Super-Resolution Microscope Phase Retrieval via Phasorgrams
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Solution Overview
Problem
Current technologies can only measure amplitude distribution, losing approximately 80% of information, as phase information is not directly measurable in the diffraction plane, making it challenging to reconstruct the complete wave front in both the output and diffraction planes.
Innovation Solution
A novel method using phasorgrams and an iterative algorithm to infer the phase distribution from amplitude data, eliminating the need for data from two Fourier conjugate planes, and employing perturbing devices like kinoform lenses to generate additional information for phase retrieval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If amplitude distribution measurement is used in the diffraction plane, then measurement simplicity is improved, but information completeness deteriorates (80% information loss due to unmeasurable phase)
Solution Approach 1:
The patent introduces phase filters as intermediary elements placed in the output plane to modulate the wavefront phase. By measuring amplitude distributions with different known phase filters and using these as mediators to infer the unknown phase distribution through iterative algorithms, the system recovers phase information without directly measuring it, thus resolving the contradiction between measurement simplicity and information completeness
Solution Approach 2:
The patent employs iterative error reduction algorithms that use feedback loops to progressively refine phase estimates. The algorithm repeatedly compares calculated amplitude distributions with measured ones, adjusts phase estimates based on the error, and converges to the correct phase distribution, enabling complete wavefront reconstruction from amplitude-only measurements
2Measurement precision
If Gerchberg-Saxton algorithm is used with two Fourier conjugate planes, then phase retrieval capability is improved, but device complexity increases (requiring access to both output and diffraction planes)
Solution Approach 1:
The patent extracts and removes the requirement for accessing the diffraction plane by developing methods that work with amplitude measurements taken solely in the output plane. By taking out the diffraction plane requirement and replacing it with phase filter measurements in the output plane, the system achieves phase retrieval with reduced device complexity while maintaining measurement precision
Solution Approach 2:
The patent segments the phase retrieval process into multiple iterative steps using different phase filters. Instead of requiring simultaneous access to both conjugate planes, the method segments the problem into sequential measurements with different known phase modulations, each contributing to the final phase reconstruction through the iterative algorithm
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
The method consistently and accurately retrieves the phase distribution, achieving phase retrieval with a significant reduction in error, demonstrating its potential for applications like X-ray crystallography and improving phase retrieval in various wavefront analysis scenarios.
Implementation Method 1
the Rayleigh-Sommerfeld scalar wave diffraction equation
Implementation Method 2
the scattered wave front propagating from output to diffraction plane along the Z axis
Implementation Method 3
a detector located at position Zd along the Z-axis
Data Source
AI summary
Methods and apparatus for reconstructing a wave, including interpolation and extrapolation of the phase and amplitude distributions, with application to imaging apparatus, such as microscopes.