1. Introduction

Comprehensive optical imaging of the intensity, phase and birefringent information of the biological sample is essential for the study and diagnosis of the diseases because the important physical or pathological changes always accompany the changes in multiple optical parameters [1–3]. Traditional optical imaging techniques such as the confocal microscopic imaging technique [4,5] (including intensity information), quantitative phase imaging technique [6,7] (including phase information) and the polarization related imaging methods [8–10] (including intensity and all the birefringent information) are only focused on one or two types of the imaging parameter of the sample (i.e., the intensity, phase and the birefringent information respectively). However, the parameter that only represents a single optical property is not sufficient to provide a comprehensive evaluation of the sample. Moreover, these imaging techniques cannot differentiate the depth information of the sample. Taking advantage of the low coherence interferometer imaging modality and the polarization detection scheme, polarization-sensitive optical coherence tomography (PS-OCT), a three-dimensional (3D) imaging technique, can provide depth-resolved intensity, phase and birefringent information (phase retardation, orientation and degree of polarization) of the biological sample simultaneously. However, these parameters can only be visualized in separate images, making it hard to give comprehensive information about the sample in one figure with additional contrast. Furthermore, the latest PS-OCT set-ups are based on Michelson interferometer combined with a polarization beam splitter (PBS) and two photo detectors [11,12] (SS-PSOCT) or two spectrometers [13] (SD-PSOCT) to detect the polarization state of the probing beam. This kind of PS-OCT techniques are based on point scanning imaging scheme, which cannot provide a real-time full-field image of the sample.

In this paper, a time domain-based polarization state synthesis tomography (PoST) method, which is based on the principle of polarization state coherent synthesis and demodulation, is proposed to achieve comprehensive 3D full-field imaging of the intensity, phase and birefringent information of the biological sample. In this method, the synthesis of the polarization state is achieved by the time-domain full-field low coherence interferometer, where the polarization states of the sample beam and the reference beam are set to be orthogonal for the synthesis of the polarization state. The synthesis of the polarization state enables two functions of the PoST system. The first one is depth information of the sample can be encoded by the synthesized polarization state. Although a time-domain low coherence interferometer configuration is utilized in this method, the principle of grasping the depth information of the sample is totally different from the time-domain PS-OCT. In this method, the polarization states of the reference and sample beams are mutually orthogonal, which do not interfere but can be coherently synthesized into a new polarization state within the coherence length of the light source. When the optical path difference between the reference and the sample arm exceeds the coherence length, there is no new polarization state but two known orthogonal mixed polarization states, which are constant and can be differentiated from the new synthesized polarization state. By utilizing this principle, the depth information of the sample can be encoded by the detected polarization state rather than the interference signal. A method called orthogonal polarization state separation (OPSS) is proposed to demodulate the new synthesized polarization state from the mixed polarization states to obtain the Stokes parameters of the synthesized polarization state at a certain depth. Based on the PoST system and the OPSS method, the depth information of the sample can be extracted based on polarization state measurement. The second function provided by the synthesis of the polarization state is that the synthesized polarization state can convey the comprehensive optical property of the sample. Since the scattering coefficient, refractive index and birefringence of the sample can modulate the intensity and phase of the sample beam, which can affect the synthesized polarization state, the synthesized polarization state is sensitive to all of these three optical parameters of the sample, enabling the comprehensive 3D optical imaging of the sample. In addition, PoST uses a micro-polarized array CCD camera (PCCD) to detect the polarization state of light. The use of the PCCD camera brought 2 advantages of the PoST system: (1) Different from the traditional PS-OCT imaging technique based on point scanning, the use of PCCD camera and the high numerical aperture lenses such as microscopy objectives allows for the real-time full-field imaging of the sample with high resolution ($\sim$ 1 micrometer) at a certain depth; (2) Different from the traditional method that used the regular camera or photodetector to measure the Jones vector of the sample (i.e., intensities and phase difference of two orthogonal polarization channels), PCCD can obtain the polarization state based on intensity measurement, mitigating the issue of instability and low signal to noise ratio (SNR) of the signals introduced by the phase measurement.

