PHASE CHANGE MATERIAL-BASED METASURFACE STRUCTURE AND RELATED METHOD

Abstract

A metasurface structure including an array of sub-wavelength structures including a phase change material (PCM), encoded with different holographic images based on different phases of the PCM, the different phases including a first phase and a second phase. Phase transition between the first phase and the second phase occurs when the metasurface structure is thermally tuned. Each sub-wavelength structure in the array has a distinctive phase difference between the first phase and the second phase of the PCM.

Claims

1. A metasurface structure comprising: an array of sub-wavelength structures including a phase change material (PCM), encoded with different holographic images based on different phases of the PCM, the different phases including a first phase and a second phase, wherein phase transition between the first phase and the second phase occurs when the metasurface structure is thermally tuned, and wherein each sub-wavelength structure in the array has a distinctive phase difference between the first phase and the second phase of the PCM.

2. The metasurface structure of claim 1, wherein the different holographic images comprise a first holographic image displayed in the first phase and a second holographic image displayed in the second phase.

3. The metasurface structure of claim 1, wherein the phase change material comprises vanadium dioxide (VO.sub.2).

4. The metasurface structure of claim 1, wherein the metasurface structure is optically excited by visible radiation.

5. The metasurface structure of claim 4, wherein the visible radiation has a wavelength which ranges between 600 nm to 800 nm.

6. The metasurface structure of claim 1, wherein the array of sub-wavelength structures comprises a plurality of sub-wavelength micro-structures or nano-structures.

7. The metasurface structure of claim 1, wherein the array of sub-wavelength structures is in the form of nano-blocks having a height, a length and a width.

8. The metasurface structure of claim 7, wherein dimensions and/or rotation states of the array of the nano-blocks are optimized based on a meta-atom library.

9. The metasurface structure of claim 8, wherein the array of the nano-blocks comprises four types of nano-blocks which are selected to have distinctive phase differences between two phases of the PCM and high cross-polarized light transmittance.

10. The metasurface structure of claim 9, wherein the four nano-blocks are different in terms of at least one of their rotation states and dimensions.

11. A method for encoding information on a metasurface structure including an array of sub-wavelength structures, comprising: selecting the array of sub-wavelength structures including a phase change material (PCM) such that each sub-wavelength structure in the array has a distinctive phase difference between a first phase and a second phase of the PCM; and encoding at least two different holographic images into the array of sub-wavelength structures based on the first phase and the second phase of the PCM, wherein the first phase and the second phase are different.

12. The method of claim 11, wherein selecting the array of sub-wavelength structures comprises: selecting dimensions and/or rotation states of respective sub-wavelength structures in the array.

13. The method of claim 11, further comprising: constructing a meta-atom library to show cross-polarized light transmittance and phase shift at different temperatures as a function of dimensions of the array of sub-wavelength structures.

14. The method of claim 13, wherein selecting the array of sub-wavelength structures comprises selecting, from the meta-atom library, four nano-blocks with distinctive phase differences and high cross-polarized light transmittance.

15. The method of claim 11, wherein the array of sub-wavelength structures is in the form of nano-blocks having a height, a length and a width.

16. The method of claim 15, wherein selecting the array of sub-wavelength structures comprises: selecting all nano-blocks with cross-polarized light transmittance higher than an allowed minimum of transmittance T.sub.min and not exceeding an allowed maximum of transmittance T.sub.max at an arbitrary wavelength in the range of 600 nm to 800 nm; comparing every two nano-blocks selected from the previous selecting step, and finding pairs with phase differences between .sub.max and .sub.max at a first temperature and .sub.max and +.sub.max at a second temperature at one wavelength where .sub.max is an allowed maximum error in phase differences; obtaining pairs of nano-blocks satisfying the state transitions of 0 to 0 and 0 to ; and exchanging the nano-block's length and width of the selected pair of nano-blocks to obtain another pair satisfying to and to 0 state transitions.

17. The method of claim 16, wherein the first temperature is a room temperature (RT) and the second temperature is a temperature higher than the room temperature (HT).

18. The method of claim 11, wherein encoding the at least two different holographic images is based on a gradient descent-based iterative approach.

19. The method of claim 18, wherein the gradient descent-based iterative approach is based on a machine learning model comprising three layers of an input layer, a hidden layer, and an output layer, corresponding to an incident light, a diffraction plane, and an image plane, respectively.

