Quantitative phase-amplitude microscopy I: optical microscopy

Structured illumination contrast transfer function for high resolution quantitative phase imaging

We report a sub-diffraction resolution imaging of non-fluorescent samples through quantitative phase imaging. This is achieved through a novel application of structured illumination microscopy (SIM), a super-resolution imaging technique established primarily for fluorescence microscopy. Utilizing our contrast transfer function formalism with SIM, we extract the high spatial frequency components of the phase profile from the defocused intensity images, enabling the reconstruction of a quantitative phase image with a frequency spectrum that surpasses the diffraction limit imposed by the imaging system. Our approach offers several advantages including a deterministic, phase-unwrapping-free algorithm and an easily implementable, non-interferometric setup. We validate the proposed technique for high-resolution phase imaging through both simulation and experimental results, demonstrating a two-fold enhancement in resolution. A lateral resolution of 0.814 µm is achieved for the phase imaging of human cheek cells using a 0.42 NA objective lens and an illumination wavelength of 660 nm, highlighting the efficacy of our approach for high-resolution quantitative phase imaging.

Quantitative phase imaging based on polarization encoding

Most optical characterization methods rely on measuring the complex optical fields emerging from the interaction between light and material systems. Nevertheless, inherent scattering and absorption cause ambiguities in both interferometric and noninterferometric attempts to measure phase. Here we demonstrate that the complete information about a probe optical field can be encoded into the states of polarization, and develop a topography measurement method by blindly varying the ambient refractive index surrounding the sample in a wedged cuvette, which is capable of simultaneously measuring the thickness and the ambient refractive index of the sample in real time, as well as extending the measurement range of the sample thickness. With the method, we have successfully measured the topography of a 136.7 µm thick coverslip by blindly changing the ambient refractive index by 0.001246, resulting in the thickest sample characterization ever achieved by quantitative phase imaging, to the best of our knowledge. An efficient and complete characterization of optical fields is critical for any high-resolution imaging approach and the technique demonstrated here should prove attractive for applications ranging from microscopy to remote sensing. Thanks to the high precision and fast response speed, this method may pave a new way for measuring the topography of the thick samples, such as biological tissues.

Relationship between Liver Stiffness and Steatosis in Obesity Conditions: In Vivo and In Vitro Studies

Obesity is a major risk factor for metabolic dysfunction such as non-alcoholic fatty liver disease (NAFLD). The NAFLD spectrum ranges from simple steatosis, to steatohepatitis, fibrosis, and cirrhosis. The aim of this study is to characterize the grade of steatosis being associated with overnutrition and obesity, both at the level of single hepatocyte and whole liver, and to correlate it with the hepatocyte/liver stiffness and dysfunction. For the in vivo study, 60 subjects were enrolled and grouped based on the stage of liver steatosis/fibrosis according to biochemical analyses, liver ultrasonography (USG) and acoustic radiation force impulse shear wave elastography (ARFI-SWE). For single hepatocyte analyses we employed in vitro models of moderate and severe steatosis on which to assess the single cell biomechanics by Single Cell Force Spectroscopy (SCFS) and Quantitative Phase Microscopy (QPM). Results show that in vivo liver stiffness depends mainly on the extent of fat accumulation and not on fibrosis. These results parallel the in vitro observations showing that hepatocyte stiffness and dysfunction increase with increasing fat accumulation and lipid droplet enlargement. Our findings indicate that the extent of steatosis markedly affects the biomechanical properties of both liver and single hepatocytes thus proving insights about the role of modulation of liver/hepatocyte elasticity as a physical mechanism transducing the obesity-dependent excess of plasmatic lipids towards liver steatosis and dysfunction.

Intermixed Time-Dependent Self-Focusing and Defocusing Nonlinearities in Polymer Solutions

Low-power visible light can lead to spectacular nonlinear effects in soft-matter systems. The propagation of visible light through transparent solutions of certain polymers can experience either self-focusing or defocusing nonlinearity, depending on the solvent. We show how the self-focusing and defocusing responses can be captured by a nonlinear propagation model using local spatial and time-integrating responses. We realize a remarkable pattern formation in ternary solutions and model it assuming a linear combination of the self-focusing and defocusing nonlinearities in the constituent solvents. This versatile response of solutions to light irradiation may introduce a new approach for self-written waveguides and patterns.

