Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials

Xuan Liu; Yang Yang; Lu Han; Cheng-Shan Guo

doi:10.1364/OE.25.007288

1. Introduction

Polarization describes the orientation of an oscillating electric field, which represents one of fundamental properties of an optical beam separating from its frequency and intensity. One important phenomenon related to polarization is the changes of the polarization state of light after passing through or reflected by polarization-sensitive or anisotropic materials. This kind of changes relies on the polarization-transforming properties of the material and can be characterized by a transmittance matrix. Precise measurements of the transmittance matrix parameters of the polarization-sensitive materials are crucial to revealing inner structures or birefringence properties of the materials [1–6], charactering the complex modulation properties of the optical devices [7–9], discovering the physical nature of the light-matter interactions [10–12] as well as furthering our understanding of biological and physical systems.

Two main formalisms describing the transmittance matrix of a polarization sensitive material are Mueller and Jones matrix. Since an intensity-based framework, Mueller formalism has been commonly used by most of the conventional polarization-based techniques, but it does not describe the field nature of light polarization and can’t directly retain the phase information of the light [13, 14]. Jones matrix approach works with the complex behavior of the light rather than its intensity and can directly describe the complex nature of electric field [15]. Furthermore, in many cases, Jones matrix can be a more compact and intuitive tool than the Mueller formalism for quickly estimating the complex responses of materials to incident polarized light. Generally, the Jones matrix measurement is more complicated than the Mueller matrix, because the Jones matrix of a general material contains at least four complex parameters which associated with four combinations of different linearly polarized state of input and output beam [16]. The traditional measurement of Jones matrix mainly aimed at some polarization-sensitive optical elements such as wave plates and prisms [17–20]. Some methods for measuring Jones matrix of general polarization-sensitive materials have also been reported [21–26], in which the amplitude and phase of each Jones matrix parameter were extracted based on multiple intensity measurements. Those methods are often associated with a significant measurement errors induced by instability of the system with multiple measurements. Recently, some polarization imaging techniques, based on holographic principle, are proposed to be able to extract spatially resolved Jones matrix of anisotropic samples [27–29].

In our previous work, we proposed a method, called Jones matrix polarization holography (JMPH), for realizing one-step measurement of two dimensional (2-D) Jones matrix parameters of polarization-sensitive materials [30]. It is based on a double-source Mach-Zehnder interferometer, in which two orthogonal gratings are utilized for realizing angular multiplexing. Although our solution provides more easily measuring procedure and simple optical arrangement than the existing methods, it also has some inherently disadvantages associated with the experiment scheme. For example, to get a four-channel angular multiplexing hologram, two orthogonal gratings and spatial filtering and imaging systems are required. Most recently, other two methods were proposed for realizing a single-shot measurement of the Jones matrix [31, 32]. The first one [31] made use of one orthogonal grating to achieve 2-D Jones matrix maps from biological samples. In this method, because the four complex field images were retrieved from different parts of an interferogram, some slightly pixel-level deviations for a same object point between two copied images involved in operation will lead to the distortion of the measurement results. The second one [32] utilize two Sagnac interferometers to generate angular and polarization multiplexing both in the object and reference arms. Although this technique uses only one coherent source in contrast to two laser sources as in the proposed methods [30, 31], the different propagation directions of the two orthogonal polarized beams illuminating to the sample will bring some trouble in real measurements.

Here, we present an improved system to overcome these disadvantages or avoid the shortcomings. The new system is designed based on optical fibers and the principle of a lensless off-axis Fresnel holographic imaging geometry to retrieve spatially resolved Jones matrix from one single-shot operation. In this system, two single-mode optical fiber splitters are used to generate the reference and illumination beams for recording the needed angular multiplexing off-axis hologram. Benefit from the fiber-based and lensless off-axis holographic design, the system possesses a quite compact arrangement and is free from lens aberrations.

