear distance given inunits of pixels.
When the phase distribution is measured using four different pixel positions on the polarization camera, the spatial resolution of the sample is worsened by a factor of 2 in each of the two
spatial directions. In order to prevent the reduced spatial sampling from creating aliasing artifacts, we defocus the image so that it is spatially bandlimited to half the Nyquist limit and employ
an interpolation method developed by Tyo et al.23 for which aliasing artifacts are zero for properly bandlimited images.15 In order to simplify the description, we expand from one dimension
ðxÞ to two dimensions ðx; yÞ. The Stokes parameters at the DIC microscope image plane are
given byS0 ðx; yÞ ¼ Iðx; y; 0 degÞ þ Iðx; y; 90 degÞ;(16)

S1 ðx; yÞ ¼ Iðx; y; 0 degÞ − Iðx; y; 90 degÞ;(17)

S2 ðx; yÞ ¼ Iðx; y; 45 degÞ − Iðx; y; 135 degÞ;(18)

EQ-TARGET;temp:intralink-;e016;116;359

EQ-TARGET;temp:intralink-;e017;116;316

EQ-TARGET;temp:intralink-;e018;116;294

where Iðx; y; φÞ is the image intensity detected by a pixel behind a micropolarizer oriented atangle φ on the polarization camera and the Si ðx; yÞ are the Stokes vector images. In this notation,
Eq. (21) becomes


 
1
−S2 ðx; yÞtan−1
θðx; yÞ ¼ F−1 W1 ðuÞF
:
(19)
Δx
S1 ðx; yÞ
EQ-TARGET;temp:intralink-;e019;116;248

where Δx is the shear distance calculated in units of pixels, as in Eq. (15).

3 Evaluation of the Phase Accuracy
Figure 3 shows a DIC microscope (Olympus BX51) using a 4-D Technology PolarCam (modelV) polarization camera. The polarization camera pixel size is 7.5 × 7.5 μm2 , and the image sizeis 648 × 460 pixels. We use a halogen lamp light source, with a 640- to 950-nm spectral bandpass filter. The quarter-wave plate is not achromatic, and thus has a variation in retardance acrossthe spectral range from 106 deg at 640 nm to 90 deg at the design wavelength of 745 nm to
69 deg at 950 nm.
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Fig. 3 The DIC microscope with a polarization camera and quarter-wave plate.

In order to demonstrate the phase quantification of the system, we image a sample of resin
beads (refractive index n1 ¼ 1.57) embedded in a specimen mounting agent medium (lacquer,
refractive index n2 ¼ 1.545). The diameter of the resin beads is 3  0.05 μm and the magnification of the objective lens is 20× (NA ¼ 0.45).
Although the experiment only involved placing the scatterer between the condenser lens andthe sample, the effect on the measurement should be similar to that if placed between the sample
and objective lens. The main difference is that we should see a reduced scatter-induced attenuation when the scatterer is placed closer to the objective lens, due to a wider range of angles
capable of collection through the objective. Unfortunately, the geometry of the microscope does
not allow easy access to insert a scattering element between the sample and objective lens, so thatthe experiment only demonstrates scattering from one side of the sample.
Figure 4 shows the measurement results by the proposed method. Figure 4(a) shows thequantitative phase image of resin beads (n1 ¼ 1.57) embedded in lacquer (n2 ¼ 1.545).
Figure 4(b) gives the enlarged view of the red box region indicated in (a). Figure 4(c) shows
the wavefront of the transmitted light through a bead. Figure 4(d) compares the measured phasewith the theoretical phase in the center of the resin bead [red line in Fig. 4(b)]. At the center of thebead, where the phase is large, the measured plots follow the theoretical curve. The artifact
appears at both sides of the bead, as indicated by blue dashed ellipses in Fig. 4(d) because thelight is deflected. Yu et al.24 showed that the light is deflected when passing through the transparent inclined surface, which affects the measurement accuracy.
Although the 640-to 950-nm bandpass limits the chromatic variation of the waveplate’s
retardance, the residual variation of þ16 deg to −21 deg from the nominal 90 deg value causesa small amount of error in the phase estimate—generally <5% when used with our light sourceand detector. If desired, this error can be further reduced by calibrating the waveplate and modifying the phase shift algorithm to incorporate the nonideal retardance.25

