This guest editorial introduces the Special Section on Holography.

The resolution optimization and sampling strategies in practical digital in-line holography (DIH) with spherical wave illumination are analytically studied by optimizing system parameters. Optimal parameters of holographic recording, including illumination wavelength, numerical aperture of the spherical illumination wave, source-sensor distance, object–sensor distance, and sampling parameters of the sensor, for achievable resolution are worked out. A formula is derived to guide the DIH system design in general cases. Different sampling strategies associated with corresponding reconstruction waves (plane wave and spherical waves with various curvatures) are analyzed. The reason why recording with spherical wave and reconstructing with plane wave works well in practice is explained in detail. We also present how to determine the reconstruction distance and magnification to reconcile the curvature difference. The analysis is carried out mathematically and verified by simulated holograms. Optical experiments with U.S. Air Force resolution target are carried out based on the analysis for further verification.

The label-free analysis of leukocytes by holographic microscopy has the potential to overcome the extensive labeling procedures of conventional analysis by automated hematology analyzers and manual blood smear analysis. For the enrichment of leukocytes, selective lysis of erythrocytes is applied in flow cytometry to minimize the background. In the case of quantitative phase measurements, lysis procedures may affect the morphology of leukocytes inducing refractive index changes, which can deteriorate the specificity and sensitivity of the method. To study the effects of selective erythrocyte lysis on phase measurements of leukocytes, we compared two widespread methods: lysis by hypotonic shock followed by magnetic depletion of erythrocytes and lysis with a commercial lysis buffer containing ammonium chloride and potassium bicarbonate. We observed that lymphocytes were less affected than granulocytes and monocytes by both methods and that the intracellular changes increased with increasing incubation times. These findings indicate a significant effect of erythrocyte lysis on leukocytes and need to be studied for future hematology applications.

A quick and accurate way for testing collimation of laser beams is desired to achieve correct results in many optical instruments. Laser beam collimation is generally performed using glass wedge plates. For better accuracy, a set of wedge plates of different thicknesses and wedge angles are required to acquire first-hand visual information about collimation of laser beams having a wide range of diameters. Use of a compact holographic lateral shearing interferometer (HLSI) is demonstrated for collimation testing of laser beams having different beam diameters. The interferometer uses two holographic optical elements (HOEs) with provision of variable tilt in one of the HOEs to maintain a constant number of fringes in the interferograms for different diameters of input test beams. An angle of rotation of interference fringes from a reference position is measured to be 0.9 deg for a test beam of diameter 2 mm and 16 deg for the test beam of diameter 35 mm. We experimentally demonstrated range of optimum number of interference fringes in the interferogram for visual inspection of the collimation state of the test beam. Thus the proposed interferometer could replace a set of wedge plates generally required for collimation testing of beams having different diameters. The functioning of the interferometer for collimation testing of beams having different diameters is discussed and experimentally demonstrated.

We introduce a technique for recording volume holographic optical elements (vHOEs) designed for operation at a wavelength different from the recording wavelength. This technique relies on our holographic wave front printer, which employs two spatial light modulators for recording wave front generation. We present the procedure for computing the required recording wave fronts accurately and noniteratively from the desired vHOE optical transformation function. We exploit this technique for the fabrication of a converging lens vHOE with an operation wavelength of 915 nm at a recording wavelength of 515 nm. Finally, we demonstrate the holographic lens functionality directly in the infrared spectral region.

To simulate the effects of multiple-longitudinal modes and rapid fluctuations in center frequency, we use sinusoidal phase modulation and linewidth broadening, respectively. These effects allow us to degrade the temporal coherence of our master-oscillator laser, which we then use to conduct digital holography experiments. In turn, our results show that the coherence efficiency decreases quadratically with fringe visibility and that our measurements agree with our models to within 1.8% for sinusoidal phase modulation and 6.9% for linewidth broadening.

In this work, we propose a combination of the Teager–Kaiser energy operator (TKEO) and the spiral phase transform (SPT) for robust instant energy estimation of amplitude-modulated and frequency-modulated (AM–FM) signals, where the energy extraction is followed by a high-frequency component, generally considered as noise. We demonstrate that this noise component can be subtracted mathematically using the SPT transformation applied to the AM–FM signal. The improvement in demodulation is tested using a simulated AM–FM image and evaluated by the image quality index. An experimental speckle fringe pattern obtained by digital speckle pattern interferometry on a hard disk is denoised using a multiband approach and demodulated using the proposed method.

The extreme computational complexity in generating a hologram makes the interactive holographic display very difficult. An optimized layered rendering method for real-time interactive holographic display based on ray-tracing technique is presented in order to overcome this challenge and realize real-time interaction of three-dimensional scenes. Ray tracing is able to render more complex and photorealistic images for different illuminations and circumstances. Rays are launched in parallel and traced to obtain ray–object intersections, and then the complex wave field of the effective pixels in different layers is determined. The occlusions between different layers are also considered to effectively reduce the overall computation. A computer-generated hologram is fused with the multilayer-hologram-diffraction results using the layered fast Fourier transform algorithm. The experimental results demonstrate the effectiveness of the proposed method. The reconstructed holographic image with real depth cues is demonstrated by the experiments, and the optical reconstruction images can be interacted in real-time.

