Siyuan Dong

Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging

Information multiplexing is important for biomedical imaging and chemical sensing. In this paper, we report a microscopy imaging technique, termed state-multiplexed Fourier ptychography (FP), for information multiplexing and coherent-state decomposition. Similar to a typical Fourier ptychographic setting, we use an array of light sources to illuminate the sample from different incident angles and acquire corresponding low-resolution images using a monochromatic camera. In the reported technique, however, multiple light sources are lit up simultaneously for information multiplexing, and the acquired images thus represent incoherent summations of the sample transmission profiles corresponding to different coherent states. We show that, by using the state-multiplexed FP recovery routine, we can decompose the incoherent mixture of the FP acquisitions to recover a high-resolution sample image. We also show that, color-multiplexed imaging can be performed by simultaneously turning on R/G/B LEDs for data acquisition. The reported technique may provide a solution for handling the partially coherent effect of light sources used in Fourier ptychographic imaging platforms. It can also be used to replace spectral filter, gratings or other optical components for spectral multiplexing and demultiplexing. With the availability of cost-effective broadband LEDs, the reported technique may open up exciting opportunities for computational multispectral imaging.

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging

We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging. The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object. The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process. We demonstrate two applications of the reported scheme. In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects. The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object. We also demonstrate a reconstruction resolution better than the detector pixel limit (i.e., pixel super-resolution). In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging. By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field. This platforms maximum achievable resolution is ultimately determined by the cameras traveling range, not the aperture size of the lens. The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy.

High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography.

Fluorescence microscopy plays a vital role in modern biological research and clinical diagnosis. Here, we report an imaging approach, termed pattern-illuminated Fourier ptychography (FP), for fluorescence imaging beyond the diffraction limit of the employed optics. This approach iteratively recovers a high-resolution fluorescence image from many pattern-illuminated low-resolution intensity measurements. The recovery process starts with one low-resolution measurement as the initial guess. This initial guess is then sequentially updated by other measurements, both in the spatial and Fourier domains. In the spatial domain, we use the pattern-illuminated low-resolution images as intensity constraints for the sample estimate. In the Fourier domain, we use the incoherent optical-transfer-function of the objective lens as the object support constraint for the solution. The sequential updating process is then repeated until the sample estimate converges, typically for 5-20 times. Different from the conventional structured illumination microscopy, any unknown pattern can be used for sample illumination in the reported framework. In particular, we are able to recover both the high-resolution sample image and the unknown illumination pattern at the same time. As a demonstration, we improved the resolution of a conventional fluorescence microscope beyond the diffraction limit of the employed optics. The reported approach may provide an alternative solution for structure illumination microscopy and find applications in wide-field, high-resolution fluorescence imaging.

Sparsely sampled Fourier ptychography

Fourier ptychography (FP) is an imaging technique that applies angular diversity functions for high-resolution complex image recovery. The FP recovery routine switches between two working domains: the spectral and spatial domains. In this paper, we investigate the spectral-spatial data redundancy requirement of the FP recovery process. We report a sparsely sampled FP scheme by exploring the sampling interplay between these two domains. We demonstrate the use of the reported scheme for bypassing the high-dynamic-range combination step in the original FP recovery routine. As such, it is able to shorten the acquisition time of the FP platform by ~50%. As a special case of the sparsely sample FP, we also discuss a sub-sampled scheme and demonstrate its application in solving the pixel aliasing problem plagued in the original FP algorithm. We validate the reported schemes with both simulations and experiments. This paper provides insights for the development of the FP approach.

Optimization of sampling pattern and the design of Fourier ptychographic illuminator.

