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Abstract
Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular-varied illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3−0.7 with a 4 × /0.1NA objective due to the geometric constraint with the declined illumination intensities and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500−1000 nm, which cannot meet the requirements of high-resolution biomedical imaging applications. Although it is possible to improve the resolution by using a high-NA objective lens, the FP approach is less appealing as the decrease of field-of-view (FOV) will far exceed the improvement of spatial resolution in this case. In this paper, we initially present a subwavelength resolution Fourier ptychography (SRFP) platform with a hemispherical digital condenser to provide high-angle programmable plane-wave illuminations of 0.95NA, attaining a 4 × /0.1NA objective with the final effective imaging performance of 1.05NA at a half-pitch resolution of 244 nm with the incident wavelength of 465 nm across a wide FOV of 14.60 mm2, corresponding to a SBP of 245 megapixels. Our work provides an essential step of FP towards high-throughput imaging applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-resolution (HR) wide-field imaging is essential for biomedical research and digital pathology, where requires a large space-bandwidth product (SBP) to provide computational data sets and statistical analyses for thousands of cells simultaneously across a large field-of-view (FOV) [1,2]. However, conventional microscopes are always subjected to the restricted SBP due to the inherent trade-offs between the spatial resolution and FOV. Therefore, mechanical scanning and digital stitching is necessary for the measurement of a large FOV HR image. Fourier ptychography (FP) [3–5] is a fast-growing computational imaging technique that applies angle diversity to expand the passband of an imaging system. Sharing roots with conventional ptychography [6,7], synthetic aperture imaging [8,9] and structured-illumination microscopy [10,11], FP iteratively synthetizes a series of low-resolution (LR) intensities captured with a low numerical aperture (NA) objective to reconstruct a large FOV HR image without multi-view stitching. Due to its flexible setup, remarkable performance without mechanical scanning and interferometric measurements, FP has wide applications in the digital pathology [12], whole slide imaging systems [13] and fluorescence imaging [14,15].
Although many significant progresses have been made in FP for improving data collection efficiency [16,17] and recovery accuracy [18–22] in the past few years, HR imaging with high synthetic NA (NAsyn) greater than unity without the loss of FOV is rarely reported. To date, the achievable imaging NA with a commercial LED board is still limited to the range of 0.3−0.7 with a 4 × /0.1NA objective due to two reasons. One is that the illumination NA (NAillu) of the LED array cannot reach 1 due to the constraint of planar geometry. The other is that the collected LED intensities are severely declined with the increasing incident angle θ (proportional to cos4θ) [23] and only parts of the scattering light can be collected when the NAillu is larger than the NA of the objective (NAobj). Therefore, the dark field images with high-angle illuminations are more easily submerged by the noise due to the attenuated signal-to-noise ratio (SNR). The highest achievable half-pitch resolution is usually constrained between 500−1000 nm, which cannot meet the requirements of HR biomedical imaging applications. Although it is possible to improve the resolution by using a higher magnification objective with larger NA, for instance, Ou et al. [24] used a 40 × /0.75NA objective to achieve the final NAsyn of 1.45, the FP approach is less appealing as the decrease of FOV far exceeds the improvement of spatial resolution in this case. Sun et al. [25] proposed a REFPM platform to achieve the final NAsyn of 1.6 with a 10 × /0.4NA objective via an oil-immersion condenser and a dense LED array, attaining a SBP of 98.5 megapixels. However, the loss of FOV is still noticeable in this method since that the lower magnification objective is not applicable due to the sampling requirements [26]. Luo et al. [27] proposed a lensless on-chip microscope to achieve the final NAsyn of 1.4 under unit magnification. However, different from FP, it needs mechanical scanning.
