Yuzhen Zhang

Sampling criteria for Fourier ptychographic microscopy in object space and frequency space

Fourier ptychographic microscopy (FPM) is a new computational super-resolution approach, which can obtain not only the correct object function, but also the pupil aberration, the LED misalignment, and beyond. Although many state-mixed FPM techniques have been proposed to achieve higher data acquisition efficiency and recovery accuracy in the past few years, little is known that their reconstruction performance highly depends on the data redundancy in both object and frequency domains. Generally, at least 35% aperture overlapping percentage in the Fourier domain is needed for a successful reconstruction using ordinary FPM method. However, the data redundancy requirements for those state-mixed FPM schemes are largely remained unexplored until now. In this paper, we explore the spatial and spectrum data redundancy requirements for the FPM recovery process to introduce sampling criteria for the conventional and state-mixed FPM techniques in both object and frequency space. Moreover, an upsampled FPM method is proposed to solve the pixel aliasing problem, and an alternative illumination-angle subsampled FPM scheme is introduced to get rid of the complexity of decoherence and achieve the expected recovery quality with reduced data quantity. All the proposed methods and sampling criteria are validated with both simulations and experiments, and our results show that state-mixed techniques cannot provide a significant performance advantage since they are much more sensitive to data redundancy. This paper provides both the guidelines for designing the most suitable FPM platform and the insights for the capabilities and limitations of the FPM approach.

Coded multi-angular illumination for Fourier ptychography based on Hadamard codes

Fourier ptychographic microscopy (FPM) is a newly developed super-resolution technique, which employs angularly varying illumination and a phase retrieval algorithm to surpass the diffraction limit of the objective lens. Specifically, FP captures a set of low-resolution (LR) images, under angularly varying illuminations, and stitches them together in the Fourier domain. However, because the requisite large number of incident illumination angles, the long capturing process becomes an obvious limiting factor. Furthermore, in order to acquire high-dynamic range images, the time can be increased several times over. In this work, utilizing the Hadamard code principle, we propose a highly efficient method, which applies coded multi-angular illumination for FPM, to shorten the exposure time of each raw image. High acquisition efficiency is achieved by employing an optimal multi-angular illumination scheme by using two set of Hadamard coded multiplexing patterns. Both simulation and experimental results indicate that the proposed multi-angular illumination process could shorten the acquisition time of conventional FPM.

Optimal principal component analysis-based numerical phase aberration compensation method for digital holography

In this Letter, an accurate and highly efficient numerical phase aberration compensation method is proposed for digital holographic microscopy. Considering that most parts of the phase aberration resides in the low spatial frequency domain, a Fourier-domain mask is introduced to extract the aberrated frequency components, while rejecting components that are unrelated to the phase aberration estimation. Principal component analysis (PCA) is then performed only on the reduced-sized spectrum, and the aberration terms can be extracted from the first principal component obtained. Finally, by oversampling the reduced-sized aberration terms, the precise phase aberration map is obtained and thus can be compensated by multiplying with its conjugation. Because the phase aberration is estimated from the limited but more relevant raw data, the compensation precision is improved and meanwhile the computation time can be significantly reduced. Experimental results demonstrate that our proposed technique could achieve both high compensating accuracy and robustness compared with other developed compensation methods.

Three-dimensional measurement based on a Greenough-type stereomicroscope using phase-shifting projection

We propose an absolute 3D micro surface profile measurement technique based on a Greenough-type stereomicroscope. The camera and the projector are fixed on the stereomicroscope, facilitating a flexible 3D measurement of objects with different heights. Experiments of both calibration and measurements are conducted, and the results show that our proposed method works well for measuring different types of geometry like spheres, ramps and planes etc. The reconstruction accuracy can achieve 4.8 μm with a measurement depth about 3 mm.

Multi-view phase unwrapping with composite fringe patterns

We introduce a high-speed 3-D shape measurement technique based on composite phase-shifting fringes and a stereo camera system. Epipolar constraint is adopted to search the corresponding point independently without additional images. Meanwhile, by analysing the 3-D position and the main wrapped phase of the corresponding point, pairs with an incorrect 3-D position or considerable phase difference are effectively rejected. Then all the qualified corresponding points are corrected, and the unique one as well as the related period order is selected through the embedded triangular wave. Finally, considering that some points can only be captured by a single camera in some shading areas, the final period order of these points in one camera and the one of their corresponding points in another camera always have different values, so left-right consistency check is employed to eliminate those erroneous period orders in this case. Several experiments on both static and dynamic scenes are performed, verifying that our method can achieve a speed of 120 frames per second (fps) with 25-period fringe patterns for fast, dense, and accurate 3-D measurement.

