Optical phase imaging using a synthetic aperture phase retrieval technique

Spherical wave illumination scanning digital holographic profilometry

In this work, we proposed what we believe to be a novel scanning solution for the assessment of high-NA samples, referred to as spherical-wave illumination scanning digital holographic profilometry (SWS-DHP). This approach introduces a 2F optimization methodology, based on the measurement of the focal length of the object to determine the spherical component of the scanning. Furthermore, re-optimization of 2F, whether it needs to be operated depends on the measured object's NA to inspect more information. Meanwhile, utilizing phase space analysis shows SWS superiority in information transfer for high-NA samples compared to plane-wave illumination scanning. In addition, this method introduces a shape reconstruction algorithm with volumetric aberration compensation based on the propagation of the aberrated object and illumination waves to obtain high-quality measurements. Finally, the imaging merits of SWS-DHP were proved through simulations and were experimentally verified for the object of NA up to 0.87.

Fast Fourier ptychographic quantitative phase microscopy for in vitro label-free imaging

Quantitative phase microscopy (QPM) is indispensable in biomedical research due to its advantages in unlabeled transparent sample thickness quantification and obtaining refractive index information. Fourier ptychographic microscopy (FPM) is among the most promising QPM methods, incorporating multi-angle illumination and iterative phase recovery for high-resolution quantitative phase imaging (QPI) of large cell populations over a wide field of-view (FOV) in a single pass. However, FPM is limited by data redundancy and sequential acquisition strategies, resulting in low imaging efficiency, which in turn limits its real-time application in in vitro label-free imaging. Here, we report a fast QPM based on Fourier ptychography (FQP-FPM), which uses an optimized annular downsampling and parallel acquisition strategy to minimize the amount of data required in the front end and reduce the iteration time of the back-end algorithm (3.3% and 4.4% of conventional FPM, respectively). Theoretical and data redundancy analyses show that FQP-FPM can realize high-throughput quantitative phase reconstruction at thrice the resolution of the coherent diffraction limit by acquiring only ten raw images, providing a precondition for in vitro label-free real-time imaging. The FQP-FPM application was validated for various in vitro label-free live-cell imaging. Cell morphology and subcellular phenomena in different periods were observed with a synthetic aperture of 0.75 NA at a 10× FOV, demonstrating its advantages and application potential for fast high-throughput QPI.

Fast and robust Fourier ptychographic microscopy with position misalignment correction

Significance

Fourier ptychographic microscopy (FPM) is a new, developing computational imaging technology. It can realize the quantitative phase imaging of a wide field of view and high-resolution (HR) simultaneously by means of multi-angle illumination via a light emitting diode (LED) array, combined with a phase recovery algorithm and the synthetic aperture principle. However, in the FPM reconstruction process, LED position misalignment affects the quality of the reconstructed image, and the reconstruction efficiency of the existing LED position correction algorithms needs to be improved.

Aim

This study aims to improve the FPM correction method based on simulated annealing (SA) and proposes a position misalignment correction method (AA-C algorithm) using an improved phase recovery strategy.

Approach

The spectrum function update strategy was optimized by adding an adaptive control factor, and the reconstruction efficiency of the algorithm was improved.

Results

The experimental results show that the proposed method is effective and robust for position misalignment correction of LED arrays in FPM, and the convergence speed can be improved by 21.2% and 54.9% compared with SC-FPM and PC-FPM, respectively.

Conclusions

These results can reduce the requirement of the FPM system for LED array accuracy and improve robustness.

Structured illumination phase and fluorescence microscopy for bioimaging

This study presents a dual-modality microscopic imaging approach that combines quantitative phase microscopy and fluorescence microscopy based on structured illumination (SI) to provide structural and functional information for the same sample. As the first imaging modality, structured illumination digital holographic microscopy (SI-DHM) is implemented along the transmission beam path. SI-DHM acts as a label-free, noninvasive approach and provides high-contrast and quantitative phase images utilizing the refractive index contrast of the inner structures of samples against the background. As the second imaging modality, structured illumination (fluorescence) microscopy (SIM) is constructed along the reflection beam path. SIM utilizes fluorescent labeling and provides super-resolution images for specific functional structures of samples. We first experimentally demonstrated phase imaging of SI-DHM on rice leaves and fluorescence (SIM) imaging on mouse kidney sections. Then, we demonstrated dual-modality imaging of biological samples, using DHM to acquire the overall cell morphology and SIM to obtain specific functional structures. These results prove that the proposed technique is of great importance in biomedical studies, such as providing insight into cell physiology by visualizing and quantifying subcellular structures.