To this end, we initially present a subwavelength resolution Fourier ptychography (SRFP) platform, equipped with an elaborate hemispherical digital condenser with the adjustable brightness and 0.95 illumination NA, breaking the geometric constraint of planar LED matrix. In contrast with traditional optical condensers, no lenses, mirrors, or mechanically scanning parts are needed for the control of NAillu [28] as the sample can be illuminated from all directions in this method. The hemispherical digital condenser also has many other applications [29–31]. The illumination device of SRFP is assembled by two 3D-printed quarter-spherical condensers, with 415 blue-light LEDs distributed uniformly in the internal surface of a rigid hollow hemisphere with a 80mm radius of curvature, aiming to satisfy the sampling criteria [26] and pattern optimization [32] of the FP technique where a moderate overlapping rate of 68.5% is required by a 4 × /0.1NA objective. Higher resolution can be obtained with a higher NA objective without any other changes in our SRFP platform at the cost of FOV and computational efficiency depending on different applications. And a higher overlapping rate will be get. The SRFP enables the imaging performance of 1.05 synthetic NA at a half-pitch resolution of 244 nm with the incident wavelength of 465 nm across a wide FOV of 14.60 mm2 via a 4 × /0.1NA objective, corresponding to a SBP of 245 megapixels. The reconstructions indicate that the SRFP dramatically improves the spatial resolution of the conventional planar-illuminated FP method without sacrificing the system FOV, expanding the SBP for dozens of times compared with the incoherent microscopy. Furthermore, in order to compensate the imperfections and uncertainties of the SRFP platform, a system calibration method is implemented in our iterative reconstruction algorithm to eliminate the artifacts caused mainly by the LED brightness fluctuations and LED positional misalignment. This work will provide an important step of FP towards high-throughput imaging applications.
2. Materials and methods
Figure 1 shows the schematic and optical setup of the traditional FP platform with LED board and our SRFP platform with hemispherical digital condensers. In the traditional FP platform, a 32 × 32 programmable R/G/B LED array (Adafruit, 4mm spacing, controlled by an Arduino) is placed at 63mm above the sample. The red, green and blue LEDs have a dominant narrow peak at the wavelength of 631nm, 516nm and 465nm within 20nm bandwidth respectively, while only the blue LEDs are used to provide angle-varied illuminations in this experiment for comparison. A compact inverted microscope is used as shown in Fig. 1(a2) with light path diagram, which can be further combined with the fluorescence imaging easily [33]. All the data are captured by a 4 × /0.1NA apochromatic objective and a 16-bits sCMOS camera (Neo 5.5, Andor, 2160 × 2560 pixels, 6.5μm pixel pitch). Many works [16,19–22] are based on the traditional FP platform in the past few years, however, the acquisition efficiency is restricted by the long exposure time (1s) due to the low electric power of 19.5 milliwatts (mW) per element, corresponding to a luminous power of 0.95mW. In addition, the synthetic NA is severely degraded as the attenuated SNR of dark-field images resulting from the decreased intensity of high-angle illuminations. Therefore, a hemispherical digital condenser is elaborately designed with 415 blue-light LEDs (XPEROY-L1-0000-00B01, Cree, 465nm, 10nm bandwidth) distributed uniformly in the internal surface of a rigid hollow hemisphere with a 80mm radius of curvature, which is placed above the sample and the edge of condenser is coincide with the plane of sample as shown in Figs. 1(b) and 1(d). The hemispherical condenser is assembled by two 3D-printed quarter-spheres with 5mm thickness as shown in Fig. 1(b1). The photograph of the condenser is shown in Fig. 1(b2) and the component design specification is presented in Table 1 with 20 rings, 24 columns and a constant step length of the NAillu of 0.05, aiming to satisfy the sampling criteria [26] and pattern optimization of FP [32] with the overlapping rate of 68.5% along the column-axis by a 4 × /0.1NA objective. The overlapping rate can be calculated as follows.
where St is the step length of the NAillu.
Fig. 1 (a) Schematic of traditional FP platform with LED board. (a1) A 32 × 32 programmable R/G/B LED matrix. (a2) The enlargement of a compact inverted microscope with light path diagram. MO: microscope objective; TL: tube lens; M1 and M2: mirrors; BS: beam splitter. (b) Schematic of our SRFP platform with hemispherical digital condensers. (b1) Assembly of two 3D-printed quarter-spherical condensers. (b2) Photography of the hemispherical digital condensers. (c) and (d) Photographs of the corresponding optical setups, respectively.
