Lens-free on-chip 3D microscopy based on wavelength-scanning Fourier ptychographic diffraction tomography.

Lens-free on-chip microscopy is a powerful and promising high-throughput computational microscopy technique due to its unique advantage of creating high-resolution images across the full field-of-view (FOV) of the imaging sensor. Nevertheless, most current lens-free microscopy methods have been designed for imaging only two-dimensional thin samples. Lens-free on-chip tomography (LFOCT) with a uniform resolution across the entire FOV and at a subpixel level remains a critical challenge.

Roadmap on computational methods in optical imaging and holography [invited].

Unlabelled: Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging.

Transport of intensity diffraction tomography with non-interferometric synthetic aperture for three-dimensional label-free microscopy.

We present a new label-free three-dimensional (3D) microscopy technique, termed transport of intensity diffraction tomography with non-interferometric synthetic aperture (TIDT-NSA). Without resorting to interferometric detection, TIDT-NSA retrieves the 3D refractive index (RI) distribution of biological specimens from 3D intensity-only measurements at various illumination angles, allowing incoherent-diffraction-limited quantitative 3D phase-contrast imaging. The unique combination of z-scanning the sample with illumination angle diversity in TIDT-NSA provides strong defocus phase contrast and better optical sectioning capabilities suitable for high-resolution tomography of thick biological samples.

Single-exposure 3D label-free microscopy based on color-multiplexed intensity diffraction tomography.

We present a 3D label-free refractive index (RI) imaging technique based on single-exposure intensity diffraction tomography (sIDT) using a color-multiplexed illumination scheme. In our method, the chromatic light-emitting diodes (LEDs) corresponding R/G/B channels in an annular programmable ring provide oblique illumination geometry that precisely matches the objective's numerical aperture. A color intensity image encoding the scattering field of the specimen from different directions is captured, and monochromatic intensity images concerning three color channels are separated and then used to recover the 3D RI distribution of the object following the process of IDT.

Accelerated Fourier ptychographic diffraction tomography with sparse annular LED illuminations.

Fourier ptychographic diffraction tomography (FPDT) is a recently developed label-free computational microscopy technique that retrieves high-resolution and large-field three-dimensional (3D) tomograms by synthesizing a set of low-resolution intensity images obtained with a low numerical aperture (NA) objective. However, in order to ensure sufficient overlap of Ewald spheres in 3D Fourier space, conventional FPDT requires thousands of intensity measurements and consumes a significant amount of time for stable convergence of the iterative algorithm. Herein, we present accelerated Fourier ptychographic diffraction tomography (aFPDT), which combines sparse annular light-emitting diode (LED) illuminations and multiplexing illumination to significantly decrease data amount and achieve computational acceleration of 3D refractive index (RI) tomography.

Accurate quantitative phase imaging by the transport of intensity equation: a mixed-transfer-function approach: erratum.

In this erratum, we correct Fig. 4 of our Letter [Opt. Lett.

Wavelength-scanning lensfree on-chip microscopy for wide-field pixel-super-resolved quantitative phase imaging.

We propose a lensfree on-chip microscopy approach for wide-field quantitative phase imaging (QPI) based on wavelength scanning. Unlike previous methods, we found that a relatively large-range wavelength diversity not only provides information to overcome spatial aliasing of the image sensor but also creates sufficient diffraction variations that can be used to achieve motion-free, pixel-super-resolved phase recovery. Based on an iterative phase retrieval and pixel-super-resolution technique, the proposed wavelength-scanning approach uses only eight undersampled holograms to achieve a half-pitch lateral resolution of 691 nm across a large field-of-view of 29.

Accurate quantitative phase imaging by the transport of intensity equation: a mixed-transfer-function approach.

As a well-established deterministic phase retrieval approach, the transport of intensity equation (TIE) is able to recover the quantitative phase of a sample under coherent or partially coherent illumination with its through-focus intensity measurements. Nevertheless, the inherent paraxial approximation limits its validity to low-numerical-aperture imaging and slowly varying objects, precluding its application to high-resolution quantitative phase imaging (QPI). Alternatively, QPI can be achieved by phase deconvolution approaches based on the coherent contrast transfer function or partially coherent weak object transfer function (WOTF) without invoking paraxial approximation.

On a universal solution to the transport-of-intensity equation.

The transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a non-interferometric, deterministic manner. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive pre-knowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions.

Multi-step phase aberration compensation method based on optimal principal component analysis and subsampling for digital holographic microscopy.

Digital holographic microscopy (DHM) is a well-known powerful technique allowing measurement of the spatial distributions of both the amplitude and phase produced by a transparent sample. Nevertheless, in order to improve the transverse resolution of the DHM system, a microscope objective has to be introduced in the object beam path, which inevitably leads to phase aberration in the object wavefront. In recent decades, a multitude of techniques have been proposed to compensate for this phase aberration, and the principal component analysis (PCA) technique has proven to be one of the most promising approaches due to its high compensation accuracy, low computational complexity, and simplicity to implement.

Optimal illumination pattern for transport-of-intensity quantitative phase microscopy.

