Polarization holographic microscope slide for birefringence imaging of anisotropic samples in microfluidics

Yang Yang; Hong-Yi Huang; Cheng-Shan Guo

doi:10.1364/OE.389973

1. Introduction

Microfluidics, as a rapidly growing field involving methods and technologies to manipulate fluids in microchannels with typical dimensions ranging from tens to hundreds of microns, offers the capability of integrating biological and chemical analysis systems on chips and has caused the development of Lab-on-a-Chip (LoC) technologies. LoCs with microchannels have been widely applied in many researches in soft matter physics, cell biology, biophysics, chemistry, and medicine [1–6], because of their advantages of good light transmission, high efficiency, high integration, low-cost and compact hardware implementation.

In microfluidic LoC technologies, imaging functionalities play an important role for quantitatively investigating the process occurring inside microfluidic channels. Much effort has been made in recent years to develop quantitative microscopy systems suitable for integrating into microfluidic LoC setups with a reduced number of optical components, in which the methods based on digital holography (DH) have drawn much attention because of the innate abilities of DH methods in quantitative label-free phase imaging and digital posteriori refocusing [7–20]. Some of LoC technologies with DH optics have been demonstrated in imaging blood cells, waterborne parasites and even fast-moving self-propelled microorganisms, including sperm.

According to the relative orientation between the object and the reference beams in recording configurations, DHs are often divided into two categories: on-axis (or in-line) and off-axis (or off-line). It is known that the on-axis configurations can reduce the spatial bandwidth of the recorded holograms and thus make full use of the resolving power of the image sensor, but the reconstructed images often suffer from the disturbances of the zero-order and twin images, which need to be removed by using phase shifting operations or other time-consuming elimination algorithms. In off-axis DHs, the zero-order and twin images are separated from the desired holographic image in spatial frequency domain and so they can be removed by a simple digital spatial filtering, but at the cost of a high bandwidth demand on the imaging sensor and the need for relatively bulky elements and complex optics that are sensitive to vibrations and misalignment. To overcome the drawback, some modified off-axis DHs with quasi-common path configurations have been developed in recent years [21–28]. For example, Mico et al. [21] proposed a wavefront division off-axis DH system with a quasi-common path configuration, in which the input plane of the imaging system is spatially divided into two regions in side-by-side configuration: the object region under test and a blank region for the reference; at the same time, an one-dimensional grating is inserted between the input and output planes of the system to realize the overlap and off-axis interference of the object and reference beams at the output plane. Yaghoubi et al. [27] developed a single-shot phase-shifting digital holographic microscopy also based on common path wavefront division using a Ronchi grating. Compared with the conventional off-axis DHs such as those based on Mach-Zehnder or Michelson interferometers, the quasi-common path configurations are more stable, relatively insensitive to mechanical vibrations and air fluctuations, and require fewer optical elements.

Recently, the research group of Ferraro [29,30] proposed an alternative quasi-common path off-axis DH imaging system that miniaturizes the interferometer optics to the chip level to achieve a compact off-axis holographic imaging configuration especially suitable for LoC microfluidic systems. In this configuration, the grating for realizing quasi-common path off-axis holographic recording is inscribed directly on a blank region near the microfluidic channel of the chip, thus creating a pocket holographic microscope slide in a cost-effective and scalable manner. However, all the existed LoC setups with DH optics are difficult to quantitatively image the polarization or birefringence information of samples moving in microfluidic channels.