Fast and stable Fourier ptychographic microscopy based on improved phase recovery strategy

Fourier ptychographic microscopy (FPM) imaging is a computational imaging technology that can reconstruct wide-field high-resolution (HR) images. It uses a series of low-resolution images captured by a camera under different illumination angles. The images are stitched in the Fourier domain to expand their spectral range. Under high-angle illumination, a dark-field image is noisy with a low signal-to-noise ratio, which significantly reduces the reconstruction quality of FPM. Conventional reconstruction algorithms often have low FPM imaging performance and efficiency due to optimization strategies. In response to these problems, this paper proposes an FPM imaging method based on an improved phase recovery strategy to optimize the alternating iterative algorithm. The technique uses an improved threshold method to reduce noise in the image preprocessing stage to maximize the retention of high-frequency sample information. Moreover, an adaptive control factor is added in the subsequent iterative update process to balance the sample spectrum function. This study verifies the effectiveness of the proposed method on both simulation and experimental images. The results show that the proposed method can effectively suppress image background noise and has a faster convergence speed and higher robustness. In addition, it can be used to reconstruct HR complex amplitude images of objects under wide field-of-view conditions.

Machine Learning Assisted Classification of Cell Lines and Cell States on Quantitative Phase Images

In this report, we present implementation and validation of machine-learning classifiers for distinguishing between cell types (HeLa, A549, 3T3 cell lines) and states (live, necrosis, apoptosis) based on the analysis of optical parameters derived from cell phase images. Validation of the developed classifier shows the accuracy for distinguishing between the three cell types of about 93% and between different cell states of the same cell line of about 89%. In the field test of the developed algorithm, we demonstrate successful evaluation of the temporal dynamics of relative amounts of live, apoptotic and necrotic cells after photodynamic treatment at different doses.

Spatial phase and polarization retrieval of arbitrary circular symmetry singular light beams using orthogonal polarization separation

Circular symmetry singular light beams (CS-SLBs) possessing spatially variant field distributions have drawn extensive attention because of their unique optical properties. However, the extraction of spatial phase and polarization distributions is always a significant but difficult issue in CS-SLB applications. Here, we propose and experimentally investigate an orthogonal polarization separation (OPS) method to retrieve the spatial phase and polarization distributions of arbitrary CS-SLBs. Theoretically, the CS-SLB, including the vortex beam (VB), cylindrical vector beam (CVB), and cylindrical vector vortex beam (CVVB), can be decomposed into two orthogonal circularly polarized sub-VBs. Therefore, once the spatial phase distributions and initial phase difference of the two components are obtained, the phase and polarization distributions of the CS-SLB can be retrieved, and its type can also be identified. Based on this analysis relationship, we first separated the CS-SLB into two circularly polarized sub-VBs and designed an astigmatic phase iterative algorithm to restore their spatial phase information. After retrieving the phases of the two components, we have experimentally obtained the spatial phase and polarization distributions of three typical CS-SLBs, including VBs, CVBs, and CVVBs. These results demonstrate that this method provides a feasible way to retrieve the variant field distributions of CS-SLBs and may have great application prospects in optical imaging, optical communication, etc.

Compressed channeled spectropolarimetry

Channeled spectropolarimetry measures the spectrally resolved Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a modulated measurement of the channeled spectropolarimeter. The state-of-the-art reconstruction algorithm uses the Fourier transform to extract the Stokes parameters from channels in the Fourier domain. While this approach is straightforward, it can be sensitive to noise and channel cross-talk, and it imposes bandwidth limitations that cut off high frequency details. To overcome these drawbacks, we present a reconstruction method called compressed channeled spectropolarimetry. In our proposed framework, reconstruction in channeled spectropolarimetry is an underdetermined problem, where we take N measurements and solve for 3N unknown Stokes parameters. We formulate an optimization problem by creating a mathematical model of the channeled spectropolarimeter with inspiration from compressed sensing. We show that our approach offers greater noise robustness and reconstruction accuracy compared with the Fourier transform technique in simulations and experimental measurements. By demonstrating more accurate reconstructions, we push performance to the native resolution of the sensor, allowing more information to be recovered from a single measurement of a channeled spectropolarimeter.

