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In holographic three-dimensional (3D) displays, the surface structures of 3D objects are reconstructed without their internal parts. In diffraction calculations using 3D fast Fourier transform (FFT), this sparse distribution of 3D objects can reduce the calculation time as the Fourier transform can be analytically solved in the depth direction and the 3D FFT can be resolved into multiple two-dimensional (2D) FFTs. Moreover, the Fourier spectrum required for hologram generation is not the entire 3D spectrum but a partial 2D spectrum located on the hemispherical surface. This sparsity of the required Fourier spectrum also reduces the number of 2D FFTs and improves the acceleration. In this study, a fast calculation algorithm based on two sparsities is derived theoretically and explained in detail. Our proposed algorithm demonstrated a 24-times acceleration improvement compared with a conventional algorithm and realized real-time hologram computing at a rate of 170 Hz.
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We propose a method to enlarge the field of view (FOV) of holographic 3D displays in both the horizontal and vertical directions. The FOV was enlarged by using two galvano mirrors and a high-speed spatial light modulator. These optical elements were placed so that the imaging relation was satisfied among them and they were synchronously driven at a high speed to implement the time-division method. Using this method, a floating 3D object could be successfully reconstructed in mid-air near the focal point of the final lens at the rate of 10 Hz. The FOV was enlarged five times and two times in the horizontal and vertical directions, respectively.
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Convex-parabolic-mirror reflection enables a very wide viewing zone in a holographic three-dimensional (3D) display. In this work, segmentation is introduced to reduce the calculation time of holograms in a convex-parabolic-mirror-reflection holographic 3D display. Wavefront segmentation can practically limit the lateral spread of the wavefront to be considered, which enables the application of geometrical approximation and conventional diffraction theories such as Fresnel diffraction. Thus, diffraction calculation via the convex parabolic mirror can be derived analytically and calculated rapidly using fast Fourier transform (FFT). Our proposed FFT-based method can calculate the diffraction integral 7000 times faster than our previous method, which involved calculating directly the diffraction integral without FFT. In addition, numerical simulation and an optical experiment are presented to verify our proposal.
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To realize a real-time interactive holographic three-dimensional (3D) display system, we synthesize a set of 24 full high-definition (HD) binary computer-generated holograms (CGHs) based on a 3D fast-Fourier-transform-based approach. These 24 CGHs are streamed into a digital micromirror device (DMD) as a single 24-bit image at 60 Hz: 1440 CGHs are synthesized in less than a second. Continual updates of the CGHs displayed on the DMD and synchronization with a rotating mirror enlarges the horizontal viewing zone to 360° using a time-division approach. We successfully demonstrate interactive manipulation, such as object rotation, rendering mode switching, and threshold value alteration, for a medical dataset of a human head obtained by X-ray computed tomography.
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A technical full-color reconstruction method is presented to develop our previous monochromatic holographic three-dimensional display with a horizontal full viewing zone. A digital micromirror device (DMD) is used as a high-speed spatial light modulator, and its modulation area is divided into three parts, which independently handle three sub-holograms corresponding to red, green, and blue components. The reconstructed images from a single frame of the DMD never form full-color images. However, given that this spatial division is combined with the time-division method for the full viewing zone, each monochromatic image is temporally mixed, and practically full-color images are reconstructed. After monochromatic reconstruction from a single frame was confirmed, full-color reconstruction with a horizontal full viewing zone was demonstrated.
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The diffraction integral onto a spherical surface is discussed in the three-dimensional (3D) Fourier domain of the 3D object used. The diffraction integral is expressed in the form of the convolution integral between the partial Fourier components of the 3D object and the kernel function defined on the sphere. This two-dimensional convolution on the sphere can be calculated rapidly based on the convolution theorem by performing spherical harmonic transform instead of Fourier transform. This paper presents a detailed derivation of this diffraction integral and analyzes the sampling pitch required for handing the data on the sphere. Our proposed method is verified using a simple simulation of Young's interference experiment. Moreover, a numerical simulation with a more complicated 3D object is demonstrated. Our proposed method speeds up the calculation of the diffraction integral by more than 6,000 times compared with the direct calculation method.
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To enlarge both horizontal (azimuthal) and vertical (zenithal) viewing zones simultaneously, a convex parabolic mirror is placed after passing through the hologram. Viewers perceive a three-dimensional (3D) object inside the parabolic mirror as a virtual image by capturing the wavefront radially reflected from the parabolic mirror. The optical experiment using the convex parabolic mirror has demonstrated an extremely wide viewing zone with an azimuthal range of 180° and zenithal range of 90°. The viewing zone and the shape of the parabolic surface are analyzed. The hologram is designed considering the parabolic mirror reflection, and its diffraction calculation method based on Fermat's principle is also proposed.
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This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.
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A method for a continuous optical rotation compensation in a time-division-based holographic three-dimensional (3D) display with a rotating mirror is presented. Since the coordinate system of wavefronts after the mirror reflection rotates about the optical axis along with the rotation angle, compensation or cancellation is absolutely necessary to fix the reconstructed 3D object. In this study, we address this problem by introducing an optical image rotator based on a right-angle prism that rotates synchronously with the rotating mirror. The optical and continuous compensation reduces the occurrence of duplicate images, which leads to the improvement of the quality of reconstructed images. The effect of the optical rotation compensation is experimentally verified and a demonstration of holographic 3D display with the optical rotation compensation is presented.
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A holographic three-dimensional display system with a viewing angle of 360°, by using a high-speed digital micromirror device (DMD), has been proposed. The wavefront modulated by the DMD enters a rotating mirror tilted vertically downward. The synchronization of the rotating mirror and holograms displayed on the DMD allows for the reconstruction of a wavefront propagating in all horizontal directions. An optical experiment has been demonstrated in order to verify our proposed system. Binocular vision is realized from anywhere within the horizontal plane. Our display system enables simultaneous observation by multiple viewers at an extremely close range.