In this work, the depth-resolved ability of the proposed method has been demonstrated by multilayer samples. Non-birefringent and birefringent sample were utilized to demonstrate that the synthesized polarization state can be modulated by the scattering coefficient, phase and birefringence of the sample simultaneously. The application of PoST in biomedical imaging was investigated by imaging onion epidermal cell samples, demonstrating that the proposed synthesized polarization state can provide additional contrast to the biological samples.

2. Setup and methods

The polarization state synthesis tomography (PoST) system is based on the free-space Linnik interferometer structure, as shown in Fig. 1. A near-infrared super-luminescent diode (SLD) (EXALOS, EXS210006-01) is used to generate broadband light, which is coupled into a single-mode fiber (SMF) to the PoST system. Then, parallel light is obtained through a non-spherical lens for sample illumination, with a power of $\sim$10mW. Before entering the polarization beam splitter (PBS), the light passed through a polarizer (LP) to become 45${\circ }$ linearly polarized light. The PBS separates the 45${\circ }$ linearly polarized light into horizontally and vertically polarized components, which are transmitted to the sample arm and reference arm, respectively. The reference arm and sample arm use two identical 0.5 NA flat-field apochromatic microscope objectives (MO1, MO2) (Olympus, UPLFLN20$\times$) to avoid chromatic aberration.

 

Fig. 1. Schematic diagram of the PoST system. (a) TL: tube lens; MTS: motorized translation stage (minimum movement is 0.05$\mu$m); MO: microscope objective; SMF: single mode fiber; PBS: polarizing beam-splitter; BS: beam-splitter; QWP: achromatic quarter-wave plate. RM: reference mirror; PCCD: micro-polarizer array CCD. The plain red lines represent the beam in the plane of the figure. The blue dashed box represents the polarization measurement module of the figure. (b) Structure of a micro-polarizer array CCD camera: Each unit consists of four differently oriented micropolarizers and covers each pixel on the light-sensitive surface.

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In the reference arm, 90${\circ }$ linearly polarized light passes through a neutral density filter before entering a quarter-wave plate (QWP1) oriented at 45${\circ }$, which converts the linearly polarized light to circularly polarized light to illuminate the reference mirror. When the reference light propagates backward through QWP1, the circularly polarized light is converted back to linearly polarized light at 0${\circ }$. In the sample arm, 0${\circ }$ linearly polarized light enters QWP2 oriented at 45${\circ }$ and is then used to provide circularly polarized light illumination to the sample through a 20$\times$ microscope objective. For backscattered light from the sample arm, the polarization state of the reflected light can be considered unchanged if the sample is isotropic or weakly anisotropic. If the sample is strongly birefringent, the reflected light from the sample becomes an arbitrary (elliptical) polarization state due to the anisotropic nature of the sample. However, for any situation, the PBS will enforce the polarization state of the sample beam to be 90${\circ }$ linearly polarized light. This is because the PBS only transmits the horizontally polarized component and reflects the vertically polarized component, ensuring the polarization directions of the reference light and sample light are perpendicular to each other. The orthogonal polarization states reflected back from the reference and sample arm are recombined and form a new polarization state when the optical path difference between the reference and sample arm is within the coherence length.