2. Principle

2.1 Principle of the experimental setup

The schematic of the proposed system is represented in Fig. 1. Two fiber-coupled laser diodes LD1 and LD2 are used as light sources, each of them is split into three fiber paths by a $1 \times 3$ single-mode optical fiber splitter (FS1 and FS2). All the beams emitted from the same optical fiber splitter travel the same distance along single-mode fibers (Nufern 630-HP), and are fixed, respectively, on specially designed fiber holders (FH1-FH4), of which one enters the sample path used as illumination beam and the other two beams enter the reference path used as reference beams. In the sample path, two illumination beams S₁ (split from FS1) and S₂ (split from FS2) are combined together on the optical axis by the polarization beam splitter PBS1 and pass through a quarter-wave plate (QWP) oriented at 45 degrees to the horizontal direction, so that the sample O is simultaneously illuminated with two mutually incoherent beams: one is right circularly polarized and the other is left circularly polarized. The beams passed through the sample serve as the sample beam of the off-axis holographic recording. In the reference path, the beams split from the two optical fiber splitters including R₁₁ and R₁₂ (from FS1), as well as R₂₁ and R₂₂ (from FS2), are respectively fixed on FH3 and FH4. The four beams are distributed as shown in Fig. 1(b), and their relative positions and tilt angles can be respectively adjusted on the FH3 and FH4. The arrows in Fig. 1(b) indicate the adjusting direction of the four beams. It should be noted that the centers of FH3 and FH4 are coaxial with point sources S₁ and S₂ after passing through the polarization beam splitters (PBS1 and PBS2) and the non-polarized beam splitter (NPBS). All the four beams R₁₁, R₁₂, R₂₁ and R₂₂ are linearly polarized by PBS2 as the reference beams for recording a four-channel angular-multiplexing polarization hologram, among which, R₁₁ and R₂₁ are horizontally polarized, and R₁₂ and R₂₂ are vertically polarized. Finally, all the sample beam and the reference beams are superimposed over one another on the recording plane and form an angular-multiplexing polarization hologram, which is recorded by the image sensor IS.

Fig. 1 (a) Schematic of the experimental setup. (b) Structure of the Fiber holders.

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Since the fiber-based and lensless design, the system has a compact configuration only with a small amount of optical elements such as three beam splitters and one quarter-wave plate. In addition, because a lensless off-axis Fresnel holographic recording geometry is adopted, the system is easy to adjust and insensitive to optical path difference or wavefront distortion.

2.2 Principle of measuring the Jones matrix

Figure 2 is the geometry of our four-channel off-axis Fresnel holographic system. In the following analysis, all the reference and illumination beams are considered to be emitted from coplanar point sources at a distance d apart from the sample plane, of which, S₁ and S₂ represent the illumination point sources (in this geometry, the point sources S₁ and S₂ is spatially coincident), and R₁₁, R₁₂, R₂₁, and R₂₂ respectively represent the four reference sources. The arrows in Fig. 2 indicate the polarization states of these beams. The coordinates in the sample plane and image sensor plane are assumed to be $(x_{o}, y_{o})$ and $(x, y)$ , respectively.

Fig. 2 Recording geometry of the fiber-based off-axis Fresnel holographic system.

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According to the conventional Jones matrix calculus, the Jones matrix of an arbitrary sample is described as

J (x_{o}, y_{o}) = [\begin{matrix} J_{xx} (x_{o}, y_{o}) & J_{xy} (x_{o}, y_{o}) \\ J_{yx} (x_{o}, y_{o}) & J_{yy} (x_{o}, y_{o}) \end{matrix}],

where

J_{xx}

,

J_{xy}

,

J_{yx}

, and

J_{yy}

are four Jones parameters of the sample. In the sample path, two mutually incoherent illumination beams emitted from point sources S₁ and S₂ are respectively right and left circularly polarized beams when they are incident on the sample. Therefore, the light field right after the sample can be described using Jones vectors as follows

\begin{array}{l} O (x_{o}, y_{o}) = O_{1} (x_{o}, y_{o}) \oplus O_{2} (x_{o}, y_{o}) \\ = \exp [\frac{i π}{λ d} (x_{o}^{2} + y_{o}^{2})] {A_{1} [\begin{matrix} J_{x x} + i J_{x y} \\ J_{y x} + i J_{y y} \end{matrix}] \oplus A_{2} [\begin{matrix} J_{x x} - i J_{x y} \\ J_{y x} - i J_{y y} \end{matrix}]}, \end{array}

in which,

\oplus

represents the incoherent superposition of the beams, A₁ and A₂ are complex constants describing the amplitudes of the two illuminating sources S₁ and S₂,

λ

is the illumination wavelength, and d is the distance between the source plane and the sample plane.