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The relation between a three-dimensional (3D) object and its diffracted wavefront in the 3D Fourier space is discussed at first and then a rigorous diffraction formula onto cylindrical surfaces is derived. The azimuthal direction and the spatial frequency direction corresponding to height can be expressed with a one-dimensional (1D) convolution integral and a 1D inverse Fourier transform in the 3D Fourier space, respectively, and fast Fourier transforms are available for fast calculation. A numerical simulation of a diffracted wavefront on cylindrical surfaces is presented. An alternative optical experiment equivalent of the optical reconstruction from cylindrical holograms is also demonstrated.
Assuntos
Simulação por Computador , Análise de Fourier , Holografia/métodos , Algoritmos , Fatores de TempoRESUMO
A fast calculation method for computer-generated holograms for hidden surface removal is proposed. In this method, a three-dimensional object is considered as a set of point light sources emitting light rays. To achieve the hidden surface removal, only appropriate light rays are selected according to their geometrical position, which are then converted into a Fourier spectrum of the wavefront. After the Fourier spectrum on the spherical surface is obtained, diffraction in arbitrary directions is calculated. Numerical simulation of a series of diffracted wavefronts onto arbitrary observation planes has been demonstrated to verify the effectiveness of our proposal.
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We have derived the basic spectral relation between a 3-D object and its 2-D diffracted wavefront by interpreting the diffraction calculation in the 3-D Fourier domain. Information on the 3-D object, which is inherent in the diffracted wavefront, becomes clear by using this relation. After the derivation, a method for obtaining the Fourier spectrum that is required to synthesize a hologram with a realistic sampling number for visible light is described. Finally, to verify the validity and the practicality of the above-mentioned spectral relation, fast calculation of a series of wavefronts radially diffracted from a 3-D voxel-based object is demonstrated.
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The theory of generalized grating imaging for a one-dimensional grating is applied to a pattern projection system in pattern projection profilometry. Contrast of the projected grating image is calculated under various conditions. The results help to determine the conditions suitable for obtaining high contrast grating images in a large space. Although the gratings required for the profilometry are hexagonal, the theory for two-dimensional gratings is prohibitively complex. Therefore, the projection system was designed using the one-dimensional theory. The projection system using two-dimensional hexagonal gratings was constructed and experiments were done with it. The result agrees approximately with the theoretical calculations for one-dimensional gratings. This suggests that the one-dimensional theory may be used for estimating the approximated behavior for hexagonal gratings for use in pattern projection profilometry. Some discussions are given for the application of the projection system for profiling the mannequin or human body.
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Algoritmos , Imageamento Tridimensional/métodos , Desenho de Equipamento , Humanos , Aumento da Imagem/métodos , Interpretação de Imagem Assistida por Computador/métodos , Imageamento Tridimensional/instrumentaçãoRESUMO
The synthesis of spherical computer-generated holograms is investigated. To deal with the staggering calculation times required to synthesize the hologram, a fast calculation method for approximating the hologram distribution is proposed. In this method, the diffraction integral is approximated as a convolution integral, allowing computation using the fast-Fourier-transform algorithm. The principles of the fast calculation method, the error in the approximation, and results from simulations are presented.
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A numerical deconvolution method to cancel lateral defocus in Fourier domain optical coherence tomography (FD-OCT) is presented. This method uses a depth-dependent lateral point spread function and some approximations to design a deconvolution filter for the cancellation of lateral defocus. Improved lateral resolutions are theoretically estimated; consequently, the effect of lateral superresolution in this method is derived. The superresolution is experimentally confirmed by a razor blade test, and an intuitive physical interpretation of this effect is presented. The razor blade test also confirms that this method enhances the signal-to-noise ratio of OCT. This method is applied to OCT images of medical samples, in vivo human anterior eye segments, and exhibits its potential to cancel the defocusing of practical OCT images. The validity and restrictions involved in each approximation employed to design the deconvolution filter are discussed. A chromatic and a two-dimensional extensions of this method are also described.
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We propose a fast calculation method for diffraction to nonplanar surfaces using the fast-Fourier transform (FFT) algorithm. In his method, the diffracted wavefront on a cylindrical surface is expressed as a convolution between the point response function and the spatial distribution of objects wherein the convolution is calculated using FFT. The principle of the fast calculation and the simulation results are presented.
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A novel method for the procurement of full-color three-dimensional (3-D) images of real objects has been developed. This method is based on extracting information from 3-D Fourier spectra, which are calculated from several projection images recorded using a white light source. 3-D Fourier spectra for three colors were obtained separately for projection images recorded with a color-CCD camera. Three computer-generated holograms (CGHs) were then synthesized from those Fourier spectra. The resulting numerically and optically reconstructed full-color images are presented.
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A new method for synthesizing a full-color computer-generated hologram (CGH) of real-existing objects has been proposed. In this method, the synthesizing process of CGHs and the adjustments of magnifications for each wavelength are considered based on parabolic sampling of three-dimensional (3-D) Fourier spectra. Our method requires only one-dimensional (1-D) azimuth scanning of objects, does not require any approximations in the synthesizing process, and can perform efficient magnification adjustments required for color reconstruction. Experimental results have been presented to verify the principle and validity of this method.
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A method of synthesizing computer-generated holograms of real existing objects is proposed that is based on a series of projection images of an incoherently illuminated object recorded from different perspectives. In accordance with the principles of computer tomography, the three-dimensional Fourier spectrum of the object is calculated by use of several projection images. A method of calculating a Fresnel hologram from the three-dimensional Fourier spectrum is proposed. Experimental results in the form of a computer simulation and optical reconstruction are presented.