Faithful reconstruction, which is a key phenomenon in optical data storage, is significant in polarization holography and has attracted much attention. It is defined as the reconstructed wave being identical to the signal wave. We design an experiment to observe the faithful reconstruction of elliptical polarization holography in which the two orthogonal elliptical polarization waves are applied in the recording stage. In the experiment, phenanthrenequinone-doped poly methyl methacrylate is used as the recording material, and the angle between the signal and reference waves is ∼56  deg. We control the exposure time of recording material to observe the faithful reconstruction of orthogonal elliptical polarization holography. How to obtain the faithful reconstruction is interesting work; therefore, we propose a prerequisite for faithful reconstruction. Although the prerequisite is derived from orthogonal elliptical polarization holography, it could also be applied in orthogonal linear and circular polarization holography. The result may be helpful for understanding the faithful reconstruction of orthogonal polarization holography.

Floating three-dimensional (3-D) display can provide a natural and realistic 3-D scene. Nowadays, because of stray light and aberration, most floating 3-D displays cannot realize a large viewing angle and high resolution simultaneously, and it directly deteriorates the viewing effect of the 3-D scene. A large viewing angle floating and high-resolution 3-D display based on multichannel and multivariable (MCMV) correction algorithm are presented. The optical system consists of a time-sequential autostereoscopic 3-D display with the directional backlight, a floating lens, and an eye tracker. The 3-D display with the directional backlight provides loss-free resolution for the system. To realize a large viewing angle floating 3-D display, MCMV correction algorithm based on eye tracking is proposed. The 3-D images can be reconstructed by the optical system within the viewing angle of 60 deg. The feasibility of the proposed display method is verified with the experimental results.

A method is proposed for multiple-image encryption based on optical scanning holography (OSH) using a random phase mask (RPM) and orthogonal compressive sensing (CS). It can destroy the linearity of the traditional OSH system and possess a superior security. On the one hand, images are preferentially preprocessed by utilizing the orthogonal CS to provide a single-layer section for OSH. Therefore, the defocus noise as well as information leakage can be controlled effectively in decryption. On the other hand, each image can be extracted separately without the others’ contents. In addition, the use of RPM can bring about a more ulterior distribution to the cyphertext, which may be better than the case without the RPM. The use of orthogonal modulation matrices and RPM can provide the additional key spaces to guarantee the security of this holography cryptosystem. Simulations and discussions are also made on the cyphertext characteristics as well as the ability of resisting occlusive attack.

A modified single-pass multiview rendering method is proposed to achieve real-time large viewing angle volume data three-dimensional (3-D) display. By modifying the volume rendering pipeline, the mapping of the synthetic image pixel and multiperspective information is directly accomplished in once rendering pass. And then shear-transformed ray is cast to integrate multiperspective information into the synthetic image used for 3-D display. Proof-of-concept experimental setups are constructed with the autostereoscopic 3-D display and the 3-D light-field display to demonstrate the proposed method without loss of generality. The experimental results show that the real-time frame rates of the autostereoscopic 3-D display and the 3-D light-field display are more than 30 and 60 fps at 4K (3840  ×  2160) resolution, respectively. The rendering efficiency of the proposed method is irrespective of the viewpoint number and viewing angle size. In addition, it is not only compatible with the volume drawing pipeline but also robust to different types of 3-D displays based on pixel coding. A feasible way of applying 3-D display to the biological and medical fields is presented.

Computer-generated holography (CGH) is a technique to generate holographic interference patterns. One of the major issues related to computer hologram generation is the massive computational power required. Hardware accelerators are used to accelerate this process. Previous publications targeting hardware platforms lack performance comparisons between different architectures and do not provide enough information for the evaluation of the suitability of recent hardware platforms for CGH algorithms. We aim to address these limitations and present a comprehensive review of CGH-related hardware implementations.

We present validation of a tilt angle illumination technique for height maps’ reconstruction using digital holography and propose a few solutions for improvement of the inclined probe wave front approach. The general algorithm of tilt angle digital holography approach is described and validated in experimental monitoring of a coin relief. Several approaches of height map quality improvement concerning tilt angle estimation, relation between measurement accuracy and dynamic range, and selective averaging algorithm are proposed and discussed.