Optical module for single-shot quantitative phase imaging based on the transport of intensity equation with field of view multiplexing

We present a cost-effective, simple, and robust method that enables single-shot quantitative phase imaging (QPI) based on the transport of intensity equation (TIE) using an add-on optical module that can be assembled into the exit port of any regular microscope. The module integrates a beamsplitter (BS) cube (placed in a non-conventional way) for duplicating the output image onto the digital sensor (field of view - FOV - multiplexing), a Stokes lens (SL) for astigmatism compensation (introduced by the BS cube), and an optical quality glass plate over one of the FOV halves for defocusing generation (needed for single-shot TIE algorithm). Altogether, the system provides two laterally separated intensity images that are simultaneously recorded and slightly defocused one to each other, thus enabling accurate QPI by conventional TIE-based algorithms in a single snapshot. The proposed optical module is first calibrated for defining the configuration providing best QPI performance and, second, experimentally validated by using different phase samples (static and dynamic ones). The proposed configuration might be integrated in a compact three-dimensional (3D) printed module and coupled to any conventional microscope for QPI of dynamic transparent samples.

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. But these methods are generally appropriate for "weakly scattering" samples in which the total phase delay induced by the object should be small. Consequently, high-resolution high-accuracy QPI of "nonweak" phase objects with fine details and large phase excursions remains a great challenge. In this Letter, we propose a mixed-transfer-function (MTF) approach to address the dilemma between measurement accuracy and imaging resolution. By effectively merging the phases reconstructed by TIE and WOTF in the frequency domain, the high-accuracy low-frequency phase "global" profile can be secured, and high-resolution high-frequency features can be well preserved simultaneously. Simulations and experimental results on a microlens array and unstained biological cells demonstrate the effectiveness of MTF.

Practical application of microsphere samples for benchmarking a quantitative phase imaging system

Quantitative phase imaging (QPI) provides an approach for monitoring the dry mass of individual cells by measuring the optical pathlength of visible light as it passes through cells. A distinct advantage of QPI is that the measurements result in optical path length quantities that are, in principle, instrument independent. Reference materials that induce a well‐defined optical pathlength shift and are compatible with QPI imaging systems will be valuable in assuring the accuracy of such measurements on different instruments. In this study, we evaluate seven combinations of microspheres embedded in index refraction matching media as candidate reference materials for benchmarking the performance of a QPI system and as calibration standards for the optical pathlength measurement. Poly(methyl metharylate) microspheres and mineral oil were used to evaluate the range of illumination apertures, signal‐to‐noise ratios, and focus positions that allow an accurate quantitative optical pathlength measurement. The microsphere‐based reference material can be used to verify settings on an instrument that are suitable for obtaining an accurate pathlength measurement from biological cells. The microsphere/media reference material is applied to QPI‐based dry mass measurements of a population of HEK293 cells to benchmark and provide evidence that the QPI image data are accurate.

Two improved defocus quantitative phase imaging methods: discussion

Multifilter phase imaging with partially coherent light (MFPI-PC) and phase optical transfer function recovery (POTFR) are two viable defocus-based, two-dimensional quantitative phase imaging (QPI) methods. While both methods use transfer function inversion, MFPI-PC is based on the in-focus intensity derivative, while POTFR is based on the intensity difference between symmetrically defocused images. This paper compares and contrasts MFPI-PC and POTFR. Six disadvantages (five in MFPI-PC and one in POTFR) are identified. Improvement strategies to overcome each of the six shortcomings are identified and implemented, and both methods are shown to be clearly improved. The revised MFPI-PC is shown to be more accurate than the original MFPI-PC and generally more accurate than the revised POTFR. The revised POTFR is shown to be inherently faster than the original POTFR and also slightly faster than the revised MFPI-PC.

Dual-mode phase and fluorescence imaging with a confocal laser scanning microscope

We present dual-mode phase and fluorescence imaging in a confocal laser scanning microscopy (CLSM) system. For phase imaging, the depth of field of the CLSM system is extended by fast axial scanning with a tunable acoustic gradient index of refraction lens. Under transillumination, intensity images of the sample are recorded at a few different defocusing distances. The phase image is reconstructed from these intensity images by using the transport-of-intensity equation. The 3D fluorescence image is obtained by confocal scanning. The dual-mode images with pixel-to-pixel correspondence yield complementary quantitative structural and functional information. Combination of the two imaging modalities enables standalone determination of the refractive index of live cells.

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. Second, the reconstructed phase tends to blur under spatially low-coherent illumination, especially when the defocus distance is beyond the near Fresnel region. Recent studies have shown that the shape of the illumination aperture has a significant impact on the resolution and phase reconstruction quality, and by simply replacing the conventional circular illumination aperture with an annular one, these two limitations can be addressed, or at least significantly alleviated. However, the annular aperture was previously empirically designed based on intuitive criteria related to the shape of PTF, which does not guarantee optimality. In this work, we optimize the illumination pattern to maximize TIE's performance based on a combined quantitative criterion for evaluating the "goodness" of an aperture. In order to make the size of the solution search space tractable, we restrict our attention to binary-coded axis-symmetric illumination patterns only, which are easier to implement and can generate isotropic TIE PTFs. We test the obtained optimal illumination by imaging both a phase resolution target and HeLa cells based on a small-pitch LED array, suggesting superior performance over other suboptimal patterns in terms of both signal-to-noise ratio (SNR) and spatial resolution.

