Fresnel Holography Research Articles

Reconstruction of images using Fresnel holograms: the relationship between the longitudinal and transverse scales of images

The article is devoted to the study of changes in the relationship between the transverse and longitudinal scales of images. The possibility of changing the classical quadratic relationship between the longitudinal and transverse scales of images is considered, while when using traditional imaging methods in classical optics this is impossible due to the homogeneity and isotropy of space. An analysis of image scale transformations for optical schemes of Fresnel holography using spatially incoherent radiation has been carried out. It is shown that recording a Fresnel hologram allows one to change the ratio between the transverse and longitudinal scales of the reconstructed image within a fairly wide range. The results are relevant for use in those areas of science and technology that require the creation of images that reflect real-world objects as accurately as possible without distortion, for example, in the field of medical imaging.

Improvement of Fresnel Diffraction Convolution Algorithm

With the development of digital holography, the accuracy requirements for the reconstruction phase are becoming increasingly high. The transfer function of the double fast transform (D-FFT) algorithm is distorted when the diffraction distance is larger than the criterion distance dt, which reduces the accuracy of solving the phase. In this paper, the Fresnel diffraction integration algorithm is improved by using the low-pass Tukey window to obtain more accurate reconstructed phases. The improved algorithm is called the D-FFT (Tukey) algorithm. The D-FFT (Tukey) algorithm adjusts the degree of edge smoothing of the Tukey window, using the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) to remove the ringing effect and obtain a more accurate reconstructed phase. In a simulation of USAF1951, the longitudinal resolution of the reconstructed phase obtained by D-FFT (Tukey) reached 1.5 μm, which was lower than the 3 μm obtained by the T-FFT algorithm. The results of Fresnel holography experiments on lung cancer cell slices also demonstrated that the phase quality obtained by the D-FFT (Tukey) algorithm was superior to that of the T-FFT algorithm. D-FFT (Tukey) algorithm has potential applications in phase correction, structured illumination digital holographic microscopy, and microscopic digital holography.

Autofocusing in off-axis digital Fresnel holography using S-th power weighted neighborhood correlation coefficient

Accurately determining the focus plane of the reconstructed image is crucial for obtaining high-quality reconstructed images in the process of digital hologram reconstruction. In this paper, a focusing evaluation function based on S-th power weighted neighborhood correlation coefficient (SPWNCC) is proposed to realize automatic focusing of the reconstructed image in off-axis digital Fresnel holography. The Fresnel transform method is utilized as the off-axis digital holographic reconstruction algorithm. Both the numerical simulation and optical experiment results are given to verify the validity of the proposed autofocusing method. The obtained focusing curve can maintain good unimodality and noise immunity performance over a large search range (approximately 800 mm). The proposed SPWNCC based focusing evaluation function has a certain guiding significance on the automatic focusing of off axis digital holographic reconstructed images of long distance recorded objects.

Research on improving holographic display quality based on phase compensation of reproduced image light energy distribution.

Liquid crystal spatial light modulator (LC-SLM) holographic display is affected by its structure, which products multi-level diffracted image with zero-order spot, resulting in low light energy utilization and poor uniformity of the reproduced image. This paper presents a method to improve the uniformity of light energy distribution in the reproduced image by using phase compensation, and the uniformity of the image can be effectively improved by using digital blazed grating to deviate the image and performing phase compensation according to the light energy distribution. Analyzing the uniformity of light energy distribution, the phase distribution is compensated, and experiments verify the phase compensation. The experimental results show that the uniformity and light energy utilization of the reproduced image after compensation has been improved. The results show that the proposed phase compensation method can be applied to both Fresnel holography and Fourier holography; both can effectively improve the uniformity and efficiency of light energy. Therefore, this method has a specific application value to enhance the quality of holographic reproduction and light field modulation based on LC-SLM.

Three-dimensional optical image encryption using phase-shifting compressive Fresnel holography

A new method of three-dimensional (3D) image optical encryption based on phase-shifting compressive Fresnel holography (PSCFH) is presented. In the optical encryption step, the 3D object is encrypted with random phase masks using phase-shifting interferometry to record three intensity images with different phase-shifting. In the decryption step, the three-step phase-shifting technique is first used to extract the complex optical field at the recording plane. Finally, the 3D object is reconstructed from the recovered complex optical field using compressive Fresnel holography with the correct key. Numerical experiments demonstrate the feasibility and robustness of our proposed PSCFH method.