20. The method of claim 18, wherein encoding the at least two different holographic images based on the gradient descent-based iterative approach comprises: calculating two binary-phase holographic images based on the gradient descent-based iterative approach; and encoding the two holographic images into the two different phases of the PCM at two temperatures.

21. The method of claim 11, wherein encoding the at least two different holographic images comprises applying additional work conditions including wavelength, polarization, and/or observation distance.

22. The method of claim 21, wherein different observation distances and/or different polarizations are assigned for respective holographic images in addition to the different temperatures.

23. The method of claim 11, wherein the phase change material (PCM) comprises vanadium dioxide (VO.sub.2).

24. The method of claim 11, wherein the at least two different holographic images are generated when the metasurface structure is optically excited by visible radiation.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0032] Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings, in which:

[0033] FIG. 1 is a graph showing real part (n) and imaginary part (k) of the complex refractive index of VO.sub.2 as a function of wavelengths and temperatures. The shaded area indicates the wavelength range of interest, where |n.sub.1n.sub.2| is relatively large and k.sub.1 and k.sub.2 are close to zero.

[0034] FIGS. 2a and 2b show schematic diagrams of a thermally tunable VO.sub.2 metasurface holography: FIG. 2a shows example holographic images generated by the holographic metasurface when optically excited at room temperature (30 C.); and FIG. 2b shows example holographic images generated by the holographic metasurface when optically excited at high temperature (90 C.), respectively. The grayscales in FIGS. 2a and 2b indicate the phase profiles at different temperatures.

[0035] FIG. 3 shows an example meta-atom library (taking =620 nm and 800 nm as an example): the cross-polarized light transmittance and phase shift at RT and HT as a function of W and L.

[0036] FIG. 4 shows holographic images with varying phase imprecision from 0 to . Peak signal-to-noise ratios (PSNRs) of the images, 11.53 dB (a), 11.06 dB (b), 9.86 dB (c), 8.43 dB (d), 7.22 dB (e), 6.44 dB (f), and 6.18 dB (g).

[0037] FIG. 5 shows holographic images with varying transmittance differences from 1:1 to 1:0. PSNRs of the images, 11.53 dB (a), 9.51 dB (b), 8.40 dB (c), and 7.99 dB (d). One can see that transmittance differences have a lower impact on image quality than phase imprecision.

[0038] FIG. 6a shows example building blocks of the four nano-blocks according to an embodiment of the invention, and FIG. 6b shows their states at RT and HT.

[0039] FIG. 7a shows an example structure of a machine learning model for hologram calculation according to an embodiment of the invention, and FIG. 7b shows an example flowchart of the machine learning model.

[0040] FIGS. 8a and 8b show binary images of the older version and the latest version of the CityU logo, respectively. FIGS. 8c and 8d present the phase profiles of the holograms at RT and HT, respectively. FIGS. 8e and 8f show details of the phase profiles under the illumination with proper chirality (top panels) and opposite chirality (bottom panels). FIGS. 8g-8j show holographic images under differently chiral illumination with PSNRs=11.38 dB (8g), 12.16 dB (8h), 7.12 dB (8i), and 8.29 dB (8j). Circle arrows spinning clockwise and counterclockwise represent RCP and LCP illumination, respectively, and d represents observation distance.

[0041] Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of embodiment and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting.

DETAILED DESCRIPTION

[0042] The embodiments of the invention are related to a tunable holographic metasurface based on phase change materials (PCMs). Specifically, the phase transition of PCMs leads to significant changes in their optical properties, allowing different holographic information to be encoded in different phases. Consequently, dynamically switching between different phases can provide dynamic images. On the other hand, the external conditions for phase transition and holographic display can be regarded as multiple keys for information encryption and decryption. The approach to the design of tunable holographic metasurfaces follows two steps: First, optimize four phase-changeable nano-blocks in morphology to fulfill the four optical phase shift transitions, i.e., 0 to 0, 0 to , to 0, and to ; second, encode two independent binary-phase holograms into the phase profiles in two different phases of the material based on the optimized nano-blocks. Overall, the embodiments of the invention offer a general way of tunable metasurface holography, which has broad prospects in dynamic display and information encryption.