The probing light of the new polarization state is focused by a cylindrical lens (TL) with a focal length of 75mm and sent to the polarization state measurement module (PSM, blue box). In the PSM, the synthesized light is split into two signals by a non-polarizing beam splitter (BS, 50:50), which are captured by two identical, 2448 $\times$ 2048 pixels, 8-bits, micro-polarized array CCD cameras (PCCD1, PCCD2) (Lucid Vision Labs, PHX050S-P). The acquisition speed of the camera is 24 Hz at full resolution but can be increased up to 340 Hz by pixel binning. The image sensor of the camera is equipped with micro-polarizer units located at each pixel, consisting of four micro-polarizers with different polarization directions (0${\circ }$, 45${\circ }$, 90${\circ }$, 135${\circ }$). Since the PoST system uses two PCCD cameras to measure the Stokes vector, it is necessary to ensure that both cameras are photographing the same region of the object and that the same pixel of both cameras must correspond to the same object point. For this purpose, we performed pixel registration on the images taken by the two PCCD cameras. We installed PCCD1 and PCCD2 on two 3D displacement platforms respectively for rough adjustment, so that the images of the two cameras are parallel and overlapping, and finally, the fast approximate nearest neighbor automatic registration algorithm [14–16] is used for image registration. In one exposure of the camera, the four intensity images with different polarization directions can be obtained simultaneously. Because a single PCCD1 cannot obtain circularly polarized components, to obtain the 4 Stokes parameters, PCCD2 is coupled with a QWP (QWP3) to detect the circularly polarized component of the probing light. As a result, PCCD1 detects the linearly polarized components (represented by I$_{0^{\circ }}$, I$_{90^{\circ }}$, I$_{45^{\circ }}$, I$_{135^{\circ }}$, I$_R$ and I$_L$), while PCCD2 detects the circularly polarized components of the synthesized light (represented by I$_R$ and I$_L$). Since the shooting of PCCD1 and PCCD2 is strictly synchronized in time, the six intensity images (I$_{0^{\circ }}$, I$_{90^{\circ }}$, I$_{45^{\circ }}$, I$_{135^{\circ }}$, I$_R$ and I$_L$) required for Stokes vector can be obtained simultaneously in one single exposure. We also use the camera’s built-in pixel binning function, Binning 2$\times$2, to improve the signal-to-noise ratio and sensitivity of the acquired images.

The entire reference arm of the PoST system is mounted on a DC servo-driven motorized translation stage (MTS1) (Thorlabs, Z812B) for axial scanning to match the optical path length of the reference light and sample light. The microscope objective on the sample arm is assembled on another identical motorized translation stage (MTS2). While the reference arm length is being scanned, the focus in the sample is adjusted to ensure dynamic focus control. To ensure that the coherence plane (zero optical path difference plane) in the sample arm and the focal plane (MO2) of the objective lens always match, the movement of MTS2 must be adjusted according to the refractive index of the sample. In order to focus at a depth z below the sample surface, starting from the focusing on the surface, the microscope objective (MO2) must be moved axially towards the sample at a certain distance [17]

In order to develop the algorithm that can extract the depth information of the sample from the detected output polarization state, the information included by the output polarization state directly detected by the PoST system should be fully discussed firstly as follows.

The output polarization state can be expressed by the Jones vector or Stokes parameters as shown in Eq. (2). Because the Jones vector requires the measurement and demodulation of the phase difference between the reference beam and sample beam, it can be easily affected by the phase noise which can lead to the instability of the signals. Hence, we detect the output polarization state by measuring the 4 Stokes parameters, which can be obtained by detecting 6 intensity signals as shown in Eq. (2). By using the Stokes parameters to express the output polarization state, the issue introduced by the instability of the measurement of the phase signals can be mitigated.

As it can be seen from Eq. (2), by using the PSM module, which can provide the intensity signals of six polarized components (i.e., I$_{0^{\circ }}$, I$_{90^{\circ }}$, I$_{45^{\circ }}$, I$_{135^{\circ }}$, I$_R$ and I$_L$) simultaneously, the output polarization state detected by the PoST system can be obtained by a single acquisition. The sample information included in the six polarized components can be represented as

As shown in Eq. (4), the detected polarization state (denoted as S$_{super\; position}$ ) not only contains the polarization information at $z_0$ depth, but also contains the polarization information at other non-target depths. $S_0$ and $S_1$ parameters include the optical information of all depths of the sample. Due to the operations ($I_{45^{\circ }} - I_{135^{\circ }}$) and ($I_R-I_L$), the incoherent term (DC term) $\sum _{z\neq z_0}E_s^2(z)$, $E_s^2(z_0)$ and $E_r^2$ are canceled out, hence the $S_2$ and $S_3$ parameters only contain the coherent terms of the reference light and sample light scattered back from the target depth $z_0$. Clearly, Eq. (4) cannot be used to represent the information of a certain layer of the sample.

To obtain the polarization state $S_{layer}(z_0)$ synthesized by light scattered back from the sample at a certain depth and the reference beam, we propose a new polarization state separation method called Orthogonal Polarization State Separation (OPSS). In this method, we reconstruct the 4 Stokes parameters of the synthesized polarization state by utilizing $S_2$ and $S_3$ in Eq. (4).

