The state-of-the-art in computer generated holography for 3D display

Holographic displays have the promise to be the ultimate 3D display technology,able to account for all visual cues.Recent advances in photonics and electronics gave rise to high-resolution holographic display prototypes,indicating that they may become widely available in the near future.One major challenge in driving those display systems is computational:computer generated holography(CGH)consists of numerically simulating diffraction,which is very computationally intensive.Our goal in this paper is to give a broad overview of the state-of-the-art in CGH.We make a classification of modern CGH algorithms,we describe different algorithmic CGH acceleration techniques,discuss the latest dedicated hardware solutions and indicate how to evaluate the perceptual quality of CGH.We summarize our findings,discuss remaining challenges and make projections on the future of CGH.

Editorial for Focus Issue on Digital and Computer Generated Holography (DCH)

This focus issue Digital and Computer Generated Holography （DCH） combines the contributions from digital holography （DH） and computer-generated holography （CGH） into a single issue. We have classified the papers into four topics： holographic microscopy, computer-generated holography,

Problems on fabrication of computer-generated holograms for testing aspheric surfaces

Interferometric optical testing using computer-generated hologram （CGH） can give highly accurate measurement of aspheric surfaces has been proved. After the system is designed, a phase function is obtained according to the CGH＇s surface plane. For the requirement of accuracy, an optimization algorithm that transfers the phase function into a certain mask pattern file is presented in this letter, based on the relationship between the pattern error of CGH and the output wavefront accuracy. Then the writing machine is able to fabricate such a mask with this kind of file. With that mask, an improved procedure on fabrication of phase type CGH is also presented. Interferometrie test results of an aspherie surface show that the whole test system obtains the demanded accuracy.

Estimation and optimization of computer-generated hologram in null test of freeform surface

Freeform surfaces are increasingly used in the design of compact optical systems. Interferometric null test with computer generated hologram （CGH）, which has been successfully used in highly accurate test of aspheric surfaces, is adopted to test the freeform surfaces. The best fitting sphere of the freeform surface under the test is firstly calculated to quickly estimate the possibility of null test. To decrease the maximum spatial frequency of the null CGH, the position of the CGH and the direction of optical axis are optimized. The estimated maximum spatial frequency of the CGH is 7.8% apart from the optimized one, which shows the validity of the best fitting sphere.

3D trapping and manipulation of micro-particles using holographic optical tweezers with optimized computer-generated holograms

A multi-plane adaptive-additive algorithm is developed for optimizing computer-generated holograms for the reconstruction of traps in three-dimensional （3D） spaces. This algorithm overcomes the converging stagnation problem of the traditional multi-plane Gerehber-Saxton algorithm and improves the diffraction efficiency of the holograms effectively, The optimized holograms are applied in a holographic optical tweezers （HOT） platform. Additionally, a computer program is developed and integrated into the HOT platform for the purpose of achieving the interactive control of traps. Experiments demonstrate that the manipulation of micro-particles into the 3D structure with optimized holograms can be carried out effectively on the HOT Dlatform.

Optical reconstruction of 3D images by use of pure-phase computer-generated holograms

A three-dimensional （3D） object reconstruction technique that uses pure-phase computer-generated holograms （CGHs） and a phase-only spatial light modulator （SLM） is proposed. The full parallax CGHs are generated by the point source method and the wave-oriented method without paraxial approximation. Different from conventional CGHs, the pure-phase information on the hologram plane is loaded on the SLM to reconstruct the 3D diffusive objects without considering the reference wave. This technique is more efficient in its utilization of the space-bandwidth product of the SLMs. Numerical simulations and experiments are performed, and the results show that our proposed method can reconstruct 3D diffusive objects successfully.

