Digital Holograms Research Articles

Frequency domain zero padding for accurate autofocusing based on digital holography

The numerical refocusing feature of digital holography enables the reconstruction of a well-focused image from a digital hologram captured at an arbitrary out-of-focus plane without the supervision of end users. However, in general, the autofocusing process for getting a highly focused image requires a considerable computational cost. In this study, to reconstruct a better-focused image, we propose the zero padding technique implemented in the frequency domain. Zero padding in the frequency domain enhances the visibility or numerical resolution of the image, which allows one to measure the degree of focus with more accuracy. A coarse-to-fine search algorithm is used to reduce the computing load, and a graphics processing unit (GPU) is employed to accelerate the process. The performance of the proposed scheme is evaluated with simulation and experiment, and the possibility of obtaining a well-refocused image with an enhanced accuracy and speed are presented.

Single-shot incoherent digital holography based on spatial light modulator

Fresnel incoherent correlation holography (FINCH) is a relatively innovative technology, which can achieve incoherent holograms by using the correlation between the object information and a Fresnel zone plate. In this method, the optical wave front scattered from an object propagates and is incident on a spatial light modulator which a phase mask is mounted on, and then the optical beam is split and phase shifted. The biggest advantage of the FINCH is that it can be matched with any standard optical imaging technology, which can realize microscopic imaging, telescopic imaging, spectroscopic imaging, etc. based on incoherent digital holography, and has important application prospect in remote sensing, astronomy, microscopy, and material analysis. In this paper, based on phase modulation characteristic of spatial light modulator, two types of masks are used. The first mask has an optical axis. And the results show that when the distribution intervals of the three phases on the spatial light modulator (SLM) are larger, the reconstruction image is clearer. On this basis, a new method of mode mounting on the SLM is put forward. The second mask has dual-lens array mode with three phases of 0°, 120°, and 240°, and the three phases respectively correspond to their corresponding optical axis, which means that the mask has three optical axes. Both of the two masks can achieve the single-shot of FINCH. By comparing the two mask forms, we find that the field-of-view of the first mask is larger, which can image the entire resolution board; however, because the sub-phase shift holograms are mixed together and cannot be extracted, the quality of the reconstructed image is worse. The second one can extract three sub-holograms, and the reconstructed image has better quality; but because of smaller imaging field of view, it is suitable for the real-time imaging of micro-organisms and objects. Experiments show that a compound digital hologram including three phase-shifting elements is recorded in charge-coupled device in this way. Three sub-holograms with different phase shift angles are extracted from the compound hologram, and there is no overlapping among the three phase shift holograms. Therefore, the three-phase-shifting technique is usually employed. The sample is reconstructed by numerical reconstruction algorithm. The proposed method may be useful in dynamic process real-time measurement and three-dimensional analysis of the object, and thus providing a new way to promote the development of incoherent digital holography.

合成孔径同轴数字全息图的相位恢复再现

合成孔径同轴数字全息图的相位恢复再现

Chirped pulse digital holography for measuring the sequence of ultrafast optical wavefronts

Optical setups for measuring the sequence of ultrafast optical wavefronts using a chirped pulse as a reference wave in digital holography are proposed and analyzed. In this method, multiple ultrafast object pulses are used to probe the temporal evolution of ultrafast phenomena and they are interfered with a chirped reference wave to record a digital hologram. Wavefronts at different times can be reconstructed separately from the recorded hologram when the reference pulse can be treated as a quasi-monochromatic wave during the pulse width of each object pulse. The feasibility of this method is demonstrated by numerical simulation.

Characterization of the reference wave in a compact digital holographic camera.

A hologram is a recording of the interference between an unknown object wave and a coherent reference wave. Providing the object and reference waves are sufficiently separated in some region of space and the reference beam is known, a high-fidelity reconstruction of the object wave is possible. In traditional optical holography, high-quality reconstruction is achieved by careful reillumination of the holographic plate with the exact same reference wave that was used at the recording stage. To reconstruct high-quality digital holograms the exact parameters of the reference wave must be known mathematically. This paper discusses a technique that obtains the mathematical parameters that characterize a strongly divergent reference wave that originates from a fiber source in a new compact digital holographic camera. This is a lensless design that is similar in principle to a Fourier hologram, but because of the large numerical aperture, the usual paraxial approximations cannot be applied and the Fourier relationship is inexact. To characterize the reference wave, recordings of quasi-planar object waves are made at various angles of incidence using a Dammann grating. An optimization process is then used to find the reference wave that reconstructs a stigmatic image of the object wave regardless of the angle of incidence.