4 Influence of Scattering on the Phase
For light passing through a singly scattering medium, we can classify the possible paths into
three different categories (see Fig. 5):(A) ballistic path (no scatter),(B) scattering out of the light collection path, and(C) light from a nearby path scattering into the ballistic path.
Although propagation path (B) simply causes a loss of signal, path (C) causes the phaseacquired along an alternative path to mix with the phase acquired along the ballistic path.
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Shear direction

(a)

(c)

30 µ m (b)

2 µm

(d)

Fig. 4 (a) The quantitative phase image of resin beads (n 1 ¼ 1.57) embedded in lacquer(n2 ¼ 1.545). The magnification of the objective lens is 20× (NA ¼ 0.45). The image is sampled
at 0.38 μm∕pixel. (b) Enlarged view of the red box region indicated in (a). (c) The wave front of thetransmitted light through a bead. (d) The cross section through the center of the resin bead [red linein (b)]. The two black curves give the theoretical value of the phase for bead diameters 2.95 and3.05 μm.

Fig. 5 The experimental set up to demonstrate the influence of scattering on the phase measurement and a schematic showing the possible light propagation paths: (a) ballistic; (b) scatter
loss; and (c) channel mixing.

Since the scatter process in the (C) path tends to alter the light’s polarization state, the polarizer atthe detector array is able to reduce the amplitude of (C) light according to the degree that its
polarization state differs from the ballistic state.
For ballistic light, the measured polarization state and phase follow the development of
Eqs. (1)–(19). For channel mixing light, however, the polarization state is largely scrambled,so that the measured light intensity at each polarization filter is independent of the input stateand object phase. Thus, if we write the input light intensity as I 0 , the ballistic component as I A ,the loss due to scattering as I B , and the channel mixing component as I C , then the ballistic
component is simply I A ¼ I 0 − I B. This component gives the amplitude for the interference
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December 2020 • Vol. 25(12)Takano et al.: Minimizing scattering-induced phase errors in differential interference contrast microscopy

contrast [Eq. (4)]. The channel mixing component is depolarized and thus does not participate in
the interference, so that the resulting light intensity measurement is simply a sum of I C with theintensity given in Eq. (19)21
I meas ¼ I C þ I A ½α21 cos2 φ þ α22 sin2 φ þ 2α1 α2 cos φ sin φ cosðΔθ þ βÞ:

EQ-TARGET;temp:intralink-;e020;116;699(20)

In order to quantify the influence of scattering on the quantitative phase estimate, we image aresin bead sample with a 0.9-mm-thick layer of intralipid placed between the sample and theobjective lens (see Fig. 5). By varying the concentration of the intralipid, we can change thedegree of scattering between the lens and the phase sample. We evaluate the phase measurementwith the conventional method (using only two polarizer angles)15 and the proposed method(using all four polarizer angles).
With the conventional method, the sample phase gradient is calculated using an approximation given byIðx; 45 degÞ − Iðx; 135 degÞIA
2α1 α2¼−
ΔθðxÞ ≈
sin½ΔθðxÞ;(21)
Iðx; 45 degÞ þ Iðx; 135 degÞ2I C þ I A
α2 2 þ α1 2
EQ-TARGET;temp:intralink-;e021;116;571