Then the sample beam travels a distance z and reaches the image sensor plane. The complex fields at the sample plane and the sensor plane satisfy Fresnel diffraction transformation

O_{z} (x, y) = F r_{z} {O (x_{o}, y_{o})},

here

F r_{z} {}

represents the Fresnel diffraction transform with diffraction distance of z. Substituting Eq. (2) into Eq. (3) gives the distribution of the sample diffraction beam at the sensor plane

\begin{matrix} O_{z} (x, y) = O_{1 z} (x, y) \oplus O_{2 z} (x, y) \\ = [\begin{matrix} A_{1} (J_{x x}^{'} + i J_{x y}^{'}) \\ A_{1} (J_{y x}^{'} + i J_{y y}^{'}) \end{matrix}] \oplus [\begin{matrix} A_{2} (J_{x x}^{'} - i J_{x y}^{'}) \\ A_{2} (J_{y x}^{'} - i J_{y y}^{'}) \end{matrix}], \end{matrix}

where

\begin{matrix} J_{x x}^{'} = F r_{z} {J_{x x} \exp [\frac{i π}{λ d} (x_{o}^{2} + y_{o}^{2})]}, & J_{x y}^{'} = F r_{z} {J_{x y} \exp [\frac{i π}{λ d} (x_{o}^{2} + y_{o}^{2})]} \\ J_{y x}^{'} = F r_{z} {J_{y x} \exp [\frac{i π}{λ d} (x_{o}^{2} + y_{o}^{2})]}, & J_{y y}^{'} = F r_{z} {J_{y y} \exp [\frac{i π}{λ d} (x_{o}^{2} + y_{o}^{2})]} \end{matrix} .

On the other side, the reference beams can be treated as spherical waves generated by four point sources located at the coordinates $(x_{mn}, y_{mn})$ $(m,n= 1, 2)$ in the source plane. Under the condition of Fresnel approximation, the reference beams incident on the sensor plane can be written as

R_{m n} (x, y) = | R_{m n} (x, y) | \begin{matrix} \times \exp {\frac{i π}{λ (z + d)} [{(x - x_{m n})}^{2} + {(y - y_{m n})}^{2}], & (m, n = 1, 2) \end{matrix} .

At the sensor plane, the recorded interference pattern formed by all the sample beam and reference beams can be expressed as

\begin{matrix} I = {| [\begin{matrix} O_{1 z_{x}} \\ O_{1 z_{y}} \end{matrix}] + R_{11} [\begin{matrix} 1 \\ 0 \end{matrix}] + R_{12} [\begin{matrix} 0 \\ 1 \end{matrix}] |}^{2} + {| [\begin{matrix} O_{2 z_{x}} \\ O_{2 z_{y}} \end{matrix}] + R_{21} [\begin{matrix} 1 \\ 0 \end{matrix}] + R_{22} [\begin{matrix} 0 \\ 1 \end{matrix}] |}^{2} \\ = I_{0} + Y_{11} + Y_{12} + Y_{21} + Y_{22} + Y_{11}^{*} + Y_{12}^{*} + Y_{21}^{*} + Y_{22}^{*}, \end{matrix}

where

I_{0} = {| O_{1 z_{x}} |}^{2} + {| O_{1 z_{y}} |}^{2} + {| O_{2 z_{x}} |}^{2} + {| O_{2 z_{y}} |}^{2} + {| R_{11} |}^{2} + {| R_{21} |}^{2} + {| R_{12} |}^{2} + {| R_{22} |}^{2},

and

\begin{matrix} Y_{11} = A_{1} R_{11}^{*} (J_{x x}^{'} + i J_{x y}^{'}), & Y_{12} = A_{1} R_{12}^{*} (J_{y x}^{'} + i J_{y y}^{'}) \\ Y_{21} = A_{2} R_{21}^{*} (J_{x x}^{'} - i J_{x y}^{'}), & Y_{22} = A_{2} R_{22}^{*} (J_{y x}^{'} - i J_{y y}^{'}) \end{matrix} .

The superscript “*” in Eqs. (7) and (9) indicates the complex conjugate operation.

Y_{mn} (m,n= 1, 2)

in Eq. (7) are the items including the complex amplitude of the sample beam

O_{mz}

. The off-axis geometry allows directly retrieving them from the recorded interference pattern via a spatial filtering algorithm [33–35]. In addition, it can be seen from Eq. (8) that the background intensity I₀ of the interference pattern contains the intensities of the two incoherent sample diffraction beams, which will reduce the fringe visibility to a certain degree compared to the case of illumination with a single light source. The following experiments will demonstrate that this kind of superposition has no effect on the reconstruction of the sample information described by Eq. (9).