Off-axis tilt compensation in common-path digital holographic microscopy based on hologram rotation.

We present a simple and effective compensation method for the off-axis tilt in common-path digital holographic microscopy (CPDHM) by introducing a rotating operation on the hologram. The proposed method mainly requires a digital reference hologram (DRH), which is a rotated version of the original one; it is assumed to be easy to obtain by rotating the specimen's hologram 180°. In this way, the off-axis tilt could be removed by subtracting the retrieved phase of DRH from the retrieved phase of the original hologram, but without any complex spectrum centering judgment, fitting procedures, or prior knowledge of the system. This highly automatic and efficient performance makes our approach available for real-time quantitative phase imaging (QPI), although it limits the field of view (FOV) of the specimen. Some experimental results of microlens array and phase plate demonstrate the feasibility and effectiveness of the proposed method.

Measurement of the refractive index of solutions based on digital holographic microscopy

A new approach for the refractive index (RI) measurement of solutions is proposed based on digital holographic microscopy. The experimental system consists of a modified Mach–Zehnder interferometer and related lab-developed analysis software. The high quality digital hologram of the tested solution is obtained by the real-time analysis software, which is firstly encapsulated into a capillary tube, and then the capillary tube is inserted in a matching fluid. An angular spectrum algorithm is adopted to extract the phase distribution from the hologram recorded by a CCD. Based on a capillary multi-layer calculation model, the RI of the tested solution is obtained at high accuracy. The results of transparent glycerol solution measured by the proposed method are more accurate than those measured by the Abbe refractometer. We also measure the RI of translucent magnetic fluid, which is not suitable to be measured by the Abbe refractometer. The relationship between the RI and the concentration of magnetic fluid is experimentally studied, and the results show that the RI is linearly related to the concentration of dilute magnetic fluid.

Chromatic aberration compensation in numerical reconstruction of digital holograms by Fresnel-Bluestein propagation.

In this Letter, we present a method for chromatic compensation in numerical reconstruction of digitally recorded holograms based on Fresnel-Bluestein propagation. The proposed technique is applied to correct the chromatic aberration that arises in the reconstruction of RGB holograms of both millimeter- and micrometer-sized objects. The results show the feasibility of this strategy to remove the wavelength dependence of the size of the numerically propagated wavefields.

Phase retrieval based on transport of intensity and digital holography.

We propose a technique in which intensity images are reconstructed from a digital hologram to provide inputs for the transport-of-intensity equation for unwrapped phase recovery. By doing this, we avoid shifting of the sample or the camera in the experiment, a method commonly employed while using the method of transport-of-intensity equation for phase retrieval. Computer simulations as well as experimental results have been demonstrated to verify the effectiveness of the proposed idea. The underlying numerical technique can also be viewed as an alternative to existing phase-unwrapping algorithms.

Two schemes for rapid generation of digital video holograms using PC cluster

Computer-generated holography (CGH), which is a process of generating digital holograms, is computationally expensive. Recently, several methods/systems of parallelizing the process using graphic processing units (GPUs) have been proposed. Indeed, use of multiple GPUs or a personal computer (PC) cluster (each PC with GPUs) enabled great improvements in the process speed. However, extant literature has less often explored systems involving rapid generation of multiple digital holograms and specialized systems for rapid generation of a digital video hologram. This study proposes a system that uses a PC cluster and is able to more efficiently generate a video hologram. The proposed system is designed to simultaneously generate multiple frames and accelerate the generation by parallelizing the CGH computations across a number of frames, as opposed to separately generating each individual frame while parallelizing the CGH computations within each frame. The proposed system also enables the subprocesses for generating each frame to execute in parallel through multithreading. With these two schemes, the proposed system significantly reduced the data communication time for generating a digital hologram when compared with that of the state-of-the-art system.

Phase distribution analysis of tissues based on the off-axis digital holographic hybrid reconstruction algorithm.

