Rationalized diffraction calculations for high accuracy and high speed with few bits.

Diffraction calculations in few-bit formats, such as single-precision floating-point and fixed-point numbers, are important because they yield faster calculations and lower memory usage. However, these methods suffer from low accuracy owing to the loss of trailing digits. Fresnel diffraction is widely known to prevent the loss of trailing digits. However, it can only be used when the paraxial approximation is valid. In this study, a few-bit diffraction calculation method that achieves high accuracy without using any approximation is proposed. The proposed method is derived only by rationalizing the numerator of conventional formulas. Even for scenarios requiring double-precision floating-point numbers using conventional methods, the proposed method exhibits higher accuracy and faster computation time using single-precision floating-point numbers.

Wavefront recording plane-like method for polygon-based holograms.

The wavefront recording plane (WRP) method is an algorithm for computer-generated holograms, which has significantly promoted the accelerated computation of point-based holograms. Similarly, in this paper, we propose a WRP-like method for polygon-based holograms. A WRP is placed near the object, and the diffracted fields of all polygons are aggregated in the WRP so that the fields propagating from the polygonal mesh affect only a small region of the plane rather than the full region. Unlike the conventional WRP method used in point-based holograms, the proposed WRP-like method utilizes sparse sampling in the frequency domain to significantly reduce the practical computational kernel size. The proposed WRP-like method and the analytical shading model are used to generate polygon-based holograms of multiple three-dimensional (3D) objects, which are then reproduced to confirm 3D perception. The results indicate that the proposed WRP-like method based on an analytical algorithm is hundreds of times faster than the reference full region sampling case; a hologram with tens of thousands of triangles can be computed in seconds even on a CPU, whereas previous methods required a graphics processing unit to achieve these speeds.

Reducing the computational complexity of high-resolution hologram calculations using polynomial approximation.

In this paper, we have proposed a hologram calculation method using polynomial approximations for reducing the computational complexity of point-cloud-based hologram calculations. The computational complexity of existing point-cloud-based hologram calculations is proportional to the product of the number of point light sources and hologram resolution, whereas that of the proposed method can be reduced to approximately proportional to the sum of the number of point light sources and hologram resolution by approximating the object wave with polynomials. The computation time and reconstructed image quality were compared with those of the existing methods. The proposed method was approximately 10 times faster than the conventional acceleration method, and did not produce significant errors when the object was far from the hologram.

Point-polygon hybrid method for generating holograms.

Computer-generated holograms (CGHs) are usually calculated from point clouds or polygon meshes. Point-based holograms are good at depicting details of objects, such as continuous depth cues, while polygon-based holograms tend to efficiently render high-density surfaces with accurate occlusions. Herein, we propose a novel point-polygon hybrid method (PPHM) to compute CGHs for the first time (to the best of our knowledge), which takes advantage of both point-based and polygon-based methods, and thus performs better than each of them separately. Reconstructions of 3D object holograms confirm that the proposed PPHM can present continuous depth cues with fewer triangles, implying high computational efficiency without losing quality.

Comparison of double-phase hologram and binary amplitude encoding: holographic projection and vortex beam generation.

Utilizing computer-generated holograms is a promising technique because these holograms can theoretically generate arbitrary waves with high light efficiency. In phase-only spatial light modulators, encoding complex amplitudes into phase-only holograms is a significant issue, and double-phase holograms have been a popular encoding technique. However, they reduce the light efficiency. In this study, our complex amplitude encoding, called binary amplitude encoding (BAE), and conventional methods including double-phase hologram, iterative algorithm, and error diffusion methods were compared in terms of the fidelity of reproduced light waves and light efficiency, considering the applications of lensless zoomable holographic projection and vortex beam generation. This study also proposes a noise reduction method for BAE holograms that is effective when the holograms have different aspect ratios. BAE is a non-iterative method, which allows holograms to be obtained more than 2 orders of magnitude faster than iterative holograms; BAE has about 3 times higher light efficiency with comparable image quality compared to double-phase holograms.

Deep hologram converter from low-precision to middle-precision holograms.

We propose a deep hologram converter based on deep learning to convert low-precision holograms into middle-precision holograms. The low-precision holograms were calculated using a shorter bit width. It can increase the amount of data packing for single instruction/multiple data in the software approach and the number of calculation circuits in the hardware approach. One small and one large deep neural network (DNN) are investigated. The large DNN exhibited better image quality, whereas the smaller DNN exhibited a faster inference time. Although the study demonstrated the effectiveness of point-cloud hologram calculations, this scheme could be extended to various other hologram calculation algorithms.

Hyperparameter tuning of optical neural network classifiers for high-order Gaussian beams.