Although the $Y_{mn} (m,n= 1, 2)$ can be retrieved from the recorded hologram, from Eq. (9) we can see that it is not directly equal to the Jones matrix parameters $J_{xx}$ , $J_{xy}$ , $J_{yx}$ , and $J_{yy}$ that we want to measure. Here we take $Y_{11}$ as an example to explain how to retrieve the tested Jones matrix parameters from the items $Y_{mn} (m,n= 1, 2)$ . Substituting Eqs. (5) and (6) into Eq. (9), we get

\begin{matrix} Y_{11} = A_{1} R_{11}^{*} ({J^{'}}_{x x} + i {J^{'}}_{x y}) \\ = A_{1} R_{11}^{*} F r_{z} {(J_{x x} + i J_{x y}) \exp [\frac{i π}{λ d} (x_{o}^{2} + y_{o}^{2})]} \\ = A_{1} | R_{11} | e x p [\frac{- i π}{λ (z + d)} (x_{11}^{2} + y_{11}^{2})] \exp [\frac{i 2 π}{λ (z + d)} (x_{11} x + y_{11} y)] \\ \times \exp [\frac{i π d}{λ z (z + d)} (x^{2} + y^{2})] \iint (J_{x x} + i J_{x y}) \\ \times \exp [\frac{i π}{λ} (\frac{1}{d} + \frac{1}{z}) (x_{o}^{2} + y_{o}^{2})] \exp [\frac{- i 2 π}{λ z} (x x_{o} + y y_{o})] d x_{o} d y_{o} . \end{matrix}

After setting the following variable transformation,

x_{o}^{'} = x_{o} (z + d) / d

,

y_{o}^{'} = y_{o} (z + d) / d

,

x_{i} = x_{o}^{'} / M

,

y_{i} = y_{o}^{'} / M

,

z_{i} = z (z + d) / d

, and

M = (z + d) / d

, Eq. (10) can be further simplified as

\begin{matrix} Y_{11} = A_{1} | R_{11} | \iint [J_{x x} (x_{o}, y_{o}) + i J_{x y} (x_{o}, y_{o})] \exp {\frac{i π d}{λ z (z + d)} \\ \times [(^{x - \frac{z + d}{d} x_{o}) 2} + (^{y - \frac{z + d}{d} y_{o}) 2}]} d x_{o} d y_{o} \\ = (^{\frac{d}{z + d}) 2} A_{1} | R_{11} | \iint [J_{x x} (\frac{x_{0}^{'}}{M}, \frac{y_{0}^{'}}{M}) + i J_{x y} (\frac{x_{0}^{'}}{M}, \frac{y_{0}^{'}}{M})] \\ \times \exp {\frac{i π d}{λ z (z + d)} [(^{x - x_{0}^{'}) 2} + (^{y - y_{0}^{'}) 2}]} d x_{0}^{'} d y_{0}^{'} \\ = C_{11} F r_{z_{i}} {J_{x x} (x_{i}, y_{i}) + i J_{x y} (x_{i}, y_{i})} . \end{matrix}

The sign M corresponds to the magnification parameter of the system. From Eq. (11), it can be seen that the magnified Jones matrix distribution

J_{x x} + i J_{x y}

can be retrieved by an inverse Fresnel diffraction transform with the diffraction distance

z_{i}

, that is,

Y_{11}^{'} = J_{x x} + i J_{x y} = I F r_{z_{i}} {\frac{Y_{11}}{C_{11}}},

where

IF r_{z_{i}} {}

indicates the inverse Fresnel diffraction transform with the diffraction distance

z_{i}

. Applying the same analysis to the items

Y_{12}

,

Y_{21}

, and

Y_{22}

, we get

\begin{array}{l} Y_{12}^{'} = J_{y x} + i J_{y y} = I F r_{z_{i}} {\frac{Y_{12}}{C_{12}}} \\ Y_{21}^{'} = J_{x x} - i J_{x y} = I F r_{z_{i}} {\frac{Y_{21}}{C_{21}}}, \\ Y_{22}^{'} = J_{y x} - i J_{y y} = I F r_{z_{i}} {\frac{Y_{22}}{C_{22}}} \end{array}

where

C_{mn} (m,n= 1, 2)

represent the complex fields of illuminating beam

S_{m}

and reference beam

R_{mn}

at the sensor plane when the sample is absent. The operation of dividing the complex field

Y_{mn}

by corresponding

C_{mn}

in Eqs. (12) and (13) can removes much of the background noise and any tilt in the image associated with the off-axis approach.