Lensless imaging through multiple phase patterns illumination

A stable optical system is required to acquire a high-quality image. A motionless lensless setup is designated to obtain high-resolution and large field of view images. The sample is sequentially illuminated with multiple random phase patterns, and the recorded images are subtracted from the system calibration images correspondingly. The resultant images are propagated to the sample plane. The summation of all images yields a final image with resolution of ∼4  μm, field of view of ∼15  mm2, and better signal-to-noise ratio. This technique provides a compact, stable, and cost-effective optical system.

Scatter-plate microscope for lensless microscopy with diffraction limited resolution

Scattering media have always been looked upon as an obstacle in imaging. Various methods, ranging from holography to phase compensation as well as to correlation techniques, have been proposed to cope with this obstacle. We, on the other hand, have a different understanding about the role of the diffusing media. In this paper we propose and demonstrate a ‘scatter-plate microscope’ that utilizes the diffusing property of the random medium for imaging micro structures with diffraction-limited resolution. The ubiquitous property of the speckle patterns permits to exploit the scattering medium as an ultra-thin lensless microscope objective with a variable focal length and a large working distance. The method provides a light, flexible and cost effective imaging device as an alternative to conventional microscope objectives. In principle, the technique is also applicable to lensless imaging in UV and X-ray microscopy. Experiments were performed with visible light to demonstrate the microscopic imaging of USAF resolution test target and a biological sample with varying numerical aperture (NA) and magnifications.

Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations

High-resolution and wide field-of-view (FOV) microscopic imaging plays a central role in diverse applications such as high-throughput screening and digital pathology. However, conventional microscopes face inherent trade-offs between the spatial resolution and FOV, which are fundamental limited by the space-bandwidth product (SBP) of the optical system. The resolution-FOV tradeoff can be effectively decoupled in Fourier ptychography microscopy (FPM), however, to date, the effective imaging NA achievable with a typical FPM system is still limited to the range of 0.4–0.7. Herein, we report, for the first time, a high-NA illumination based resolution-enhanced FPM (REFPM) platform, in which a LED-array-based digital oil-immersion condenser is used to create high-angle programmable plane-wave illuminations, endowing a 10×, 0.4 NA objective lens with final effective imaging performance of 1.6 NA. With REFPM, we present the highest-resolution results with a unprecedented half-pitch resolution of 154 nm at a wavelength of 435 nm across a wide FOV of 2.34 mm², corresponding to an SBP of 98.5 megapixels (~50 times higher than that of the conventional incoherent microscope with the same resolution). Our work provides an important step of FPM towards high-resolution large-NA imaging applications, generating comparable resolution performance but significantly broadening the FOV of conventional oil-immersion microscopes.

Surface wave illumination Fourier ptychographic microscopy

We propose a novel microscopy method, combining surface wave illumination and the Fourier ptychographic microscopy (FPM) algorithm to achieve super-resolution (SR) imaging. In our system, an oil-immersion objective lens is used to excite both the total internal reflection (TIR) evanescent waves and the surface plasmon waves (SPWs), which illuminate the sample with large wave vectors. Through the FPM algorithm, a resolution approximately twice that of conventional wide-field microscopy is obtained. Meanwhile, we could retrieve the sample's quantitative phase map in order to obtain its surface profile. Importantly, the field enhancement from a SPW has improved the contrast of the reconstructed images, which is critical for revealing the finer structural details of the specimen. In our experiments, we have imaged metallic gratings with a 120 or 150 nm wide line and trench features. We accurately retrieved their axial dimensions with a lateral resolution better than 240 nm that is close to the theoretical resolution of 215 nm, thus demonstrating the quantitative phase imaging capability of our technique. As this approach provides a label-free solution for intensity and phase imaging of samples with lateral resolution exceeding the limit introduced by the optical system, it can be potentially used in a wide range of noninvasive biological imaging applications.

