Multi-dimensional optical imaging systems exploit different degrees of freedom of scattering photons from an object scene, such as polarization, depth, and spectrum, to reveal different information [1–3]. For instance, spectral characteristics reflect the elemental composition, while the polarimetric characteristics contain the surface’s roughness and conductance . The information can be helpful for object inspection and classification in remote sensing and industry applications. However, most existing approaches require mechanical moving parts or multiple modulation processes (e.g., polarizers of different orientations, diffractive gratings, or spectrum filters), which leads to long acquisition time, large volume size, high system complexity, or low sampling resolution.
In recent years, lensless imaging systems have gradually unfolded their advantages compared with traditional lens-based imaging systems. Unlike the point-to-point imaging manner in the latter systems, lensless imaging systems, acting as new paradigms in imaging, are replacing the conventional lenses with encoding masks and directly recording the coded pattern of an object on the sensor. Then after the post-process reconstruction, the information of the object can be recovered. Benefiting from this typical architecture, lensless imaging systems are usually more flexible, light weight, and with less cost than traditional lens-based imaging systems. It has been demonstrated that lensless imaging systems can be used in super-resolution imaging [5,6], three-dimensional imaging [7,8], multispectral  and hyperspectral imaging , and so on. Diffuser-based scattering imaging has drawn attention since much optical field information can be retrieved during the scattering process. However, there will be a random speckle in the transmittance of conventional diffusers , and their optical properties may be unstable with time , which makes the scattering effect of the conventional diffuser unpredictable and unrepeatable. Therefore, the time-consuming and tedious characterizations are unavoidable before utilization. Furthermore, due to the limited optical field engineering ability, it is also a great challenge to realize multiple-dimensional imaging for conventional lensless imaging systems owing to the wavelength and polarization insensitivity.
Digital optics could play an important role to conquer these challenges. Digital optics is a new concept that leverages discrete micro-/nano-optical elements to realize optical field manipulation with higher flexibility and resolution. As a core of digital optics, metasurfaces are planar devices comprising arrays of subwavelength meta-atoms. By locally tailoring the geometries of each meta-atom, the metasurface can manipulate the phase, amplitude, and polarization at will [13–24]. The metasurface-based devices have been successfully demonstrated and utilized in numerous applications, e.g., light-field imaging , depth sensing , planar synthetic aperture , polarization detection and imaging [27,28], multispectral imaging , and wide field-of-view imaging and detection [18,30]. The concept of the metasurface diffuser has been well established lately to achieve high-resolution bio-imaging  and complex optical field imaging . Compared with the conventional diffuser, the predesigned metasurface diffuser significantly simplifies the characterization procedure and shows stable and reliable optical properties. More importantly, by exploiting sensitivities of wavelength and polarization at subwavelength scales, the metasurface has the potential to realize multi-dimensional imaging . Nevertheless, preparing the metasurfaces comprising great nano-pillars or nano-holes is facing enormous challenges, especially in large-area manufacturing. Alternatively, a common and straightforward approach is to develop the geometric phase elements with controllable liquid crystal (LC) orientations [34–38]. On the one hand, the gradual maturity of LC production lines provides low-cost and large-scale production. On the other hand, compared to conventional diffraction optical elements, LCs also revealed unparalleled superiority in terms of operation efficiency, processing difficulty , and wavelength-polarization sensitivity.
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In this paper, we propose and demonstrate the concept of multi-dimensional computational imaging (MCI) by combining the principles of both lensless computational imaging and metasurface optics. A flat LC-based diffuser fabricated through a standard photoalignment technology and a digital micro-mirror device (DMD) is used to encode spatial–spectral–polarization five-dimensional (5D) object information. The generated point spread functions (PSFs) exhibit linear translation invariance within the memory effect range, which promises the post-processing algorithm to recover two-dimensional information on the plane. The variation of depth along the axis will result in phase delays, leading to different PSFs with low correlation, which makes depth information able to be retrieved. Owing to the spin-reversed wavefront coding and dispersive diffraction character of the LC-based geometric phase diffuser, PSFs among different chirality and wavelength are highly irrelevant, benefiting to reveal polarization and spectrum information. Therefore, MCI can be easily achieved by the conventional deconvolution technique. Our proposal has been demonstrated in the visible band, with the merits of snapshot acquisition, multi-dimensional perception ability, simple optical configuration, compact device size, and high fabrication efficiency.
