Speckle is a well-known and inevitable phenomenon exhibiting in optical coherence tomography (OCT). However, conventional OCT imaging formula cannot isolate the speckles from a meaningful OCT image. Here we introduce a new formulation of OCT to mathematically explicitly represent the meaningful image and speckle. We represent an intensity OCT image as a collection of complex contributions from scatterers. This formulation clarified that the intensity OCT image is the summation of a meaningful OCT image and speckles. In addition, it was found that the meaningful OCT image is equivalent to the incoherent image of the sample. This equation also recapitulates well-known properties of speckle.
We construct a universal image formation theory that covers almost all optical imaging systems with diverse (coherent, incoherent, linear, and nonlinear) light-matter interactions, by utilizing Feynman diagrams. To deal with all optical systems ranging from classical to cutting-edge instruments including OCT in one framework, we reformulate the theory in four dimensions. We incorporate the vacuum field to treat incoherent interactions by using the operator for electric field.
KEYWORDS: Optical coherence tomography, Point spread functions, Speckle, Signal processing, Signal analyzers, In vivo imaging, Artificial intelligence, Refractive index, Microscopy, Mathematical modeling
A new formulation of Optical Coherence Tomography (OCT) is presented. This formulation can represent a meaningful OCT image and speckles as two independent mathematical entities. In addition, by using the same formulation strategy, a new imaging modality to generate a spatially differential image, similar to differential interferometric contrast microscopy is demonstrated.
Differential interference microscopy (DIC) is a method to obtain the refractive index distribution of a sample as contrast. It is suitable for biological cells, however, DIC can only obtain 2D images from thin samples. Therefore, we introduce a new imaging method, volumetric differential contrast (VDC) imaging using optical coherence tomography (OCT). This method enables getting 3D differential contrast of thick samples. VDC was designed based on the disperse scatterer model (DSM), a new theoretical model of OCT, and obtains differential contrast by complex numerical processing of OCT signal. DSM represents the sample as a spatially distributed refractive index with dispersed random scatterers, and OCT signal was formulated from this model. VDC uses two complex OCT signals, s1 and s2 at two laterally slightly distant positions, and the final image is defined as Im[s1 s2. This signal forms a spatially differential image of the product of the refractive index distribution and the scatterer density. According to the formulation, the size of the differentiation kernel, corresponding to the shear amount of DIC, is proportional to the defocus of the probe beam and the separation between s1 and s2. This method was validated by an in vitro spheroid sample and an in vivo zebrafish sample, measured by spectral domain OCT with a center wavelength of 830 nm. VDC images were obtained from refocused and defocused signals.
We construct a universal image formation theory that generalized individual optical imaging systems including OCT by stepping up to the four-dimensional (4-D) coordinate system. We show how the unified image formation theory is formulated by applying the modern physics to imaging systems. A bird’s-eye view from the four dimensions brightens up the perspective of the image formations in almost all optical systems simultaneously, even though different types of imaging systems seem entirely distinct and unrelated. We define a 4-D aperture in the 4-D frequency domain as an instrumental function that indicates a spatial-temporal resolution, which allows for the comparison of 4-D optical resolution in all imaging systems that includes a time response stemming from the light-matter interaction. In virtue of a strict definition of a 4-D frequency cutoff, the optical resolution can be evaluated and compared to other imaging systems in the frequency domain more clearly than in the real-space domain. The unification of individual imaging systems has been achieved with the 4-D aperture. It can easily be visualized how the 4-D aperture captures a certain region in an object frequency, and how the image formation is performed with the captured 4-D frequency region by stepping down to the 3-D frequency domain. We will show that some types exist in terms of the image formation, which means that how to drop one dimension to form the 3-D image depends on the optical system. We will find that our new framework can explain each individual existing approach.
