1. INTRODUCTION

For their rarity and unique effulgence, pearls have been cherished by humanity since ancient times [1]. Since the production of genuine pearls is less than the demand from consumers, imitation pearls have been distributed to the market. Sellers should accurately inform the customers about the type and value of the pearls, but this reality is not always practiced. For this reason, objective discrimination methods of genuine pearls from imitation pearls have been researched. In the early days, imitation pearls were distinguished [2] by observing appearance, touching, and analyzing the fluorescence irradiation. In the case of observing appearance, however, it is difficult to quantify by merely observing the surface with unaided eyes [3]. The touching causes friction on the surface of the pearl by biting or scratching it. However, this is a destructive method and easily damages the surface of the pearl, which degrades its commercial value as a gemstone. Lastly, the fluorescence irradiation method analyses the fluorescence spectrum emitted from the pearl, but this is difficult to apply for pigmented or dyed pearls [4,5]. The shape and texture of imitation pearls, along with the development of production techniques, are not much different from the genuine ones. Therefore, we can say that the conventional distinction methods have limit in discriminating between genuine and imitation pearls. Recently, optical coherence tomography (OCT), which gives non-destructive three-dimensional tomographic images with micrometer level spatial resolutions [6,7], was used to evaluate pearls [8–10]. However, they offered only structural information, which was not enough to discriminate imitation from genuine pearls. Therefore, in order to distinguish between imitation and genuine pearls, we need to concentrate more on the inner structure of the pearls.

Pearls are composed of two major parts: the nacre and nucleus. The nacre is made of multiple layers of calcium carbonate (${\mathrm{CaCO}}_3$) and conchiolin [11,12], but the pearl nucleus is a foreign object. When the foreign substance enters inside of the shell, in general the nacre forms around the foreign body as a defense mechanism. On the other hand, imitation pearls, which copy the appearance of genuine ones, are created in factories rather than gathered or cultured from shells. Figures 1(a) and 1(b) are exterior photographs of South Sea and imitation pearls; they have very similar appearances. Figures 1(c) and 1(d) are cross-sectional images of the nacre parts that were scanned by a field emission scanning electron microscope (FE SEM, S-4700, Hitachi). We can see extreme differences in their internal structures. In general, the nacre of the South Sea pearl is composed of stacked micro-bricks of ${\mathrm{CaCO}}_3$ [13,14] 300–500 nm [15] in thickness, and the conchiolin acts as a cement among the brick-shaped ${\mathrm{CaCO}}_3$. Moreover, the nacre of a genuine pearl grows at different rates in different directions, so it has unique forms of optical birefringence. However, the nacre structures are not found in the imitation pearl, as in Fig. 1(d); there is just a single layer that may have artificial dye in it. Therefore, in the case of imitation pearls, the optical birefringence in the nacre region cannot be expected or is very small if it exists.

 

Fig. 1. (a) and (b) are exterior photographs of South Sea and imitation pearls, respectively. (c) and (d) are cross-sectional images of nacre parts scanned by a field emission scanning electron microscope (FE SEM) of the South Sea and the imitation pearls, respectively.

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In order to inspect the optical birefringence of pearls, polarization-sensitive OCT (PS-OCT) can be employed. PS-OCT can provide birefringence information such as the phase retardation in addition to the conventional intensity profile information [16–22]. This additional information is meaningful in evaluating pearls because the nacre of a genuine pearl is a birefringent material in general.

In this paper, we propose a simple and robust optical polarization-based method for discriminating between genuine and imitation pearls. We obtain the intensity and phase retardation images of several kinds of genuine and imitation pearls with a custom PS-OCT system. Since the nacre of a genuine pearl has unique birefringence, this can be easily distinguished by examining the birefringence properties. As a quantitative indicator for discriminating pearls, the phase retardation entropy is devised and adapted. Although the concept of entropy was introduced for use in the Jones matrix [23] and depolarization [24], our use of the concept of entropy for phase retardation is the first to our best knowledge. For the case of a birefringent material, the phase retardation entropy is calculated as higher than for an isotropic material. Based on these characteristics, we experimentally confirm that the phase retardation entropy can be a robust quantitative discrimination indicator between genuine and imitation pearls.