Adaptive dual-exposure fusion-based transport of intensity phase microscopy

Via the transport of intensity phase microscopy, quantitative phase can be retrieved directly from captured multi-focal intensities. The accuracy of the retrieved phases depends highly on the quality of the recorded images; therefore, the exposure time should be carefully chosen for high-quality intensity captures. However, it is difficult to record well-exposure intensities to maintain rather a high signal to noise ratio and to avoid over-exposure due to the complex samples. In order to simplify the exposure determination, here the adaptive dual-exposure fusion-based transport of intensity phase microscopy is proposed: with captured short- and long-exposure images, the well-exposure multi-focal images can be numerically reconstructed, and then high-accurate phase can be computed from these reconstructed intensities. With both simulations and experiments provided in this paper, it is proved that the adaptive dual-exposure fusion-based transport of intensity phase microscopy not only provides numerically reconstructed well-exposure image with simple operation and fast speed but also extracts highly accurate retrieved phase. Moreover, the exposure time selection scope of the proposed method is much wider than that based on single exposure, and even though there is an over-exposure region in the long-exposure image, a well-exposure image can still be reconstructed with high precision. Considering its advantages of high accuracy, fast speed, simple operation, and wide application scope, the proposed technique can be adopted as quantitative phase microscopy for high-quality observations and measurements.

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. The reconstruction result of the benchmark quantitative phase microscopy target (QPT^TM) demonstrates a half-pitch lateral resolution of 775 nm across a large field-of-view of ∼29.84  mm², surpassing 2.15 times that of the theoretical Nyquist-Shannon sampling resolution limit imposed by the pixel size of the imaging sensor (1.67 μm). The proposed approach is also evaluated by imaging unstained HeLa cells, suggesting it is a promising toolset for high-throughput monitoring and quantitative analysis of unlabeled biological samples.

Solvent-Dependent Light-Induced Structures in Gem-Dichlorocyclopropanated Polybutadiene Solutions

The formation of permanent structures upon mild red laser illumination in transparent polydiene solutions is examined in the case of gem-dichlorocyclopropanated polybutadiene (gDCC-PB) polymers bearing 15% functional units of the dichlorocyclopropane groups. The response was found to be distinct from the precursor PB. Whereas fiber-like patterns were clearly observed in both precursor and gDCC-PB solutions in cyclohexane, these were absent in the case of gDCC-PB/chloroform but were present in the precursor PB/chloroform solutions. The involved mechanical stresses were not sufficient for the gDCC activation to be detected by NMR spectroscopy. Remarkably, addition of even 10 wt % gDCC-PB into the latter solution sufficed to suppress the light-induced patterning. The importance of the chemical environment on the response to light irradiation was further checked and confirmed by use of other PB copolymers. Different diameter patterns and kinetics were observed. The strong solvent and comonomer mediated effect was reflected neither in solvency nor in optical polarizability differences of the polymers solvent couples.

Comparative study of quantitative phase imaging techniques for refractometry of optical waveguides

A comparative study of quantitative phase imaging techniques for refractometry of optical waveguides is presented. Three techniques were examined: a method based on the transport-of-intensity equation, quadri-wave lateral shearing interferometry and digital holographic microscopy. The refractive index profile of a SMF-28 optical fiber was thoroughly characterized and served as a gold standard to assess the accuracy and precision of the phase imaging methods. Optical waveguides were inscribed in an Eagle2000 glass chip using a femtosecond laser and used to evaluate the sensitivity limit of these phase imaging approaches. It is shown that all three techniques provide accurate, repeatable and sensitive refractive index measurements. Using these phase imaging methods, we report a comprehensive map of the photosensitivity to femtosecond pulses of Eagle2000 glass. Finally, the reported data suggests that the phase imaging techniques are suited to be used as precise and non-destructive refractive index shift measuring tools to study and control the inscription process of optical waveguides.

