This paper proposes a novel approach for high-resolution light field microscopy imaging by using a camera array. In this approach, we apply a two-stage relay system for expanding the aperture plane of the microscope into the size of an imaging lens array, and utilize a sensor array for acquiring different sub-apertures images formed by corresponding imaging lenses. By combining the rectified and synchronized images from 5 × 5 viewpoints with our prototype system, we successfully recovered color light field videos for various fast-moving microscopic specimens with a spatial resolution of 0.79 megapixels at 30 frames per second, corresponding to an unprecedented data throughput of 562.5 MB/s for light field microscopy. We also demonstrated the use of the reported platform for different applications, including post-capture refocusing, phase reconstruction, 3D imaging, and optical metrology.
© 2015 Optical Society of America
Light field microscopy (LFM)  is a scanless 3D computational imaging approach that records both 2D spatial and 2D angular distribution of light passing through a specimen. This kind of spatio-angular data allows for computationally synthesizing focal stacks, flexibly controlling depth of field and achieving full volumetric reconstruction, and hence has important applications in optical bioimaging . The current optical schematic of LFM, which can be dated back to 1908 by Lippmann , is implemented by inserting a microlens array at the intermediate image plane of an optical microscope so that sensor pixels capture the rays of 4D light field during a single exposure. However, microlens array based light field microscopy (MALM) suffers from inherent trade-offs between sensor spatial resolution and angular resolution measurement , which degrades the final achievable image resolution by orders of magnitude compared with the raw sensor resolution.
To address the drawback of the decreased spatial resolution of LFM, 3D deconvolution  has been proposed to reconstruct volumetric data with improved spatial resolution, which requires a computationally intensive process and results in non-uniform lateral resolution across the depth of field. The resulting non-uniform lateral resolution across the depth of field can be mitigated with additional phase masks for wavefront coding . Accounting for the application of high-resolution post-capture refocusing, aperture scanning  or LED scanning methods [8, 9] can be employed alternatively to achieve full sensor resolution digital refocusing at the sacrifice of temporal resolution. By incorporating prior knowledge about the object, for example, Gaussian angular distribution assumption for light field moment imaging [10, 11], Lambertian reflectance priors with super-resolution [12–14] or learning an over-complete dictionary to exploit its intrinsic redundancy [15, 16], high-resolution light fields can be computationally reconstructed. Unfortunately, these empirical assumptions do not always hold for microscopic samples.
In this paper, we report a new LFM configuration for addressing the intrinsic resolution trade-offs of the conventional LFM. The reported approach, termed camera array based light field microscopy (CALM), utilizes a 5 × 5 camera array to simultaneously capture different perspective images of the sample, corresponding to different sub-apertures of the two-stage relay system. We show that high-resolution light fields can be obtained by simply rectifying the captured sub-aperture images without further processing or enforcing any prior assumptions on the microscopic specimens.
We provide three key insights on the optical system comparison between our approach and the MALM as follows:
First, our approach can achieve much higher data transmission capability by using a parallel data acquisition and storage scheme. The space-bandwidth product (SBP)  of an optical system places an upper bound on the product of spatial and angular resolution in light fields (i.e. the total pixel count of employed sensors). Conventional microscope objective has a SBP of tens of mega-pixels, on the same order of pixel number of conventional image sensor. However, higher SBP lens system exists , for example, the SBP of Olympus MVX10 stereoscopic objective lens (MVPLAPO2XC) is approximate 0.7 billion; and a simple closed-circuit television (CCTV) lens reported in  has a SBP of 0.5 billion which is orders of magnitude higher than existing sensor resolution. In this regard, CALM can achieve higher resolution and higher SBP by using a camera sensor array at detection path. In contrast, MALM utilizes a single sensor and the final achievable SBP is determined by the sensor, not the employed optics.
Second, our approach provides more flexible optical configurations. Perspective images are highly redundant and humans are more tolerant of low angular resolution than low spatial resolution . Under a SBP-limited objective lens, CALM can be easily configured to capture low angular but high spatial resolution light fields, while it is challenging for MALM to manufacture the microlens array with small pitch and suitable focal length for the same goal. On the other hand, under a high SBP objective lens, utilizing a microlens array with large pitch to increase the angular resolution will reduce the final spatial resolution of light field; however, capturing more angular resolutions can be simply implemented by adding more cameras in our approach without sacrificing the spatial resolution.