2. PRINCIPLE AND METHODS
A. Geometric Phase and LC Metasurface Diffuser Design
The designed metasurface diffuser is composed of anisotropic liquid crystal molecules (LCMs), based on the Pancharatnam–Berry (PB) phase [40,41], which is also called the geometric phase. The transmission property of the LCMs with a fast axis and slow axis along the and directions can be calculated with the Jones matrix, which can be written as
For circularly polarized (CP) incidence, the output field after passing through the LCMs can be calculated as
Based on the PB phase, we designed an LC metasurface diffuser with a random phase distribution due to the random wavefront achieving better-reconstructed results and showing more sensitivity to multi-dimensional information during the post-processing algorithm (see Appendix A for details). The designed phase profile was discretized into a four-order phase (i.e., 0, , , ), which is enough for the spin-reversed wavefront coding. Figure 1(a) shows the designed phase profile of the LC metasurface diffuser, 10.3 mm long and 5.8 mm wide. Figures 1(b) and 1(c) indicate the local phase distribution with four-order phase and the LCMs with four different orientations correspondingly. The LC metasurface diffuser was then fabricated through a DMD-based photoalignment technology. The polarized optical microscope (POM) image of the metasurface diffuser is shown in Fig. 1(d), and Fig. 1(e) shows the local magnification images of Fig. 1(d) under different polarization states.
Figure 1.Design of LC metasurface diffuser. (a) Designed phase distribution of the LC metasurface diffuser. (b) Local phase distribution of the LC metasurface diffuser with the four-order phase. (c) The four LCMs with different rotation angles corresponding to the four-order phase distribution. (d) The POM image of the metasurface diffuser. (e) The local magnification POM images under different polarization states, and the blue and red arrows denote the input and output polarization states of light.
B. Multiple-Dimensional PSFs through a Single Diffuser
The functionalities and performances of an imaging system can be quantified by calculating its PSF. Our crucial intuition is to build a diffuser whose PSFs change with chirality, wavelengths, and position so that the associated information can be recorded into a snapshot speckle, and the polarization, spectral, and spatial information can be recovered through the conventional deconvolution technique, shown in Fig. 2. Suppose an object point is at a distance of from the diffuser. The optical field passes through the diffuser resulting in phase changes. Subsequently, the field propagates to the sensor at the distance , resulting in the PSF , which is the squared magnitude of the complex wave field at the sensor plane :
Figure 2.Schematic of the spatial–spectral–polarization meta-optical imaging system. (a) Light from two multispectral objects with different spatial and polarization (left, left-circularly polarized; right, right-circularly polarized) information propagating through the designed LC metasurface diffuser generates a speckle pattern on a monochromatic camera. (b) Speckle patterns produced by two-point objects with respective spatial and polarization information of the two multi-dimensional objects, taken as corresponding multi-dimensional PSFs. (c) Reconstructed multi-dimensional images from the monochromatic speckle images using corresponding PSFs. (d) The recovered image of the two objects by superimposing individual reconstructed images.
C. Image Formation and Recovery
Our Snapshot 5D Imaging system is mainly based on Fresnel diffraction and Fourier optics , and for an incoherent imaging system, it is described as
The speckle pattern with all the spatial distribution, wavelength, and chirality information of the object is the composite response of the LC metasurface diffuser. It can be expressed as
Therefore, the object with interesting spatial–spectral–polarization information can be reconstructed from the image overlapping diverse factors by deconvoluting PSF with respect 5D property as follows:
D. Deconvolution Algorithm
We use Wiener deconvolution for image reconstruction, and it is expressed as follows :
A. Spatial Resolution
As an imaging system, the spatial resolution of MCI is measured first. The setup of MCI is shown in Fig. 3(a). A projector (Acer X118H) is used to generate object patterns. The magnification lens of the projector is removed, and an iris is set to filter out background light from the projector. The LC metasurface diffuser then modulates the light that comes from the projector, and a monochromatic camera (Daheng, MER-500-7UM) is used to capture the intensity profile. The exposure time to capture PSFs was set to 80 ms, and that to capture objects was set to 16 ms. The distance from the object patterns to the metasurface is 15 cm, and the camera is placed 2 cm behind the metasurface. To decide the resolution of this system, resolution chart patterns with different gaps, shown in Fig. 3(c), are loaded on the center area of the projector. The recovered images and their profiles are shown in Fig. 3(d), illustrating that the spatial resolution of this system is around 28 μm, as the peak–valley ratio is about 1.52 at this scale. The deconvolution algorithm takes 0.43 s to reconstruct information from the PSF and the corresponding speckle pattern pair. The axial resolution and spectral resolution are discussed in Appendix A, and more experimental results are exhibited in Appendix C.