2. MEASUREMENT SETUP AND METHODS

A. Measurement Setup

The measurement setup is illustrated in Fig. 2, a custom PS-OCT system, whose technical details are described in previous works [22]. The swept-source laser (HSL-2000, Ver. 1.0, Santec) has a center wavelength of 1310 nm with a bandwidth of 110 nm. The repetition rate and the average output power are 20 kHz and 10 mW, respectively. The laser light is split with a 90:10 coupler after passing an optical circulator (C). The 10% portion is delivered to a fiber Bragg grating (FBG) for stable optical triggering [25], and the other 90% light is collimated by a collimator lens (CL) and then vertically polarized with a linear polarizer (LP). With a non-polarizing beam splitter (NPBS), the light is split into the sample and the reference arms with equal optical powers. In the sample arm, the vertically polarized light is changed to circularly polarized light by a quarter-wave plate 1 (QWP1) oriented at 45°, and then the backscattered light from the sample is returned to the NPBS through the QWP1. In the reference arm, the vertically polarized light is changed to 45° linearly polarized light after a round trip of QWP2, oriented at 22.5°, which gives the same power in the horizontal and vertical polarization directions. The lights returned from the sample arm and the reference arm are combined at the NPBS and make interference with each other. To analyze the interference signal, the recombined light is redivided with a polarizing beam splitter (PBS) into horizontal and vertical states. The two interference signals are detected by photoreceivers (PRs), and then captured by a dual-channel digitizer (PCI-5142, National Instruments) having a 14-bit resolution and a 100 MS/s sampling rate. The experimentally measured axial and lateral resolutions of the system were 8.8 μm and 29 μm in air, respectively.

 

Fig. 2. Schematic of the polarization sensitive optical coherence tomography (PS-OCT) system: PC, polarization controller; C, optical circulator; FBG, Fiber Bragg grating; PR, photo receiver; CL, collimator lens; LP, linear polarizer; PBS, polarizing beam splitter; NPBS, non-polarizing beam splitter; QWP, quarter-wave plate; L, objective lens; MRS, motorized rotation stage; AP, aperture; and M, mirror.

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B. Measurement Methods

The signal processing follows the common procedure of PS-OCT: background noise reduction, wavenumber linearization, dispersion compensation, windowing, zero padding, and fast Fourier transform. The spectral interferograms are acquired for both horizontal and vertical polarization states, and the relative phase retardation information of the sample is obtained by using the Jones calculus [16–22]. In general, the complex depth-resolved OCT signal is analytically expressed as

With the phase retardation information of Eq. (3), we devise and propose the phase retardation entropy, which statistically measures the degree of distribution [26] as

In our study, the phase retardation value is quantized by 256 ($2^8$) levels. Therefore, the entropy $E$ could have a value from 0 to 8 depending on the development of birefringence in the sample. Of course, the entropy can be normalized to have values from 0 to 1. The important thing is that if the sample has a well-developed birefringence, the entropy $E$ becomes maximized, 8 in this case. Conversely, if the sample has no or little birefringence, the phase retardation values are close to 0 for most of the pixels, and the entropy $E$ becomes diminished or very small. Therefore, it can be expected that the entropy value of a genuine pearl is higher than the one of an imitation pearl. However, when the tomogram is obtained with high noise, the phase retardation value is fully or randomly distributed from 0 to $\pi /2$, and the entropy $E$ approaches to the maximal value again. To avoid this ambiguity, the randomness of phase retardation is reduced by applying a moving average filter [27] along the lateral direction rather than the depth direction before taking the phase retardation histogram.

Several pearls have been characterized by using the PS-OCT system of Fig. 2; the reflected intensity image and the phase retardation image were extracted at the same time. Three types of genuine cultured pearls (South Sea pearl from Australia, Akoya pearl from Japan, and freshwater pearl from China) were imaged along with various imitation pearls received from Saehan Pearl, Republic of Korea. The B-scan of the OCT images was made by rotating the pearl with a motorized rotation stage. The size of each cross-sectional image for a single round rotation, from 0° to 360°, was about $2.75\mathrm{mm}\times 25\mathrm{mm}$ ($500\text{pixels}\times 2300\text{pixels}$, $\text{depth}\times \text{lateral}$). We collected the phase retardation histogram for the first 100 μm depth [28] of each pearl and calculated the phase retardation entropy by using Eq. (4). The examination thickness was chosen for the proper comparison with the imitation pearls.

3. EXPERIMENTAL RESULTS

Figure 3 shows the PS-OCT images of genuine cultured pearls: South Sea pearl [(a), (d)], Akoya pearl [(b), (e)], and freshwater pearl [(c), (f)]. From the intensity images in the left column [(a), (b), (c)], we can clearly see the boundary between the nacre and the pearl nucleus in the (a) South Sea and (b) Akoya pearls. But the (c) freshwater pearl does not show a clear boundary; instead, we can see some cracks in some deep regions. In general, freshwater pearls do not have manmade nuclei in them. In the right column for the phase retardation images [(d), (e), (f)], we can see that all the genuine cultured pearls have slowly varying phase retardation values ranging from 0 to $\pi /2$ in the depth direction.

 

Fig. 3. PS-OCT images of genuine cultured pearls: (a), (d) South Sea pearl; (b), (e) Akoya pearl; (c), (f) freshwater pearl. The left column [(a), (b), (c)] shows the intensity images, and the right column [(d), (e), (f)] shows the phase retardation images with a 0 to $\pi /2$ scale.

