Three-dimensional Optical Transfer Function Research Articles

DeepRegularizer: Rapid Resolution Enhancement of Tomographic Imaging Using Deep Learning.

Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor axial resolution due to limited access to the three-dimensional optical transfer function. This missing cone problem has been addressed through regularization algorithms that use a priori information, such as non-negativity and sample smoothness. However, the iterative nature of these algorithms and their parameter dependency make real-time visualization impossible. In this article, we propose and experimentally demonstrate a deep neural network, which we term DeepRegularizer, that rapidly improves the resolution of a three-dimensional refractive index map. Trained with pairs of datasets (a raw refractive index tomogram and a resolution-enhanced refractive index tomogram via the iterative total variation algorithm), the three-dimensional U-net-based convolutional neural network learns a transformation between the two tomogram domains. The feasibility and generalizability of our network are demonstrated using bacterial cells and a human leukaemic cell line, and by validating the model across different samples. DeepRegularizer offers more than an order of magnitude faster regularization performance compared to the conventional iterative method. We envision that the proposed data-driven approach can bypass the high time complexity of various image reconstructions in other imaging modalities.

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.

Three-dimensional optical transfer function in differential confocal microscopy.

To reveal the fundamental characteristics of differential confocal microscopy (DCM), its imaging properties were analysed by studying the 3D optical transfer function (OTF). The zero transfer at zero frequency along the axial direction in DCM, which has not been well understood and is considerably different from the transfer behaviour in conventional confocal microscopy (CM), was elucidated. The integral expressions of the OTFs for CM and DCM and the subsequent simulation results showed that DCMs have higher transfer capability than CM in the axial direction at medium and high frequencies. Conventionally, the relative optimal defocusing amount in DCMs are determined through calculations of the gradient of the point spread functions in the spatial domain. In contrast, in this study, the OTF performances were compared and the optimal defocusing amount was found to be between 5 and 7.

Three‐dimensional optical transfer functions in the aberration‐corrected scanning transmission electron microscope

In the scanning transmission electron microscope, hardware aberration correctors can now correct for the positive spherical aberration of round electron lenses. These correctors make use of nonround optics such as hexapoles or octupoles, leading to the limiting aberrations often being of a nonround type. Here we explore the effect of a number of potential limiting aberrations on the imaging performance of the scanning transmission electron microscope through their resulting optical transfer functions. In particular, the response of the optical transfer function to changes in defocus are examined, given that this is the final aberration to be tuned just before image acquisition. The resulting three-dimensional optical transfer functions also allow an assessment of the performance of a system for focal-series experiments or optical sectioning applications.

Study of the imaging property of a fluorescent confocal microscopy with a phase-only filter in an extended source

The phase information of an enlarged source is reconstructed with an annular two-zone phase-only filter in a fluorescent confocal scanning optical microscope for resolution improvement. The dependences of its resolution on the source size and on the phase transmission of the outer annular zone of the filter are investigated theoretically by use of its three-dimensional optical transfer function (3D OTF). The increased source size and the required phase value of the outer annular zone of the phase-only filter for an optimal 3D OTF of the optical system are presented.

The sampling limit in fluorescence microscopy

Sampling in fluorescence microscopy is treated using the concept of the three-dimensional (3D) optical transfer function (OTF). The border of the OTF frequency surface defines the required minimum sampling. The shape of the OTF is derived from simple considerations and valid for far-field high numerical aperture, vector theory. Optimal regular sampling is achieved by a hexagonal grid in 2D, and corresponding hexagonal structures, body-centered cubic (bcc) and hexagonal close-packed (hcp) structures, in 3D. As compared to standard (rectilinear grid) sampling a reduction of 13.4% in 2D and 29.3% in 3D can be achieved with optimized sampling. This reduction in data size is also accompanied by an imaging speed improvement, a reduction of sample bleaching, and can lead to imaging with better signal to noise ratio.