Multi-focus TIE algorithm including partial spatial coherence and overlapping filters

The transport of intensity equation (TIE) relates the variation of intensity of a wave-front along its mean direction of propagation with its phase. In experimental application, characteristic artefacts may affect the retrieved phase. These originate from inadequacies in estimating the axial derivative and the amplification of noise in the inversion of the TIE. To tackle these issues, images recorded at multiple planes of focus can be integrated into a multi-focus TIE (MFTIE) solution. This methodology relies on the efficient sampling of phase information in the spatial-frequency domain, typically by the definition of band pass filters implemented as a progression of sharp spatial frequency cut-offs. We present a convenient MFTIE implementation which avoids the need for recording images at very specific planes of focus and applies overlapping cut-offs, greatly simplifying the experimental application. This new approach additionally also accounts for partial spatial coherence in a flux-preserving framework. Using simulated data as well as experimental data from optical microscopy and electron microscopy we show that the frequency response of this MFTIE algorithm recovers efficiently a wide range of spatial frequencies of the phase that can be further extended by simple iterative refinement.

Clarification and unification of the obliquity factor in diffraction and scattering theories: discussion

Two-dimensional (2D) and three-dimensional (3D) diffraction theories form the underlying basis of quantitative phase imaging. This paper reviews how 2D and 3D diffraction theories are developed based on thin and thick object requirements. However, some previously reported work has mixed 2D and 3D theories. This discussion shows that it is possible to enable consistent mixed use of 2D and 3D theories by applying appropriate obliquity factor (OF) modifications. The discussion is concluded with an overall unifying representation for the usage of the OF modifications in 2D and 3D diffraction theories as applied to both thin and thick objects.

Efficient quantitative phase microscopy using programmable annular LED illumination

In this work, we present an efficient quantitative phase imaging (QPI) approach using programmable annular LED illumination. As a new type of coded light source, the LED array provides flexible illumination control for noninterferometric QPI based on a traditional microscopic configurations. The proposed method modulates the transfer function of system by changing the LED illumination pattern, which provides noise-robust response of transfer function and achieves twice resolution limit of objective NA. The quantitative phase can be recovered from slightly defocused intensity images through inversion of transfer function. Moreover, the weak object transfer function (WOTF) of axis-symmetric oblique source is derived, and the noise-free and noisy simulation results validate the predicted theory. Finally, we experimentally confirm accurate and repeatable performance of our method by imaging calibrated phase samples and cellular specimens with different NA objectives.

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. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.

Wavefront-sensing-based autofocusing in microscopy

Massive image acquisition is required along the optical axis in the classical image-analysis-based autofocus method, which significantly decreases autofocus efficiency. A wavefront-sensing-based autofocus technique is proposed to increase the speed of autofocusing and obtain high localization accuracy. Intensities at different planes along the optical axis can be computed numerically after extracting the wavefront at defocus position with the help of the transport-of-intensity equation method. According to the focus criterion, the focal plane can then be determined, and after sample shifting to this plane, the in-focus image can be recorded. The proposed approach allows for fast, precise focus detection with fewer image acquisitions compared to classical image-analysis-based autofocus techniques, and it can be applied in commercial microscopes only with an extra illumination filter.

Kinetics of Light-Induced Concentration Patterns in Transparent Polymer Solutions

When exposed to weak visible laser light, solutions of common polymers like poly(isoprene) and poly(butadiene) respond by local concentration variations, which in turn lead to refractive index changes. Various micropatterns have been recently reported, depending mostly on the solvent environment and the irradiation conditions. Here, we focused on the simpler case of single polymer-rich filaments and we employed phase contrast microscopy to systematically investigate the influence of laser illumination and material parameters on the kinetics of the optically induced local concentration increase in the polydiene solutions. The refractive index contrast of the formed filaments increased exponentially with the laser illumination time. The growth rate exhibited linear dependence on the laser power and increased with polymer chain length in semidilute solutions in good solvents. On the contrary, the kinetics of the formed filaments appeared to be rather insensitive to the polymer concentration. Albeit the origin of the peculiar light field-polymer concentration coupling remains yet elusive, the new phenomenology is considered necessary for the elucidation of its mechanism.

Calibrated brightfield-based imaging for measuring intracellular protein concentration

Intracellular protein concentration is an essential cell characteristic, which manifests itself through the refractive index. The latter can be measured from two or more mutually defocused brightfield images analyzed using the TIE (transport-of-intensity equation). In practice, however, TIE does not always achieve quantitatively accurate results on biological cells. Therefore, we have developed a calibration procedure that involves successive imaging of cells in solutions containing different amounts of added protein. This allows one to directly relate the output of TIE (T) to intracellular protein concentration C (g/L). The resultant relationship has a simple form: C ≈ 1.0(T/V), where V is the cell volume (μm³ ) and 1.0 is an empirical coefficient. We used calibrated TIE imaging to characterize the regulatory volume increase (RVI) in adherent HeLa cells placed in a hyperosmotic solution. We found that while no RVI occurs over the first 30-60 min, the protein concentration fully recovers after 20 h. Because interpretation of such long experiments may depend on whether protein concentration varies significantly throughout the cell cycle, we measured this parameter in three cell lines: HeLa, MDCK and DU145. Our data indicate that protein concentration remains relatively stable in these cells. © 2017 International Society for Advancement of Cytometry.

Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC)

We present a new technique for quantitative phase and amplitude microscopy from a single color image with coded illumination. Our system consists of a commercial brightfield microscope with one hardware modification-an inexpensive 3D printed condenser insert. The method, color-multiplexed Differential Phase Contrast (cDPC), is a single-shot variant of Differential Phase Contrast (DPC), which recovers the phase of a sample from images with asymmetric illumination. We employ partially coherent illumination to achieve resolution corresponding to 2× the objective NA. Quantitative phase can then be used to synthesize DIC and phase contrast images or extract shape and density. We demonstrate amplitude and phase recovery at camera-limited frame rates (50 fps) for various in vitro cell samples and c. elegans in a micro-fluidic channel.

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. Such information may provide tremendous flexibility to emulate various microscopy modalities computationally without requiring specialized hardware components. We develop a requisite theory to describe such a hybrid computational multimodal imaging system, which yields quantitative phase, Zernike phase contrast, differential interference contrast, and light field moment imaging, simultaneously. It makes the various observations for biomedical samples easy. Then we give the experimental demonstration of these ideas by time-lapse imaging of live HeLa cell mitosis. Experimental results verify that a tunable lens-based TIE system, combined with the appropriate postprocessing algorithm, can achieve a variety of promising imaging modalities in parallel with the quantitative phase images for the dynamic study of cellular processes.

Quantitative phase imaging method based on an analytical nonparaxial partially coherent phase optical transfer function

Multifilter phase imaging with partially coherent light (MFPI-PC) is a promising new quantitative phase imaging method. However, the existing MFPI-PC method is based on the paraxial approximation. In the present work, an analytical nonparaxial partially coherent phase optical transfer function is derived. This enables the MFPI-PC to be extended to the realistic nonparaxial case. Simulations over a wide range of test phase objects as well as experimental measurements on a microlens array verify higher levels of imaging accuracy compared to the paraxial method. Unlike the paraxial version, the nonparaxial MFPI-PC with obliquity factor correction exhibits no systematic error. In addition, due to its analytical expression, the increase in computation time compared to the paraxial version is negligible.

Phase retrieval deblurring for imaging of dense object within a low scattering soft biological tissue

Tissues are characterized by a strong scattering of visible optical radiation, which prevents one from achieving deep-tissue imaging. We propose a computational imaging technique for the inference of specific macroscopic, spatial phase distribution features of the scattering media. The spatial phase distribution is reconstructed from several defocused intensity images. We empirically demonstrate the method by reconstructing the location of two fibula chicken bones, embedded within chicken breast tissue. The suggested technique is safe, using visible laser illumination, and noninvasive. It is also cost-effective since a simple optical system is used and the images are acquired using a conventional camera, and it does not require interferometric detection as well as direct access to the object in absence of the layer.

Quantitative phase imaging using transport of intensity equation with multiple bandpass filters

A phase imaging based on the transport of intensity equation using multiple bandpass filters is proposed. The proposed method enables us to measure a phase distribution quantitatively from through-focus intensity images obtained by using a white light source and multiple bandpass filters. The technique improves the accuracy of a phase measurement by increasing the number of intensity images obtained at different defocused positions. The feasibility of the phase measurement and the improvement in the accuracy with the increasing the through-focus images are confirmed by numerical simulations and optical experiments.

Three-dimensional block-based restoration integrated with wide-field fluorescence microscopy for the investigation of thick specimens with spatially variant refractive index

Development of a block-based restoration (BBR) method that addresses spatially variant (SV) imaging in wide-field fluorescence microscopy of thick samples is presented. The BBR method is based on a block-based imaging model, which approximates SV imaging using an efficient orthonormal basis decomposition of multiple SV point-spread functions computed at block vertices. The effect of reducing the number of blocks needed to account for SV imaging on the restoration accuracy was investigated with simulations using a numerical lung tissue phantom relevant to biological studies. Results show that reducing the number of blocks by 82% and 98% resulted in a 19% and 27% reduction in restoration accuracy, respectively, thereby establishing a reasonable tradeoff between computational resources and accuracy. Comparison of the BBR method to existing methods (deconvolution) that do not account for SV imaging demonstrates a 90% improvement in restoration accuracy. BBR results from synthetic and experimental images of a controlled test sample with SV refractive index (RI) show consistency, providing a validation of the BBR approach. In this study, information from DIC and fluorescence images was combined to identify regions with changing RI within the imaging volume. The BBR method provides a first step toward computationally tractable reconstruction of images from thick samples.