It is known that birefringence is an important optical property of anisotropic materials arising from anisotropies of tissue microstructures. As a non-destructive, non-intrusive method that can provide anisotropic structural information of samples, birefringence measurement or polarization imaging has been widely studied in many researches [31–49], in which the applications of birefringence imaging in microfluidic environment have drawn much attention in recent years because microfluidic chips, as good platforms for imaging birefringence of samples in microfluids, have advantages of good light transmission, small size, high efficiency and high integration. For examples, Sengupta et al. explored the flow of a nematic liquid crystal in microfluidic channels and found that the flow-induced effective birefringence can be characterized using polarizing optical microscopy on a microfluidic platform [41–43]. Sun et al. [45] demonstrated the use of a microscopic circular polariscope to directly measure the flow-induced birefringence in a microfluidic device; they proved that both extensional and shear strain rates contributed to the flow induced birefringence and that the birefringence retardation measurement provides a quantitative and non-invasive representation of the fluid deformation and stress in microfluidics. Alizadehgiashi et al. [47] developed a single-droplet microfluidic oscillatory platform integrated with polarized optical microscopy for in situ studies of shear-induced alignment of cellulose nanocrystals in their aqueous shear-thinning suspensions. Wang et al. [48] proposed a microfluidic polarization imaging and analysis method and demonstrated that their method could effectively detect and classify cancer-associated fibroblasts and two kinds of non-small cell lung cancer cells [49]. In these researches different polarization imaging systems were designed to image the 2D birefringence information of the samples in microfluidic channels. However, all of them belong to multi-frame methods; that is, multiple step measurements (often accompanied with different polarization configurations) are required for extracting the full birefringence information (both including the birefringence phase retardation δ and the optic axis orientation θ) of the samples, which hinders their application under unsteady-flow conditions.

In this paper, we propose a scheme to miniaturize a double-channel polarization holographic interferometer optics to create a pocket polarization holographic microscope slide (P-HMS) suitable for integrating with microfluidic LoC setups. Based on the P-HMS combined with a simple reconstruction algorithm described in the next section, we can not only simultaneously realize holographic imaging of two orthogonal polarization components of dynamic samples in a microfluidic channel but also quantitative measurement of 2D birefringence information (both including the birefringence phase retardation and optic-axis orientation). This chip interferometer allows for off-axis double-channel polarization DH recording using only a single illumination beam without need of any beam splitter or mirror. Its quasi-common path configuration and self-aligned design also make it tolerant to vibrations and misalignment.

2. Working principle

When an optical beam passes through a birefringence sample, its amplitude and phase distributions as well as its polarization state will be changed in general. The relationship between the transmitted beam E_t and the incident beam E_i can be described as

(1)$${{\textbf E}_t} = {\textbf J}{{\textbf E}_\textrm{i}}\;,\textrm{ or, }\left( {\begin{array}{c} {{E_{tx}}}\\ {{E_{ty}}} \end{array}} \right) = \left( {\begin{array}{cc} {{J_{xx}}}&{{J_{xy}}}\\ {{J_{yx}}}&{{J_{yy}}} \end{array}} \right)\left( {\begin{array}{c} {{E_{ix}}}\\ {{E_{iy}}} \end{array}} \right),$$

where (E_tx, E_ty) and (E_ix, E_iy) are, respectively, the complex amplitudes of two orthogonal polarization components of E_t and E_i; the matrix J is often called as Jones matrix or, in general, transmittance matrix (J_xx, J_xy, J_yx and J_yy are four elements of the matrix), which is determined by the birefringence properties of the sample.

Birefringence of the sample is also often characterized quantitatively by the parameters of the optic-axis orientation (θ) and the birefringence phase retardation

(2)$$\delta = {{2\pi s({n_e} - {n_o})} \mathord{\left/ {\vphantom {{2\pi s({n_e} - {n_o})} \lambda }} \right.} \lambda },$$

where s is the thickness of the sample, λ is the wavelength of the incident beam; n_e and n_o are the refractive indices of the sample for incident polarization components respectively parallel and vertical to the optic axis. The Jones matrix J and the birefringence parameter (δ and θ) have the relationship of

(3)$$\begin{array}{ll} {\textbf J} &= \left[ {\begin{array}{cc} {{J_{xx}}}&{{J_{xy}}}\\ {{J_{yx}}}&{{J_{yy}}} \end{array}} \right] = {t_0}\left[ {\begin{array}{cc} {\cos \theta }&{ - \sin \theta }\\ {\sin \theta }&{\cos \theta } \end{array}} \right]\left[ {\begin{array}{cc} {{e^{i\delta /2}}}&0\\ 0&{{e^{ - i\delta /2}}} \end{array}} \right]\left[ {\begin{array}{cc} {\cos \theta }&{\sin \theta }\\ { - \sin \theta }&{\cos \theta } \end{array}} \right]\\ &= {t_0}\left[ {\begin{array}{cc} {\cos (\frac{\delta }{2}) + i\sin (\frac{\delta }{2})\cos (2\theta )}&{i\sin (2\theta )\sin (\frac{\delta }{2})}\\ {i\sin (2\theta )\sin (\frac{\delta }{2})}&{\cos (\frac{\delta }{2}) - i\sin (\frac{\delta }{2})\cos (2\theta )} \end{array}} \right], \end{array}$$