Third, compared with MALM that employs a single camera, the parameters of each camera in CALM can be set independently for different applications, such as compensating the angularly non-uniform illumination or inconsistent focal positions. Marginal views usually have lower light intensity compared with center views, especially when the numerical aperture of the illumination is smaller than that of the employed objective lens. In our approach, the uniform illuminated light field images can be obtained by setting different exposure time for different perspective views. By setting different focal positions for different cameras and placing them at a curved surface, we can correct for the non planar focal aberration of the objective lens.
2. Light field imaging using a camera array
In this section, we will first demonstrate the optical schematic of the our CALM prototype in Section 2.1. We will then evaluate the imaging performance using a USAF resolution target in Section 2.2
2.1. System design of the CALM
Figure 1 shows a schematic of the proposed optical system and a photograph of the prototype system. To facilitate the prototype system building, we adopted a commercially available inverted microscope (Olympus IX73) for producing a magnified image of the specimen at the image plane. A partially coherent white LED light source with a green interference filter (central wavelength λ = 550 nm) is used to provide illumination for the system, and the numerical aperture of the condenser lens is 0.55. We used a 10× air objective lens (Olympus, UPLSAPO10X2, N.A. = 0.4, F.N. = 26.5) for all experiments in this paper. The image plane of microscope is relayed by a two-stage relay system to form the aperture plane whose diameter is equivalent to the diagonal line of the lens array, as shown in Fig. 1(bottom). The first-stage relay lens (Canon EF, 85 mm, f/1.8, USM) is used to generate the aperture plane and it is magnified by the second-stage relay lens (Computar M0814-MP2, 8 mm, f/1.4). The magnification factor is determined by the ratio of two focal lengths of the relay lens; and N.A. is matched by keeping the N.A. of the second-stage relay lens larger than the first-stage relay lens. Finally, we placed the imaging lens array (CCTV SV-10035V, 100 mm, f/3.5) at the aperture plane to obtain sub-aperture images that are recorded with the sensor array. The sensor is a PointGray Flea2-08S2C-C RGB color sensor with pixel pitch 4.65 μm, operated at resolution 1024 × 768 pixels with frame rate 30 fps. Since the light propagation in our system is no longer under the paraxial approximation, we adopted the arc configuration of the sensor array in this implementation. The lens array and sensor array are placed on the spherical surface with its center at the second-stage relay lens. The radius of tube holder we used for fixing the camera array is 472mm in this design, which is determined with a single camera before the manufacture. Finally, we established the master-slave server architecture to synchronize between sensors, acquire large-capacity light field videos and provide user interface ( Visualization 1).
The SBP of a microscope objective can be given asFig. 1(bottom), the SBP of the objective lens in our setup SBP1 is about 31.3 mega-pixels and the SBP for camera array arranged as square in the center SBP2 is about 19.9 mega-pixels. Therefore, we employed 25 sensors, which have the total number of 19.6 mega-pixels, to make full use of the information capacity of our optical system, resulting in 5 × 5 angular resolution in this implementation. And the N.A. of imaging lenses are set to 1/7.0 (the effective N.A., f/# = 7.0) for N.A. matching of the second-stage relay lens and reducing the ambient light. The system performs near the diffraction limit. Since the diffraction limit d of our objective lens is 0.84μm, the lateral resolution imposed by diffraction limit is approximately 4.20μm for each view.
Since we used the same model sensors in our implementation, besides the focal position, we set other parameters (white balance, exposure time, gain, aperture size, etc) the same for all cameras to compensate for the difference. For geometric calibration, we first aligned the optical axis of the camera array, relay system and the camera port of microscope, and assembled the camera array by converging the optical axis of each camera to the center of the second-stage relay lens. During the assembly, we precisely adjusted the direction of each camera, glued its tube onto the tube holder and assembled cameras one by one. A checkerboard was mounted on the imaging plane during the calibration, and the captured perspective images were registered with the simple planar parallax procedure as described in  to obtain the rectified light field. Light field L(x, y, u, v) describes a mapping from rays to radiance, as a function of position (x, y) and direction (u, v) in the free space (shown in Fig. 1(top)).