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. Then, we can directly reconstruct a high-quality phase map through inverse Fourier transform. What's more, in order to compensate the phase discrepancy resulted from strong absorption in the intensity, an iterative compensation algorithm is proposed. Both the simulation and experimental results demonstrate that our iterative OFC (IOFC) method can give a computationally efficient and noise-robust phase reconstruction for absorptive phase objects with higher accuracy and fewer defocus planes.

Quantitative phase microscopy via optimized inversion of the phase optical transfer function

Although the field of quantitative phase imaging (QPI) has wide-ranging biomedical applicability, many QPI methods are not well-suited for such applications due to their reliance on coherent illumination and specialized hardware. By contrast, methods utilizing partially coherent illumination have the potential to promote the widespread adoption of QPI due to their compatibility with microscopy, which is ubiquitous in the biomedical community. Described herein is a new defocus-based reconstruction method that utilizes a small number of efficiently sampled micrographs to optimally invert the partially coherent phase optical transfer function under assumptions of weak absorption and slowly varying phase. Simulation results are provided that compare the performance of this method with similar algorithms and demonstrate compatibility with large phase objects. The accuracy of the method is validated experimentally using a microlens array as a test phase object. Lastly, time-lapse images of live adherent cells are obtained with an off-the-shelf microscope, thus demonstrating the new method's potential for extending QPI capability widely in the biomedical community.

The influence of the microscope lamp filament colour temperature on the process of digital images of histological slides acquisition standardization

Background

The aim of this study is to compare the digital images of the tissue biopsy captured with optical microscope using bright field technique under various light conditions. The range of colour's variation in immunohistochemically stained with 3,3'-Diaminobenzidine and Haematoxylin tissue samples is immense and coming from various sources. One of them is inadequate setting of camera's white balance to microscope's light colour temperature. Although this type of error can be easily handled during the stage of image acquisition, it can be eliminated with use of colour adjustment algorithms. The examination of the dependence of colour variation from microscope's light temperature and settings of the camera is done as an introductory research to the process of automatic colour standardization.

Methods

Six fields of view with empty space among the tissue samples have been selected for analysis. Each field of view has been acquired 225 times with various microscope light temperature and camera white balance settings. The fourteen randomly chosen images have been corrected and compared, with the reference image, by the following methods: Mean Square Error, Structural SIMilarity and visual assessment of viewer.

Results

For two types of backgrounds and two types of objects, the statistical image descriptors: range, median, mean and its standard deviation of chromaticity on a and b channels from CIELab colour space, and luminance L, and local colour variability for objects' specific area have been calculated. The results have been averaged for 6 images acquired in the same light conditions and camera settings for each sample.

Conclusions

The analysis of the results leads to the following conclusions: (1) the images collected with white balance setting adjusted to light colour temperature clusters in certain area of chromatic space, (2) the process of white balance correction for images collected with white balance camera settings not matched to the light temperature moves image descriptors into proper chromatic space but simultaneously the value of luminance changes. So the process of the image unification in a sense of colour fidelity can be solved in separate introductory stage before the automatic image analysis.

Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks

We report theoretical and experimental results for imaging of electromagnetic phase edge effects in lithography photomasks. Our method starts from the transport of intensity equation (TIE), which solves for phase from through-focus intensity images. Traditional TIE algorithms make an implicit assumption that the underlying in-plane power flow is curl-free. Motivated by our current study, we describe a practical situation in which this assumption breaks down. Strong absorption gradients in mask features interact with phase edges to contribute a curl to the in-plane Poynting vector, causing severe artifacts in the phase recovered. We derive how curl effects are coupled into intensity measurements and propose an iterative algorithm that not only corrects the artifacts, but also recovers missing curl components.

Low-noise phase imaging by hybrid uniform and structured illumination transport of intensity equation

We demonstrate a new approach to the transport of intensity equation (TIE) phase retrieval method which uses structured illumination to improve low-frequency noise performance. In the hybrid scheme, two phase images are acquired: one with uniform and one with sinusoidal grating illumination intensity. The former preserves the high spatial frequency features of the phase best, whereas the latter dramatically increase the response at low spatial frequencies (where traditional TIE notoriously suffers). We then theoretically prove the design of a spectral filter that optimally combines the two phase results while suppressing noise. The combination of uniformly and structured illuminated TIE (hybrid TIE) phase imaging is experimentally demonstrated optically with a calibrated pure phase object.