Off-axis digital holography (DH) has great potential in histopathology for its high efficiency and precision. Phase distribution, usually extracted by the angular spectrum (AS) algorithm from a digital hologram, reflects important structural information of biological tissues. However, the complex structure of tissues introduces spectrum aliasing of the hologram, making the AS algorithm hard to realize and accurate phase analysis difficult to conduct. Here, we present a hybrid reconstruction algorithm, combining Fresnel reconstruction in spatial domain with the AS algorithm in frequency domain, to solve aliasing by spatial filtering. Through simulation, we demonstrate the feasibility and superiority of the hybrid algorithm and verified the precision (10-3 rad) of the hybrid algorithm with spectrum aliasing. We extract phase distributions from normal urothelial and bladder cancer tissues by the hybrid algorithm and make quantitative analysis through histogram and standard deviation. The result shows the hybrid algorithm in off-axis DH has great advantage for the high-precision phase extraction of tissues and supplies significant information for cancer diagnosis.

Digital hologram transformations for RGB color holographic display with independent image magnification and translation in 3D.

A new framework for in-plane transformations of digital holograms (DHs) is proposed, which provides improved control over basic geometrical features of holographic images reconstructed optically in full color. The method is based on a Fourier hologram equivalent of the adaptive affine transformation technique [Opt. Express18, 8806 (2010)OPEXFF1094-408710.1364/OE.18.008806]. The solution includes four elementary geometrical transformations that can be performed independently on a full-color 3D image reconstructed from an RGB hologram: (i)transverse magnification; (ii)axial translation with minimized distortion; (iii)transverse translation; and (iv)viewing angle rotation. The independent character of transformations (i) and (ii) constitutes the main result of the work and plays a double role: (1)it simplifies synchronization of color components of the RGB image in the presence of mismatch between capture and display parameters; (2)provides improved control over position and size of the projected image, particularly the axial position, which opens new possibilities for efficient animation of holographic content. The approximate character of the operations (i) and (ii) is examined both analytically and experimentally using an RGB circular holographic display system. Additionally, a complex animation built from a single wide-aperture RGB Fourier hologram is presented to demonstrate full capabilities of the developed toolset.

Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

Numerous experiments have been conducted with success in the field of compressive digital holography, but the theory to determine optimal measurement conditions is lagging behind. In contrast to a prior study that expects object wavefields to be sparse in the spatial domain, we investigate how the configuration of the interferometer influences the reconstruction of wavefields that are sparse in a multiresolution orthogonal wavelet basis. In particular, we derive expressions for the coherence between the free-space wave propagation operator and the basis functions of a Shannon multiresolution representation as a function of the wavelength, the propagation distance, the image sensor's pixel pitch, and the scale of the basis functions. These expressions reveal that the coherence as a function of the Fresnel number is subject to specific scaling and translating rules as the scale of the basis functions changes. For a multiresolution orthogonal wavelet representation and digital holograms that are recorded in the near field, we deduce subsequently the optimal configuration of the interferometer and we show by means of hypothesis testing that the associated phase transition bound coincides with the weak threshold for block-sparse compressive sensing with a block length of 2, which is an optimal bound for the class of complex-valued compressive sensing problems. By means of experiments with a USAF 1951 resolution target and an angle grid, we validate our findings and demonstrate that the reconstructed object wavefields are resilient to sparsity defects and additive noise.

Quality of reconstruction of compressed off-axis digital holograms by frequency filtering and wavelets.

Compression of digital holograms can significantly help with the storage of objects and data in 2D and 3D form, its transmission, and its reconstruction. Compression of standard images by methods based on wavelets allows high compression ratios (up to 20-50 times) with minimum losses of quality. In the case of digital holograms, application of wavelets directly does not allow high values of compression to be obtained. However, additional preprocessing and postprocessing can afford significant compression of holograms and the acceptable quality of reconstructed images. In this paper application of wavelet transforms for compression of off-axis digital holograms are considered. The combined technique based on zero- and twin-order elimination, wavelet compression of the amplitude and phase components of the obtained Fourier spectrum, and further additional compression of wavelet coefficients by thresholding and quantization is considered. Numerical experiments on reconstruction of images from the compressed holograms are performed. The comparative analysis of applicability of various wavelets and methods of additional compression of wavelet coefficients is performed. Optimum parameters of compression of holograms by the methods can be estimated. Sizes of holographic information were decreased up to 190 times.

Simultaneous generation of multiple vector beams on a single SLM.