Figure 3.Spatial resolution of the MCI system. (a) Schematic diagram of the experimental setup. (b) The diagonal length of the DMD chip used in the projector is 0.55 in., and the pixel size is 14 μm. (c) The resolution chart loaded on the projector and the recovered images. The gaps of each line are 1, 2, and 3 pixels, respectively. (d) Intensity profile of lines in (c). Scale bar: 50 μm in (c).
B. Multispectral Imaging
The same setup shown in Fig. 3(a) is used to generate object patterns for multispectral imaging of MCI. By loading different patterns with different RGB values, objects’ spatial and spectral information could be changed conveniently. In practice, seven different capital letters with different colors are projected respectively. The speckle patterns captured by the camera are shown in Fig. 4(a) (Pseudocolore is applied for convenient exhibition). Then, a single central pixel with the aforesaid colors is lightened up respectively, and the captured speckles are taken as multispectral PSFs of MCI, as shown in Fig. 4(b). The reconstructed multispectral images are finally obtained by deconvolving different spectral PSFs with different speckle patterns, exhibited in Fig. 4(c). The ground truth patterns loaded on the projector are shown in Fig. 4(d). As expected, each speckle pattern is smoothly reconstructed. Figure 4(e) demonstrates the composite multispectral image superimposing with seven individual spectral images of Fig. 4(c).
Figure 4.Schematic of MCI’s multispectral imaging. (a) The raw speckle patterns generated by different chromatic objects. (b) The PSFs generated by a central point object with corresponding colors. (c) The images reconstructed from the speckle patterns using corresponding PSFs. (d) The ground truth pictures projected on the projector, which are projected respectively. (e) The full reconstructed image by superimposing seven individual spectral images in (c). Scale bar: 1000 μm in speckle patterns and PSFs, and 100 μm in reconstructed images.
C. Polarization Imaging
For verifying the polarization selective ability of MCI, we leverage the setup shown in Figs. 5(a) and 5(b). Different from the setup in Fig. 3, two pairs of the polarizer and the quarter-wave plate were employed. The first pair of the polarizer and quarter-wave plate translates the incident light into CP light. By rotating the quarter-wave plate, LCP light or RCP light can be generated. Then the CP light transmits through the metasurface diffuser and converts incident CP light to the opposite chirality. The LC metasurface diffuser can obtain a high polarization conversion efficiency () at the designed wavelength, which is about 532 nm, but the efficiency will decrease away from that wavelength. So the second pair of the polarizer and the quarter-wave plate is applied to filter out the co-polarized light remaining in transmitted light. In the experiment, two letters, “H” and “E,” with the same color, were loaded on the projector. Figure 5(c) shows the raw speckle patterns captured by the camera. The rotation arrows in the upper left indicate the polarization of each pattern (blue for RCP, red for LCP). Figure 5(d) shows the PSFs with different polarizations. Figures 5(e) and 5(f) show the reconstructed images by deconvolving the different polarization speckle patterns with different polarization PSFs. There are two rotation arrows in the upper left. The first indicates the polarization of the speckle pattern, and the second indicates the polarization of the PSF used for deconvolving [e.g., the upper picture in Fig. 5(f) has two arrows, blue on the left and red on the right, indicating this picture is the result of the RCP speckle pattern deconvolving with the LCP PSF]. According to these experimental observations, MCI shows high sensitivity to the polarization of incident objects, and objects can be recovered only when the speckle patterns and PSFs are at the same polarization.