Firstly, the light scattered back from a certain depth $z_0$ of the sample $E_{s}^2(z_0)$ can be demodulated by $S_2$ and $S_3$ as follow

Then we can reconstruct the Stokes parameters of the synthesized polarization state. Due to the use of the PBS, the reference beam $E_{r}^2$ and the light scattered back from $z_0$ of the sample $E_{s}^2(z_0)$ provide the orthogonal polarized components for the synthesis of the polarization state $S_{layer}(z_0)$. To reconstruct $S_{layer}(z_0)$, the Stokes parameters of the synthesized polarization state at the target layer can be reconstructed and demodulated as follows

According to Eq. (4), $S_2$ and $S_3$ already represent the information of the sample at the depth of $z_0$ of the sample and hence, the synthesized polarization state at a certain layer can be represented

From Eq. (8), it can be seen that the synthesized polarization state of a certain depth of the sample can be obtained by the PSM module. In other words, the proposed PoST system and the OPSS method can extract the depth information of the sample. Moreover, according to Eq. (5) and (8), the synthesized polarization state is modulated by $E_{r}^2$, $E_{s}^2(z_0)$ and $\delta$. $E_r$ is constant and $\delta$ is related to the refractive index of the sample. Because only the 90$\circ$ polarized component of the light scattered back from the sample can be detected, both the scattering coefficient and the birefringent property of the sample can modulate $E_{s}^2(z_0)$. Hence, the scattering coefficient, birefringent property, and the refractive index of the sample can modulate the synthesized polarization state. In other words, the synthesized polarization state represents the comprehensive optical information of the sample at a certain depth. To visualize the synthesized polarization state and present the comprehensive optical information of the sample in a figure, we apply three primary colors, red, green, and blue, to encode the normalized Stokes parameters in color space to obtain a polarization chromaticity value (PCV) image, which integrates the complete information of the three Stokes parameters [18]. Through Eqs. (9) and (10), the three normalized Stokes parameters (with a range of [-1, 1]), which quantitatively represent the polarization state, can be uniquely mapped to the values of the three primary colors (with a range of [0, 1]).

As shown in Fig. 2, the color encoding method using polarization state as the imaging parameter displays all polarization states at the surface of the Poincaré sphere. The polarization state can be visualized by a unique color.

 

Fig. 2. Mapping relation between the polarization state of the combined Poincare sphere and RGB color space. (a) The color-encoded Poincare sphere and the path of changes in a polarization state; (b) The PCV and Stokes parameters for some points in the corresponding path.

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3. System performance characterization

3.1 Spatial resolution

The lateral resolution of the PoST system depends on the numerical aperture (NA) of the objective lens. In the PoST system, both objective lenses have an NA of 0.5. The lateral resolution of the imaging system is typically defined as the full width at half maximum (FWHM) of the point spread function (PSF) in the lateral direction. In traditional diffraction-limited optical systems, the theoretical lateral resolution $d_x$ is [19]

In air (n=1), with an NA of 0.5 and a wavelength of $\lambda _0$ = 840 nm, the theoretical lateral resolution in the PoST system is 1.02 $\mu$m.

In order to test the actual lateral resolution of the PoST system, we used a standard resolution test chart (1951 USAF, Thorlabs) as the PoST imaging sample as shown in Fig. 3(a). The actual lateral resolution was measured by recording the intensity profile of the edge response of the line in the sixth group (as indicated by the green line as shown in Fig. 3(a)). The edge response with a 0.5 NA microscope objective was shown in Fig. 3(b). We define the lateral resolution of the image as the 20%-80% width of the intensity profile of the measured edge [20]. The 20%-80% width of the normalized intensity profile (Fig. 3(b)) was 1.32 $\mu$m $\pm$ 0.01 $\mu$m, which is slightly larger than the theoretical value of 1.02 $\mu$m, mainly due to optical aberrations [21].

 

Fig. 3. Measurements of the spatial resolution of the PoST system. (a) 1951 USAF resolution test chart; (b) Measurement of the lateral resolution of the PoST system by recording the intensity profile of the edge of the line (indicated by the green line); (c) Typical interference signal a slide acquired by one pixel of a PCCD camera; (d) The curve of the axial point spread function, which is obtained from the digital demodulation of the interference fringes shown in (c).