Table 1. Component design specification of hemispherical digital condensers
The LEDs will be dense in the center and sparse near the edge of the condenser, which breaks the artifacts caused by constant overlapping rate of the traditional FP platform [31]. And the sampling rate in space of FP is given by
where mag is the magnification of the objective, λ is the incident wavelength, Δx is the pixel size of camera and the sampling rate Rcam is 1.43 in our platform. The dimension of each LED element is 3.45 × 3.45 × 2mm3 and the maximum electric power is 3.5W with a luminous power of 500mW. In our design scheme, the maximum simultaneous lighting LED elements in one ring are 20 with 1.65W per element in case of burning out. Repeated experiments indicate that the real power of 465mW is the optimal power value for a 4 × /0.1NA objective with 10ms exposure time per frame. During the data acquisition process, 415 LED elements on the hemispherical digital condenser are lighted up sequentially as shown in Visualization 1 and all of them are driven statically by a self-made LED controller board with an FPGA unit (Altera FPGA EP3C25Q240) to provide the logical control through the GPIO interface. The EPRY-FPM reconstruction algorithm [18] embedded with adaptive step-size strategy [19] is applied to both traditional FP and SRFP in the experiment.3. Experimental results of USAF targets
The imaging results and reconstructions by the incoherent microscopy, planar-illuminated FP and SRFP are demonstrated in Fig. 2, Fig. 3 and Fig. 4 respectively. The experimental results are summarized in the Table 2 for comparison. The Extreme resolution target (Ready Optics Company, Calabasas, California, USA), 1951 USAF board from Group 4 to Group 11 with the minimum linewidth of 137nm, is embedded in a standard microscope slide as shown in the top-right of Fig. 3(a). We lighten all the LEDs for the bright-field microscopy (i.e., incoherent microscopy) since the illumination is incoherent. Generally, the measured resolution should be improved with the increasing NAsyn of the imaging system, but many factors, such as the modulation characteristic of optical transfer function (OTF), the aberrations and the sampling rate in space, should be taken into account in the real situation. Detailed comparison between these factors with respect to the final resolution can be referred to Refs [25,34,35]. Since the pixel size of our camera is 6.5μm, the sampling rates in bright-field microscopy with 4 × /0.1NA, 10 × /0.3NA and 20 × /0.45NA objectives are all less than 1. Thus the final resolution of these objectives is limited by the sampling rate in space. The full FOV and spatially-resolved line-pair of the conventional microscopy with different objectives are demonstrated in Fig. 2 for comparison. The measured half-pitch resolution are 1740nm (Group 8, element 2), 775nm (Group 9, element 3), 548nm (Group 9, element 6) and 388nm (Group 10, element 3), respectively, for 4 × /0.1NA, 10 × /0.3NA, 20 × /0.45NA and 40 × /0.6NA objectives, corresponding to SBP of 4.8, 3.9, 1.9 and 1.0 megapixels, respectively. We can see that the improvement of spatial resolution is at the cost of FOV and SBP in the conventional incoherent microscopy. Generally, it is not easy to compare the resolution between the incoherent microscopy and coherent microscopy since there is the effect of phase in coherent case. The half-pitch resolution Reshalf is popularly used for quite fair comparison [24,25], which is given by
Fig. 2 Imaging results of conventional bright-field microscopy for the USAF resolution target. (a), (b), (c) and (d) The full FOV of the incoherent microscopy by using a 4 × /0.1NA, 10 × /0.3NA, 20 × /0.45NA and 40 × /0.6NA objective, respectively. (a1), (b1), (c1) and (d1) The corresponding zoom-in sections.
Fig. 3 Experimental results of the USAF resolution target with traditional FP platform. (a) The full FOV captured with a 4 × /0.1NA objective. (a1) and (a2) Enlarged sub-regions of Fig. 2(a) and Fig. 2(a1), respectively. (b), (b1)-(b6) and (c1)-(c6) The recovery results of the same sub-region with different NAsyn and their close-up, respectively. (d1)-(d6) and (e1)-(e6) The recovered spectrum and their corresponding LR segments at the highest illumination angle of different NAsyn respectively.
Fig. 4 Experimental results of the USAF resolution target with SRFP platform. (a1)-(a5) and (d1)-(d5) The recovery results of the same sub-region with different NAsyn under different brightness respectively. (b1)-(b5), (c1)-(c5), (e1)-(e5) and (f1)-(f5) The recovered spectrum and their corresponding LR segments at the highest illumination angle of different NAsyn under different brightness respectively.