Synthetic aperture microscopy based on referenceless phase retrieval with an electrically tunable lens

Phase imaging microscopy, based either on holography or nonholographic methods such as phase retrieval, has seen considerable attention recently. Phase retrieval offers the advantage of being free of a reference arm and enables a more stable and compact setup. We present an optical setup that provides enhanced resolution by implementing synthetic aperture imaging based on phase retrieval using an electrically tunable lens (ETL). The ETL is a more compact and less expensive alternative to computerized translation stages and spatial light modulators. Before applying phase retrieval, we discuss a general calibration algorithm, which performs image registration, corrects for magnifications, and determines the axial locations of image planes. Finally, we obtain resolution-enhanced images of a phase grating and of cells to demonstrate the practical application of our technique.

Modal-based phase retrieval for adaptive optics

We consider using phase retrieval (PR) to correct phase aberrations in an optical system. Three measurements of the point-spread function (PSF) are collected to estimate an aberration. For each measurement, a different defocus aberration is applied with a deformable mirror (DM). Once the aberration is estimated using a PR algorithm, we apply the aberration correction with the DM, and measure the residual aberration using a Shack-Hartmann wavefront sensor. The extended Nijboer-Zernike theory is used for modelling the PSF. The PR problem is solved using both an algorithm called PhaseLift, which is based on matrix rank minimization, and another algorithm based on alternating projections. For comparison, we include the results achieved using a classical PR algorithm, which is based on alternating projections and uses the fast Fourier transform.

Phase microscopy using light-field reconstruction method for cell observation

The refractive index (RI) distribution can serve as a natural label for undyed cell imaging. However, the majority of images obtained through quantitative phase microscopy is integrated along the illumination angle and cannot reflect additional information about the refractive map on a certain plane. Herein, a light-field reconstruction method to image the RI map within a depth of 0.2 μm is proposed. It records quantitative phase-delay images using a four-step phase shifting method in different directions and then reconstructs a similar scattered light field for the refractive sample on the focus plane. It can image the RI of samples, transparent cell samples in particular, in a manner similar to the observation of scattering characteristics. The light-field reconstruction method is therefore a powerful tool for use in cytobiology studies.

Versatile optical microscopy using a reconfigurable hemispherical digital condenser

We present a computer-controlled hemispherical digital condenser and demonstrate that a single device can be used to implement a variety of both well established and novel optical microscopy techniques. We verified the condenser capabilities by imaging fabricated periodic patterned structures and biological samples.

High numerical aperture Fourier ptychography: principle, implementation and characterization

Fourier ptychography (FP) utilizes illumination control and computational post-processing to increase the resolution of bright-field microscopes. In effect, FP extends the fixed numerical aperture (NA) of an objective lens to form a larger synthetic system NA. Here, we build an FP microscope (FPM) using a 40X 0.75NA objective lens to synthesize a system NA of 1.45. This system achieved a two-slit resolution of 335 nm at a wavelength of 632 nm. This resolution closely adheres to theoretical prediction and is comparable to the measured resolution (315 nm) associated with a standard, commercially available 1.25 NA oil immersion microscope. Our work indicates that Fourier ptychography is an attractive method to improve the resolution-versus-NA performance, increase the working distance, and enlarge the field-of-view of high-resolution bright-field microscopes by employing lower NA objectives.

Overlapped Fourier coding for optical aberration removal

We present an imaging procedure that simultaneously optimizes a camera's resolution and retrieves a sample's phase over a sequence of snapshots. The technique, termed overlapped Fourier coding (OFC), first digitally pans a small aperture across a camera's pupil plane with a spatial light modulator. At each aperture location, a unique image is acquired. The OFC algorithm then fuses these low-resolution images into a full-resolution estimate of the complex optical field incident upon the detector. Simultaneously, the algorithm utilizes redundancies within the acquired dataset to computationally estimate and remove unknown optical aberrations and system misalignments via simulated annealing. The result is an imaging system that can computationally overcome its optical imperfections to offer enhanced resolution, at the expense of taking multiple snapshots over time.