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The axial resolution of the PoST system is determined by the bandwidth of the broadband light source. For a Gaussian-type source, the axial resolution is defined as half of the coherence length, but for a broadband spectrum light source, the theoretical axial resolution $d_z$ is defined by the following formula [22]

The low-coherence light source used in our system has a center wavelength $\lambda _0$ of 840 nm and an effective bandwidth $\nabla \lambda$ of 46 nm. In the air (n=1), the theoretical axial resolution is $d_z$ = 6.75 $\mu$m. The actual axial resolution of the PoST system is measured by imaging the interference signal of the surface of the glass slide. The FWHM of the signal of the glass slide is 7.8 $\mu$m $\pm$ 0.1 $\mu$m, which is considered to be the axial imaging resolution (Fig. 3(c)). If a light source with a wider bandwidth, such as a halogen lamp that is inexpensive and conducive to long-term observation of tissue activity, is used, the axial resolution can be improved to the sub-micron level.

3.2 Calibration and error correction of the PSM

Due to the imperfection of the optical components in the PCCD camera, the PSM (indicated by the blue box in Fig. 1) should be calibrated to enhance the measurement accuracy of the synthesized polarization state $S_{layer (z_0 )}$. According to Eq. (8), the accuracy of the OPSS method is determined by the accuracy of $S_2 (z_0 )$ and $S_3 (z_0 )$. Therefore, the key is to measure and correct the errors in these two parameters. The details of the calibration process are included in the Supplementary materials.

In the absence of any errors in the PSM, the measured polarization state $S_{out}(\alpha )$ should match exactly with the $S_{in}(\alpha )$ generated by the test module. However, due to the imperfection of the optical components in the PCCD camera, there exists errors in the PSM which can reduce the measurement accuracy of the synthesized polarization state. Therefore, it is necessary to calibrate the PSM based on actual measurement results, so as to correct the errors in the $S_2$ and $S_3$ components. At the same time, since the reconstructed $S_1$ is determined by $S_2$ and $S_3$, the error in $S_1$ can be calibrated when $S_2$ and $S_3$ are calibrated. Figure 4 shows the results of the Stokes parameters of the polarization state before and after calibration. In Figs. 4(a)–4(c), the theoretical curves of $S_1$, $S_2$ and $S_3$ of the polarization state are plotted as the solid lines and the corresponding measured values without the calibration are plotted as the dash lines. It can be seen that the errors between the theoretical value and the measured value cannot be neglected.

 

Fig. 4. Comparison of the actual measured Stokes parameters with theoretical values before and after calibration. The curves of theoretical and measured values of (a)$S_1$ (b)$S_2$ (c)$S_3$ before calibration. The curves of theoretical and measured values of (d)$S_1$ (e)$S_2$ (f)$S_3$ after calibration. The red, green and blue represent the three parameters of the Stokes vector in turn($S_1$,$S_2$,$S_3$), where the solid line represents the theoretical values and the dashed line represents the actual measured and calibrated values.

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By using the calibration method, the maximum errors of the corrected Stokes parameters compared to the theoretical values were reduced from 0.11 to 0.09, from 0.28 to 0.09, and from 0.19 to 0.06. Figure 4 shows that the calibrated Stokes parameters are much closer to the standard values, demonstrating the high accuracy of the PoST system and the feasibility and necessity of error correction.

3.3 Validation experiments of method feasibility

3.3.1 Demonstration of the tomographic ability of the PoST system

To demonstrate the depth-resolved ability of the PoST system, we first performed the tomographic imaging on a test sample model which is composed of two identical micrometers (Zhuzhou Carter Photoelectric Instrument) (Fig. 5(a)). One micrometer is engraved with a line facing down, and the other micrometer is engraved with a line facing up as shown in Fig. 5(b). A cover glass (Fisher brand) with a thickness of 0.17 mm is placed between them and fixed with transparent tape to form the test sample (see Fig. 5(b)). Due to the high scattering coefficient of the engraved lines (metal coating), the sample mainly consists of two resolvable layers: the first layer contains horizontally-oriented engraved lines, while the second layer contains vertically-oriented engraved lines. By imaging the two resolvable layers, the depth-resolved ability of the proposed PoST system can be verified.