in which t₀ is an isotropic complex transmittance coefficient.

From Eqs. (1) to (3) it can be seen that precise measurement of the Jones matrix or birefringence parameters of an anisotropic sample in microfluidic environment is more difficult than imaging of an isotropic sample. Here we found an approach to create a pocket P-HMS for realizing a single-shot 2D measurement of the birefringence parameters of dynamic anisotropic samples in microfluidic channel suitable for integrating with microfluidic LoC systems.

Figure 1(a) shows an example of the pocket P-HMSs designed through combining a wavefront division interferometer with angular multiplexing polarization holography. This P-HMS is implemented by integrating three microlenses (L_o, L_r1 and L_r2) and two film polarizers (P₁ and P₂) onto a chip surface. The objective lens L_o is layered above the microfluidic channels to form the image of the sample moving in the channel onto the recording plane. The lenses L_r1 and L_r2 with the same focal lengths are posted on one side of the lens Lo as shown in Fig. 1; they are used to generate two reference beams with different orientations to the recording plane. The film polarizers P₁ and P₂, with orthogonal polarization directions, are respectively attached below the reference lenses L_r1 and L_r2 to control the polarization states of the beams passed through the two reference lenses.

Fig. 1. (a) Example of the proposed scheme to miniaturize a double-channel polarization holographic interferometer optics to the chip level to create a pocket P-HMS suitable for integrating with microfluidic LoC setups. (b) Coordinate geometry of the system.

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When the P-HMS is illuminated by a single collimated beam, as shown in Fig. 1, the input wavefront will be divided into three interesting parts: the object beam part passed through the objective lens L_o and the two reference beam parts transmitted through the two reference lenses with orthogonal polarizers. By choosing suitable separation distance between the lenses, the three beams can be superimposed each other with different orientations in the downstream recording plane. The three overlapped beams will interfere with each other to form a multi-beam polarization interference pattern. If the illumination beam is set to be a right circularly polarized light, the three lenses on the slide surface are arranged with the same distance and the system has the coordinate geometry as shown in Fig. 1(b), the total intensity of the interference pattern on the recording plane can be expressed as [50]

(4)$$\begin{array}{ll} {I_h} &= \left|{{A_o}\exp \{ \frac{{j\pi ({x^2} + {y^2})}}{{\lambda (L - f)}}\} {\textbf J}(\frac{{ - x}}{M},\frac{{ - y}}{M})\left( {\begin{array}{c} 1\\ i \end{array}} \right) + {{\mathop{\rm R}\nolimits}_1}\exp \{ \frac{{j\pi [{{(x + {{\sqrt 3 a} \mathord{\left/ {\vphantom {{\sqrt 3 a} 2}} \right.} 2})}^2} + {{(y - {a \mathord{\left/ {\vphantom {a 2}} \right.} 2})}^2}]}}{{\lambda (L - f)}}\} \left( {\begin{array}{c} 1\\ 0 \end{array}} \right)} \right.\\ &{\left. { + {{\mathop{\rm R}\nolimits}_2}\exp \{ \frac{{j\pi [{{(x + {{\sqrt 3 a} \mathord{\left/ {\vphantom {{\sqrt 3 a} 2}} \right.} 2})}^2} + {{(y + {a \mathord{\left/ {\vphantom {a 2}} \right.} 2})}^2})}}{{\lambda (L - f)}}\} \left( {\begin{array}{c} 0\\ i \end{array}} \right)} \right|^2}, \end{array}$$

in which, (x,y) are orthogonal Cartesian coordinates at the recording plane, f is the focal length of the three lenses, L is the image distance from the lens L_o to the recording plane, a is the separation distance of the optical centres of the three lenses with each other and M is the image magnification determined by $M = {{(L - f)} \mathord{\left/ {\vphantom {{(L - f)} f}} \right.} f}$; A_o, R₁ and R₂ are three constants determined by the intensity of the illumination beam. After removing the same quadratic phase factor, Eq. (4) can be simplified as