[0043] According to an embodiment of the invention, vanadium dioxide (VO.sub.2) is chosen as the PCM. VO.sub.2, a volatile temperature-sensitive PCM, has been demonstrated to exhibit reversible insulator-to-metal phase transition around 68 C. with significant changes in optical properties [34], leading to various applications of VO.sub.2 metasurfaces in color generation [35], polarization control [36, 37], perfect absorption [38], etc. VO.sub.2 exhibits reversible insulator-to-metal phase transition around 68 C. with significant changes in its refractive index across the visible and infrared spectrum (FIG. 1). FIG. 1 shows real part (n) and imaginary part (k) of the complex refractive index of VO.sub.2 as a function of wavelengths and temperatures. The shaded area indicates the wavelength range of interest, where |n.sub.1n.sub.2| is relatively large and k.sub.1 and k.sub.2 are close to zero. To build a tunable holographic metasurface containing two independent binary-phase (0, ) profiles, four types of constituent nano-blocks with distinctive phase differences (0 to 0, 0 to , to 0, and to ) and high cross-polarized light transmittance should be selected from a VO.sub.2 meta-atom library. Here, the high cross-polarized light transmittance may refer to the cross-polarized light transmittance of 5% or more. In the full-wave finite-element-method simulations for building such a meta-atom library, periodic VO.sub.2 nano-blocks with a fixed period (P=400 nm) and height (H=600 nm) and varying widths and lengths (W, L from 50 nm to 350 nm) are illuminated by circularly polarized light at 30 C. (room temperature, RT) and 90 C. (high temperature, HT), respectively. The incident wavelength ranges from 600 nm and to 800 nm, where VO.sub.2 has sufficiently large refractive index differences between RT and HT and relatively low extinction coefficients.

[0044] VO.sub.2 nano-blocks are patterned to realize a thermally tunable transmissive holographic metasurface working at 620 nm, where the refractive index difference between 30 C. and 90 C. allows sufficient change in propagation phase, and the extinction coefficients remain low (FIG. 1). A gradient descent-based iterative approach is developed to calculate two binary-phase (0, ) holograms separately, which are then encoded into the two different phases of the VO.sub.2 metasurface. The nano-blocks are elaborately optimized in morphology to fulfill all possible state transitions, i.e., 0 to 0, 0 to , to 0, and to , under thermal regulation. The proposed design approach can be promisingly adopted in a broad range of tunable device designs, such as optical data processors, LiDAR, anti-counterfeit packaging, etc.

Method

Design of Nano-Blocks

[0045] The functionality of the thermally tunable VO.sub.2 metasurface is illustrated in FIGS. 2a and 2b: The older CityU logo appears when the metasurface is optically excited at room temperature (RT, 30 C.), while when it operates at high temperature (HT, 90 C.), the latest CityU logo is displayed. To build such a tunable holographic metasurface containing two independent binary-phase (0, ) profiles, four sets of constituent nano-blocks should be specially engineered to fulfill the four possible state transitions, i.e., 0 to 0, 0 to , to 0, and to . Taking the amplitude into consideration, there is a combination of 10 parameters (T.sub.RT (i), .sub.RT (i), T.sub.HT (i), .sub.HT (i), .sub.RT (i).sub.RT (j), .sub.HT (i).sub.HT (j)) to investigate for one single nano-block, where T.sub.R(H)T and P.sub.R(H)T are the transmittance and phase shift of cross-polarized light at R(H)T, respectively, and i, j=1, 2, 3, or 4 (i<j). This will be further described with reference to Tables 2 and 3 and the relevant discussion below.

[0046] For this purpose, a VO.sub.2 meta-atom library is constructed, from which four sets of nano-blocks with distinctive phase differences and high cross-polarized light transmittance can be selected. Full-wave finite-element-method simulations are performed with COMSOL Multiphysics 5.5, where periodic VO.sub.2 nano-blocks with a fixed period (P=400 nm) and height (H=600 nm) and varying widths and lengths (W, L from 50 nm to 350 nm) are illuminated by circularly polarized light at 30 C. and 90 C., respectively. The incident wavelength ranges from 600 nm to 800 nm, where VO.sub.2 has sufficiently large refractive index differences between RT and HT and relatively low extinction coefficients [34]. The structure-dependent transmittance and phase shift of nano-blocks at 620 nm and 800 nm are shown as an example in FIG. 3.