Figure 5.Schematic of MCI’s polarization selective characterization. (a) Schematic diagram of the experimental setup. The first pair of the polarizer and quarter-wave plate converts incident light to LCP light (indicated by the red rotation spinning arrow). Then the LCP light transmits through the metasurface and is converted to RCP light (indicated by the blue rotation spinning arrow). Limited by the polarization conversion efficiency of the metasurface, some LCP light is left in transmitted light. The second pair of the polarizer and the quarter-wave plate is employed to remove LCP light. (b) has the same experimental setup as (a), except the rotation angle of two quarter-wave plates is changed for the generation and removal of RCP light. (c) The raw speckle patterns with different polarization (blue for RCP, red for LCP). (d) The PSFs with different polarization. (e) The reconstructed images from the speckle patterns by deconvolution with PSFs of the same polarization. (f) The reconstructed images from the speckle patterns by deconvolution with PSFs of the orthogonal polarization (there are two rotation spinning arrows in the upper left; the left and right arrows indicate polarization of speckle pattern and PSF). Scale bar: 1000 μm in speckle patterns and PSFs, and 100 μm in reconstructed images.
D. 5D Imaging
To evaluate the performance of our MCI in spatial–spectral–polarization 5D imaging, two objects with different 5D properties are projected and superimposed on the sensor. The experimental setup is shown in Fig. 6(a). The two patterns with different colors are loaded on the left and right areas of the projector. After transmitting through a diaphragm and a polarizer, the beam from the projector becomes polarized light. The left part of the beam is reflected by a mirror to another path. Beams in two paths are polarized into orthogonal circular polarizations while transmitting through quarter-wave plates with different fast axis orientations. Then two beams are superimposed by a beam combiner and modulated by the metasurface diffuser. Finally, the raw speckle pattern is recorded by a camera, shown in Fig. 6(b). Before recovering the actual pattern, a two-point source with different colors was loaded on the projector to generate corresponding 5D PSFs respectively, shown in the upper part of Figs. 6(c) and 6(d). The reconstructed images obtained by deconvolving the PSFs with speckle patterns in Fig. 6(b) were exhibited in the lower parts of Figs. 6(c) and 6(d). The experimental results shown above illustrate that the two objects with different 5D information can be reconstructed from the overlapped speckle pattern. PSFs with different 5D information can retrieve different objects in the superimposed speckle pattern. Note that the quality of reconstructed images in Figs. 6(c) and 6(d) is not as good as shown in Figs. 4(c) and 5(e), which is likely due to the polarization conversion efficiency of our metasurface diffuser. Although the metasurface converts polarization of incident light into the opposite handedness, some co-polarized light remains in transmitted light, causing minor deterioration for recognizing objects with orthogonal polarization.
Figure 6.Schematic of MCI’s 5D imaging. (a) Schematic diagram of the experimental setup. Two objects (left and right) are projected simultaneously and transmitted through a diaphragm and polarizer, which blocks stray light and converts to linear polarization. M1, M2, and M3 are mirrors, and M1 and M2 reflect the left object to another path. Quarter-wave plates circularly polarize both objects. The two quarter-wave plates are set to orthogonal rotation angles to produce different circularly polarized objects. Following M3 reflects the left object to the main path and the beam splitter superimposes both objects together. Then the superimposed beam transmits through the metasurface and is recorded by the camera. (b) The superimposed speckle pattern of two objects with different 5D information. (c) The individual measured PSF of the right path and the reconstructed image from the superimposed speckle pattern by deconvolution. (d) The individual measured PSF of the left path and the reconstructed image from the superimposed speckle pattern by deconvolution. Scale bar: 1000 μm in speckle patterns and PSFs, and 100 μm in reconstructed images.
We demonstrate a lensless snapshot 5D imaging system by employing a computational technique and the metasurface’s spatial–spectral–polarization sensitivity. The 5D information of the object is encoded by the metasurface as speckle patterns, which allow us to apply a deconvolution algorithm to reconstruct the 5D information of interest by corresponding PSFs. Our demonstrations present a compact and inexpensive technique for snapshot 5D imaging that might be promising for material classification and identification, biomedicine, and industry applications. As a general framework of imaging and detection, our proposal is promising to promote the next generation of engineering optics [45,46].