From Eqs. (12) and (13), the wanted Jones matrix parameters of the sample can be determined by the following formulas:

\begin{matrix} J_{x x} = \frac{1}{2} (Y_{11}^{'} + Y_{21}^{'}), & J_{x y} = - \frac{i}{2} (Y_{11}^{'} - Y_{21}^{'}) \\ J_{y x} = \frac{i}{2} (Y_{12}^{'} - Y_{22}^{'}), & J_{y y} = \frac{1}{2} (Y_{12}^{'} + Y_{22}^{'}) \end{matrix} .

3. Experiments

3.1 Jones matrix of a composite polarizer

For further demonstrating the feasibility of our method by experiments, we constructed a real experimental setup as shown in Fig. 3. In the experiments, two independent fiber-coupled laser diodes, with the central wavelength of 650 nm, are adopted as the light sources. The four-channel angular-multiplexing polarization hologram (AMPH) of the sample is recorded by a CMOS image sensor with pixel size of 6.45 × 6.45 um and pixel number of 1024 × 1024.

Fig. 3 Photograph of the experimental setup.

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The sample used for the first experimental example is a composite polarizer composed of two polyvinyl alcohol (PVA) film polarizers with different polarizing directions (one −18 degree and another + 27 degree relative to horizontal direction). The distance parameters d and z are, respectively, equal to about 95 mm and 135 mm, and the magnification of the system is about 2.4.

Figure 4(a) shows an example of the AMPHs recorded in the experiments. The detailed interferometric fringe structure of the hologram can be seen from the zoom-in picture shown in Fig. 4(b). Figure 4(c) shows the Fourier spectrum of the AMPH obtained via a 2D fast Fourier transformation. The dashed circles shown in Fig. 4(c) indicate the Fourier spectra of the complex field $Y_{mn} (m,n= 1, 2)$ , which can be easily extracted by a spatial filtering algorithm. A similar operation can be performed on the background hologram to retrieve the terms $C_{mn} (m,n= 1, 2)$ . Using the formula given by Eqs. (12)-(14), the sample’s Jones matrix parameters $J_{xx}$ , $J_{xy}$ , $J_{yx}$ , and $J_{yy}$ can be obtained, respectively. In calculating the inverse diffraction transform related in Eqs. (12) and (13), the diffraction distance $z_{i}$ is taken as 326.8 mm.

Fig. 4 (a) Example of an AMPH recorded in our experiments; (b) zoom-in image of the rectangular areas of the hologram shown in (a); (c) spatial frequency of the AMPH.

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Figures 5(a) and 5(b) show, respectively, the amplitude and phase maps of the four Jones matrix parameters retrieved from the AMPH shown in Fig. 4(a). The arrows in Fig. 5(a) represent the polarization direction of different regions of the sample. It should be noted that the upper region in the phase map of $J_{yy}$ is very noisy. This is because the amplitude of $J_{yy}$ at that region is close to be zero and so the corresponding phase value is naturally indefinite. Figures 5(c) and 5(d) respectively show the amplitude and phase of the Jones matrix of the sample obtained by theoretical calculation, which is consistent basically with the experimental results as shown in Figs. 5(a) and 5(b).

Fig. 5 Measured Jones matrix parameters of the composite polarizer, from left to right: $J_{xx}$ , $J_{xy}$ , $J_{yx}$ , and $J_{yy}$ . (a) and (b) are, respectively, the amplitude and phase maps measured in experiments; (c) and (d) are the corresponding amplitude and phase maps by theoretical calculation. The scale bar is the same in all images.

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3.2 Measurement of stress birefringence

As the second example, we measured the Jones matrix parameters of a polymethyl methacrylate (PMMA) sample with stress birefringence. The tested PMMA sample with a slit and a size of 20mm*10mm*1mm is fixed on a specially designed loading platform, as shown in Fig. 6. The direction of the external force applied to the sample is indicated by the arrows shown in Fig. 6. The circle area indicated in Fig. 6 is the measuring zone in the experiments.

Fig. 6 Stressed PMMA sample. The circle is the illuminated area.

