Holographic Display Virtual Image Intensity via Inverse Fourier Transform
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Solution Overview
Problem
In holographic display technologies, particularly in head-up and head-mounted displays, the twin-image problem limits the separation of real and virtual images due to the limited resolution of spatial light modulators, making it difficult to emphasize the virtual image effectively.
Innovation Solution
A method involving the inverse Fourier transform of an object field with a negative quadratic phase exponential, followed by processing with a Gerchberg-Saxton type algorithm in the Fresnel domain, to optimize the virtual image in the hologram, and restricting hologram pixel values to enhance the virtual image intensity while reducing the real image intensity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Illumination intensity
If a conventional Fourier transform hologram is used, then the hologram can be reconstructed, but the twin-image problem causes both real and virtual images to appear with equal intensity, making it difficult to emphasize the virtual image
Solution Approach 1:
The patent changes the mathematical parameters of the hologram calculation by using an inverse Fourier transform with a negative quadratic phase exponential instead of the conventional forward Fourier transform. This parameter change fundamentally alters the diffraction pattern to produce a virtual image with significantly higher intensity than the real image, resolving the twin-image problem where both images previously appeared with equal intensity
Solution Approach 2:
The patent inverts the conventional hologram calculation approach by using the inverse Fourier transform rather than the forward Fourier transform. This inversion of the mathematical operation, combined with the negative quadratic phase exponential, flips the intensity relationship between the real and virtual images, making the virtual image prominent while suppressing the real image
2Measurement precision
If high resolution is required to separate twin images in 3D space using off-axis reference beam, then image separation is achieved, but the limited resolution of spatial light modulators prevents effective separation
Solution Approach 1:
The patent changes the hologram calculation parameters to produce an asymmetric diffraction pattern where the virtual image has much higher intensity than the real image. This parameter change eliminates the need for high-resolution spatial light modulators to separate twin images, as the intensity difference naturally emphasizes the virtual image even with limited SLM resolution
3Ease of operation
If the hologram is encoded on a spatial light modulator with limited resolution, then the hologram can be displayed, but the possibility for separating twin images in 3D space is more limited
Solution Approach 1:
The patent modifies the hologram calculation parameters using inverse Fourier transform and negative quadratic phase exponential to create a diffraction pattern where the virtual image dominates in intensity. This parameter modification allows the hologram to be effectively displayed on spatial light modulators with limited resolution while maintaining the ability to emphasize the virtual image, eliminating the need for precise twin image separation
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 approach allows for the formation of a holographic reconstruction with a prominent virtual image, simplifying the optical viewing system and improving image quality in displays by iteratively enhancing the virtual image intensity while minimizing the real image, suitable for augmented reality applications.
Implementation Method 1
Light modulation may be achieved using electrically-addressable liquid crystals, optically-addressable liquid crystals or micro-mirrors, for example
Implementation Method 2
Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well-known interference techniques to form a holographic recording
Implementation Method 3
The hologram may be reconstructed by illumination with suitable light to form a two-dimensional or three-dimensional holographic reconstruction
Implementation Method 4
A computer-generated hologram may be calculated by a technique based on a mathematical transformation such as a Fresnel or Fourier transform
Data Source
AI summary
A holographic display method includes calculating a hologram, displaying it on a spatial light modulator (SLM) and illuminating it with coherent light. The hologram includes hologram pixels each having a hologram pixel value. The hologram is calculated using steps including: performing the inverse Fourier transform of the product of an object field and a negative quadratic phase exponential representative of positive optical power; and restricting each calculated hologram pixel value to one of a plurality (greater than two) of allowable pixel values to form a constrained hologram, which is displayed on the SLM. Each light-modulating pixel of the SLM is operable in a plurality of light-modulation levels corresponding to the plurality of allowable pixel values. The SLM is illuminated with coherent light to form a replay field including conjugate images: a real holographic reconstruction and a virtual holographic reconstruction having greater intensity than that of the real holographic reconstruction.