(5)$$\begin{array}{ll} {I_h} &= \left|{{A_o}{\textbf J}(\frac{{ - x}}{M},\frac{{ - y}}{M})\left( {\begin{array}{c} 1\\ i \end{array}} \right) + {{\mathop{\rm R}\nolimits}_1}\exp [\frac{{j\pi a}}{{\lambda (L - f)}}(\sqrt 3 x - y)]\left( {\begin{array}{c} 1\\ 0 \end{array}} \right)} \right.\\ &{\left. { + {{\mathop{\rm R}\nolimits}_2}\exp [\frac{{j\pi a}}{{\lambda (L - f)}}(\sqrt 3 x + y)]\left( {\begin{array}{c} 0\\ i \end{array}} \right)} \right|^2}. \end{array}$$

Equation (5) can be further written as

(6)$$\begin{array}{ll} {I_h} &= {H_0} + {H_1}\exp [\frac{{ - j\pi a}}{{\lambda (L - f)}}(\sqrt 3 x - y)] + {H_2}\exp [\frac{{ - j\pi a}}{{\lambda (L - f)}}(\sqrt 3 x + y)]\\ &+ H_1^\ast \exp [\frac{{j\pi a}}{{\lambda (L - f)}}(\sqrt 3 x - y)] + H_2^\ast \exp [\frac{{j\pi a}}{{\lambda (L - f)}}(\sqrt 3 x + y)]\;, \end{array}$$

where the superscript star ‘*’ indicates the complex conjugate operation, H₀ is the sum of all the autocorrelation terms, H₁ and H₂ can be expressed as follows:

(7)$$\left\{ {\begin{array}{{c}} {{H_1} = O{R_1}[{J_{xx}}( - \frac{x}{M}, - \frac{y}{M}) + i{J_{xy}}( - \frac{x}{M}, - \frac{y}{M})]}\\ {{H_2} ={-} iO{R_2}[{J_{yx}}( - \frac{x}{M}, - \frac{y}{M}) + i{J_{yy}}( - \frac{x}{M}, - \frac{y}{M})]} \end{array}} \right.\quad .$$

The interference pattern I_h given in Eqs. (5) and (6) can be recorded by an image sensor in a single shot to form a double-channel angular-multiplexing polarization digital hologram (AMPDH). As Eq. (7) shows, the complex amplitudes of the terms H₁ and H₂ are proportional to the two orthogonal polarization components of the sample image, containing the information of the birefringence parameters of the sample we interested in. From Eq. (6) it can be found that the interferogram of the AMPDH is composed of two groups of interference fringes inclined to one another at a 60 degree angle; the fringe period of each group can be simply estimated by the following formula:

(8)$$\Lambda = \frac{{\lambda (L - f)}}{a}.$$

The complex amplitudes of the two orthogonal polarization components of the sample image as shown in Eq. (7) are carried respectively by the two groups of interference fringes. Thus simultaneously recording of the two polarization components of the image is performed by multiplexing two off-axis interferograms into one single double-channel AMPDH. This kind of angular multiplexing technique for digital holograms has already been shown to be feasible and has been used for many applications [31–35,40]. The terms H₁ and H₂ in Eq. (7) can be respectively extracted from the AMPDH by using a simple spatial filtering algorithm for reconstruction of such an angular-multiplexing off-axis hologram.