where α1 and α2 are the amplitudes of the two interfering beams, respectively [see Eq. (2)]. The
two factors in parentheses are present here but not in Eq. (4), though we can see that both factors
approach 1 as the amount of scattering approaches zero. Thus, in the conventional algorithm,
scattering will cause a reduction in the estimated phase. In the four-angle approach, however, thealgorithm is able to compensate for scattering effects so that the only problem remaining is anincrease in the noise, and a decrease in the ballistic fraction, with an increase in scatter.
Figure 6 shows the measurement results by the conventional method (shown on the left sideof this figure) and the proposed method (shown on the right-hand side of this figure) at an intralipid concentration of 2.0%. Although imaging through nonscattering volumes (e.g., pure water)
has no effect on the contrast, imaging through the scattering induced by the intralipid causes aloss of contrast in the conventional method. The proposed method, on the other hand, experiences only an increase in noise and a decrease in signal (due to a reduction in the ballistic fraction) in the presence of scattering, but does not experience a change in the mean of theestimated phase.
Figure 7(a) shows the change of the phase measured at the center of the bead with increased
scattering (intralipid concentration). We can see that the phase calculated with the conventional
method decreases sharply with increase in scatter, whereas the phase calculated with the proposed method is more robust to scatter.
One way to quantify the severity of scatter is to measure the change in the degree of linear
polarization (DoLP) of light transmitted by the sample. As the scatter increases, the ballistic
photons retain their polarization state but the scattered photons do not, so DoLP is an estimateof the ballistic fraction. The DoLP is given by
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
S1 2 ðx; yÞ þ S2 2 ðx; yÞ:(22)
DoLP ¼S0 ðx; yÞ
EQ-TARGET;temp:intralink-;e022;116;262

Figure 7(b) shows the change of the maximum phase, at the middle of a 2-μm glass beadsample, with the average DoLP in the image. Although the phase obtained with the conventional
method rapidly decreases with reduced DoLP, the proposed method maintains the phase value
for DoLP of ∼0.45 or more. Below DoLP ¼ 0.45, we see that scattering can induce errors ofmore than 10% in the phase estimate.
Because each sample presents different scattering behaviors, it is not easy to establish limits
on the maximum depth in which accurate phase estimation is possible. However, if the scattering
coefficient μs of the sample is known, then one can estimate the maximum depth from the resultof Figure 7(b). For example, using established estimates of the intralipid scattering coefficient26
for the wavelength range of our measurements, we have
EQ-TARGET;temp:intralink-;sec4;116;94

μs ð745 nmÞ ¼ 325 mm−1 ;Journal of Biomedical Optics

μs ð1064 nmÞ ¼ 181 mm−1 ;123703-8

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December 2020 • Vol. 25(12)Takano et al.: Minimizing scattering-induced phase errors in differential interference contrast microscopy(a)

30 µ m(b)

30 µ m

(c)

2 µm

(d)

2 µm

(e)

(f)

Fig. 6 The quantitative phase of resin beads (n1 ¼ 1.57) embedded in lacquer (n2 ¼ 1.545) at the
intralipid concentration of 2.0% where the phase is calculated using [(a), (c), and (e)] the conventional method and [(b), (d), and (f)] the proposed method. The magnification of the objective lens is
20× (NA ¼ 0.45). The image is sampled at 0.38 μm∕pixel. Subimages (c) and (d) are enlarged
images of the red squares indicated in (a) and (b), respectively. Subimages (e) and (f) are thecross sections through the centers of the glass beads [red lines of (c) and (d)].

(b)

(a)

Fig. 7 Influence of the scattering intensity of an intralipid sample on (a) the maximal phase and(b) the DoLP on the maximal phase. In both figures, the phase value is normalized to the value withno intralipid (water only sample).