Design and fabrication of computer-generated holograms for testing optical freeform surfaces

Freeform optical surfaces （FOSs） will be the best elements in the design of compact optical systems in the future. However, it is extremely difficult to measure freeform surface with sufficient accuracy, which im- pedes the development of the freeform surface. The design and fabrication of computer-generated hologram （CGH） , which has been successfully applied to the tests for aspheric surfaces, cannot be directly adopted to test FOSs due to their non-rotational asymmetry. A novel ray tracing planning method combined with successively optimizing even and odd power coefficients of phase polynomials in turn is proposed, which can successfully design a non-rotational asymmetry CGH for the tests of FOSs with an F-O lens. A new eight-step fabrication process is also presented aiming to solve the problem that the linewidth on the same circle of the CGH for testing freeform surface is not uniform. This problem cannot be solved in the original procedure of CGH fabrication. The test results of the step profiler show that the CGH fabricated in the new nrocedure meets the reauirements.

Fast numerical generation and hybrid encryption of a computer-generated Fresnel holographic video sequence

Research demonstrates that a Fresnel hologram can be generated and simultaneously encrypted numerically based on a secret symmetric key formed by the maximal length sequence （M-sequence）. The method can be directly extended to encrypt a video holographic clip in a frame-by-frame manner. However, given the limited combination of signals in the family of M-sequence, hacking the secret key through trial and error can be time consuming but not difficult. In this letter, we propose a method that is difficult to crack with brute force for enerypting a holographic video sequence. An M-sequence is first randomly assigned to enerypt each frame of the holographic video signal. Subsequently, the index of the selected M-sequence, which is necessary to decrypt the hologram~ is encrypted with the RSA algorithm before transmitting to the receiving end. At the receiving end, the decoder is provided with a private key to recover the index for each frame, and the corresDonding M-se（mence is used to decrvDt the encoded hologram.

Computer-generated-hologram-accelerated computing method based on mixed programming

Component object model technology is used to solve problems encountered when using three-dimentional （3D） objects to conduct computer-generated hologram （CGH） fast coding. MATLAB and C/C＋＋ are combined for relevant programming under experimental conditions. The proposed method effectively reduces the time required for holographic encoding of large amounts of 3D object data. The CGH- accelerated computing method based on mixed programming is proven to be highly reliable and practical by testing the 3D data of different data volumes. According to the test results, the proposed method improves the efficiency of holographic encoding. The higher the data volume is, the more significantly the computation speed is improved.

Speckle noise reduction in digital holography by use of multiple polarization holograms

A novel speckle reduction technique for digital holography is proposed. Multiple off-axis holograms are recorded using a circularly polarized illumination beam and a rotating linearly polarized reference beam. The speckle noise in the reconstructed images is suppressed by averaging these fields. We demonstrate the effectiveness of this technique experimentally and conduct additional statistical evaluation.

Quality evaluation of phase reconstruction in LED-based digital holography

An approach, based on the correlation between the intensity distribution of object wave of the directly recorded by charge-coupled device and the one reconstructed by computer, is proposed to evaluate the quality of the phase reconstruction in light emitting diode （LED） based phase-shifting digital holography. This method enables us to find out the optimal reconstructed phase even though the peak wavelength of LED, which is used for calibrating the phase-shifter, is inconvenient to be determined and tends to shift with temperature and driving current. The feasibility of this method is verified by both computer simulations and experiments.

Improvement of speckle noise suppression in digital holography by rotating linear polarization state

An improved polarization recording approach to reduce speckle noise in digital holography is proposed. Multiple off-axis holograms are obtained by rotating the linear polarization state of both illumination and reference wave simultaneously. By averaging the intensity fields, the speckle noise in the reconstructed images is well suppressed. Statistical evaluation of the experimental results shows the effectiveness and improvement of the proposed method.

Numerical correction of splicing dislocation between sub-holograms in synthetic aperture digital holography using convolution approach

We propose a new correction method for the splicing dislocation of sub-holograms in synthetic aperture digital holography. By adjusting the splicing distances between sub-holograms during the numerical recon- struction process using the convolution approach, the influence of non-paraxial aberration for the quality of the synthetic reconstructed image is avoided and synthetic reconstructed images corresponding to different splicing distances are obtained. Then, the accurate splicing distance between sub-holograms is determined by evaluating the quality of the corresponding synthetic reconstructed images. Accurate correction for the splicing dislocation of sub-holograms is achieved and high-quality reconstructed images without non- Daraxial aberration are obtained.

