Complex Index Refraction Tomography Super-Resolution Microscopy
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Solution Overview
Problem
Current microscopy techniques face limitations in achieving high-resolution imaging due to bandwidth constraints and noise sensitivity, particularly in coherent microscopy, which affects the ability to distinguish closely spaced objects and reconstruct accurate three-dimensional refractive index distributions of biological samples.
Innovation Solution
The method involves complex deconvolution using the Synthetic Coherent Transfer Function (SCTF), which accesses the object's scattered complex field and deconvolves it with the reconstructed complex transfer function, incorporating experimental parameters of the microscope objective and Amplitude Point Spread Functions to improve resolution beyond the Rayleigh limit.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional coherent microscopy techniques are used, then the imaging system is simpler to operate, but the resolution is limited by the Rayleigh criterion and bandwidth constraints
Solution Approach 1:
The patent pre-calculates and stores the coherent transfer function (CTF) and amplitude point spread function (APSF) for the specific microscopy system before actual imaging. This preliminary characterization allows the complex deconvolution process to use predetermined system parameters, making the resolution improvement achievable without requiring real-time complex calculations during image acquisition.
Solution Approach 2:
The patent introduces an intermediary computational processing step that acts as a bridge between the raw microscopy data and the final high-resolution image. The complex deconvolution algorithm serves as this intermediary, using pre-characterized system functions (CTF and APSF) to transform the limited-resolution raw data into super-resolution images, thereby resolving the contradiction between simplicity and resolution.
2Measurement precision
If the spectrum is extended to improve resolution, then the bandwidth limitations are overcome, but noise amplification increases
Solution Approach 1:
The patent applies partial deconvolution by selectively extending the spectrum only to the extent necessary to achieve the desired resolution improvement, rather than attempting to fully recover all high-frequency components. This partial action approach recovers sufficient spatial frequency information to surpass the Rayleigh limit while avoiding the excessive noise amplification that would result from attempting to recover the complete high-frequency spectrum.
3Measurement precision
If iterative algorithms are used for phase retrieval, then the complex wavefield can be determined, but the problem becomes ill-posed and computationally intensive
Solution Approach 1:
The patent replaces iterative computational algorithms with a direct mathematical solution using pre-calculated system transfer functions. Instead of using computationally intensive iterative phase retrieval methods, the invention uses a closed-form deconvolution approach based on the measured CTF and APSF, substituting mechanical/computational iteration with a direct calculation that achieves the same goal much faster.
4Loss of information
If quantitative phase imaging techniques are used, then phase information can be extracted, but the methods are sensitive to noise and artifacts due to derivative computations
Solution Approach 1:
The patent creates a copy of the system's impulse response (APSF) through direct measurement using a sub-resolution object, rather than attempting to computationally derive phase information from intensity gradients. This measured copy of the system behavior is then used in the deconvolution process to recover phase information directly from the complex field, avoiding the noisy derivative computations inherent in traditional quantitative phase imaging methods.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables super-resolution imaging by extending the limit of resolution to λ/6 or smaller, improving image quality and accuracy in three-dimensional refractive index reconstruction, and reducing noise amplification, thus overcoming the limitations of conventional microscopy techniques.
Implementation Method 1
the angular spectrum: complex amplitude as a function of the unit vector of the beam diffracted by the object
Implementation Method 2
Digital Holographic Microscopy: DHM is based on the holographic approach, i.e. the determination of the complex field of the radiated wave from its interference (hologram) with some reference wave
Data Source
Figure 1(a)~1(d)
Figure 2(a)~2(f)
Figure 3
AI summary
The present invention discloses a method to improve the image resolution of a microscope. This improvement is based on the mathematical processing of the complex field computed from the measurements with a microscope of the wave emitted or scattered by the specimen. This wave is, in a preferred embodiment, electromagnetic or optical for an optical microscope, but can be also of different kind like acoustical or matter waves. The disclosed invention makes use of the quantitative phase microscopy techniques known in the sate of the art or to be invented. In a preferred embodiment, the complex field provided by Digital Holographic Microscopy (DHM), but any kind of microscopy derived from quantitative phase microscopy: modified DIC, Shack- Hartmann wavefront analyzer or any analyzer derived from a similar principle, such as multi-level lateral shearing interferometers or common-path interferometers, or devices that convert stacks of intensity images (transport if intensity techniques: TIT) into quantitative phase image can be used, provided that they deliver a comprehensive measure of the complex scattered wavefield. The hereby-disclosed method delivers superresolution microscopic images of the specimen, i.e. images with a resolution beyond the Rayleigh limit of the microscope. It is shown that the limit of resolution with coherent illumination can be improved by a factor of 6 at least. It is taught that the gain in resolution arises from the mathematical digital processing of the phase as well as of the amplitude of the complex field scattered by the observed specimen. In a first embodiment, the invention teaches how the experimental observation of systematically occurring phase singularities in phase imaging of sub-Rayleigh distanced objects can be exploited to relate the locus of the phase singularities to the sub-Rayleigh distance of point sources, not resolved in usual diffraction limited microscopy. In a second, preferred imbodiment, the disclosed method teaches how the image resolution is improved by complex deconvolution. Accessing the object's scattered complex field - containing the information coded in the phase - and deconvolving it with the reconstructed complex transfer function (CTF) is at the basis of the disclosed method. In a third, preferred imbodiment, it is taught how the concept of "Synthetic Coherent Transfer Function" (SCTF), based on Debye scalar or Vector model includes experimental parameters of MO and how the experimental Amplitude Point Spread Functions (APSF) are used for the SCTF determination. It is also taught how to derive APSF from the measurement of the complex field scattered by a nanohole in a metallic film. In a fourth imbodiment, the invention teaches how the limit of resolution can be extended to a limit of λ/6 or smaller based angular scanning. In a fifth imbodiment, the invention teaches how the presented method can generalized to a tomographic approach that ultimately results in super-resolved 3D refractive index reconstruction.