2.2. System characterization of the CALM
Synthetic refocusing is one of the most important applications of light field imaging, which can be implemented by shearing the 4D light field and projecting along its angular dimension . The minimum refocusing step size along the axial dimension that determines the axial resolution of 3D reconstructions in this paper can be formulated as
Figure 2 evaluates the resolution and depth of field of the prototype system by imaging a standard USAF 1951 resolution target and measuring the normalized average contrast from group 4.1 to group 5.6 of stripes . We translated the focal plane above the native object plane (z = 0 μm) in 20 μm increments, captured light fields at each increment and performed sample refocusing. Top row of Fig. 2 demonstrates the large focal range of our system. For the light field captured at z = 0 μm, we synthetically refocus it with 20 μm increment and compare it with the conventional microscopy in Fig. 2 (middle and bottom rows). Our synthetic refocusing images get out-of-focus quickly as expected, which is comparable to the conventional microscopy indicating the good optical sectioning of our system. Due to the optical aberration and sensor pixel size, the resolvable group of stripes for each view of our system and conventional microscopy are 5.6 (line width 8.77 μm) and 6.6 (line width 4.38 μm), respectively.
3. Experimental results
To demonstrate the imaging performance of the reported approach and its application to optical metrology, we capture the light field of a rose petal and an integrated circuit board as shown in Fig. 3. We used an epi-illumination configuration for capturing the integrated circuit board due to its opaque material property and applied a trans-illumination to other experiments in this paper. Since the diffuser used in the trans-illumination configuration hardly produces the isotropic illumination, the epi-illumination configuration achieves more uniform illumination for different views. The parallaxes for different views are successfully recorded (first and third column) and they allow for post-capture refocusing (second and fourth column, top). In order to facilitate the depth recovery without calibrating the intrinsic and extrinsic camera parameters, we applied the depth-from-defocus method  to estimating its depth and 3D structure from the synthesized defocused images (second and fourth column, bottom). The final spatial resolution of rose petal dataset is 880 × 768. For the integrated circuit board dataset, the actual depth range measured by the vernier calipers is 459 μm. It matches the depth range obtained by synthetic refocusing (front focus to rear focus) which is 451 μm. The detailed 3D structures of the chromatic specimens are faithfully reconstructed ( Visualization 2 and Visualization 3).
Since the employed sensor has a frame rate of 30 fps, we conducted the light field video acquisition for various living specimens. Figure 4 demonstrates the light field video of a living drosophila larva ( Visualization 4); and the movement of large numbers of Caenorhabditis elegans (C. elegans) in the water is shown in Fig. 5 ( Visualization 5). The 3D differential phase-contrast (DPC) videos  of drosophila larva are computed as the normalized difference between opposite halves of the perspective images (Fig. 4(middle rows)), which indicates the two direction derivatives of the light field. It represents the object’s phase gradient along the axis of asymmetry, so the phase can be quantitatively recovered from the gradient fields of DPC videos, with the result shown in Fig. 4(bottom row). Phase reconstruction results φ are displayed as the height h of the object in the axial dimension for better visualization, where h = φλΔn/2π and Δn is the differential refractive index between the specimen and environment. Our quantitative phase retrieval video reveals the morphological changing of translucent drosophila larva body during its movement. The light field and synthetic refocusing videos of the C. elegans in Fig. 5 demonstrate the relative spatial locations of different C. elegans along the axial dimension.
We also quantitatively evaluate the accuracy of light fields captured by our approach in Fig. 6 ( Visualization 6). We adopted a custom-made plano-convex microlens array, which is made of a plastic material (Cyclic Olefin Copolymer) with excellent optical properties, as the target sample (100 μm pitch, refractive index n = 1.53). With the captured light field in Fig. 6(top-left), the phase of microlens array is quantitatively recovered as shown in Fig. 6(top-right) by using the method proposed in . The normalized root-mean-square error (NRMSE) of the reconstructed shape with respect to the result measured by scanning confocal microscopy (Olympus FV1200) is 0.0851. In addition, the comparison of the microlens thickness cross-sections obtained by our approach (the average of three line profiles indicated in top-right) and confocal microscopy is shown in Fig. 6(bottom). The result indicates that our light field data can achieve high-accuracy phase reconstruction that has good agreement to the confocal microscopy.