Table 2. Comparison of the measured half-pitch resolution, FOV, and SBP with different illuminators and objectives. (λ = 465nm)
and the corresponding SBP can be calculated as follows:
In our planar-illuminated FP platform, the overlapping rate Roverlap is 60.35% and the sampling rate Rcam is 1.59. The LR raw image captured by a 4 × /0.1NA objective with the normal illumination is shown in Fig. 3(a). A small segment (200 × 200 pixels) in the FOV is indicated in Fig. 3(a1) and its close-up (50 × 50 pixels) is shown in Fig. 3(a2). Figures 3(b), 3(b1)-3(b6) and 3(c1)-3(c6) present the reconstructions of intensity with different NAsyn and their close-up, respectively. The recovered spectrum of Figs. 3(b1)-3(b6) and their zoom-in segments at the highest illumination angle with different NAsyn are shown in Figs. 3(d1)-3(d6) and 3(e1)-3(e6) respectively. A series of data preprocessing methods [20] have been used to remove the noise from all the LR segments. The maximum measured half-pitch resolution with a 4 × /0.1NA objective is 388nm (Group 10, Element 3) with the NAsyn of 0.73, corresponding to a SBP of 97 megapixels. It can be observed that the achievable resolution remains unchanged with the increase of NAsyn that beyond 0.73, and most of the high-frequency component is submerged in the background as indicated in Figs. 3(e4)-3(e6) due to the attenuated SNR of edge-illuminated dark-field images, verifying the geometric constraint of planar LED matrix and the resolution limit in the conventional FP platform.
Generally, only parts of the scattering light can be collected when the NAillu is beyond the NAobj, since the condenser of the microscope is replaced with the LED board in traditional FP platform due to the large size of the LED board. Therefore, the LR images of those high-angle illuminations have weak SNR inevitably. To address the resolution limit in the conventional planar-illuminated FP setup, Sun et al. [25] proposed a REFPM platform with a 10 × /0.4NA objective to overcome this problem without replacing the condenser, but it needs a dense and special LED array, which is quite small to match the size of the condenser. However, it cannot use a lower magnification objective due to the overlapping rate and sampling requirements [25] and there is still the loss of FOV to a certain degree. While in our SRFP platform, we use the opposite approach to enhance the SNR of dark-field images by providing a constant LED brightness with the increase of incident angle via a hemispherical digital condenser. The brightness I can be adjustable continuously and we’ve tested different intensities. For illustration the reconstructions with two different intensities are shown in Fig. 4. The maximum measured resolution with the electric power of 230mW per LED element is 308nm (Group 10, Element 5), and the resolution will not be improved when the NAillu is beyond around 0.75. The recovered spectrum and their zoom-in segments at the highest illumination angle with different NAsyn are shown in Figs. 4(b1)-4(b5) and 4(c1)-4(c5) respectively. Most of the high-frequency component is submerged in the background as indicated in Figs. 4(c4) and 4(c5). However, the maximum measured resolution with the electric power of 465mW per LED element is 244nm (Group 11, Element 1) with a 4 × /0.1NA objective, which corresponding to a SBP of 245.2 megapixels. It can be seen from the comparisons that sufficient brightness is indispensable for the enhancement of FP imaging performance. The LED intensities should be carefully chosen according to the practical situations to ensure the sufficient illumination while to avoid overexposure. Compared with the traditional FP platform, the SRFP platform can improve the resolution from 388nm to 244nm without the sacrifice of FOV. The amount of LEDs is less than the traditional FP platform with the same NAsyn, and the energy utilization is more efficient. Compared with conventional incoherent microscopy, the SRFP facilitates a higher SBP with 65 times’ increase and 245 times’ increase respectively with 4 × /0.1NA objective and 40 × /0.60NA objectives.
4. System calibration methods
We use the EPRY-FPM algorithm [18] with the adaptive step-size strategy [19] for the reconstructions. However, there are parts of artifacts in our previous experimental results of USAF targets. Several system calibration methods [21,22] have been proposed to analyze and eliminate the artifacts in the traditional FP platform. Here we propose two system calibration methods for the LED brightness fluctuations and LED positional misalignment respectively, which are the main errors in our platform.