Coherent confocal microscope with a phase-only filter in its extended source

The phase information of an extended source is reconstructed by use of a two-zone (annular) phase-only filter in a coherent confocal scanning optical microscope. The dependence of its resolution on its source size is investigated theoretically by its three-dimensional optical transfer function (3D OTF). The results show that the resolution is improved, even though the source size is enlarged.

Parameterized code SHARM-3D for radiative transfer over inhomogeneous surfaces

The code SHARM-3D, developed for fast and accurate simulations of the monochromatic radiance at the top of the atmosphere over spatially variable surfaces with Lambertian or anisotropic reflectance, is described. The atmosphere is assumed to be laterally uniform across the image and to consist of two layers with aerosols contained in the bottom layer. The SHARM-3D code performs simultaneous calculations for all specified incidence-view geometries and multiple wavelengths in one run. The numerical efficiency of the current version of code is close to its potential limit and is achieved by means of two innovations. The first is the development of a comprehensive precomputed lookup table of the three-dimensional atmospheric optical transfer function for various atmospheric conditions. The second is the use of a linear kernel model of the land surface bidirectional reflectance factor (BRF) in our algorithm that has led to a fully parameterized solution in terms of the surface BRF parameters. The code is also able to model inland lakes and rivers. The water pixels are described with the Nakajima-Tanaka BRF model of wind-roughened water surface with a Lambertian offset, which is designed to model approximately the reflectance of suspended matter and of a shallow lake or river bottom.

Enlargement of source size and improvement of resolution in fluorescent confocal microscope

Since the larger source size causes the worse optical resolution in a fluorescent confocal optical scanning microscope, a two-zone (annular) phase-only filter is employed to modify the phase information of each annular zone of the enlarged coherent source. The three-dimensional optical transfer function (3D OTF) of the above optical system is derived. The calculated results of the 3D OTF show that the source size is enlarged and the optical resolution is improved.

Quantitative phase amplitude microscopy IV: imaging thick specimens.

The ability to image phase distributions with high spatial resolution is a key capability of microscopy systems. Consequently, the development and use of phase microscopy has been an important aspect of microscopy research and development. Most phase microscopy is based on a form of interference. Some phase imaging techniques, such as differential interference microscopy or phase microscopy, have a low coherence requirement, which enables high-resolution imaging but in effect prevents the acquisition of quantitative phase information. These techniques are therefore used mainly for phase visualization. On the other hand, interference microscopy and holography are able to yield quantitative phase measurements but cannot offer the highest resolution. A new approach to phase microscopy, quantitative phase-amplitude microscopy (QPAM) has recently been proposed that relies on observing the manner in which intensity images change with small defocuses and using these intensity changes to recover the phase. The method is easily understood when an object is thin, meaning its thickness is much less than the depth of field of the imaging system. However, in practice, objects will not often be thin, leading to the question of what precisely is being measured when QPAM is applied to a thick object. The optical transfer function formalism previously developed uses three-dimensional (3D) optical transfer functions under the Born approximation. In this paper we use the 3D optical transfer function approach of Streibl not for the analysis of 3D imaging methods, such as tomography, but rather for the problem of analysing 2D phase images of thick objects. We go on to test the theoretical predictions experimentally. The two are found to be in excellent agreement and we show that the 3D imaging properties of QPAM can be reliably predicted using the optical transfer function formalism.

Three-dimensional optical-transfer-function analysis of fiber-optical two-photon fluorescence microscopy.

The three-dimensional optical transfer function is derived for analyzing the imaging performance in fiber-optical two-photon fluorescence microscopy. Two types of fiber-optical geometry are considered: The first involves a single-mode fiber for delivering a laser beam for illumination, and the second is based on the use of a single-mode fiber coupler for both illumination delivery and signal collection. It is found that in the former case the transverse and axial cutoff spatial frequencies of the three-dimensional optical transfer function are the same as those in conventional two-photon fluorescence microscopy without the use of a pinhole.However, the transverse and axial cutoff spatial frequencies in the latter case are 1.7 times as large as those in the former case. Accordingly, this feature leads to an enhanced optical sectioning effect when a fiber coupler is used, which is consistent with our recent experimental observation.

