Phase Retrieval from Defocused Color Images
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Solution Overview
Problem
Current phase imaging techniques, such as interferometry and the Transport of Intensity Equation, face challenges in providing real-time measurements and high spatial resolution due to the need for coherent illumination, stable reference beams, and mechanical stability, making them unsuitable for adaptive optical systems and applications requiring quick feedback.
Innovation Solution
Measuring intensity at different wavelengths using a detector array allows for the calculation of phase differences in a single plane, enabling the estimation of phase and refractive index profiles without coherent illumination or reference beams, suitable for adaptive optics and real-time measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If interferometry is used to achieve quantitative phase imaging, then measurement precision is improved, but device complexity and stability requirements increase due to the need for coherent illumination and stable reference beams
Solution Approach 1:
The patent extracts and removes the reference beam component from the interferometric system, using only the object beam that passes through the transparent object. This eliminates the need for beam splitting, reference beam stabilization, and complex interferometric alignment while retaining phase measurement capability through intensity derivative analysis
Solution Approach 2:
The patent replaces the mechanical/optical interferometric system with a computational approach based on the Transport of Intensity Equation. Instead of using physical interference patterns and stable mechanical setups, the phase is retrieved by calculating intensity derivatives along the optical axis from intensity measurements at different defocus positions
2Device complexity
If the Transport of Intensity Equation approach is used to avoid reference beams, then device complexity is reduced, but measurement time increases due to the need for multiple sequential measurements at varying depths
Solution Approach 1:
The patent uses periodic action by capturing images at regular defocus intervals along the optical axis. The systematic sampling of intensity at multiple z-positions enables the calculation of intensity derivatives needed for phase retrieval through the TIE approach
Solution Approach 2:
The patent performs preliminary action by capturing all necessary intensity images at different defocus positions simultaneously or in rapid sequence before phase calculation. This pre-capture of depth-resolved intensity data enables subsequent real-time phase computation without requiring additional measurements during the feedback loop
3Reliability
If Shack-Hartmann sensors are used for noninterferometric phase measurement, then reference beam stability is improved, but spatial resolution deteriorates due to the limited number of lenslets
Solution Approach 1:
The patent transitions from the spatial domain to the depth dimension by measuring intensity variations along the optical axis at multiple z-positions. This additional dimensional information enables phase retrieval without requiring a dense lenslet array, achieving high spatial resolution through computational methods rather than dense physical sampling
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 method provides improved spatial resolution and enables real-time phase measurements, suitable for adaptive optics, nondestructive testing, and other applications by deriving phase information from a single defocused color image, overcoming limitations of existing techniques.
Implementation Method 1
Phase differences associated with a defocused wavefront can be determined by measuring the intensity of the defocused wavefront at first and second wavelengths with a detector array
Implementation Method 2
Phase, however, carries information about an object's optical density and thickness. The phase of reflected waves can also be used to derive information about the topology, or surface profile, of the object from which the waves were reflected
Data Source
AI summary
Phase differences associated with a defocused wavefront can be determined from a single color image. The color image, which is a measurement of intensity as a function of wavelength, is used to calculate the change in intensity with respect to wavelength over the image plane. The change in intensity can then be used to estimate a phase difference associated with the defocused wavefront using two-dimensional fast Fourier transform solvers. The phase difference can be used to infer information about objects in the path of the defocused wavefront. For example, it can be used to determine an object's shape, surface profile, or refractive index profile. It can also be used to calculate path length differences for actuating adaptive optical systems. Compared to other techniques, deriving phase from defocused color images is faster, simpler, and can be implemented using standard color filters.