Boundary-artifact-free phase retrieval with the transport of intensity equation II: applications to microlens characterization

Boundary conditions play a crucial role in the solution of the transport of intensity equation (TIE). If not appropriately handled, they can create significant boundary artifacts across the reconstruction result. In a previous paper [Opt. Express 22, 9220 (2014)], we presented a new boundary-artifact-free TIE phase retrieval method with use of discrete cosine transform (DCT). Here we report its experimental investigations with applications to the micro-optics characterization. The experimental setup is based on a tunable lens based 4f system attached to a non-modified inverted bright-field microscope. We establish inhomogeneous Neumann boundary values by placing a rectangular aperture in the intermediate image plane of the microscope. Then the boundary values are applied to solve the TIE with our DCT-based TIE solver. Experimental results on microlenses highlight the importance of boundary conditions that often overlooked in simplified models, and confirm that our approach effectively avoid the boundary error even when objects are located at the image borders. It is further demonstrated that our technique is non-interferometric, accurate, fast, full-field, and flexible, rendering it a promising metrological tool for the micro-optics inspection.

Multifilter phase imaging with partially coherent light

A novel quantitative phase imaging method is shown to estimate phase accurately over a wide range of length scales using Köhler illumination from an extended incoherent source. The method is based on estimating the longitudinal intensity derivative in the transport-of-intensity equation via convolution with multiple Savitzky-Golay differentiation filters and generalizes methods previously developed for coherent imaging to the practical scenario of partially coherent imaging. The resulting noise and resolution performance are evaluated via numerical simulation and demonstrated experimentally using a blazed transmission grating as well as a single-mode fiber as test objects.

Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform

The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications.

Direct imaging of phase objects enables conventional deconvolution in bright field light microscopy

In transmitted optical microscopy, absorption structure and phase structure of the specimen determine the three-dimensional intensity distribution of the image. The elementary impulse responses of the bright field microscope therefore consist of separate absorptive and phase components, precluding general application of linear, conventional deconvolution processing methods to improve image contrast and resolution. However, conventional deconvolution can be applied in the case of pure phase (or pure absorptive) objects if the corresponding phase (or absorptive) impulse responses of the microscope are known. In this work, we present direct measurements of the phase point- and line-spread functions of a high-aperture microscope operating in transmitted bright field. Polystyrene nanoparticles and microtubules (biological polymer filaments) serve as the pure phase point and line objects, respectively, that are imaged with high contrast and low noise using standard microscopy plus digital image processing. Our experimental results agree with a proposed model for the response functions, and confirm previous theoretical predictions. Finally, we use the measured phase point-spread function to apply conventional deconvolution on the bright field images of living, unstained bacteria, resulting in improved definition of cell boundaries and sub-cellular features. These developments demonstrate practical application of standard restoration methods to improve imaging of phase objects such as cells in transmitted light microscopy.

Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope

We demonstrate a single-camera imaging system that can simultaneously acquire brightfield, darkfield, and phase contrast images in real time. Our method uses computational illumination via a programmable light-emitting diode (LED) array at the source plane, providing flexible patterning of illumination angles. Brightfield, darkfield, and differential phase contrast images are obtained by changing the LED patterns, without any moving parts. Previous work with LED array illumination was only valid for static samples because the hardware speed was not fast enough to meet real-time acquisition and processing requirements. Here, we time multiplex patterns for each of the three contrast modes in order to image dynamic biological processes in all three contrast modes simultaneously. We demonstrate multicontrast operation at the maximum frame rate of our camera (50 Hz with 2160 × 2560 pixels).

High-speed transport-of-intensity phase microscopy with an electrically tunable lens

We present a high-speed transport-of-intensity equation (TIE) quantitative phase microscopy technique, named TL-TIE, by combining an electrically tunable lens with a conventional transmission microscope. This permits the specimen at different focus position to be imaged in rapid succession, with constant magnification and no physically moving parts. The simplified image stack collection significantly reduces the acquisition time, allows for the diffraction-limited through-focus intensity stack collection at 15 frames per second, making dynamic TIE phase imaging possible. The technique is demonstrated by profiling of microlens array using optimal frequency selection scheme, and time-lapse imaging of live breast cancer cells by inversion the defocused phase optical transfer function to correct the phase blurring in traditional TIE. Experimental results illustrate its outstanding capability of the technique for quantitative phase imaging, through a simple, non-interferometric, high-speed, high-resolution, and unwrapping-free approach with prosperous applications in micro-optics, life sciences and bio-photonics.

Noninterferometric single-shot quantitative phase microscopy

We present a noninterferometric single-shot quantitative phase microscopy technique with the use of the transport of intensity equation (TIE). The optical configuration is based on a Michelson-like architecture attached to a nonmodified inverted transmission bright field microscope. Two laterally separated images from different focal planes can be obtained simultaneously by a single camera exposure, enabling the TIE phase recovery to be performed at frame rates that are only camera limited. Precise measurement of a microlens array validates the principle and demonstrates the accuracy of the method. Investigations of chemical-induced apoptosis and the phagocytosis process of macrophages are then presented, suggesting that the method developed can provide promising applications in the dynamic study of cellular processes.