Acknowledgment. Y. Lei thanks Dr. Dongliang Tang for his help in LC metasurface fabrication and experimental design.
APPENDIX A: CONTRAST RANDOM PHASE PROFILE WITH FOCUS PHASE PROFILE IN THE ALGORITHM’S PERFORMANCE
To determine an efficient LC metasurface design, we evaluate two different phase profiles for the sensitivity of multi-dimensional information in the algorithm’s performance. First, we compare the random and focus phase profiles’ wavelength resolution. We simulate the imaging results under these two phase profiles with a center wavelength of 532 nm and deconvolve these images with their PSFs at different wavelengths [the simulated PSFs are according to Eq. (
Figure 7.Wavelength resolution comparison of random and focus phase profiles. We simulate the imaging results under these two phase profiles with a center wavelength of 532 nm and deconvolve these images with their PSFs of varying wavelengths. (a) and (c) are the reconstructed results under different PSFs with corresponding phase profiles at different wavelengths. (b) and (d) show the simulated PSFs for each phase profile. (e) The Jaccard index of the reconstructed results compared with the ground truth image. (f) The Pearson correlation coefficient of the reconstructed results compared with the ground truth image.
Figure 8.Spatial resolution comparison of random and focus phase profiles. We simulate the imaging results under these two phase profiles at the distance of 15 cm along the
Furthermore, we should consider the object–image relationship when using a focusing lens for spatial perception. When the object is located at a location in front of the focal point, there will be no image on the sensor. When the object is located at a location beyond the focal length, the size of images on the sensor will be reduced leading to loss of information detail. In summary, a random phase profile is a better option for spatial perception than a focus phase profile.
APPENDIX B: ANALYSIS OF SPATIAL–SPECTRAL–POLARIZATION DEPENDENCY OF LC METASURFACE DIFFUSER
Figure 9.For LCP incidence, the Pearson correlation coefficients between PSFs with different object depths and wavelengths of incidence.
Figure 10.For RCP incidence, the Pearson correlation coefficients between PSFs with different object depths and wavelengths of incidence.
APPENDIX C: EXPERIMENT OF AXIAL PSF DEPENDENCY AND AXIAL RESOLUTION MEASUREMENT
To verify the simulation results of Appendices
Figure 11.Axial resolution experimental result. (a) Scheme of
APPENDIX D: MEMORY EFFECT OF MCI SYSTEM
Light passing through a scattering medium produces a random speckle pattern. “Memory effect” describes the phenomenon that the speckle pattern changes linearly when the incidence angle changes in a limited angle. The memory effect induces the shift invariance of PSFs. Within the memory effect region, the captured speckle pattern could be deconvolved with one PSF. According to our experiment results, the edge of the DMD in the projector is within the memory effect range. To test the memory effect range of our MCI system, we measured a set of speckles of the same object at different distances from the center area. To expand the moving range out of the limitation of the DMD’s size, we move the projector vertically and horizontally. Then these patterns were deconvolved by the same PSF recorded at the center area. The results are shown in Fig.
Figure 12.Test of memory effect range. (a) Scheme of memory effect range measurement. Objects are shifting out of the original position along with the projector moving, and the moving step is 0.5 mm. (b) Reconstructed images of objects in different positions. (c)–(h) Enlarged images of (b). Scale bar: 100 μm.
LC metasurfaces were fabricated using a DMD exposure system and the fabrication process is kept in a dust-free environment to obtain high-quality samples. Photoalignment materials we used in the fabrication are dimethylformamide (DMF) and sulfonated azo dye (SD1), mixed with a ratio of 99.5:0.5. First, the glass substrate was washed by ultrasonic cleaning, adequately heated, UV-light exposed, and compressed air blown. Second, the mixed solution of DMF and SD1 was dropped uniformly on the constant rotating glass substrate to form an evenly distributed orientation layer. Third, the samples were exposed by a DMD to achieve the expected rotation angles of the LC molecules. Fourth, a solution of LC materials consisting of RM257 (14%), Irgacure184 (1%), and methylbenzene (85%) was dropped on an orientation layer and rotated uniformly. Finally, the LC metasurfaces were completed after solidification within the unpolarized light with a wavelength of 365 nm.
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