For eliminating the undesired coefficients and finding the interested birefringence parameters of the sample from the reconstructed H₁ and H₂, we can further calculate the following ‘relative deviation’ of H₁ and H₂:

(9)$$\Gamma = \frac{{{H_1}/{H_{10}} - {H_2}/{H_{20}}}}{{{H_1}/{H_{10}} + {H_2}/{H_{20}}}}\;,$$

where H₁₀ and H₂₀ correspond to the reconstructed values from one background AMPDH, which can be obtained by performing a measurement without the object to be tested. After substituting Eq. (7), Eq. (9) can be simplified to

(10)$$\Gamma = \frac{{({J_{xx}} - {J_{yy}}) + i({J_{xy}} + {J_{yx}})}}{{({J_{xx}} + {J_{yy}}) + i({J_{xy}} - {J_{yx}})}}\;.$$

It can be seen that the quantity Γ will be not equal to zero only when the object is anisotropic, because the parameters of J_xx-J_yy, J_xy and J_yx will be always equal to zero for any isotropic object. If we further substitute the Jones elements defined in Eq. (3) into Eq. (10) and after some mathematical simplifications, it can be proved that the quantity Γ has a simple relationship with the birefringence parameters of δ and θ as follows:

(11)$$\Gamma = \tan (\frac{\delta }{2})\exp [i(2\theta + \frac{\pi }{2})]\;.$$

Equation (11) reveals that, for birefringence materials with Jones matrix given in Eq. (3), the quantity Γ calculated by measured data H₁ and H₂ is generally complex. And its module is determined by the birefringence retardation parameter δ, while its argument is just proportional to the optic axis orientation parameter θ.

From the above analyses, we can arrive at the prediction that, using the simple pocket P-HMS as shown in Fig. 1, the complex amplitudes of two orthogonal polarization components of a sample image can be recorded in a single-shot AMPDH and can be respectively reconstructed in computer by a simple spatial filtering algorithm. Based on the retrieved data, the birefringence parameters of the imaged sample can be quantitatively worked out using the formulas given in Eqs. (9) to (11).

3. Experiments

For demonstrating the feasibility of our proposed P-HMS system, we established an experimental setup as shown in Fig. 2(a). In this setup, a 10 mW fiber-coupled laser diode (LD), with the central wavelength of 650 nm and the spectral bandwidth of 1 nm, are adopted as the light sources. The beam from the LD is first collimated by a collimating lens and then passes through a circular polarizer to generate the required input circular polarization sate. The P-HMS was fabricated by integrating three glass plano-convex micro lenses and two film polarizers with orthogonal polarization directions on one optical glass slider with the thickness of 0.5 mm. The aperture diameter and focal length of the three lenses are the same with the value of 6 mm, and the distance a between the optical centres of the lenses with each other is set to be 8 mm. Then the P-HMS was attached to a microfluidic chip with the channel width of 1 mm and the height of 200 µm. The AMPDH formed by the beams passed through the P-HMS is recorded by an image sensor, with pixel size of 3.45µm × 3.45µm, and pixel number of 2048 × 2048. The image distance L from the P-HMS to the recording plane is taken as 180 mm. With this configuration, the system has the image magnification of 29 × and the period Λ of the interference fringes determined by Eq. (8) is equal to be about 14 µm. For satisfying the coherent condition of holographic recording in the whole photosensitive surface of the image sensor, the coherence length of the input source should be larger than 0.16 mm at least. The wavelength bandwidth of the LD adopted in our experiment is about 1.0 nm (corresponding to a coherence length of 0.42 mm), satisfying the coherence requirement of the requirement.

Fig. 2. (a) Photo of the experimental setup designed according to the principle scheme shown in Fig. 1. (b) Example of the AMPDHs recorded in experiments. (c) Example of the spatial spectrum of the AMPDHs, in which the frequency components corresponding to the terms H1 and H2 in Eqs. (5) and (6) are indicated by two dotted circles. Scale bars: 60 µm.