Generally, the error of the LED brightness nonuniformity is caused by the inconsonant propagation distance and the processing technology. The model of planar LED array and hemispherical digital condenser are shown in Fig. 5(a) and Fig. 5(b) respectively. The measured intensity at the sample plane is declined with the increase of incident angle θ in the planar LED matrix, which can be expressed as I(θ) = I0 cos2θ and I0 is the central intensity with the normal illumination. The second drawback of the LED board comes from the fact that LEDs have significant angular variation in intensity (typically emitting more light in the forward direction), while all LEDs are radially oriented in the hemispherical digital condenser. Besides, in both the condenser and LED board we note that intensity further decreases with a final factor of cosθ due to the smaller profile of objective window when viewed off-axis. Therefore, combining these factors and assuming a Lambertian (~cosθ) angular dependence for physical (non-point-source) LEDs [23] results in an expected intensity falloff of ~cos4θ for the planar geometry but only ~cosθ for the hemispherical model, a vast improvement at high incidence angles. The difference between two geometries is proportional to cos3θ, or a factor of >50% at 40° and 99% at 77° incidence, having a substantial impact on the exposure time and lighting efficiency.
Fig. 5 The LED intensity correction method. (a) and (b) The model of planar LED array and hemispherical digital condenser respectively. (c) and (d) Normalized measured intensity falloff as a function of incident angle with the LED board and the condenser respectively. Falloff is proportional to cos4θ for the LED board and cosθ for the condenser (black line). (e) and (f) Top view of the normalized illumination brightness of each LED element for the planar LED array and the condenser respectively.
Generally, the system calibration method for the LED brightness fluctuations is to utilize the adaptive algorithm [36,37], but it is less effective when dealing with multiple error sources [22]. In our method, we use a much higher NA objective, a 20 × /0.75NA objective for the LED board and a 100 × /1.25NA for the hemispherical condenser respectively, to collect all the LR images without loading the sample. Since the NA of the objective is larger than the NAillu we set, emergent lights from all the incident angles can be collected by the objective and recorded as bright-field images. The normalized intensity distributions of planar-illuminated FP and the SRFP method are demonstrated in the top and bottom of Fig. 5 respectively, with the incident angles varying from −50° to 50° for comparison. Here the averaged intensity of each LR raw image is considered as the corresponding LED brightness. The measured intensity falloff in Figs. 5(c) and 5(d) is well agreed with the theoretical analyses, and we can see that the SRFP facilitates a larger NAillu and higher lighting efficiency. In order to compensate the difference of the illumination brightness, a compensation factor is multiplied to each LR image during the experiments, which can be given by the reciprocal of the normalized illumination brightness.
Another system error in our platform is the LED positional misalignment, which is also an important issue in the traditional FP platform. Even a little positional errors can cause severe image degradation and lead to reconstruction failure [21,38]. Therefore, the condenser should be carefully fabricated with a small tolerance. But the error comes from the installation cannot be ignored when putting the condenser above the sample stage. In our previous work, we proposed a scFPM algorithm [22], based on the adaptive step-size strategy, simulated annealing and non-linear regression algorithm, to calibrate this error for the traditional FP platform. Four global parameters, namely the shift factors of center LED along x- and y- axis ∆x, ∆y, height factor h, and rotation factor 𝜑, are required for system modeling. Similarly, in SRFP platform we use three global parameters, shift factors ∆x, ∆y and rotation factor 𝜑, to describe the off-axis error of the center LED to improve convergence and robustness of the iterative reconstruction algorithm.
where xm,n, ym,n denote the position of the LED element on the ring m, column n, rm is the lateral radius of each ring, δn is the lateral angle to the coordinate axis x. For illustration 20% intensity fluctuation is artificially introduced by multiplying each raw image with a random constant ranging from 0.9 to 1.1 in simulations. The positional misalignment is introduced by setting the ∆x = 1mm, ∆y = 1mm, and 𝜑 = 5°, while the ∆x = 0mm, ∆y = 0mm, and 𝜑 = 0° is the ideal condition. The simulations and experimental results with and without system calibration methods are shown in Fig. 6. The numbers listed in the bottom right indicate the root mean square errors (RMSE) relative to the simulation ground truth to evaluate the image quality. It can be seen that the intensity fluctuation and positional misalignment can lead to severe artifacts in the reconstruction results as indicated in Figs. 6(a1)-6(e1), and the positional errors shown in Figs. 6(a2)-6(e2) may cause a worse degradation compared with the brightness nonuniformity shown in Figs. 6(a3)-6(e3). After processed by the calibration method mentioned above, an improved imaging performance can be obtained both in the simulation and experiment with a higher resolution and lower noise level as indicated in Figs. 6(a4)-6(e4).Fig. 6 Simulations and experimental results with system calibration methods in SRFP platform. (a) and (b) The group truth of intensity and phase in simulations respectively. (a1)-(a4), (b1)-(b4) and (c1)-(c4) The recovered results of intensity, phase and spectrum with different processing procedures in simulations. The numbers listed in the bottom right indicate the RMSE relative to the simulation ground truth. (d1)-(d4) and (e1)-(e4) The recovered results of intensity and spectrum of USAF resolution target with different processing procedures in experiments. A: LED intensity correction method; B: LED position correction method.