[0047] Based on the simulation results, it is found that the nano-blocks with high conversion efficiency always exhibit limited phase shift changes between RT and HT. This indicates an unavoidable trade-off between high transmittance and high precision in phase differences. Further study of imprecision in phase difference and transmittance imbalance reveals that the former has a greater impact on holographic images than the latter (FIGS. 4 and 5). On the other hand, it is well known that the Pancharatnam-Berry (PB) phase of a rotated nano-block .sub.PB=2 changes in sign with the reversal of incident light's chirality [39]. Therefore, the phase imprecision can be compensated by rotating the orientation of the nano-blocks by =|0.5| and reversing the circularity of incident light at HT, if the phase shift of nano-blocks without rotation remains constant in value while changes its sign when transitioning from RT to HT. The optical properties and the schematic of the building blocks of the four selected nano-blocks are shown in Table 1 and FIGS. 6a and 6b, respectively. FIG. 6a shows building blocks of the four nano-blocks, and FIG. 6b shows their states at RT and HT.

TABLE-US-00001 TABLE 1 Selected nano-blocks with the required phase differences and high cross- polarized light transmittance. T, transmittance; , phase shift; and 2, additional PB phase. In our case, = 0.35, = 0.175, 2 at RT and +2 at HT for illumination with the proper chirality, and +2 at RT and 2 at HT for the opposite chirality. = 620 nm W (nm) L (nm) T.sub.RT (%) .sub.RT (rad) T.sub.HT (%) .sub.HT (rad) Type 50 220 19.6 0.35 (2) 5.9 0.35 (2) 0 .Math. 0 220 110 10.2 0 6.1 0 .Math. 220 50 19.6 1.35 (2) 5.9 0.65 (2) .Math. 110 220 10.2 6.1 0 .Math. 0

[0048] The method of selecting nano-blocks with required phase differences and high cross-polarized light transmittance from the VO.sub.2 meta-atom library is shown in Table 2, which follows two steps: 1) Select all nano-blocks with cross-polarized light transmittance higher than T.sub.min and not exceeding T.sub.max at an arbitrary wavelength in the range of 600 nm to 800 nm; 2) compare every two nano-blocks selected from step 1, then find the pairs with phase differences between .sub.max and .sub.max at RT and .sub.max and +.sub.max at HT at a specific wavelength (i.e., one wavelength, in other words, the phase differences should be compared under the same wavelength). After the above process, several pairs of nano-blocks satisfying the state transitions of 0 to 0 and 0 to are obtained (Output of Method in Table 3). To minimize the impact of the imperfections in phase differences and transmittance, |.sub.HT (i).sub.HT (j)|=|.sub.RT (i).sub.RT (j)| (=2), T.sub.RT (i)T.sub.RT (j), and T.sub.HT (i)T.sub.HT (j) are prioritized in determining the optimal pair. Finally, exchanging the nanoblock's length and width of the selected pair of nano-blocks obtains another pair satisfying to and to 0 state transitions, which complies with the principle of geometric phase (Final result in Table 3). The output of the Method with T.sub.min=0.059, T.sub.max=0.215, and .sub.max=0.35 (rad/) and the final result are listed in Table 3.

TABLE-US-00002 TABLE 2 Method of selecting nano-blocks from the meta-atom library. Method: Selecting nano-blocks from the meta-atom library Input: MAL (, W, L, T.sub.RT, .sub.RT, T.sub.HT, .sub.HT) - Meta-atom library; T.sub.min - Allowed minimum of transmittance; T.sub.max - Allowed maximum of transmittance; .sub.max - Allowed maximum error in phase differences (rad/T). Initialization: n - Number of wavelengths number of nano-blocks; Set temp to empty list; Set result to empty list. Output: Pairs of nano-blocks with required phase differences and transmittance. for i = 1 : 1 : n if (T.sub.RT (i) T.sub.min) and (T.sub.RT (i) T.sub.max) and (T.sub.HT (i) T.sub.min) and (T.sub.HT (i) T.sub.max) then temp = [temp; MAL (i)] end if end for for j = 1 : 1 : size (temp,1) for k = i + 1 : 1 : size (temp,1) if ( (j) = (k)) and ((|.sub.RT (j) .sub.RT (k)| .sub.max) or (|.sub.RT (j) .sub.RT (k)| 2 .sub.max)) and ((|.sub.HT(j) .sub.HT (k)| 1+ .sub.max) and (|.sub.HT (j) .sub.HT (k)| 1 .sub.max)) then result = [result, temp (j), temp (k)] end if end for end for return result

