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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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Guest editors Toyohiko Yatagai, Osamu Matoba, Yoshihisa Aizu, Yasuhiro Awatsuji, and Yuan Luo introduce the articles in the Special Series on Biomedical Imaging and Sensing.

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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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Guest editors introduce the special section of Journal of Biomedical Optics Volume 25, Issue 3, entitled "Biomedical Imaging and Sensing II," a collection of papers related to the topics of the conference "Biomedical Imaging and Sensing Conference 2019" (BISC'19), which was held in April 2019, in Yokohama, Japan.

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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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This guest editorial introduces the special section on Biomedical Imaging and Sensing.

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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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A parallel computation method for large-size Fresnel computer-generated hologram (CGH) is reported. The method was introduced by us in an earlier report as a technique for calculating Fourier CGH from 2D object data. In this paper we extend the method to compute Fresnel CGH from 3D object data. The scale of the computation problem is also expanded to 2 gigapixels, making it closer to real application requirements. The significant feature of the reported method is its ability to avoid communication overhead and thereby fully utilize the computing power of parallel devices. The method exhibits three layers of parallelism that favor small to large scale parallel computing machines. Simulation and optical experiments were conducted to demonstrate the workability and to evaluate the efficiency of the proposed technique. A two-times improvement in computation speed has been achieved compared to the conventional method, on a 16-node cluster (one GPU per node) utilizing only one layer of parallelism. A 20-times improvement in computation speed has been estimated utilizing two layers of parallelism on a very large-scale parallel machine with 16 nodes, where each node has 16 GPUs.

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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 new phase shifting digital holographic technique using a purely geometric phase in Michelson interferometric geometry is proposed. The geometric phase in the system does not depend upon either optical path length or wavelength, unlike dynamic phase. The amount of geometric phase generated is controllable through a rotating wave plate. The new approach has unique features and major advantages in holographic measurement of transparent and reflecting three-dimensional (3D) objects. Experimental results on surface shape measurement and imaging of 3D objects are presented using the proposed method.

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In the multiple-plane phase retrieval method, a tedious-to-fabricate phase diffuser plate is used to increase the axial intensity variation for a nonstagnating iterative reconstruction of a smooth object wavefront. Here we show that a spatial light modulator (SLM) can be used as an easily controllable diffuser for phase retrieval. The polarization modulation at the SLM facilitates independent formation of orthogonally polarized scattered and specularly reflected beams. Through an analyzer, the polarization states are filtered enabling beam interference, thereby efficiently encoding the phase information in the axially diverse speckle intensity measurements. The technique is described using wave propagation and Jones calculus, and demonstrated experimentally on technical and biological samples.

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Optical design and testing have numerous applications in industrial, military, consumer, and bio-medical settings. This issue features original research ranging from the optical design of image and nonimage optical stimuli for human perception, optics applications, bio-optics applications, displays, and solar energy systems to novel imaging modalities from deep UV to infrared spectral imaging, a systems perspective to imaging, as well as optical measurement. In addition, new concepts and trends for optics and further optical systems will be especially highlighted in this special issue.

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We propose ultra-high resolution optical coherence tomography to study the morphological development of internal organs in medaka fish in the post-embryonic stages at micrometer resolution. Different stages of Japanese medaka were imaged after hatching in vivo with an axial resolution of 2.8 µm in tissue. Various morphological structures and organs identified in the OCT images were then compared with the histology. Due to the medaka's close resemblance to vertebrates, including humans, these morphological features play an important role in morphogenesis and can be used to study diseases that also occur in humans.

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A method has been proposed to reduce the communication overhead in computer-generated hologram (CGH) calculations on parallel and distributed computing devices. The method uses the shifting property of Fourier transform to decompose calculations, thereby avoiding data dependency and communication. This enables the full potential of parallel and distributed computing devices. The proposed method is verified by simulation and optical experiments and can achieve a 20 times speed improvement compared to conventional methods, while using large data sizes.