Fan Beam Resection Positioning Using Direct Linear Transform

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Solution Overview

Problem

Existing fan-beam resection methods are limited by the assumption that detectors are arranged in a plane with the fan-beam axis perpendicular to it, restricting their utility in various applications.

Innovation Solution

A method for resection-based positioning of a rotating fan beam transmitter that detects the fan beam using a cluster of detectors in a detector space where the axis of rotation intersects a reference plane at an arbitrary angle, processing detection signals to determine the axis of rotation and calculate the 2D or 3D position and orientation of the detector cluster.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If detectors are arranged in a plane with the fan-beam axis perpendicular to it, then the positioning method is simple to implement, but the applicability is limited

Engineering Contradiction:

Improvesimplicity of implementationVSAvoidapplicability

Core Design Contradiction:

Ease of manufactureVSAdaptability or versatility

Solution Approach 1:

The patent transitions from a 2D planar detector arrangement to a 3D spatial configuration where detectors are distributed in three-dimensional space. The fan-beam axis can intersect the detector space at arbitrary angles rather than being constrained to perpendicular orientation, enabling the system to handle complex spatial relationships and expand applicability to diverse positioning scenarios

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Solution Approach 2:

The positioning method is designed to universally handle various detector configurations and beam intersection angles. By using a cluster of detectors in 3D space with arbitrary angle accommodation, the system becomes multi-functional, capable of positioning in different geometric configurations without requiring separate specialized methods for each case

Inventive Principle:

Principle #6Universality (Multi-functionality)

2Adaptability or versatility

If the fan-beam axis intersects the reference plane at an arbitrary angle, then the versatility is enhanced, but the calculation complexity increases

Engineering Contradiction:

ImproveversatilityVSAvoidcalculation complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent replaces complex geometric calculations with linear algebra operations. By formulating the positioning problem as a system of linear equations using the Direct Linear Transform (DLT) method, the solution substitutes iterative geometric computations with efficient matrix operations, significantly reducing calculation complexity while maintaining versatility for arbitrary angles

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the mathematical parameters from geometric coordinates to matrix representations. By expressing detector positions and beam intersections in terms of homogeneous coordinates and transformation matrices, the system simplifies the handling of arbitrary intersection angles through standardized linear algebra operations rather than case-by-case geometric analysis

Inventive Principle:

Principle #35Parameter changes

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

Enables accurate determination of the fan beam's axis of rotation and position within the detector space, allowing for effective resection-based positioning regardless of the angle of intersection, enhancing the versatility of fan-beam resection techniques.

Implementation Method 1

a fan beam rotating about a single axis of rotation

Methodology Applied

Scientific EffectLaser: Laser

Implementation Method 2

detecting the rotating fan beam by using a plurality of detectors; processing a set of detection signals to obtain a set of time-strike tags

Methodology Applied

Scientific EffectPhotoelectric detection: Photoelectric Effect

Data Source

PatentUS8472015B1Fan beam resection using direct linear transform and singular value decomposition

Publication Date: 2013.06.25 TRIMBLE NAVIGATION LTD

AI summary

A method of resection-based positioning of a rotating fan beam transmitter is provided. The fan beam is rotating about a single axis of rotation. The rotating fan beam is being detected in a detector space including a detector cluster further including a plurality of detectors. The single axis of rotation intersects a reference plane in the detector space at an arbitrary angle. The method comprises: (A) detecting the rotating fan beam by using a plurality of detectors; (B) processing a set of detection signals to obtain a set of time-strike tags; and (C) determining the axis of rotation of the rotating fan beam in the detector space by using the set of time-strike tags. At least minimum number of detectors is stricken by the rotating fan beam. Each stricken detector generates a detection signal having a time-strike tag corresponding to a timing coordinate of the strike by the rotating fan beam.