Imaging theory and resolution improvement of two-photon confocal microscopy

The nonlinear effect of two-photon excitation on the imaging property of two-photon confocal microscopy has been analyzed by the two-photon fluorescence intensity transfer function derived in this paper. The two-photon fluorescence intensity transfer function in a confocal microscopy is given. Furthermore the three-dimensional point spread function (3D-PSF) and the three-dimensional optical transfer function (3D-OTF) of two-photon confocal microscopy are derived based on the nonlinear effect of two-photon excitation. The imaging property of two-photon confocal microscopy is discussed in detail based on 3D-OTF. Finally the spatial resolution limit of two-photon confocal microscopy is discussed according to the uncertainty principle.

Three-dimensional transfer functions of coherent anti-Stokes Raman scattering microscopy.

The three-dimensional coherent transfer function of confocal coherent anti-Stokes Raman scattering microscopy was derived theoretically. The three-dimensional optical transfer function was also derived under the weak-contrast assumption. The effect of a pinhole in front of the detector on the optical transfer function was estimated, and it was found that the cutoff frequency of the optical transfer function is independent of the pinhole. Micrometer-order spatial resolution along the optical axis was also experimentally demonstrated.

THE IMAGING THEORY OF TWO-PHOTON AND MULTI-PHOTON CONFOCAL SCANNING MICROSCOPY

The Imaging theory of two-photon and multi-photon confocal scanning microscopy is presented. The three-dimensional point spread function and three-dimensional optical transfer function of two-photon confocal scanning microscopy is derived. By using the three-dimensional point spread function and three-dimensional optical transfer function theory, we have proved that the horizontal and vertical resolutions of two-photon confocal scanning microscopy are higher than those of the single photon confocal scanning microscopy, and the space resolution of multi-photon confocal scanning microscopy is higher than that of two-photon confocal scanning microscopy.

Optical transfer function in three dimensions for a large numerical aperture

Abstract We calculate the three-dimensional optical transfer function for an ordinary microscope with a large numerical aperture by elementary mathematical methods. The support of this function has been found before but not its values. Numerical Fourier transformation gives the corresponding point spread function.

Optical transfer function in three dimensions for a large numerical aperture

We calculate the three-dimensional optical transfer function for an ordinary microscope with a large numerical aperture by elementary mathematical methods. The support of this function has been found before but not its values. Numerical Fourier transformation gives the corresponding point spread function.

Image formation in three-photon fluorescence microscopy

Image formation in three-photon fluorescence microscopy is analysed. The point spread function, three-dimensional optical transfer function and axial resolution are considered. The results are generalized to multiphoton fluorescence. Three-photon fluorescence is particularly amenable to resolution improvement by use of pupil filters.

Resolution in three-photon fluorescence scanning microscopy

Resolution in potential three-photon fluorescence scanning microscopy is discussed in terms of the threedimensional optical transfer function. Images of layers and sharp edges are presented for a comparison of the resolution with that in two-photon fluorescence microscopic imaging. For the same fluorescence wavelength the resolution is almost the same in both cases. However, for a given illumination wavelength the resolution for imaging a thick object in the case of three-photon fluorescence imaging can be improved by as much as 40-50% relative to that in two-photon imaging.

Differential phase-contrast microscope with a split detector for the readout system of a multilayered optical memory

A transmission differential phase-contrast microscope with a split detector is used as a readout system for a multilayered three-dimensional optical memory. The system is applicable to data recorded as refractive-index changes. The system is compact and easy to use. The three-dimensional optical transfer function for the system is derived. This shows that the spatial bandwidth of the system is the same as that of a conventional microscope with incoherent illumination but with much improved contrast. Six layers of information are recorded in a photopolymer and are read out with little cross talk and high contrast.

Three-dimensional Optical Transfer Function for Weak Aberrations

Abstract The phase variations of the three-dimensional optical transfer function for incoherent optical systems with weak aberrations of different types are developed in algebraic form. Both single Seidel terms and Zernike sums are considered.