 

Fig. 5. The diagram of test sample. (a) The photograph image of the test sample. The red small red box indicates the imaging area, and the large red box indicated by the arrow is the microscopic image of the sample; (b) The schematic diagram of the structure of the test sample and related parameters; (c) The depth-resolved intensity tomographic image of the first layer of inscribed lines; (d) The depth-resolved intensity tomographic image of the second layer of inscribed lines. Scale bars: 50 $\mu$m.

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The insert in Fig. 5(a) shows the microscopic image of the sample, which was reconstructed using $S_0$ of the $S_{superpostion}$. Both of the two micrometers at different layers are presented, indicating that the traditional microscopic imaging without the OPSS method cannot provide the depth information of the sample. By using the OPSS method to reconstruct $S_{0} (z_0)$ of the $S_{layer} (z_0 )$, two micrometers at different layers can be differentiated as shown in Fig. 5(c) and 5(d). This result demonstrates that the OPSS method can extract the depth information of the sample, verifying the tomographic ability of PoST system. The total acquisition time for a whole 3D volume of the test sample is 0.1 s.

3.3.2 Demonstration of the phase-sensitive property of the synthesized polarization state

To demonstrate that the phase information of the sample can modulate the synthesized polarization state, we reconstructed the phase images and the synthesized polarization state PVC images of the sample at different depths (Fig. 6).

 

Fig. 6. En-face images of test samples captured by the PoST system. (a) The phase tomographic image of the first layer of inscribed lines; (b) The phase tomographic image of the second layer of inscribed lines. (color bar:-3 to 3 (rad.)); (c) The synthesized polarization state tomographic PCV image of the first layer of inscribed lines; (d) The synthesized polarization state tomographic PCV image of the second layer of inscribed lines (PCV). Scale bars: 50 $\mu$m. Color bar: color-encoded Poincare sphere shown in Fig. 2(a).

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In the phase images (Fig. 6(a) and 6(b)), the phase signals of the background of the sample at different depths are totally different because phase difference between the reference arm and the sample is continuously changing when moving the reference mirror to match the imaging depth. In the synthesized polarization state PVC images (Fig. 6(c) and 6(d)), the colors of the background of the micrometers are different at two different layers. Since the intensity signals of the glass background, which are related to the scattering coefficient and the birefringent property of the glass sample, are similar at the two different layers as shown in Fig. 5(c) and 5(d), the difference of the colors of the background at different layers in the synthesized polarization state images should be caused by the difference of the phase signals. These results demonstrate that the synthesized polarization state is sensitive to the phase information of the sample.

3.3.3 Demonstration of the intensity-sensitive property of the synthesized polarization state

To demonstrate that the intensity of the sample can modulate the synthesized polarization state, a standard resolution test chart (1951 USAF, Thorlabs) has been imaged by the PoST system.

By blocking the reference arm to image the test chart, the PoST system can be used as a polarized light microscopy which can show the birefringent property of the sample alone. Figures 7(a)–7(c) show the microscopic image, the polarized light image and the synthesized polarization state PVC image of the sample. In the microscopic image (Fig. 7(a)), the scattering coefficient of the coated lines is much higher than that of the glass background as expected. However, in the polarized light image (Fig. 7(b)), the birefringent properties of the coated lines and the glass background are similar, demonstrating that the traditional polarized-related image cannot provide the intensity information of the sample. In the synthesized polarization state image (Fig. 7(c)), the coated lines and the glass background can be differentiated clearly even when the birefringent properties of these two materials are similar, demonstrating that the synthesized polarization state is also sensitive to the intensity information of the sample.

 

Fig. 7. En-face imaging results of a standard resolution test chart (1951 USAF, Thorlabs) by the PoST system. (a) The depth-resolved intensity image; (b) The polarization state image of the 1951 USAF by blocking the reference beam; (c) The synthesized polarization state PCV image of the 1951 USAF with the use of PoST method. Scale bars: 50 $\mu$m. Color bar: color-encoded Poincare sphere shown in Fig. 2(a).