Transport-of-intensity phase imaging using Savitzky-Golay differentiation filter--theory and applications

Several existing strategies for estimating the axial intensity derivative in the transport-of-intensity equation (TIE) from multiple intensity measurements have been unified by the Savitzky-Golay differentiation filter--an equivalent convolution solution for differentiation estimation by least-squares polynomial fitting. The different viewpoint from the digital filter in signal processing not only provides great insight into the behaviors, the shortcomings, and the performance of these existing intensity derivative estimation algorithms, but more important, it also suggests a new way of improving solution strategies by extending the applications of Savitzky-Golay differentiation filter in TIE. Two novel methods for phase retrieval based on TIE are presented--the first by introducing adaptive-degree strategy in spatial domain and the second by selecting optimal spatial frequencies in Fourier domain. Numerical simulations and experiments verify that the second method outperforms the existing methods significantly, showing reliable retrieved phase with both overall contrast and fine phase variations well preserved.

Nonlinear diffusion regularization for transport of intensity phase imaging

We demonstrate a nonlinear diffusion (NLD) regularization method to solve the transport of intensity equation (TIE). A novel NLD regularization function is proposed to enforce piecewise-constant priors and to remove low-frequency artifacts in the TIE solution.

Self-induced transparency in diblock copolymer dispersions

We report on the versatile effect of weak red laser light impinging on diblock copolymer [poly(isoprene-b-styrene)] dispersions in two selective solvents for each block. In the strongly scattering but transparent micellar solutions in hexane (a good solvent for polyisoprene), higher refractive index copolymer-rich fibers were formed. In the turbid dispersions of the same copolymer in ethyl acetate (a good solvent for polystyrene), the effect of self-induced transparency was observed. A two-step patterning mechanism caused the generation of a transparent microchannel, increasing light transmission. The analogy between the current effect and that observed in homopolymer polyisoprene solutions in different solvents is discussed toward an understanding of the unanticipated light-soft-matter interaction.

Laser oblique scanning optical microscopy (LOSOM) for phase relief imaging

The visualization of optical phase can provide abundant information when imaging transparent specimen. We present a novel phase sensitive imaging design capable of obtaining phase contours of transparent biological cells through laser oblique scanning optical microscope (LOSOM). LOSOM is based on the introduction of a fluorescent medium behind the specimen to generate a differential phase-sensitive image, thus, the complicated phase retardation alignment procedure associated with differential interference contrast (DIC) microscopy can be eliminated. Moreover, multi-modality fluorescence and phase relief imaging can be attained in a single system with fluorescently labeled specimens.

Maskless imaging of dense samples using pixel super-resolution based multi-height lensfree on-chip microscopy

Lensfree in-line holographic microscopy offers sub-micron resolution over a large field-of-view (e.g., ~24 mm2) with a cost-effective and compact design suitable for field use. However, it is limited to relatively low-density samples. To mitigate this limitation, we demonstrate an on-chip imaging approach based on pixel super-resolution and phase recovery, which iterates among multiple lensfree intensity measurements, each having a slightly different sample-to-sensor distance. By digitally aligning and registering these lensfree intensity measurements, phase and amplitude images of dense and connected specimens can be iteratively reconstructed over a large field-of-view of ~24 mm2 without the use of any spatial masks. We demonstrate the success of this multi-height in-line holographic approach by imaging dense Papanicolaou smears (i.e., Pap smears) and blood samples.

Label-free intracellular transport measured by spatial light interference microscopy

We show that applying the Laplace operator to a speckle-free quantitative phase image reveals an unprecedented level of detail in cell structure, without the gradient artifacts associated with differential interference contrast microscopy, or photobleaching and phototoxicity limitations common in fluorescence microscopy. This method, referred to as Laplace phase microscopy, is an efficient tool for tracking vesicles and organelles in living cells. The principle is demonstrated by tracking organelles in cardiomyocytes and vesicles in neurites of hippocampal neurons, which to our knowledge are the first label-free diffusion measurements of the organelles in such cells.

Refractive index determination of transparent samples by noniterative phase retrieval

We present a simple method to determine the refractive indices of transparent specimens. The refractive index of an object under investigation is received by evaluating the optical path difference introduced by the object, while taking into account geometric parameters. The optical path difference that corresponds to the phase distribution is obtained by a noninterferometric, noniterative phase retrieval method based on Green's functions. It will be shown that this technique is a highly accurate and quantitative method for refractive index determination.