The transport-of-intensity equation (TIE) is a well-established non-interferometric phase retrieval approach, which enables quantitative phase imaging (QPI) of transparent sample simply by measuring the intensities at multiple axially displaced planes. Nevertheless, it still suffers from two fundamentally limitations. First, it is quite susceptible to low-frequency errors (such as "cloudy" artifacts), which results from the poor contrast of the phase transfer function (PTF) near the zero frequency.

Wide-field anti-aliased quantitative differential phase contrast microscopy.

Differential phase contrast (DPC) microscopy is a popular methodology to recover quantitative phase information of thin transparent samples under multi-axis asymmetric illumination patterns. Based on spatially partially coherent illuminations, DPC provides high-quality, speckle-free 3D reconstructions with lateral resolution up to twice the coherent diffraction limit, under the precondition that the pixel size of the imaging sensor is small enough to prevent spatial aliasing/undersampling. However, microscope cameras are in general designed to have a large pixel size so that the intensity information transmitted by the optical system cannot be adequately sampled or digitized.

Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations.

We demonstrate a three-dimensional (3D) optical diffraction tomographic technique with multi-frequency combination (MFC-ODT) for the 3D quantitative phase imaging of unlabeled specimens. Three sets of through-focus intensity images are captured under an annular aperture and two circular apertures with different coherence parameters. The 3D phase optical transfer functions (POTF) corresponding to different illumination apertures are combined to obtain a synthesized frequency response, achieving high-quality, low-noise 3D reconstructions with imaging resolution up to the incoherent diffraction limit.

Lensfree dynamic super-resolved phase imaging based on active micro-scanning.

In this Letter, we present a new active micro-scanning-based imaging platform and associated super-resolution (SR) phase retrieval method in lensfree microscopy to achieve SR dynamic phase imaging. The samples are illuminated by a nearly coherent illumination system, where two orthogonal parallel plates are inserted into the light path and rotate to achieve controllable source micro-scanning, permitting sub-pixel shifts of the holograms on x- and y-axis directions independently. Then sequential low-resolution sub-pixel-shifted holograms are processed to enhance spatial resolution and reconstruct quantitative phase images of the sample simultaneously.

Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography.

We present a single-shot quantitative phase imaging (QPI) method based on color-multiplexed Fourier ptychographic microscopy (FPM). Three light-emitting diode (LED) elements with respective R/G/B channels in a programmable LED array illuminate the specimen simultaneously, providing triangle oblique illuminations matching the numerical aperture of the objective precisely. A color image sensor records the light transmitted through the specimen, and three monochromatic intensity images at each color channel are then separated and utilized to recover the phase of the specimen.

High-speed Fourier ptychographic microscopy based on programmable annular illuminations.

High-throughput quantitative phase imaging (QPI) is essential to cellular phenotypes characterization as it allows high-content cell analysis and avoids adverse effects of staining reagents on cellular viability and cell signaling. Among different approaches, Fourier ptychographic microscopy (FPM) is probably the most promising technique to realize high-throughput QPI by synthesizing a wide-field, high-resolution complex image from multiple angle-variably illuminated, low-resolution images. However, the large dataset requirement in conventional FPM significantly limits its imaging speed, resulting in low temporal throughput.

Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy.

High-resolution wide field-of-view (FOV) microscopic imaging plays an essential role in various fields of biomedicine, engineering, and physical sciences. As an alternative to conventional lens-based scanning techniques, lensfree holography provides a new way to effectively bypass the intrinsical trade-off between the spatial resolution and FOV of conventional microscopes. Unfortunately, due to the limited sensor pixel-size, unpredictable disturbance during image acquisition, and sub-optimum solution to the phase retrieval problem, typical lensfree microscopes only produce compromised imaging quality in terms of lateral resolution and signal-to-noise ratio (SNR).

High-resolution transport-of-intensity quantitative phase microscopy with annular illumination.

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one.

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.

Multimodal computational microscopy based on transport of intensity equation.

Transport of intensity equation (TIE) is a powerful tool for phase retrieval and quantitative phase imaging, which requires intensity measurements only at axially closely spaced planes without a separate reference beam. It does not require coherent illumination and works well on conventional bright-field microscopes. The quantitative phase reconstructed by TIE gives valuable information that has been encoded in the complex wave field by passage through a sample of interest.

Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy.

The incremental gradient approaches, such as PIE and ePIE, are widely used in the field of ptychographic imaging due to their great flexibility and computational efficiency. Nevertheless, their stability and reconstruction quality may be significantly degraded when non-negligible noise is present in the image. Though this problem is often attributed to the non-convex nature of phase retrieval, we found the reason for this is more closely related to the choice of the step-size, which needs to be gradually diminishing for convergence even in the convex case.

Efficient positional misalignment correction method for Fourier ptychographic microscopy.

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.

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.

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.

Iterative optimum frequency combination method for high efficiency phase imaging of absorptive objects based on phase transfer function.

In this work, an optimum frequency combination (OFC) method is proposed to reconstruct high quality phase information of the complex light field, which is really valuable for many objects such as optical elements and cells. It is shown that the difference image between two symmetrical separated, larger 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 combines different frequency components with high Signal-to-Noise Ratio (SNR) together to estimate a more accurate frequency spectrum of the object's phase distribution without any complicated linear or nonlinear regression.