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3.3.4 Demonstration of the birefringent-sensitive property of the synthesized polarization state

To demonstrate that the birefringent information of the sample can modulate the synthesized polarization state, the silver wires (diameter $\sim$ 25 $\mu$m), which are birefringent [23], was imaged by the PoST system. The silver wires were stacked vertically and were embedded within the agarose gel. The vertical spacing between adjacent wires was about 1 $\mu$m. The depths of the four silver wires are marked as $z_{1}$ - $z_{4}$ from top to bottom. The total acquisition time for a whole 3D volume of the silver sample is 1 s.

Figure 8 show the microscopic images $S_{0}$ of the $S_{super\;postion}$, Fig. 8(a)-8(d)), depth-resolved intensity images $S_{0}(z_0)$ of the $S_{layer}(z_0)$, Fig. 8(e)-8(h)) and synthesized polarization state tomographic PVC images (Fig. 8(i)-8(l)) of the sample were reconstructed by using the OPSS method. Figures 8(a)-8(d) show microscopic imaging results focused on different layers of the sample. In the microscopic images, the intensity signals of the silvers at different depths are superimposed and the depth information of the sample cannot be extracted. In the depth-resolved intensity images (Fig. 8(e)-8(h)), the image of the silver at each depth can be reconstructed separately, demonstrating the tomographic ability of the PoST system and the OPSS method. Figures 8(j)-8(i) show the synthesized polarization state PCV images of different layers of the sample. It’s hard to visualize the birefringent property of the sample in the intensity images while in the synthesized polarization state PCV images, the typical band-like birefringent pattern can be observed in the silver wire, indicating that the synthesized polarization state can also present the birefringent information of the sample.

 

Fig. 8. The results of the silver wire sample were obtained by microscopic and PoST imaging. (a-d) The microscopic images with different focus depths of $z_{1}$ - $z_{4}$ achieved by MST2 shown in Fig. 1(a); (e–h) The depth-resolved intensity tomographic images at depths of $z_{1}$ - $z_{4}$ respectively; (i-l) The synthesized polarization state PCV images at depths of $z_{1}$ - $z_{4}$. Scale bars: 50 $\mu$m. Color bar: color-encoded Poincare sphere shown in Fig. 2(a).

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3.4 Application to biological tissue imaging

To validate the performance of PoST in biological tissue imaging, we performed ex vivo live cell imaging. Onion epidermal cells were used as the sample. Before fixing the tissue on the glass plate, a drop of water was added to the tissue to maintain cell viability and provide index matching to minimize light reflection at the interface. The total acquisition time for a whole 3D volume of the onion cell is 0.69 s.

Microscopic image (without depth information), depth-resolved intensity image, phase image and the synthesized polarization state PVC image of the onion cell at the depth of 20 $\mu$m are shown in Fig. 9 respectively. In the microscopic image (Fig. 9(a)), although the cell wall (dark area between each cell) and cell nucleus (as indicated by the white box) can be roughly differentiated, the contrast of these microstructures is low because the depth information is superimposed. In the depth-resolved intensity image (Fig. 9(b)), the contrast of the microstructure is enhanced but still, some of the components such as the cell membrane and cytoplasm (indicated by the blue arrow) cannot be visualized clearly. The phase image (Fig. 9(c)) provides additional contrast for the cell membrane and cytoplasm. However, it’s hard to differentiate the cell wall (indicated by the black arrow) and the cytoplasm (indicated by the red arrow) since the phase values between these two components are similar, indicating that the refractive index between these two components is similar. These results demonstrate that the parameter that only represents a single optical property is not sufficient to contrast all the components within the onion cells. Since the synthesized polarization state is sensitive to multiple optical parameters, the cell wall, cell nucleus, cell membrane, and cytoplasm can be visualized and differentiated clearly in the synthesized polarization state image (Fig. 9(d)). The contour and shape of the nucleus and the shape and thickness of the cell membrane (as indicated by the green arrow) can be clearly identified. The difference between the cytoplasm (red arrow) within the cell and the cell wall (black arrow) can be differentiated by different colors as shown in Fig. 10(d). These results demonstrate that the synthesized polarization state includes the comprehensive information of the probing light and hence provides additional contrast for the biological sample, which can provide a reference for further understanding of the cell microstructure and various subcellular activities.