High-order Gaussian beams with multiple propagation modes have been studied for free-space optical communications. Fast classification of beams using a diffractive deep neural network (D2NN) has been proposed. D2NN optimization is important because it has numerous hyperparameters, such as interlayer distances and mode combinations. In this study, we classify Hermite-Gaussian beams, which are high-order Gaussian beams, using a D2NN, and automatically tune one of its hyperparameters known as the interlayer distance. We used the tree-structured Parzen estimator, a hyperparameter auto-tuning algorithm, to search for the best model. As a result, the proposed method improved the classification accuracy in a 16 mode classification from 98.3% in the case of equal spacing of layers to 98.8%. In a 36 mode classification, the proposed method significantly improved the classification accuracy from 84.9% to 94.9%. In addition, we confirmed that accuracy by auto-tuning improves as the number of classification modes increases.

HORN-9: Special-purpose computer for electroholography with the Hilbert transform.

Holography is a technology that uses light interference and diffraction to record and reproduce three-dimensional (3D) information. Using computers, holographic 3D scenes (electroholography) have been widely studied. Nevertheless, its practical application requires enormous computing power, and current computers have limitations in real-time processing. In this study, we show that holographic reconstruction (HORN)-9, a special-purpose computer for electroholography with the Hilbert transform, can compute a 1, 920 × 1, 080-pixel computer-generated hologram from a point cloud of 65,000 points in 0.030 s (33 fps) on a single card. This performance is 8, 7, and 170 times more efficient than a previously developed HORN-8, a graphics processing unit, and a central processing unit (CPU), respectively. We also demonstrated the real-time processing and display of 400,000 points on multiple HORN-9s, achieving an acceleration of 600 times with four HORN-9 units compared with a single CPU.

Real-valued layer-based hologram calculation.

Layer-based hologram calculations generate holograms from RGB and depth images by repeating diffraction calculations using complex Fourier transforms (FTs). Holograms generated as such are suitable for near-eye display and can be easily reconstructed with good image quality, but they are computationally expensive because of multiple complex-valued operations, including complex FTs. In this study, we propose an acceleration method for layer-based hologram calculations by reducing time-consuming complex-valued operations using the real-valued FT and Hartley transform as real linear transformations. Real linear transformations transform real input data to real output data; thus, the proposed method generates amplitude holograms. Thus, we also propose a technique to convert holograms generated by real linear transformations into phase-only holograms using the half-zone plate process and digitalized single-sideband method while maintaining the calculation acceleration. The proposed method can speed up hologram calculations by a factor of around three while maintaining the same image quality as the conventional method.

Variable-intensity line 3D images drawn using kinoform-type electroholography superimposed with phase error.

Three-dimensional (3D) display using electroholography is a promising technology for next-generation television systems; however, its applicability is limited by the heavy computational load for obtaining computer-generated holograms (CGHs). The CG-line method is an algorithm that calculates CGHs to display 3D line-drawn objects at a very high computational speed but with limited expressiveness; for instance, the intensity along the line must be constant. Herein, we propose an extension for drawing gradated 3D lines using the CG-line method by superimposing phase noise. Consequently, we succeeded in drawing gradated 3D lines while maintaining the high computational speed of the original CG-line method.

Accelerating hologram generation using oriented-separable convolution and wavefront recording planes.

Recently, holographic displays have gained attention owing to their natural presentation of three-dimensional (3D) images; however, the enormous amount of computation has hindered their applicability. This study proposes an oriented-separable convolution accelerated using the wavefront-recording plane (WRP) method and recurrence formulas. We discuss the orientation of 3D objects that affects computational efficiency, which is overcome by reconsidering the orientation, and the suitability of the proposed method for hardware implementations.

Temporal super-resolution high-speed holographic video recording based on switching reference lights and angular multiplexing in off-axis digital holography.

We develop a temporal super-resolution high-speed holographic video recording method based on the angular multiplexing in off-axis digital holography that can achieve an acquisition rate greater than the frame rate of image sensors. We realize a high-speed switching of reference lights with different incident angles using two acousto-optic modulators. We successfully double the frame rate of the hologram recording using a rotating circular protractor and demonstrate its practical application in compressed gas flow injection; we achieve a frame rate of 175,000 fps using a high-speed image sensor triggered at 87,500 Hz.

FFT-based simulation of the hologram-recording process for light-in-flight recording by holography.

We propose a numerical simulation method of the hologram-recording process for light-in-flight recording by holography (LIF holography) based on fast Fourier transform (FFT) to improve the efficiency of the simulation. Because it is crucial to consider the difference in the optical-path length between the object and reference light pulses, we modify a point-spread function by considering the optical-path lengths of the object and reference light pulses and whether both pulses interfere with each other in LIF holography. The computational time was shortened by 5.5×105 times for the 4,096×4,096 resolution of the hologram using the proposed method. We evaluate the proposed method by calculating the root mean square error (RMSE) of the reconstructed holographic images. The RMSEs were relatively small considering the effect of speckle noise; these results effectively demonstrate the validity of the proposed method. Moreover, we reconstruct the moving pictures of light pulse propagation from the hologram generated by the proposed method. We compare the simulation and experimental results, and succeed in qualitatively demonstrating the validity of the proposed method.

Single-pixel imaging for edge images using deep neural networks.

