Bayesian Framework for 3D Particle Tracking and PSF Reconstruction
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Solution Overview
Problem
Current 3D particle localization and tracking techniques face challenges due to optical aberrations caused by inhomogeneous refractive indices in biological samples, leading to distorted point spread functions (PSFs) and poor localization accuracy, especially when using pre-calibrated PSFs that do not account for sample-induced aberrations.
Innovation Solution
A computer-implemented system using a Bayesian framework for simultaneous particle tracking, phase retrieval, and PSF reconstruction directly from data sets, which propagates uncertainty from all sources and does not require additional optical hardware, employing a bi-plane microscope setup to break degeneracy in particle trajectory estimation and correct for optical aberrations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If pre-calibrated PSFs are used for particle tracking, then the tracking process is simplified and faster, but localization accuracy deteriorates due to sample-induced optical aberrations
Solution Approach 1:
The system performs preliminary phase retrieval and PSF reconstruction from the actual imaging data before particle tracking. By pre-processing the optical aberrations present in the sample, the system creates accurate, sample-specific PSFs that account for refractive index inhomogeneities, thereby maintaining both tracking efficiency and localization precision
Solution Approach 2:
The system dynamically adjusts PSF parameters based on the actual imaging conditions by retrieving the phase information from the sample. Instead of using fixed pre-calibrated PSFs, the system modifies the PSF parameters to match the specific optical aberrations present in each sample, improving localization accuracy without sacrificing tracking speed
2Measurement precision
If adaptive optics hardware is added to correct optical aberrations, then localization accuracy improves, but device complexity and cost increase
Solution Approach 1:
The system replaces complex mechanical adaptive optics hardware with a computational approach. By using phase retrieval algorithms and PSF reconstruction from imaging data, the system corrects optical aberrations through software processing rather than physical optical components, thereby maintaining localization accuracy while avoiding additional hardware complexity
Solution Approach 2:
The system uses the imaging data itself to correct the optical aberrations present in that same data. By performing phase retrieval and PSF reconstruction directly from the acquired images, the system self-corrects for sample-induced aberrations without requiring external correction hardware or additional calibration samples
3Ease of operation
If conventional particle tracking methods are used, then the system is simpler to operate, but reliability deteriorates due to distorted PSFs in inhomogeneous refractive index environments
Solution Approach 1:
The system automatically performs phase retrieval and PSF reconstruction from the imaging data without requiring manual intervention or complex setup. This self-calibrating approach maintains ease of operation while significantly improving tracking reliability by adapting to the specific optical conditions of each sample
Solution Approach 2:
The system uses the acquired imaging data as feedback to reconstruct accurate PSFs that account for sample-induced aberrations. By continuously adapting the PSF model based on the actual imaging conditions, the system maintains high tracking reliability while keeping the operation simple through automated feedback-driven correction
4Measurement precision
If additional optical components are introduced for aberration correction, then PSF distortion is reduced, but photon loss increases
Solution Approach 1:
The system replaces physical optical correction components with computational phase retrieval methods. By processing the acquired photons through algorithms that reconstruct the phase information, the system achieves accurate PSFs without introducing additional optical elements that would cause further photon loss
Data Source
AI summary
3D particle tracking and localization provide direct means to monitor details within nano-scale environments. However, a major shortcoming of 3D techniques is the sample induced aberrations due to inhomogeneous refractive index, resulting in distortion of point spread functions (PSFs), which are an important measurement tool required for these tasks in the field. This issue is particularly important when using pre-calibrated PSFs that do not take into account the sample induced aberrations. A system incorporates a Bayesian framework for simultaneous particle tracking and PSF inference directly from a given data. The system is data efficient by taking into account existing sources of uncertainty, such as uncertainty in the shape of the PSF, which is often ignored. The system is benchmarked using a wide range of synthetic and experimental data.