Beyond Born-Rytov limit for super-resolution optical diffraction tomography

Roadmap on Label-Free Super-Resolution Imaging

Label-free super-resolution (LFSR) imaging relies on light-scattering processes in nanoscale objects without a need for fluorescent (FL) staining required in super-resolved FL microscopy. The objectives of this Roadmap are to present a comprehensive vision of the developments, the state-of-the-art in this field, and to discuss the resolution boundaries and hurdles which need to be overcome to break the classical diffraction limit of the LFSR imaging. The scope of this Roadmap spans from the advanced interference detection techniques, where the diffraction-limited lateral resolution is combined with unsurpassed axial and temporal resolution, to techniques with true lateral super-resolution capability which are based on understanding resolution as an information science problem, on using novel structured illumination, near-field scanning, and nonlinear optics approaches, and on designing superlenses based on nanoplasmonics, metamaterials, transformation optics, and microsphere-assisted approaches. To this end, this Roadmap brings under the same umbrella researchers from the physics and biomedical optics communities in which such studies have often been developing separately. The ultimate intent of this paper is to create a vision for the current and future developments of LFSR imaging based on its physical mechanisms and to create a great opening for the series of articles in this field.

3D scattering microphantom sample to assess quantitative accuracy in tomographic phase microscopy techniques

In this paper we present a structurally-complex biomimetic scattering structure, fabricated with two-photon polymerization, and utilize this object in order to benchmark a computational imaging system. The phantom allows to tailor the scattering by modifying its degrees of freedom i.e. refractive index contrast and scattering layer dimensions and incorporates a 3D imaging quality test, representing a single cell within tissue. While the sample may be used with multiple 3D microscopy techniques, we demonstrate the impact of scattering on three tomographic phase microscopy (TPM) reconstruction methods. One of these methods assumes the sample to be weak-scattering, while the other two take multiple scattering into account. The study is performed at two wavelengths (visible and near-infrared), which serve as a scaling factor for the scattering phenomenon. We find that changing the wavelength from visible into near-infrared impacts the applicability of TPM reconstruction methods. As a result of reduced scattering in near-infrared region, the multiple-scattering-oriented techniques perform in fact worse than a method aimed for weak-scattering samples. This implies a necessity of selecting proper approach depending on sample's scattering characteristics even in case of subtle changes in the object-light interaction.

Scalar approximation of Maxwell equations: derivation and accuracy

Replacing Maxwell equations by a scalar wave equation is often used in computational imaging to simulate the light-sample interaction. It significantly reduces the computational burden but provides field maps that are insensitive to the polarization of the incident field, provided the latter is constant throughout the sample. Here, we develop a scalar approximation that accounts for the polarization of the incident field. Comparisons with rigorous simulations show that this approach is more accurate than the classical scalar approximation with similar computational cost.

Optimizing sample illumination scanning for reflection and 4Pi tomographic diffractive microscopy

Tomographic diffractive microscopy (TDM) is increasingly gaining attention, owing to its high-resolution, label-free imaging capability. Fast acquisitions necessitate limiting the number of holograms to be recorded. Reconstructions then rely on optimal Fourier space filling to retain image quality and resolution, that is, they rely on optimal scanning of the tomographic illuminations. In this work, we theoretically study reflection TDM, and then the 4Pi TDM, a combination of transmission and reflection systems. Image simulations are conducted to determine optimal angular sweeping. We found that three-dimensional uniform scanning fills Fourier space the best for both reflection and 4Pi configurations, providing a better refractive index estimation for the observed sample.

Holotomography: Refractive Index as an Intrinsic Imaging Contrast for 3-D Label-Free Live Cell Imaging

Live cell imaging provides essential information in the investigation of cell biology and related pathophysiology. Refractive index (RI) can serve as intrinsic optical imaging contrast for 3-D label-free and quantitative live cell imaging, and provide invaluable information to understand various dynamics of cells and tissues for the study of numerous fields. Recently significant advances have been made in imaging methods and analysis approaches utilizing RI, which are now being transferred to biological and medical research fields, providing novel approaches to investigate the pathophysiology of cells. To provide insight into how RI can be used as an imaging contrast for imaging of biological specimens, here we provide the basic principle of RI-based imaging techniques and summarize recent progress on applications, ranging from microbiology, hematology, infectious diseases, hematology, and histopathology.

Three-dimensional phase optical transfer function in axially symmetric microscopic quantitative phase imaging

Three-dimensional quantitative phase imaging (3D QPI) is widely recognized as a potentially high-impact microscopic modality. Central to determining the resolution capability of 3D QPI is the phase optical transfer function (POTF). The magnitude of the POTF over its spatial frequency coverage (SFC) specifies the intensity of the response for each allowed spatial frequency. In this paper, a detailed analysis of the POTF for an axially symmetric optical configuration is presented. First, a useful geometric interpretation of the SFC, which enables its visualization, is presented. Second, a closed-form 1D integral expression is derived for the POTF in the general nonparaxial case, which enables rapid calculation of the POTF. Third, this formulation is applied to disk, annular, multi-annuli, and Gaussian illuminations as well as to an annular objective. Taken together, these contributions enable the visualization and simplified calculation of the 3D axially symmetric POTF and provide a basis for optimizing QPI in a wide range of applications.