A positional misalignment correction method for Fourier ptychographic microscopy based on simulated annealing

Fourier ptychographic microscopy (FPM) is a newly developed super-resolution technique, which employs angularly varying illuminations and a phase retrieval algorithm to surpass the diffraction limit of a low numerical aperture (NA) objective lens. In current FPM imaging platforms, accurate knowledge of LED matrix’s position is critical to achieve good recovery quality. Furthermore, considering such a wide field-of-view (FOV) in FPM, different regions in the FOV have different sensitivity of LED positional misalignment. In this work, we introduce an iterative method to correct position errors based on the simulated annealing (SA) algorithm. To improve the efficiency of this correcting process, large number of iterations for several images with low illumination NAs are firstly implemented to estimate the initial values of the global positional misalignment model through non-linear regression. Simulation and experimental results are presented to evaluate the performance of the proposed method and it is demonstrated that this method can both improve the quality of the recovered object image and relax the LED elements’ position accuracy requirement while aligning the FPM imaging platforms.

Spatial-spectral data redundancy requirement for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a new computational super-resolution approach, which can obtain not only the correct object function, but also the pupil aberration, the LED misalignment, and beyond. Although many state-mixed FPM techniques have been proposed to achieve higher data acquisition efficiency and recovery accuracy in the past few years, little is known that their reconstruction performance highly depends on the data redundancy in both object and frequency domains. In this paper, we explore the spatial and spectrum data redundancy requirements for the FPM recovery process to introduce sampling criteria for the conventional and state-mixed FPM techniques in both object and frequency space.

A compact and lensless digital holographic microscope setup

We design a holographic system which is lensless and compact. There is a beam expander in conventional holographic setup to produce parallel light and then with a beam splitter to separate the light into two parts. One is used to illuminate the objects and the other one as the reference light. In our system, instead of utilizing beam expander to generalize parallel beam, the laser is directly produced by a fiber, which provides a spherical wave with a center in the out port of fiber. For this reason, our system contains less optical components so that the setup would be more compact. The only needed processing is to eliminate the second-order aberration caused by different distance between two path and the off-axis to a small extent. An experiment of aberration compensation by using principle component analysis is given, and the result shows that the system works well.

Optimum defocus planes selection method for transport of intensity phase imaging based on phase transfer function

In recent years, medical, biological and scientific fields have been benefited from phase information, which can reveal the hidden features of various objects. By solving the transport of intensity equation (TIE), the phase distribution of an object can be obtained from a series of intensity measurements. Assuming the solving process is correct, the reconstruction accuracy is depending on the distances between planes, the number of planes, and the level of noise. Increasing the number of planes or utilizing multi-frame de-noise algorithm could improve the reconstruction accuracy certainly, but neither of them is a time-efficient strategy. In this work, an optimum defocus planes selection (OPS) method is proposed for reconstructing high quality phase information by solving the transport of intensity equation. It is shown that the difference image between two symmetrical separated, lager defocused planes contains a lot of lower frequency components of the phase distribution and the higher frequency components can be easily observed in the difference image between two nearly focused planes. Based on the phase transfer function (PTF), our method estimate a more accurate frequency spectrum of the object phase distribution, which is combined with different frequency components from the stack of through–focus intensity images. Both the simulation and experimental results demonstrate that this optimum defocus planes selection method can give a computationally efficient and noise-robust phase reconstruction with higher accuracy and fewer defocus planes.

Optimized multiplexing super resolution imaging based on a Fourier ptychographic microscope

Fourier ptychographic microscopy (FPM) is a recently developed super-resolution technique by using angularly varying illumination and a phase retrieval algorithm to surpass the diffraction limit of the objective lens. To be specific, FP captures a set of low-resolution (LR) images under angularly varying illuminations, and combines them into one high-resolution (HR) image in the Fourier domain. However, the long capturing process becomes an obvious limitation since there are large number of images need to be acquired. Furthermore, the time can be increased several times over in order to acquire high-dynamic range images. Utilizing the multiplexing principle, we propose an optimized multiplexing FP algorithm, which is highly efficient, to shorten the exposure time of each raw image in this work. High acquisition efficiency is achieved by employing two set of optimized multiplexing patterns for bright-field and dark-field imaging respectively. Experimental results demonstrated that this method could improve the quality of reconstructed HR intensity distributions in a faster measuring process.