TABLE-US-00003 TABLE 3 Pairs of nano-blocks selected by Method with T.sub.min = 0.059, T.sub.max = 0.215, and .sub.max = 0.35 (rad/) and the final result. Two phase values of 0.59 and 0.02 are added to the phase of the selected nano-blocks at RT and HT, respectively, as the anormal refraction dictated by the generalized Snell's law is determined by phase gradients rather than absolute phase values. Output of Method: W L T.sub.RT .sub.RT T.sub.HT .sub.HT (nm) (nm) (nm) (%) (rad/) (%) (rad/) Type 620 50 220 19.6 0.24 5.9 0.33 0 .Math. 0 620 220 110 10.2 0.59 6.1 0.98 0 .Math. 630 70 210 20.5 0.17 6.0 0.32 0 .Math. 0 630 250 120 6.6 0.47 5.9 0.97 0 .Math. 640 70 220 21.2 0.24 6.0 0.38 0 .Math. 0 {close oversize brace} Not selected 640 260 120 7.3 0.57 6.1 0.94 0 .Math. Final result: W L T.sub.RT .sub.RT + 0.59 T.sub.HT .sub.HT 0.02 (nm) (nm) (nm) (%) (rad/) (%) (rad/) Type 620 50 220 19.6 0.35 5.9 0.35 0 .Math. 0 620 220 110 10.2 0 6.1 1 0 .Math. 620 220 50 19.6 1.35 5.9 0.65 .Math. * 620 110 220 10.2 1 6.1 0 .Math. 0 * The phase shift changes by when W and L are exchanged.

Calculation of Binary-Phase Holograms

[0049] Images from binary holograms usually suffer from poor quality due to binarization. Here, the binary-phase holograms with 0 and phases are calculated by a gradient descent-based iterative approach. FIGS. 7a and 7b show the structure (FIG. 7a) and flowchart (FIG. 7b) of the machine learning model (i.e., the gradient descent-based iterative approach for hologram calculation) are shown in FIGS. 7a and 7b. SIGN is the sign function in FIG. 7b. The model consists of three layers with the size 10001000: an input layer, a hidden layer, and an output layer, corresponding to an incident light, a diffraction plane, and an image plane, respectively. An all-ones matrix representing plane waves serves as the input. Initialized random complex amplitude (real numbers in the range of 1 to 1, where represents a phase delay) is updated by Adam Optimizer (a conventional stochastic gradient descent optimization algorithm) with a learning rate 0.01 combined with the mean squared error (MSE) loss function. The forward propagation is based on the Fresnel diffraction theory

[00001]$\begin{array}{cc}I\left(x,y\right)={.Math.F^{-1}\left\{F\left\{u_0\left(x_0,y_0\right)\right\}H\left(f_x,f_y\right)\right\}.Math.}^2,& \left(1a\right)\end{array}$$\begin{array}{cc}H\left(f_x,f_y\right)=e^{\mathrm{ikz}\left[1-\frac{{}^2}{2}\left(f_x^2+f_y^2\right)\right]},& \left(1b\right)\end{array}$

where F and F.sup.1 represent the Fourier transform and inverse Fourier transform, respectively; x, y, and z are the spatial coordinates; x.sub.0 and y.sub.0 are the spatial coordinates in the diffraction plane; f.sub.x and f.sub.y are the spatial frequencies; and u.sub.0, I, H, , and k=2/ are the complex amplitude of the source field, intensity of the diffraction field at z, transfer function of Fresnel diffraction, wavelength, and wavenumber respectively. The MSE loss value evaluating the difference between the output and the target image converges to 0 after 250 epochs of training. The resultant binary phase profile is taken from the complex amplitude obtained in the last epoch by the sign function. Instead of binarizing the retrieved phase during each iterative process in the GS algorithm [24], the phase profiles in the iterative process are always binary, resulting in less loss of quality.