Deep Learning Diffuse Optical Tomography

Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon scattering physics and ill-posedness, the conventional reconstruction algorithms are sensitive to imaging parameters such as boundary conditions. To address this, here we propose a novel deep learning approach that learns non-linear photon scattering physics and obtains an accurate three dimensional (3D) distribution of optical anomalies. In contrast to the traditional black-box deep learning approaches, our deep network is designed to invert the Lippman-Schwinger integral equation using the recent mathematical theory of deep convolutional framelets. As an example of clinical relevance, we applied the method to our prototype DOT system. We show that our deep neural network, trained with only simulation data, can accurately recover the location of anomalies within biomimetic phantoms and live animals without the use of an exogenous contrast agent.

Fast multiple-scattering holographic tomography based on the wave propagation method

We develop a time-efficient computation scheme for a holographic tomography reconstruction technique that accounts for multiple scattering by applying the forward model based on the wave propagation method (WPM). The computational efficiency is achieved by employing adjoint equations for calculation of the gradient of the data fidelity term in the gradient descent optimization procedure. In the paper we provide a general computation scheme that is suitable for various forward models that can be represented in the form of an iterative equation. Next, we provide the complete solution for the time-efficient reconstruction utilizing WPM. In the considered reconstruction case, the proposed algorithm enables the 114-fold speed-up of computations with respect to the original tomographic method.

3D-printed biological cell phantom for testing 3D quantitative phase imaging systems

As the 3D quantitative phase imaging (QPI) methods mature, their further development calls for reliable tools and methods to characterize and compare their metrological parameters. We use refractive index engineering during two-photon laser photolithography to fabricate a life-scale phantom of a biological cell with internal structures that mimic optical and structural properties of mammalian cells. After verification with a number of reference techniques, the phantom is used to characterize the performance of a limited-angle holographic tomography microscope.

High-fidelity optical diffraction tomography of multiple scattering samples

We propose an iterative reconstruction scheme for optical diffraction tomography that exploits the split-step non-paraxial (SSNP) method as the forward model in a learning tomography scheme. Compared with the beam propagation method (BPM) previously used in learning tomography (LT-BPM), the improved accuracy of SSNP maximizes the information retrieved from measurements, relying less on prior assumptions about the sample. A rigorous evaluation of learning tomography based on SSNP (LT-SSNP) using both synthetic and experimental measurements confirms its superior performance compared with that of the LT-BPM. Benefiting from the accuracy of SSNP, LT-SSNP can clearly resolve structures that are highly distorted in the LT-BPM. A serious limitation for quantifying the reconstruction accuracy for biological samples is that the ground truth is unknown. To overcome this limitation, we describe a novel method that allows us to compare the performances of different reconstruction schemes by using the discrete dipole approximation to generate synthetic measurements. Finally, we explore the capacity of learning approaches to enable data compression by reducing the number of scanning angles, which is of particular interest in minimizing the measurement time.

Partially coherent illumination engineering for enhanced refractive index tomography

Optical diffraction tomography based on partially coherent illumination (PC-ODT) is a quantitative label-free imaging technique that allows reconstructing of the object's 3D refractive index from measured through-focus intensity images. PC illumination provides advantages such as speckle noise-free imaging and inherent compatibility with conventional wide-field microscopes. Here we experimentally demonstrate that a proper design of the PC illumination, different from the familiar bright-field one, and the use of more realistic optical transfer functions (OTFs) have crucial importance in PC-ODT to significantly increase the accuracy in 3D refractive index reconstruction. While realistic OTFs properly account for the real experimental illumination conditions, the proposed PC illumination design allows for gathering the object spatial-frequency content attenuated when bright-field illumination is used.

Refractive index of adipose tissue and lipid droplet measured in wide spectral and temperature ranges

This study presents refractive index measurements of human and porcine adipose tissues and lipid droplet content in the visible and near-infrared. The coefficients of the Sellmeier formula were calculated for approximation of tissue dispersion. For the first time, to the best of our knowledge, the phase transition temperatures and temperature increments dn/dT of adipose tissue were quantified for a wide wavelength range from 480 to 1550 nm and from room temperature up to 50°C. For human abdominal adipose tissue, the refractive index increment averaged across all wavelengths is dn/dT=-(3.54±0.15)×10^-4°C^-1, for porcine tissue dn/dT=-7.92(0.74)×10^-4°C^-1, and for porcine lipid droplet dn/dT=-6.01(0.29)×10^-4°C^-1. Data available in literature for refractive indices of adipose tissues measured by different techniques are summarized and compared with the received data.