5. Experimental results of biological samples
In addition, we also test our platform with the biological samples. Figure 7(a) presents the FOV of the rabbit tongue tissue section via a 4 × /0.1NA objective, while Figs. 7(b1)-7(b3) present the imaging of conventional bright-field microscopy with a 40 × /0.6NA objective and recovery results by traditional FP and SRFP platforms respectively for the same segment (blue rectangle, 100 × 100 pixels). The FOV with 4 × objective is hundredfold larger than that with 40 × objective (black rectangle). The intensity distribution along the solid line in Figs. 7(b1)-7(b3) is demonstrated in Fig. 7(c). We can see from Figs. 7(b1)-7(b3) and Fig. 7(c) that the SRFP methods facilitates a higher spatial resolution and better image contrast compared with bright-field microscopy and traditional FP due to the nature of coherent imaging. In addition, some small features indicated by the purple arrows in Fig. 7(c) can be observed in the SRFP platform. The phase reconstructions by traditional FP and SRFP are indicated in Figs. 7(d1)-7(d4), with the top FOV of 200 × 200 pixels and bottom FOV of 100 × 100 pixels, and a shaper phase can be obtained by the proposed SRFP method as shown in Fig. 7(d4). To conclude, the SRFP enables the joint advantages of large FOV in low-magnification objective and high resolution in high-NA objective, offering a promising tool for biomedical imaging applications.
Fig. 7 Imaging and recovery results of conventional bright-field microscopy, traditional FP and SRFP platforms for the same rabbit tongue tissue section. (a) The full FOV captured with a 4 × /0.1NA objective. (b1)-(b3) Imaging and recovery results of the same sub-region (blue rectangle, 100 × 100 pixels) using different platforms. (c) Intensity distributions along the solid line in Figs. 7(b1)–(b3). (d1)-(d4) Phase reconstructions with traditional FP and SRFP within a fixed sub-region (red rectangle 200 × 200 pixels).
6. Discussions and conclusions
In this paper, we have proposed a subwavelength resolution FP platform, termed SRFP, to generate HR large-SBP reconstructions with an elaborate hemispherical digital condenser to provide high-angle programmable plane-wave illuminations of 0.95 NA. It has been demonstrated that the SRFP platform can further improve the resolution compared with the traditional FP with a LED board, and achieve the final effective imaging performance of 1.05 NA with a 4 × /0.1NA objective at a half-pitch resolution of 244 nm with a wavelength of 465 nm across a wide FOV of 14.60 mm2, corresponding to a SBP of 245 megapixels. Compared with the bright-field microscopy, it has a higher resolution and a larger SBP no matter with the same objective or the same theoretical NAsyn. If pursuing higher resolution in despite of the FOV, a higher NA objective can be utilized in the SRFP platform without any other changes at the cost of FOV and computational efficiency. Since the LED elements are sequentially lighted up, there is still the space to reduce the acquisition time. Future work may utilize the multiplexing scheme or sparse lighting scheme to improve the efficiency of data collection to achieve the sub-second imaging for a more practical SRFP platform. And besides, it is possible to simultaneously add several imaging modes to the setup for dark-field, bright-field, and phase contrast imaging and quantitative 3D phase imaging, since the illumination modes of the setup are easy to change. The hemispherical digital condenser has been designed with these further applications in mind, so that these new capabilities can be added to enrich the platform.
Funding
National Natural Science Foundation of China (NSFC) (81427802 and 61377008).
Acknowledgments
An Pan thanks Prof. Chao Zuo (Nanjing University of Science and Technology, China) for helpful discussions and comments, and Dr. Yuege Xie (University of Texas at Austin, USA) for support and encouragement all the time.
Disclosures
The authors have no relevant financial interests in this article and no potential conflicts of interest to disclose.
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