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Figure 2(b) shows an example of the AMPDHs recorded in our experiments. The detailed interferometric fringe structure of the hologram can be seen from its zoom-in image shown in top-right corner of the figure. Figure 2(c) gives the spatial spectrum of the hologram, in which the frequency components corresponding to the terms H₁ and H₂ in Eqs. (6) and (7) are indicated by two dotted circles. The algorithm for retrieval of the birefringence parameters from the AMPDH mainly contains following three steps: (1) calculate the spatial frequency of the AMPDH by a 2D fast Fourier transform; (2) crop the two terms H₁ and H₂, respectively, from the spatial frequency as shown in Fig. 2(c), and inversely transform them back to the spatial domain, thus obtaining the complex amplitudes of the two orthogonal polarization components of the sample; and (3) calculate the quantity Γ based on Eq. (9). The module and the argument of Γ will reveal the birefringence properties of the sample and further the birefringence retardation δ and the axis orientation θ can be quantitatively retrieved respectively according to Eq. (11).

To verify the birefringence imaging concept of the proposed setup based on the designed P-HMS, we first measured the birefringence parameters of a thin mica sheet with a known thickness of about 23 µm. Figure 3 shows an example of the experimental results, in which the upper part of the image field corresponds to the measured mica sheet. Figures 3(a)–3(b) and 3(c)–3(d) are, respectively, the amplitude and phase distributions of the two orthogonal polarization components reconstructed from one AMPDH recorded in experiments, while Figs. 3(e) and 3(f) show, respectively, the optic-axis orientation and birefringence retardation distributions retrieved from the above reconstructed components based on Eq. (11). The mean value of the measured birefringence phase retardation δ is about 1.007 ± 0.015 rad. In this measurement, the phase referencing and temporal averaging techniques are adopted to suppress the phase noises caused by the laser source and image sensor to improve the phase measurement accuracy [51]. Because the thickness of the mica sheet is measured to about 23 µm and the central wavelength of the illumination beam is about 650 nm, we can get the size of birefringence of mica (n_e-n_o) to be about 0.0045. This measured result is in agreement with the previous experimental results within a reasonable error range [52,53]. The optic-axis orientation of the tested mica sheet retrieved from Fig. 3(e) is equal to be about 30.4 degree, which is also in agreement with mica orientation of about 30 degree in actual experiments.

Fig. 3. An example of the experimental results for measurement of the birefringence parameters of a thin mica sheet. (a) (b) and (c) (d) are, respectively, the reconstructed amplitude and phase distributions of the two orthogonal polarization components of the sample image; (e) and (f) show, respectively, the retrieved optic-axis orientation and birefringence retardation distributions. Scale bar: 60 µm.

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Fig. 4. Example of holographic birefringence imaging of potato starch granules in fluids flowing in microfluidic channels. (a) (b) and (c) (d) are, respectively, the reconstructed amplitude and phase distributions of two orthogonal polarization components of the image field; (e) and (f), respectively, the retrieved optic-axis orientation and birefringence retardation distributions. Scale bar: 60 µm.

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From Fig. 3(f) it can be noted that the birefringence retardation in the lower part of the image field retains almost a zero value. This result is also as expected, because in this region only exists an isotropic glass substrate with no mica sample. In this situation, the argument of Γ is indefinite, which causes the values of this region shown in Fig. 3(e) to be random and meaningless.

Then we carried out experiments to test the P-HMS on imaging birefringence properties of moving specimens in fluids flowing in microfluidic channels. Visualization 1 gives a video example of time-lapse birefringence imaging obtained in experiments when the specimen is potato starch granules in distilled water flowing in a microfluidic channel with the channel width of 1 mm and the height of 200 µm. The frame rate of acquisition was set to 5 Hz. A typical frame extracted from Visualization 1 is shown in Fig. 4, in which, (a) (b) and (c) (d) are, respectively, the amplitude and phase distributions of two orthogonal polarization components of the image field reconstructed from one AMPDH recorded in the experiments, while (e) and (f) are, respectively, the optic-axis orientation and birefringence retardation distributions calculated by Eqs. (9) and (11) using the two reconstructed components. From Fig. 4(f) it can be seen that, the birefringence retardation of the fluid around the starch granule keeps a zero value, which means the flowing fluid keeps to an isotropic medium. As expected, the potato starch granules in water possess a strong birefringence. Its maximum birefringence retardation reached to about 2.0 rad in our experimental condition. At the same time, small dark areas of the calculated birefringence retardation distributions can be found at the hylums of the starch granules, which means that the birefringence is markedly weaker in this area than other part of a starch granule. Maybe it is because there is a water-filled hole at the hylum of a starch granule as reported in Ref. [54].