 

Fig. 9. En face PoST images of an onion cell. (a)The microscopic images without the depth information; (b) The depth-resolved intensity images; (c) The phase tomographic images (color bar:-3 to 3 (rad.)); (d) The synthesized polarization state tomographic images at the depth of 20 $\mathrm{\mu}$m . Scale bars: 50 $\mu$m. Color bar: color-encoded Poincare sphere shown in Fig. 2(a).

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4. Discussion

In the PoST prototype, the distribution of the synthesized polarization state at a certain depth can be obtained by a single acquisition. The time required to acquire an en-face tomographic image is $1/f_{camera}$ = 0.04 s, where $f_{camera}$ = 24 Hz is the frame rate of the PCCD camera under full resolution. Different from the traditional OCT based on the point scanning, which can only obtain the en-face image after the 3D scan is finished ($\sim$several seconds), the proposed PoST can provide the en-face tomographic image within 0.04 s, which is short enough to avoid partial motion artifacts and signal distortion for an en-face image at a certain depth. This advantage is attractive for the real-time visualization of the dynamic process of biological samples.

Compared with the current full-field OCT imaging technique, the proposed PoST imaging technique can provide a similar lateral resolution ($\sim 1\mu$m). A motorized translation state is also assembled into the reference arm to achieve auto focus during the axial scanning. The frame rate of the proposed PoST system is 24 Hz with the pixel of 2048*2448, which is limited by the PCCD camera (PHX050S-P) we used. Actually, the current commercial PCCD camera (MV-CH050-10UP(EoL)) can provide a higher frame rate at 74 Hz which is competing with that of the current full-field OCT system. Hence, the PoST technique has competitive performances compared with the traditional full-field OCT while it possesses unique advantage of providing comprehensive optical information (intensity, phase, birefringence) of the sample.

In this paragraph, we further discuss the new metric provided by the PoST method. As three fundamental properties of the light, intensity, phase and polarization of the probing light can convey important information about the biological sample from different perspectives. By using the synthesized polarization state as the imaging parameter, the intensity, phase and birefringent information of the sample can be comprehensively presented in one figure, which can provide additional contrast for the sample. In this work, by using the synthesized polarization state as the imaging parameter, different components within the cell such as the cell wall, cell nucleus and cell membrane can be differentiated with improved contrast. In future work, this technique may help to reveal the cellular dynamic physiology process. However, there are still limitations of this method that need to be mitigated. Firstly, the accumulation effect introduced by the birefringent property of the sample can lead to the difficulty of determining the local birefringent information at deeper layers. To mitigate this issue, the polarization state tracing method [24] based on PS-OCT can be utilized to derive the local phase retardation and local axis orientation of the sample. The second issue in this work is that although the synthesized polarization state can be used to contrast the comprehensive optical property of the sample, it still lacks the quantitative analysis of the optical property of the sample. In future work, demodulation algorithms that can extract the scattering coefficient, refractive index and the birefringent property of the samples from the synthesized polarization state are needed to be developed.

5. Conclusion

In summary, a PoST imaging system and an OPSS demodulation algorithm are proposed in this work to provide full-field tomographic imaging for the comprehensive optical property of the sample. The PoST imaging system is achieved by a time-domain full field polarization sensitive Michelson interferometer combined with a PSM, which is composed by two identical PCCD cameras to parallelly measure the output polarization states in a single exposure. Using a 0.5NA objective lens, the lateral resolution of $\sim$1 $\mu$m has been achieved. The OPSS demodulation algorithm utilizes the Stokes parameters directly detected by the PSM to derive the optical information at a certain depth. Imaging of the stacked micrometers and silver wires demonstrated the tomographic ability of the proposed method. The phase-sensitive property, intensity-sensitive property and birefringent-sensitive property of the synthesized polarization state have been demonstrated by the standard samples. Onion epidermal cells are imaged by the PoST system, demonstrating that the proposed method can provide a unique contrast for the microstructure of cells (i.e., cell membrane, nucleus, cytoplasm). These results demonstrate that PoST can provide real-time en-face images with sufficient resolution and additional contrast, which may have useful and practical applications in the investigations of the birefringent cells.