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An example of the measurement results is shown in Fig. 7, in which, Figs. 7(a)-7(d) give the amplitude distributions of the four Jones matrix parameters $J_{xx}$ , $J_{xy}$ , $J_{yx}$ , and $J_{yy}$ while Figs. 7(e)-7(h) present their phase distributions. From Figs. 7(a)-7(d), it can be seen that in the slit part (corresponding to the air background), the measured Jones matrix has the values of $J_{xx} \approx J_{yy} \approx 1$ and $J_{xy} \approx J_{yx} \approx 0$ , which is good agreement with the theoretical prediction for the isotropic free space. In the region occupied by the sample, the measured Jones matrix distributions reveal the anisotropic field induced by the exerted stress. From the phase maps shown in Figs. 7(e)-7(h), we can find that all the Jones matrix parameters in the sample region have noticeable changes in phase, which reflect an inhomogeneous refractive index of the stressed sample, and the refractive index fluctuates violently near the slit. Moreover, the orientation of fringes also reflects the spatial orientation of the change in sample’s birefringence under the influence of the external force, and reveals that the stressed sample has significant anisotropy that originated from the exerted stress.

Fig. 7 Measurement results for the PMMA sample. (a)-(d) are, respectively, the amplitude maps of the Jones matrix parameters $J_{xx}$ , $J_{xy}$ , $J_{yx}$ , and $J_{yy}$ ; (e)-(h) are the corresponding phase maps. The scale bar is the same in all images.

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3.3 Measurement of a mica fragment

As the third example of our experiments, we measured a mica flake with non-uniform thickness. The measurement is performed by simply changing the sample without need any additional adjustments to the system. Figures 8(a)-8(d) and Figs. 8(e)-8(h) show the amplitude and phase maps of the Jones matrix of the sample, respectively. The measured Jones matrix parameters of the blank region without the sample at the upper right corner are also consistent with the polarization response of the free space. The sample region have a low amplitude contrast except for the boundary areas of each layer, and the amplitudes of the diagonal elements ( $J_{xx}$ and $J_{yy}$ ) and off-diagonal elements ( $J_{xy}$ and $J_{yx}$ ) are distributed symmetrically; while the phase maps show that there are four different thickness steps in the sample region and each of them has a uniform phase distribution.

Fig. 8 Experimental results for the mica sample. (a)-(d) are, respectively, the amplitude maps of the measured Jones matrix parameters $J_{xx}$ , $J_{xy}$ , $J_{yx}$ , and $J_{yy}$ ; (e)-(h) are the corresponding phase maps. (i) and (j) are the phase maps of the two eigenvalues; (k) is the phase retardation map between the two eigenvector directions.

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The measured spatially resolved Jones matrix provides a feasible way to further analyze the birefringent properties of the sample. A typical processing is to diagonalize the Jones matrix to obtain the eigenvector distribution and the corresponding eigenvalues. When the polarization direction of an input beam is the same as an eigenvector direction, the polarization state of the input beam will remain unchanged after passing through the sample. So the direction of an eigenvector refers to the direction of a principal axes and the phase difference between the two eigenvalues reveals the birefringent property of the sample. Figures 8(i) and 8(j) are the phase maps of the two eigenvalues obtained from the measured Jones matrix, respectively. The phase difference of the two eigenvalues, as shown in Fig. 8(k), represents the phase retardation between the two eigenvector directions and reveals the different birefringence because of the different thickness of the sample.

4. Conclusion

In summary, we reported a fiber-based lensless holographic imaging system to realize a single-shot measurement of two dimensional Jones matrix parameters of polarization-sensitive materials. In this system, a multi-source lensless off-axis Fresnel holographic recording geometry is adopted, and two optical fiber splitters are used to generate the multiple reference and illumination beams required for recording a four-channel AMPH. Using this system and the method described above, spatially resolved Jones matrix parameters of a polarization-sensitive material can be retrieved from one single-shot AMPH. We demonstrate the feasibility of the method by extracting a 2-D Jones matrix of a composite polarizer. Applications of the method to measure the Jones matrix maps of a stressed polymethyl methacrylate sample and a mica fragment are also presented. Benefit from the fiber-based, angular-multiplexing and lensless holographic design, the system may have the advantages that it possesses compact configuration, can be easy to implement and free from lens aberrations. We believe that it will provide a feasible approach for development of an integrated and portable system suitable for real-time measuring the complex Jones matrix maps of polarization-sensitive materials as well as dynamic polarization imaging [36–38]. Given slight modification, the system can also be operated in reflection mode to accommodate opaque samples.

Founding

National Natural Science Foundation of China (NSFC) (11474186).

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Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials

Abstract

1. Introduction

2. Principle

2.1 Principle of the experimental setup

2.2 Principle of measuring the Jones matrix

3. Experiments

3.1 Jones matrix of a composite polarizer

3.2 Measurement of stress birefringence

3.3 Measurement of a mica fragment

4. Conclusion

Founding

References and links

Cited By

Figures (8)

Equations (14)

Optics Express