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Figure 4 shows the three imitation pearls; each was made by different techniques. The first one [IM1, (a), (d)] is a cheap imitation pearl made by painting a plastic ball with a synthetic dye. The second imitation pearl [IM2, (b), (e)] is made by using very thick paint that makes it look very close to authentic with naked eyes. The third imitation pearl [IM3, (c), (f)] is made by painting a plastic ball several times. In the intensity image, IM1 looks like a genuine pearl having a very thin nacre layer. The IM2 appears to be a freshwater pearl that consists of a thick nacre without a pearl nucleus. IM3 has multiple nacre layers, but it is not being found with genuine pearls. However, it is difficult to evaluate whether it is a genuine or imitation pearl with only the intensity images; it is just a qualitative, and not a quantitative, judgment. On the other hand, in the phase retardation images [(d), (e), (f)], none of the imitation pearls show appreciable phase variation in the depth direction. With the IM2 (e), we can see some foreign material that may be mixed with the coating dye. Although it is possible to distinguish genuine from imitation pearls with the phase retardation information, we have tried to quantify the difference by taking the phase retardation histogram and introducing the entropy of Eq. (4).

 

Fig. 4. PS-OCT images of various imitation pearls; (a), (d) first imitation pearl (IM1); (b), (e) second imitation pearl (IM2); and (c), (f) third imitation pearl (IM3). The left column [(a), (b), (c)] shows the intensity images, and the right column [(d), (e), (f)] shows the phase retardation images with a 0 to $\pi /2$ scale.

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Figure 5 is the phase retardation histogram of the above six pearls: (a) South Sea pearl, (b) Akoya pearl, (c) freshwater pearl, (d) IM1, (e) IM2, and (f) IM3. The phase retardation histograms of the genuine cultured pearls, Figs. 5(a)–5(c), show that the phase retardation is almost evenly distributed from 0 to $\pi /2$. However, those of the three imitation pearls, Figs. 5(d)–5(f), show that almost all data points are gathered near the 0 phase. To analyze more quantitatively, we calculated the phase retardation entropy $E$ and get: South Sea pearl 7.56, Akoya pearl 7.45, freshwater pearl 7.49, IM1 5.68, IM2 4.59, and IM3 5.29. The average entropy for the three genuine cultured pearls and the imitation pearls are 7.5 and 5.19, respectively. This shows that the phase retardation entropy in the nacre region can give a criterion for distinguishing between genuine and imitation pearls. In order to confirm this finding, we have calculated the phase retardation entropy of nine pearls for each type (total 36 pearls) and compared them in the box chart in Fig. 6. We can clearly see that the entropy of the genuine pearl is always higher than that of the imitation pearl. Interestingly, any phase retardation entropy of genuine pearls was not lower than 7.15, and any phase retardation entropy of imitation pearls was higher than 6.25; there was a gap of 0.9. From these measurements, the phase retardation entropy can be used as a proper quantitative criterion for discriminating genuine pearls. However, clearly distinguishing among genuine pearls from different species was not possible by using only the entropy measurement.

 

Fig. 5. Phase retardation histogram for the first 100 μm depth from the pearl surface. (a) South Sea pearl, (b) Akoya pearl, (c) freshwater pearl, (d) IM1, (e) IM2, (f) IM3.

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Fig. 6. Box chart of phase retardation entropy in nacre region; nine samples of South Sea (black), Akoya (red), freshwater (blue), and imitation (pink) pearls.

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4. CONCLUSION

We have presented a non-destructive method for discriminating genuine and imitation pearls by using PS-OCT. Conventional methods such as observing the appearance, causing friction, or measuring the fluorescence irradiation are not sufficient for accurate discrimination of pearls. To overcome the drawbacks of conventional methods, we have analyzed the polarization characteristics of pearls by using PS-OCT, which provided a reliable quantitative criterion for evaluating pearls. For our experiments, we have taken PS-OCT images of several kinds of genuine and imitation pearls and compared their intensity and phase retardation images. We confirmed that the nacres of all genuine pearls were birefringent. On the other hand, the imitation pearls did not show any birefringence. In the phase retardation image of an imitation pearl, we could see only limited values in the phase retardation and no appreciable variation along the depth. However, the phase retardation histograms of genuine pearls were well distributed from 0 to $\pi /2$. Therefore, by introducing the phase retardation entropy $E$, we could quantify the development of the birefringence in a pearl. Interestingly, the entropies of genuine pearls were not lower than 7.15 and the ones of imitation pearls were not higher than 6.25; there was a gap of 0.9. Therefore, the devised phase retardation entropy can be utilized as a criterion for distinguishing between genuine and imitation pearls. Although some imitation pearls can be distinguished by using conventional OCT only, it becomes more and more difficult with the development of the pearl-imitating process. Since the pearl-specific birefringence information is difficult to imitate, however, the quantitative distinction method will be considered as a valuable criterion continuously. However, the entropy by itself was not sufficient to distinguish genuine pearls of different kinds. For future works, we will focus attention on the local birefringence and optical axis variation for more accurate discrimination and evaluation of pearls.