Complex vector light fields, classically entangled in polarization and phase, have become ubiquitous in a wide variety of research fields. This has triggered the demonstration of a wide variety of generation techniques. Of particular relevance are those based on computer-controlled devices due to their great flexibility. In particular, spatial light modulators have demonstrated their high capabilities to generate any vector beam, with various spatial profiles and polarization distributions. Here, we put forward a novel technique that exploits the superposition principle in optics to enable the simultaneous generation of many vector beams using a single digital hologram. As proof-of-principle, we demonstrated the simultaneous generation of sixteen vector vortex beams with various polarization distributions and spatial shapes on a single SLM, each with their own spatial shape and polarization distribution.

Single camera shot interferenceless coded aperture correlation holography.

We propose a new scheme for recording an incoherent digital hologram by a single camera shot. The method is based on a motionless, interferenceless, coded aperture correlation holography for 3D imaging. Two random-like coded phase masks (CPMs) are synthesized using the Gerchberg-Saxton algorithm with two different initial random phase profiles. The two CPMs are displayed side by side and used as the system aperture. Light from a pinhole is introduced into the system, and two impulse responses are recorded corresponding to the two CPMs. The two impulse responses are subtracted, and the resulting intensity profile is used as a reconstructing hologram. A library of reconstructing holograms is created corresponding to all possible axial locations. Following the above training stage, an object is placed within the axial limits of the library, and the intensity patterns of a single shot, corresponding to the same two CPMs, are recorded under identical conditions to generate the object hologram. The image of the object at any plane is reconstructed by a cross-correlation between the object hologram and the corresponding reconstructing hologram from the library.

Simultaneous forward and backward digital holography of microparticles

This work explores several techniques in digital holography to image 10–300 μm sized particles and provide information useful for their morphological characterization. In particular, digital holograms are formed with both forward and backward-scattered light from samples fixed to a glass stage. Images of these particles are then rendered from the holograms demonstrating that front and back perspectives of a particle can be acquired simultaneously. In addition, holography’s large depth of field is used to investigate the potential for stand-off interrogation of particles of different types.

Orthoscopic real-image display of digital holograms.

We present a practical solution for the long-standing problem of depth inversion in real-image holographic display of digital holograms. It relies on a field lens inserted in front of the spatial light modulator device addressed by a properly processed hologram. The processing algorithm accounts for pixel size and wavelength mismatch between capture and display devices in a way that prevents image deformation. Complete images of large dimensions are observable from one position with a naked eye. We demonstrate the method experimentally on a 10-cm-long 3D object using a single full-HD spatial light modulator, but it can supplement most holographic displays designed to form a real image, including circular wide angle configurations.

Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses

We present a lensless, interferenceless incoherent digital holography technique based on the principle of coded aperture correlation holography. The acquired digital hologram by this technique contains a three-dimensional image of some observed scene. Light diffracted by a point object (pinhole) is modulated using a random-like coded phase mask (CPM) and the intensity pattern is recorded and composed as a point spread hologram (PSH). A library of PSHs is created using the same CPM by moving the pinhole to all possible axial locations. Intensity diffracted through the same CPM from an object placed within the axial limits of the PSH library is recorded by a digital camera. The recorded intensity this time is composed as the object hologram. The image of the object at any axial plane is reconstructed by cross-correlating the object hologram with the corresponding component of the PSH library. The reconstruction noise attached to the image is suppressed by various methods. The reconstruction results of multiplane and thick objects by this technique are compared with regular lens-based imaging.

Excitation of high-radial-order Laguerre–Gaussian modes in a solid-state laser using a lower-loss digitally controlled amplitude mask

In this paper we experimentally demonstrate selective excitation of high-radial-order Laguerre–Gaussian (LGp or LG) modes with radial order p = 1–4 and azimuthal order l = 0 using a diode-pump solid-state laser (DPSSL) that is digitally controlled by a spatial light modulator (SLM). We encoded an amplitude mask containing p-absorbing rings, of various incompleteness (segmented) on grey-scale computer-generated digital holograms, and displayed them on an SLM which acted as an end mirror of the diode-pumped solid-state digital laser. The various incomplete (α) p-absorbing rings were digitally encoded to match the zero-intensity nulls of the desired LGp mode. We show that the creation of LGp, for p = 1 to p = 4, only requires an incomplete circular p-absorbing ring that has a completeness of ≈37.5%, giving the DPSSL resonator a lower pump threshold power while maintaining the same laser characteristics (such as beam propagation properties).