Results

[0050] The behavior of the phase change VO.sub.2 metasurface under different temperature conditions is illustrated in FIGS. 2a and 2b: Image 1 (the older CityU logo) appears when the metasurface is optically excited at RT as shown in FIG. 2a, while when it operates at HT, Image 2 (the latest CityU logo) is displayed as shown in FIG. 2b. FIGS. 8a and 8b show binary images of the older version and the latest version of the CityU logo, respectively. FIGS. 8c and 8d present the phase profiles of the metasurface hologram with 10001000 pixels at RT and HT, respectively. The reconstructed images at 620 nm are displayed in FIGS. 8g-8j, all of which are calculated by the Fresnel diffraction integral with concrete optical properties of the nano-blocks listed in Table 1. To avoid holographic image crosstalk, different observation distances of 1.2 mm and 0.8 mm are purposely assigned to the holograms at RT and HT, respectively. FIGS. 8e and 8f show details of the phase profiles under the illumination with proper chirality (top panels) and opposite chirality (bottom panels). Under the illumination with proper chirality (left-handed circular polarization (LCP) at RT and right-handed circular polarization (RCP) at HT), the holograms have the correct binary-phase distribution (top panels of FIGS. 8e and 8f), and targeted images are reconstructed with sharp edges and high peak signal-to-noise ratios (PSNRs), as shown in FIGS. 8g and 8h. FIGS. 8g to 8j show holographic images under differently chiral illumination with PSNRs=11.38 dB (FIG. 8g), 12.16 dB (FIG. 8h), 7.12 dB (FIG. 8i), and 8.29 dB (FIG. 8j). Here, circle arrows spinning clockwise and counterclockwise represent RCP and LCP illumination, respectively, and d represents observation distance. It should be noted that the larger transmittance imbalance between nano-blocks at RT results in the brighter background of FIG. 8g as compared to FIG. 8h. On the contrary, incident waves with opposite handedness double the phase imprecision (as revealed by the bottom panels in FIGS. 8e and 8f), thus reconstructing images with lower PSNRs and intensity (FIGS. 8i and 8j). As a consequence, all the parameters for generating the holographic images, including the wavelength, polarization, observation distance, and temperature, can be regarded as multiple keys for information encryption and decryption.

CONCLUSION

[0051] The quality of holographic images generated by spatial light modulators (SLMs) can be degraded due to modulation errors, high-order diffraction, and narrow viewing angles. Metasurfaces are capable of generating high-quality and large-viewing-angle holographic images without unwanted diffraction orders. Recent developments show that PCMs such as germanium antimony tellurium (GST) and VO.sub.2 have been studied for their tunability in metasurface holography. For example, in references [42,43], rewriting refractive index profiles on GST films always involves femtosecond laser scanning, making real-time dynamic display difficult to achieve. Reference proposes a metasurface composed by three-level switchable aluminum and GST stacked nano-blocks; however, only one encrypted holographic image is demonstrated. VO.sub.2 integrated split-ring resonators in reference are difficult to work in the visible and infrared region due to their large size.

[0052] The embodiments of the invention present a general approach to the design of thermally tunable VO.sub.2 metasurfaces. The phase transition characteristics of VO.sub.2 and the elaborately chosen and rotated nano-blocks enable the phase profile of VO.sub.2 metasurfaces to be switchable between two arbitrary binary phase profiles by thermal tuning. As a proof of concept, two binary-phase holograms calculated by a gradient descent-based iterative approach are encoded into the phase profiles of the VO.sub.2 metasurface at two temperatures. More degrees of freedom could be further exploited with multi-level phase difference switching. The proposed design approach could also be used with other actively tunable materials, e.g., germanium antimony tellurium, liquid crystals, or graphene. The proposed design can be used for dynamic display, optical processing, LiDAR, and information encryption/decryption.

[0053] It will be appreciated by a person skilled in the art that variations and/or modifications may be made to the described and/or illustrated embodiments of the invention to provide other embodiments of the invention. The described/or illustrated embodiments of the invention should therefore be considered in all respects as illustrative, not restrictive. Example optional features of some embodiments of the invention are provided in the summary and the description. Some embodiments of the invention may include one or more of these optional features (some of which are not specifically illustrated in the drawings). Some embodiments of the invention may lack one or more of these optional features (some of which are not specifically illustrated in the drawings). While some embodiments relate to human point clouds, it should be appreciated that methods/framework of the invention can be applied to other point clouds (not limited to human point clouds).

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