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

FPscope: a field-portable high-resolution microscope using a cellphone lens

The large consumer market has made cellphone lens modules available at low-cost and in high-quality. In a conventional cellphone camera, the lens module is used to demagnify the scene onto the image plane of the camera, where image sensor is located. In this work, we report a 3D-printed high-resolution Fourier ptychographic microscope, termed FPscope, which uses a cellphone lens in a reverse manner. In our platform, we replace the image sensor with sample specimens, and use the cellphone lens to project the magnified image to the detector. To supersede the diffraction limit of the lens module, we use an LED array to illuminate the sample from different incident angles and synthesize the acquired images using the Fourier ptychographic algorithm. As a demonstration, we use the reported platform to acquire high-resolution images of resolution target and biological specimens, with a maximum synthetic numerical aperture (NA) of 0.5. We also show that, the depth-of-focus of the reported platform is about 0.1 mm, orders of magnitude longer than that of a conventional microscope objective with a similar NA. The reported platform may enable healthcare accesses in low-resource settings. It can also be used to demonstrate the concept of computational optics for educational purposes.

Microscopy illumination engineering using a low-cost liquid crystal display

Illumination engineering is critical for obtaining high-resolution, high-quality images in microscope settings. In a typical microscope, the condenser lens provides sample illumination that is uniform and free from glare. The associated condenser diaphragm can be manually adjusted to obtain the optimal illumination numerical aperture. In this paper, we report a programmable condenser lens for active illumination control. In our prototype setup, we used a

Incoherent Fourier ptychographic photography using structured light

15 liquid crystal display as a transparent spatial light modulator and placed it at the back focal plane of the condenser lens. By setting different binary patterns on the display, we can actively control the illumination and the spatial coherence of the microscope platform. We demonstrated the use of such a simple scheme for multimodal imaging, including bright-field microscopy, darkfield microscopy, phase-contrast microscopy, polarization microscopy, 3D tomographic imaging, and super-resolution Fourier ptychographic imaging. The reported illumination engineering scheme is cost-effective and compatible with most existing platforms. It enables a turnkey solution with high flexibility for researchers in various communities. From the engineering point-of-view, the reported illumination scheme may also provide new insights for the development of multimodal microscopy and Fourier ptychographic imaging.

Resolution doubling with a reduced number of image acquisitions.

Controlling photographic illumination in a structured fashion is a common practice in computational photography and image-based rendering. Here we introduce an incoherent photographic imaging approach, termed Fourier ptychographic photography, that uses nonuniform structured light for super-resolution imaging. In this approach, frequency mixing between the object and the structured light shifts the high-frequency object information to the passband of the photographic lens. Therefore, the recorded intensity images contain object information that is beyond the cutoff frequency of the collection optics. Based on multiple images acquired under different structured light patterns, we used the Fourier ptychographic algorithm to recover the super-resolution object image and the unknown illumination pattern. We demonstrated the reported approach by imaging various objects, including a resolution target, a quick response code, a dollar bill, an insect, and a color leaf. The reported approach may find applications in photographic imaging settings, remote sensing, and imaging radar. It may also provide new insights for high-resolution imaging by shifting the focus from the collection optics to the generation of structured light.

Fourier Ptychography for Brightfield, Phase, Darkfield, Reflective, Multi-Slice, and Fluorescence Imaging

Structured illumination technique enhances the lateral resolution by projecting non-uniform intensity patterns on a sample. In a typical implementation, three lateral phase shifts (0, 2π/3, 4π/3) are needed for each orientation of the sinusoidal pattern, and 3 different orientations are needed to double the bandwidth isotopically in the Fourier domain. To this end, 9 incoherent images are needed in the acquisition process. In this paper, we discuss an imaging strategy for the structured illumination technique and demonstrate the use of a modified incoherent Fourier ptychographic procedure for reducing the number of acquisitions. In the first implementation, we used complementary sinusoidal patterns for sample illumination. We show that, the number of lateral phase shifts can be reduced from 3 to 2 for each orientation of the sinusoidal pattern and the total number of image acquisitions can be reduced to 6 with 3 orientations. In the second implementation, we further reduce the number of image acquisitions to 4. We also show that, the resolution-doubled image can be recovered even with unknown phases of the sinusoidal patterns. We validate the proposed imaging procedure with non-fluorescence samples. The reported approach may shorten the acquisition time of super-resolution imaging and reduce phototoxicity of biological samples.