so that our 0.9-mm-thick intralipid sample introduces scattering-induced transmission of 0.42
and 0.78, respectively, when diluted to our 2% concentration. Taking the average of these two asa representative value over our spectral range gives a transmission of 0.60. Assuming that scattered light is unpolarized and ballistic light remains fully polarized, this represents a DoLP of
0.6. This is somewhat higher than our measured DoLP of 0.45, but considering the variations inintralipid properties, and difficulties of accurately quantifying such small samples, it provides
rough agreement. As a result, users should be able to use DoLP as a proxy for the ballistic
fraction.
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5 Examples of Real-Time Phase Analysis
In order to demonstrate how the improved phase robustness allows us to quantify phase structures deeper within biological tissues, we perform real-time phase analysis of heart and blood
motion within a living medaka egg (Fig. 8). The egg is ∼1 mm in diameter, and the sectioned
image plane containing the heart appears roughly at the center of the egg, so that the phase image
represents a section that is 500-μm deep inside the tissue surface.
Figure 9 shows an image taken from one frame of a 17-Hz video of the medaka’s heart
movement and blood flow. In order to reduce clutter in the image, we take the average of all
the images in the video sequence and subtract the mean phase image from each frame, so that theresults are phase difference images rather than phase images. In the resulting video, we canobserve the ventricle and atrium movement, the valve movement between the ventricle andatrium, and blood flow within the heart clearly despite the presence of scattering in the layers
above and below the section plane.
Next, we perform real-time phase analysis on the whole body of a living hatched medaka(Fig. 10). Because the 300-μm field of view of the microscope is too small to fit the entire 4-mmlength of the medaka’s body into one frame, we measure each individual field of view in realtime, move the medaka, and then later stitch together all of the various fields of view into a single

Fig. 8 The intensity image of a living medaka egg used as the sample for real-time analysis.
(This is the Stokes parameter s 0 image from the DIC microscope’s polarization camera.)Fig. 9 Two frames from a video of a living medaka heart in (a) contraction and (b) expansion
phases, captured at 17 Hz frame rate. The white arrows at the top right of each image indicate
the DIC shear direction. The average of all the images in the video is subtracted from each raw
frame in order to remove clutter. The spatial sampling is 0.38 μm∕pixel (Video S1, MPEG, 5.5 MB[URL: https://doi.org/10.1117/1.JBO.25.12.123703.1]).
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Fig. 10 The movement within a horizontal section of a living recently hatched whole medaka
captured at 17 Hz frame rate. The spatial sampling is 0.75 μm∕pixel (Video S2, Moving
Picture Experts Group (MPEG), 8.2 MB [URL: https://doi.org/10.1117/1.JBO.25.12.123703.2] andVideo S3, MPEG, 8.0 MB [URL: https://doi.org/10.1117/1.JBO.25.12.123703.3]).

video mosaic. Figure 10 shows one frame from the resulting 17-Hz video measurement. In the
result, we can observe the detailed structure of blood flow through the various parts of the medaka’s body: the mouth, heart, fins, and tail. Because the subimages were collected at different
times, nonperiodic motion by the mouth, head, and fins are unsynchronized. However, despite
these time gaps, the repetitive motion of blood through the medaka’s circulatory system gives theappearance of continuity, so that one can watch individual blood cells moving from veins behindthe head to the tip of the tail fin, and then all the way back.

6 Conclusion
We have shown that by adding a quarter-wave plate to a DIC microscope using a polarization
camera it is possible to improve quantitative phase accuracy in the presence of scattering. If only
two orthogonal polarization angles are used to analyze the light transmitted through the DIC
microscope, the estimated sample phase decreases with an increase in scattering (i.e., DoLP < 1).
The proposed method, on the other hand, maintains accurate phase measurement for deeper
locations inside samples. Once the ballistic (unscattered) fraction of transmitted light drops
below about 0.45, however, the loss in signal corrupts the phase estimate beyond the algorithm’s
ability to compensate. Our imaging of the heart in a 1-mm-diameter medaka egg shows that thephase retains high contrast for imaging semitransparent biological tissues at depths of 500 μm
and more.
The proposed method maintains compatibility with video measurement, allowing users to
capture the phase motion of living samples at a rate limited only by the frame rate of the detector.
Although the polarization camera used in our system operates at 17 Hz, more recent 5-megapixel
polarization cameras can operate at speeds of 75 Hz.

Disclosures
The authors declare that there are no conflicts of interest.

Acknowledgments
We would like to thank Dr. Hiroshi Ishiwata of Olympus Corporation for useful discussion
about DIC microscopes.

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