Edge images are often used in computer vision, cellular morphology, and surveillance cameras, and are sufficient to identify the type of object. Single-pixel imaging (SPI) is a promising technique for wide-wavelength, low-light-level measurements. Conventional SPI-based edge-enhanced techniques have used shifting illumination patterns; however, this increases the number of the illumination patterns. We propose two deep neural networks to obtain SPI-based edge images without shifting illumination patterns. The first network is an end-to-end mapping between the measured intensities and entire edge image. The latter comprises two path convolutional layers for restoring horizontal and vertical edges individually; subsequently, both edges are combined to obtain full edge reconstructions, such as in the Sobel filter.

Real-valued diffraction calculations for computational holography [Invited].

Computational holography, encompassing computer-generated holograms and digital holography, utilizes diffraction calculations based on complex-valued operations and complex Fourier transforms. However, for some holographic applications, only real-valued holograms or real-valued diffracted results are required. This study proposes a real-valued diffraction calculation that does not require any complex-valued operation. Instead of complex-valued Fourier transforms, we employ a pure real-valued transform. Among the several real-valued transformations that have been proposed, we employ the Hartley transformation. However, our proposed method is not limited to this transformation, as other real-valued transformations can be utilized.

Acceleration of polygon-based computer-generated holograms using look-up tables and reduction of the table size via principal component analysis.

In this study, we first analyze the fully analytical frequency spectrum solving method based on three-dimensional affine transform. Thus, we establish a new method for combining look-up tables (LUTs) with polygon holography. The proposed method was implemented and proved to be accelerated about twice compared to the existing methods. In addition, principal component analysis was used to compress the LUTs, effectively reducing the required memory without artifacts. Finally, we calculated very complex objects on a graphics processing unit using the proposed method, and the calculation speed was higher than that of existing polygon-based methods.

GPU-accelerated calculation of computer-generated holograms for line-drawn objects.

The heavy computational burden of computer-generated holograms (CGHs) has been a significant issue for three-dimensional (3D) display systems using electro-holography. Recently, fast CGH calculation methods of line-drawn objects for electro-holography were proposed, which are targeted for holography-based augmented reality/virtual reality devices because of their ability to project object contours in space with a small computational load. However, these methods still face shortcomings, namely, they cannot draw arbitrary curves with graphics processing unit (GPU) acceleration, which is an obstacle for replaying highly expressive and complex 3D images. In this paper, we propose an effective algorithm for calculating arbitrary line-drawn objects at layers of different depths suitable for implementation of GPU. By combining the integral calculation of wave propagation with an algebraic solution, we successfully calculated CGHs of 1, 920 × 1, 080 pixels within 1.1 ms on an NVIDIA Geforce RTX 2080Ti GPU.

Hologram computation using the radial point spread function.

Holograms are computed by superimposing point spread functions (PSFs), which represent the distribution of light on the hologram plane. The computational cost and the spatial bandwidth product required to generate holograms are significant; therefore, it is challenging to compute high-resolution holograms at the rates required for videos. Among the possible displays, fixed-eye-position holographic displays, such as holographic head-mounted displays, reduce the spatial bandwidth product by fixing eye positions while satisfying almost all human depth cues. In eye-fixed holograms, by calculating a part distribution of the entire PSF, we observe reconstructed images that maintain the image quality and the depth of focus almost as high as those generated by the entire PSF. In this study, we accelerate the calculation of eye-fixed holograms by engineering the PSFs. We propose cross and radial PSFs, and we determine that, out of the two, the radial PSFs have a better image quality. By combining the look-up table method and the wavefront-recording plane method with radial PSFs, we show that the proposed method can rapidly compute holograms.

Mitigating ringing artifacts in diffraction calculations using average subtractions.

Fourier transform-based diffraction calculations are essential for computational optics. However, the diffraction calculations can be corrupted by the introduction of strong ringing artifacts due to the introduction of zero-padding to avoid circular convolution or to control the sampling intervals. We propose a simple de-ringing method using average subtractions for application to on-axis and off-axis diffraction calculations. To verify the effectiveness of the proposed method, we compared the diffracted fields obtained using zero-padding, a flat-top window method, a mirror expansion method, and the whole and border average subtractions proposed. Furthermore, we confirmed the effectiveness of the proposed method for hologram calculations using double phase encoding and image reconstructions of inline digital holography.

Incoherent color digital holography with computational coherent superposition for fluorescence imaging [Invited].

We present color fluorescence imaging using an incoherent digital holographic technique in which holographic multiplexing of multiple wavelengths is exploited. Self-interference incoherent digital holography with a single-path in-line configuration and the computational coherent superposition scheme are adopted to obtain color holographic three-dimensional information of self-luminous objects with a monochrome image sensor and no mechanical scanning. We perform not only simultaneous color three-dimensional sensing of multiple self-luminous objects but also color fluorescence imaging of stained biological samples. Color fluorescence imaging with an improved point spread function is also demonstrated experimentally by adopting a Fresnel incoherent correlation holography system.