Phase retrieval from double axially displaced holograms for dual-wavelength in-line holography

A phase retrieval method for dual-wavelength in-line digital holography is presented with double axially displaced holograms.A synthetic wavelength is used during iterative propagations to retrieve wrap-free phase distributions with a much extended measurement range.The simulation and experimental results demonstrate a better elimination of the twin image,a faster rate of convergence of the iterative routine and less number of wavelengths are compared with previously reported multiple-wavelength in-line holography.

Non-invasive monitoring of living cell culture by lensless digital holography imaging

A non-invasive detection method for the status analysis of cell culture is presented based on digital holography technology.Lensless Fourier transform digital holography （LFTDH） configuration is developed for living cell imaging without prestaining.Complex amplitude information is reconstructed by a single inverse fast Fourier transform,and the phase aberration is corrected through the two-step phase subtraction method.The image segmentation is then applied to the automatic evaluation of confiuency.Finally,the cervical cancer cell TZMbl is employed for experimental validation,and the results demonstrate that LFTDH imaging with the corresponding image post-processing can provide an automatic and non-invasive approach for monitoring living cell culture.

Spatiotemporal double-phase hologram for complex-amplitude holographic displays

This Letter describes an approach to encode complex-amplitude light waves with spatiotemporal double-phase holograms(DPHs) for overcoming the limit of the space-bandwidth product(SBP) delivered by existing methods. To construct DPHs, two spatially macro-pixel encoded phase components are employed in the SBP-preserved resampling of complex holograms. Four generated sub-DPHs are displayed sequentially in time for high-quality holographic image reconstruction without reducing the image size or discarding any image terms when the DPHs are interweaved. The reconstructed holographic images contain more details and less speckle noise, with their signal-to-noise ratio and structure similarity index being improved by 14.64% and 78.79%,respectively.

Generation and motion control of optical multi-vortex

The generation and propagation dynamics of multiple optical vortices hosted in a Gaussian beam are experimentally demonstrated by use of the computer-generated holography. Fluid-like motions of the multi-vortex beam are observed owing to the helical phase structure. The multi-vortex beam with identical topological charge presents rotation, which can be suppressed by changing the sign of the topological charge alternately. In addition, the transverse motion control of the multi-vortex is proved by inserting an additional vortex. Finally, rotary and stationary vortex lattices with different periodic arrays are experimentally constructed. The results exhibit potential applications in inducing twisted or stable waveguide arrays and new types of optical traps.

Phase correction and resolution improvement of digital holographic image in numerical reconstruction with angular multiplexing

A phase correction method is presented to remove the phase slope of the sub-holograms caused by the multi-direction illumination on object in digital holography. To improve the resolution of the reconstructed holographic images, two sub-holograms are recorded by using angular multiplexing and their phase slope parameter is obtained by theoretical analysis. Introducing a phase correction parameter to this phase slope, the ideal complex reconstructed image can be obtained by superposing the reconstructed object wave fields of the two sub-holograms. Experimental results demonstrate that the resolution of the reconstructed image can be effectively enhanced.

Dual-wavelength digital holographic phase reconstruction based on a polarizationmultiplexing configuration

We present a polarization-multiplexing off-axis Mach-Zehnder configuration for dual-wavelength digital holography to achieve phase imaging in one shot. In this configuration, two orthogonal linear-polarized waves with respect to different wavelengths are employed to record respective holograms synchronously, where two recording waves transmit independently through the same optical paths of the interferometer, and by installing two analyzer polarizers each to filter off either of two wavelengths, and filtering through the other, the holograms are acquired, respectively, by a pair of CCDs at the same time. The unwrapped phase image of a grating with groove depth 7.i ~m is retrieved via spatial frequency filtering.

Analysis of optical characteristics of modulation devices with square and circle pixels for 3D holographic display

With the development of the micro/nanolithography, the optic-optic or optic-electronic modulation devices with different pixel shapes and sizes can be used for three-dimensional （3D） dynamical holographic display. The influence of different parameters of the modulation devices on the image quality of the 3D reconstructed object is analyzed for two cases： the phase-only computer-generated holography （CGH） and the complex amplitude CGH. The results quantitatively show that the pixel shape of the modulation devices will affect the quality of the holographic image.