Non-interferometric phase retrieval is a fundamental technique for phase-modulated holographic data storage due to its advantages of easy implementation, simple system setup, and robust noise tolerance. Usually, the iterative algorithm of non-interferometry needs hundreds of iteration numbers to retrieve phase accurately, which decreased the data transfer rate severely. Strong constraint conditions, such as embedded data, can be used on the phase data page to reduce the iteration numbers. However, introducing embedded data will reduce the code rate of the system. We proposed a method that combined the single-shot interferometric method with the non-interferometric iterative Fourier transform algorithm method. We used the phase decoding result by single-shot interferometry as the embedded data in the process of non-interferometry. Therefore, no extra embedded data are needed in the signal code. We realized the code rate improvement as well as keeping fast data transfer rate. In the demonstration, we recorded a four-level phase pattern and retrieved the phase correctly. The bit error rate of phase retrieval is less than 1% within 20 iterations, which proves our approach is practical. In our case, the code rate is increased by two times.

For many years, the use of advanced composite materials in aeronautics, automotive, and sports applications has been well established. The characteristics of composite materials in terms of weight reduction, fatigue, and corrosion resistance make them competitive in many cases with respect to conventional ones (i.e., metal alloys). On the other hand, the fabrication process of the most employed composites reinforced by carbon or glass fibers requires complex steps that are not always environmentally friendly. In fact, such composite materials are not themselves “green.” For these reasons, in the last decades, the use of natural reinforcing fibers has gained increasing attention, allowing the development of new materials sharing the same advantages with conventional composite systems while respecting the environment. Due to their structural complexity, these materials are not always compatible with the use of standard nondestructive evaluation methods, e.g., ultrasounds testing. The effective use of speckle holographic techniques as nondestructive evaluation methods in full field and noncontact modality is proved on “green” composite materials. In particular, electronic speckle pattern interferometry is tested on different kinds of specimens preliminarily subjected to flexural tests. Results show that, in most cases, the damage appears more severe on the back side of specimens, opposite to the loaded one, with the sole exception of basalt laminates.

We demonstrate an application of digital holography for detection of a new type of defect, i.e., delamination of polyurethane pads on a polishing tool used on a high-speed computerized numerical control machine for production of precision optics. The method enabled us to acquire both qualitative and quantitative information about the delaminated region in the polishing pad. A delaminated region of 13.6  mm  ×  10.8  mm is detected and measured on the surface of the polishing pad. An increase in the delaminated region by 30% is noticed after completion of the polishing process with the delaminated polishing pad. The effect of delamination of the polishing pad on an optical surface is experimentally demonstrated using it for polishing a BK-7 glass substrate. These investigations may enable production of improved quality precision optics at the commercial level.

A self-contained platform for realistic modeling of digital holographic microscopy (DHM) is presented. Amplitude and phase samples, imaged in different architectures, can be modeled to produce numerical DHM holograms that include all the parameters that are present in real experiments, providing an accessible way for newcomers to have a first approach to this research field. The platform is based on considering the imaging arm of the DHM that produces the object wave as the result of the convolution process between the geometrical-optics image prediction of the sample with the point spread function introduced by diffraction. The DHM hologram is produced by the amplitude superposition of complex-valued object wave with a reference wave of arbitrary description. The sampling of the analytically produced DHM holograms is set from the input discretized image according to the specifications of the digital camera aimed to be used. The feasibility of the realistic platform is exemplified by contrasting the wrong results of a nonrealistic simulation with experimental results to show the need for using a complete realistic simulation like the one presented; further applications of the platform to numerical modeling speckle noise reduction over samples with controlled levels of roughness, and phase-shifting DHM techniques, are included.

In computer-generated holograms (CGH), a random phase (RP) is usually introduced to spread the object information in the hologram and avoid the frequency-filtering effect in the reconstructed image. However, this action introduces speckle noise in the reconstructed image but also permits one to reconstruct objects with bigger size than the hologram. In recent years, alternative RPs have been proposed to reduce the speckle noise in comparison with the uniform distributed RP that is usually applied. However, its effects in different types of holograms, its capacity to reconstruct big objects, and its capability to eliminate the frequency-filtering effect have not been reviewed in detail. We present an analysis of the normal distributed, pink, brown, and Perlin phases in Fourier and Fresnel holograms coded as amplitude and phase (Kinoform and complex amplitude encoded). Only in the Kinoform holograms, the RP is required to eliminate the frequency-filtering effect. In other cases, the phase is useful to record big objects in the hologram. The Perlin phase had a better performance than the other phases, achieving the reconstruction of objects with bigger size than the hologram and reducing the speckle noise. We present a quantitative and qualitative analysis of each distribution, including simulated and experimental results that confirm the numerical analysis. We believe these results could be helpful in the selection of an adequate RP in CGH, according to the hologram configuration.

We dealt with the problem of shading of dense polydispersed aerosol particles during registration of holographic images. It is a suggested technique that is based on the three-wave holographic recording of a cloud of micron and submicron particles. We present the calculated and experimental results of effective reconstruction of cloud particles with concentration of up to 100  ×  10⁶  /  cm³. Simultaneous use of three-wave scheme provides complete analysis of the resulting holograms and more effectively restore the volume distribution of dense aerosol formatting.