We introduce volumetric differential contrast (VDC) imaging using optical coherence tomography (OCT). This method was designed based on a new theoretical model of OCT, the disperse scatterer model (DSM). VDC gives the differential image of “the product of the refractive index distribution and the scatterer density” through complex numerical processing of OCT signals.
The method was validated by in-vitro and in-vivo samples measured by spectral domain OCT. Differential contrast images with arbitrary shear amount and shear direction were obtained at arbitrary depth positions by a single measurement by numerically applying defocus by holographic signal processing after the signal acquisition.
We formulate a four-dimensional (4-D, space-time dimension) image formation theory of all laser microscopy and optical coherence tomography (OCT) by using 4-D Fourier optics. We define a Fourier transform pair: a 4-D amplitude spread function in space-time domain and a 4-D aperture in spatiotemporal frequency domain. To calculate the 4-D aperture, we also define 4-D pupil functions that include the information on light source spectra in addition to NAs of excitation and detection systems in microscopy. The 4-D aperture is a new concept indicating the sensitivity to object frequencies that contribute to the image formation in microscopy including OCT.
In this work, we study the influence of optical process on the resolution limit of laser microscopy. We formulate the calculation rules of the resolution limits for all types of laser microscopy that employ a variety of optical processes occurring in a sample. By replacing the field with the creation/annihilation operators, we develop a theoretical framework to unify the image-forming formulas that cover all interactions between molecules in the sample and the excitation light including vacuum field. To determine the simple rules for the evaluation of optical resolution, our theoretical framework provides the diagram method that describes linear, nonlinear, coherent, and incoherent optical processes. According to our formulas, the type of optical process decisively influences the resolution limit if no a priori information on the sample exists.
We proposed superresolution nonlinear fluorescence microscopy with pump-probe setup that utilizes repetitive stimulated absorption and stimulated emission caused by two-color laser beams. The resulting nonlinear fluorescence that undergoes such a repetitive stimulated transition is detectable as a signal via the lock-in technique. As the nonlinear fluorescence signal is produced by the multi-ply combination of incident beams, the optical resolution can be improved. A theoretical model of the nonlinear optical process is provided using rate equations, which offers phenomenological interpretation of nonlinear fluorescence and estimation of the signal properties. The proposed method is demonstrated as having the scalability of optical resolution. Theoretical resolution and bead image are also estimated to validate the experimental result.
We propose a two-photon imaging system and formulate the property of the system into an image-formation formulae. The idea of two-photon image-formation, in which the entangled photon pairs are utilized, unveils the possibility of the advancement in resolution. We show that the two-photon microscopy beats the diffraction limit and discuss the resolution of this high-resolving optical system.
We formulate an image-forming optical theory of quantum lithography in which Entangled-photon pairs generated by spontaneous parametric down-conversion play an important role. Our optical system consists of an image-forming system, an illumination system with a second-order nonlinear medium, and two-photon absorbing materials. We evaluate the resolution of the quantum lithography system by using the optical transfer function and show a super-resolving condition which is, however, difficult to achieve.
At the end of last century, the name of “quantum lithography” has been emerged. This exciting approach was proposed for making a resolution two times higher than that of the conventional optics without changing a wavelength and a numerical aperture. For those who want optical lithography to last long, this has been thought to be a great technology. However, an applicability of the proposed method to the current exposure system i.e., reduced projection exposure system has not yet been examined clearly. We have investigated the proposed quantum lithography to apply into the current exposure system using reticle. For simplicity, coherent illumination i.e. sigma is zero condition is used for calculation. Our quantum lithography compatible to mask exposure system explains probability of one and two photon absorption on the image plane i.e. on wafer. We have shown that the half-wavelength quantum lithography using conventional mask exposure system is impossible because diffraction at the mask makes biphoton into two photon. We have found that there is still super-resolution quantum lithography using mask exposure, however, there is little possibility of quantum lithography practically today because biphoton light source is as dark as stars. To realize quantum lithography practically, further development of not only biphoton light source but also two-photon absorption resist is indispensable.
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