After getting rid of the meaningless data corresponding to the surrounding isotropic fluid in the map shown in Fig. 4(e), it is can be found that the calculated birefringence optic-axis orientations of the starch granules are almost distributed radially around the center of the dark spot of the birefringence retardations shown in Fig. 4(f), which is also supported by the molecular growth model of a starch granule [55].

As a further example for demonstrating the feasibility of birefringent imaging in living creatures, we also applied the system with the P-HMS optics to imaging the birefringent structures of live adult C. elegan worms moving in the microfluidic channel in our experiments. Figure 5 gives our example of quantitative birefringence imaging of a C. elegan worm swimming in the microfluidic channel using our system, in which, not only the amplitude (a, b) and phase (c, d) maps of the two-orthogonal polarization components of the C. elegan image, but also its optic-axis orientation (e) and birefringence retardation (f) distributions are obtained from one single-shot recorded AMPDH at the same time. It is known that intestinal cells of worms are densely packed with lipidic vesicles involved in metabolism and a fraction of these vesicles have been observed to be birefringent, lysosome-related organelles [56]. From Figs. 5(e) and 5(f), it can be seen that some organelles in the cells of live C. elegans do exhibit birefringence as expected. These quantitative birefringence distributions combined with the amplitude and phase maps of the C. elegan image provide us more information to research the birefringent gut granules of C. elegans for understanding the formation of specialized, lysosome-related organelles.

Fig. 5. Example of quantitative birefringence imaging of C. elegan worms swimming in the microfluidic channel using the PHMS system, in which, not only the amplitude (a, b) and phase (c, d) maps of the two-orthogonal polarization components of the C. elegan image, but also its birefringence retardation (f) and optic-axis orientation (e) distributions are obtained from one single-shot recorded AMPDH at the same time. (g) Local enlargement of the retrieved birefringence retardation shown in (f). Scale bars: 60 µm

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4. Conclusions

In this work, we demonstrated a scheme to miniaturize a double-channel polarization holographic interferometer optics to the chip level to create a P-HMS suitable for integrating with microfluidic LoC setups. In the experimental example, the P-HMS is designed and implemented by integrating three plano-convex microlenses and two film polarizers onto the surface of a glass slide. When the P-HMS is attached to a microfluidic chip and illuminated by a single collimated beam with circular-polarization state, a single-shot double-channel AMPDH can be obtained by recording the beams passed through the specimen and the P-HMS in the downstream recording plane. This P-HMS is modular, reusable and easy to operate; its quasi-common path configuration and self-aligned design make the system tolerant to vibrations and misalignment. In comparison with the existed holographic microscopy systems suitable for integrating into microfluidic LoC systems such as the holographic microscope slide proposed by Ferraro’s group [29,30] that can realize holographic imaging of the complex amplitude of only one polarization component of the specimen image, our scheme can not only realize holographic imaging of complex amplitudes of two-orthogonal polarization components of the specimen image from a single-shot recorded AMPDH, but also retrieve the birefringence parameters (such as the birefringence phase retardation and the optic-axis orientation) from the same AMPDH based on a simple algorithm. Because the birefringence parameters have been found to be important to understand optical anisotropic architecture of many materials and polarization imaging has been applied in many researches in the field of biology and medicine, our work about the P-HMS could play a positive role in promoting the application of the polarization and birefringence imaging in microfluidic LoC technology.

Funding

National Natural Science Foundation of China (91750105).

Acknowledgments

The authors thank Professor Yingying Zhang from College of Traditional Chinese Medicine, Shandong University of Traditional Chinese Medicine for the useful discussion and the support in providing C. elegans specimens.

Disclosures

The authors declare no conflicts of interest.

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Polarization holographic microscope slide for birefringence imaging of anisotropic samples in microfluidics

Abstract

1. Introduction

2. Working principle

3. Experiments

4. Conclusions

Funding

Acknowledgments

Disclosures

References

Supplementary Material (1)

Cited By

Figures (5)

Equations (11)

Optics Express