Hologram Adaptation via Ray Transfer Matrices
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Solution Overview
Problem
Existing digital holography technologies fail to adapt pre-existing holograms to holographic reproduction systems with different resolutions and sizes, leading to deformation or unusability, especially in wearable devices like head-mounted displays.
Innovation Solution
A method using Linear Canonical Transform theory to calculate overall ray transfer matrices, transforming input holograms into output holograms that match the display device's resolution and size, by applying linear integral operators to compensate for optical distortions through the reproduction system's optical elements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a pre-existing hologram is displayed directly on a holographic screen with different resolution and size, then the display process is simple, but the hologram appears deformed or unusable
Solution Approach 1:
The patent applies preliminary action by performing hologram adaptation processing before display. The system calculates ray transfer matrices and applies linear integral operators to transform the input hologram into an output hologram that matches the screen's resolution and size, preventing deformation before it occurs
Solution Approach 2:
The patent changes parameters by transforming the hologram's resolution and size parameters through mathematical operations. The linear integral operators modify the hologram's spatial frequency distribution to match the target screen parameters while preserving the visual content
2Reliability
If optical elements are added to the reproduction system to adjust light field propagation, then the light field characteristics can be optimized, but the system complexity increases
Solution Approach 1:
The patent replaces the mechanical/optical system with a computational system. Instead of physically adjusting optical elements to optimize light field propagation, the system uses ray transfer matrix calculations and linear integral operators to achieve the same effect through mathematical transformation of the hologram data
Solution Approach 2:
The patent creates a computational model (ray transfer matrix) that copies the optical propagation characteristics. This mathematical model allows the system to simulate and compensate for optical effects without requiring the physical optical elements to be perfectly aligned or optimized
3Adaptability or versatility
If the hologram resolution and size match the screen exactly, then no adaptation is needed, but the system lacks flexibility for different display devices
Solution Approach 1:
The patent achieves universality by creating a general-purpose adaptation framework that works with any holographic screen regardless of its resolution or size. The ray transfer matrix approach provides a unified method to transform holograms to match any target display parameters, making the system adaptable to different devices
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 the simple adaptation of pre-existing holograms to any holographic reproduction system, ensuring accurate display without deformation, and is suitable for real-time applications in wearable devices by updating transformations based on user movement and visibility.
Implementation Method 1
The invention is based on a so-called 'Linear Canonical Transform' (LCT) theory... This theory makes the link between two types of mathematical transformations... The obtained operator performs the transformation operated on the light field by the optical element in question
Implementation Method 2
The ray transfer matrices, linear transformations expressing the ray direction change induced by the passing through an optical element... a cascade of optical elements can be represented by an overall ray transfer matrix, product of the ray transfer matrices of the optical elements successively passed through
Implementation Method 3
The resulting overall matrix that is obtained can be interpreted as a transform of the space/frequency distribution of the light field... To each transfer matrix is associated an integral operator T that, to a function f representing a field, associates a function f'
Data Source
AI summary
Disclosed is a method for processing an input hologram HE associated with an input plane, to obtain an output hologram displayable on a holographic screen placed in a plane called the output plane of a display system, viewable from a viewing plane of the system. The method includes: receiving the input hologram and a position of the input plane; obtaining a first transfer matrix representative of a propagation between the input plane and the viewing plane; obtaining a second transfer matrix representative of a propagation between the viewing plane and the output plane; calculating an overall matrix of transfer of a light field emitted by the input hologram, between the input plane and the output plane, by taking the product of the two matrices; and converting the input hologram into the output hologram by applying an operator dependent of the input hologram and on the screen.