To the best of our knowledge, we are the first to apply a camera array for light field imaging in microscopy, which can achieve high-resolution and high frame rate light field videos acquisition with high accuracy. The optical schematics of camera array based light field imaging in macro-scenarios  and microscope are different. In microscopic imaging, we applies objective lens to magnify the specimen, which requires the re-design of relay optics, and needs to consider the N.A. and SBP matching of different components due to the diffraction. We claim that our multiple cameras design can provide higher data transmission bandwidth, more flexible optical configurations and independent camera settings controlling. Such flexibilities cannot be achieved using a single lenslet array. Under current implementations, we have successfully demonstrated the acquisition of color light field videos for various fast-moving microscopic specimens with a spatial resolution of 0.79 megapixels, angular views of 25, and a temporal resolution of 33 ms (30 fps). The data throughput of the our platform is 562.5 MB/s, 5 times higher than that of the latest commercial light field camera – Lytro Illum and the frame rate is 10 times faster. Lytro Illum has the 40 megapixels raw sensor resolution with only 3 fps temporal resolution (around 114.4 MB/s data transmission,), which limits its applications in imaging dynamic biological specimens, such as neural activities. We have demonstrated different applications of the reported platform, including higher resolution post-capture refocusing, phase reconstruction and 3D imaging of fast-moving microscopic samples. With our design, we hope to bridge the gap between computer vision and optics community so that various computer vision algorithms that based on multi-view or camera array can be applied to microscopy and facilitate various biological and metrological applications that require high-resolution, high-speed monitoring.
Yet, our current prototype has several limitations. First, the SBP of the Olympus objective imposes the limit angular resolution. Although the 5 × 5 angular resolution is good enough for most of the applications as presented, aliasing will occur when dealing with large-depth-range and thin-structures samples as an example shown in Fig. 7 ( Visualization 7). In this example, the estimated depth range of the sample is 1.21 mm and the number of pixel shifting during the refocusing is 1.21 mm/18.8 μm=64 for marginal views. Here, we used all perspective images for refocusing (third column) while adopting center 3 × 3 views for synthetic aperture (forth column). Such aliasing can be reduced by using angular interpolation or light field super-resolution method  under current implementation. We can also simply increase cameras by using a high SBP objective lens. Second, the field number of the Olympus IX73 camera port is smaller than the objective lens, which produces the edge resolution loss in this implementation and causes the image cropping of some marginal views. Using the microscope with larger field number could eliminate this problem. Third, the sensors are synchronized in software in our prototype, which can be implemented with external hardware trigger to achieve higher accuracy synchronization. Finally, the proposed prototype system is more expensive and bulkier compared with the single lenslet array based approach. However, the camera array is becoming widely used in macro-scenarios, such as the commercial product – Point Grey ProFUSION 25 (5 × 5 digital camera array), and we believe that our approach could be practical for microscopic imaging in the future.
5. Conclusion and future work
In summary, the proposed camera array based light field microscopy (CALM) can achieve high-resolution and high frame rate light field videos acquisition with high accuracy. We validated the proposed approach with a standard commercial light microscope and demonstrated various applications by using the designed prototype system.
In the future, we would like to extend our approach to high-performance microscopy by combining views with different camera settings as a single view, such as high dynamic range imaging by setting different camera exposure times, and high speed imaging by staggering the camera trigger times. Furthermore, our method can be applied to fluorescence microscopy, and the axial and lateral resolution of light field can be further improved with 3D deconvolution algorithm for imaging the large-scale and high-speed neuronal activities in 3D [2, 5]. Combining Fourier ptychographic approach  for dynamic wide-field and high-resolution imaging is the other interesting avenue of future work.
This work was supported by the Project of NSFC (No. 61327902, No. 61120106003 and No. 61035002). The authors thank Yebin Liu and Gordon Wetzstein for insightful discussions, and Xiao Liu for the C. elegans used in this paper.
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