Deep convolutional neural network for three-dimensional objects classification using off-axis digital Fresnel holography

A Deep Convolutional Neural Network (CNN)-based three-dimensional (3D) objects classification using an augmented holographic phase image dataset is proposed. Off-axis Fresnel digital holography is used for retrieving 3D object information as phase images. The phase image dataset of the five different 3D objects considered in this study is prepared under various recording distances and rotational angles. The CNN based architecture classifies the 3D objects into two sets comprising of TRUE and FALSE classes with higher accuracy and minimal loss on the training set for the phase image dataset. The CNN has achieved higher precision, lower recall, and higher F1-score for the TRUE class on the test set. The experimental results demonstrate that the proposed CNN is capable of classifying 3D objects with an overall accuracy of 86% and AUC of 96% for the phase image dataset. The feasibility and classification performance are deduced from a proof of the concept experiment.

Optimal Fresnelet sparsification for compressive complex wave retrieval from an off-axis digital Fresnel hologram

Complex wave retrieval (CWR) from an off-axis digital Fresnel hologram proposed by Liebling et al. is a single-exposure scheme in which a non-linear holographic process is modeled using simultaneous linear equations. This linear model fits well into the compressive sensing (CS) framework. We propose a method in which the CS is applied to a CWR method with Fresnelet sparsification. This approach compensates for the noise in the retrieved Fresnel field that is aroused due to the linear modeling approximations involved in the reconstruction process. As a result, a superior intensity and phase reconstruction were obtained by this method. Four methods including the direct CWR (conventional) method, compressive CWR method without sparsification, compressive CWR method with Haar wavelet, and compressive CWR method were compared with Fresnelet sparsification. The simulation and the optical experimental results converge to the same conclusion: the Fresnelet sparsified case is the best choice for quantitative phase imaging using compressive off-axis digital Fresnel holography.

Compressive complex wave retrieval from a single off-axis digital Fresnel hologram for quantitative phase imaging and microlens characterization

A compressive sensing (CS) approach is proposed for the complex wave retrieval algorithm from single off-axis digital Fresnel holography to improve the accuracy of quantitative phase measurement. The linear model of non-linear holographic process used in the complex wave retrieval algorithm is utilized to meet the linearity requirement of the proposed CS implementation presented in this paper. The error in object wave reconstruction due to the approximations used in complex wave retrieval algorithm is compensated by combining it with CS approach. A Mach–Zehnder interferometric geometry in transmission and off-axis mode in the Fresnel domain is used to record the digital hologram. The numerical simulations and experimental results are presented to demonstrate and validate the proof of the concept and to compare CS frame work with conventional complex wave retrieval algorithm. The proposed algorithm is tested for the microlens sample characterization by considering the parameters such as height, diameter and radius of curvature. A Haar wavelet based object wave sparsification is used in the experiment for the prudent phase reconstruction in the CS approach. The proposed method enables an improved and accurate object phase reconstruction, with minimal noise such as distortions or speckles with respect to the conventional complex wave retrieval method.

X-Ray On-Axis Fresnel Holography Using Three-Block Fresnel Zone Plate Interferometer

An experimental setup for X-ray on-axis Fresnel holography is suggested. It is based on a three-block Fresnel zone plate interferometer. As a test object, for numerical simulation, a stencil with the text ‘X-RAY OPTICS’ printed on it is considered. Although the quality of the reconstructed image is limited, which should be expected in case of on-axis holography, it is still good enough for clear imaging of the text mentioned.

基于深度学习的离轴菲涅耳数字全息非线性重构

基于深度学习的离轴菲涅耳数字全息非线性重构

Holographic multiplane near-eye display based on amplitude-only wavefront modulation.

We present a holographic multiplane near-eye display method based on Fresnel holography and amplitude-only wavefront modulation. Our method can create multiple focal images across a wide depth range while maintaining a high resolution (1080P) and refresh rate (60 Hz). To suppress the DC and conjugation signals inherent in amplitude-only wavefront modulation, we develop an optimization algorithm which completely separates primary diffracted light from DC and conjugation at a pre-defined intermediate plane. Spatial filtering at this plane leads to a dramatic increase in the image contrast. The experimental results demonstrate our approach can create continuous focus cues in complex 3D scenes.

Fresnel incoherent digital holography with large field-of-view

Incoherent digital holography (IDH) is a recently proposed technique to record three-dimensional (3D) information about the object under incoherent illumination, which breaks the limitation that the holographic recording must be illuminated by coherent light sources and thus makes it usable in white-light and fluorescence illuminating circumstance. In particular, the fresnel incoherent correlation holography (FINCH) is an exemplary method which improves the imaging resolution power and efficiency of incoherent digital holography, and it can obtain 3D distribution of objects swiftly without scanning and moving. However, compared with the conventional optical holography, the FINCH system has a very small field-of-view due to the limitation of the pixel number and size of spatial light modulator (SLM). Therefore, expanding the recording field-of-view of FINCH system is very significant for the application of IDH. In the FINCH, the SLM is used as a diffractive beam splitter so that each spherical beam, originating from each object point, is split into two spherical beams with two different curve radii. Then the interference fringes between the two beams are recorded by CCD. In this paper, the field-of-view angle recorded by the SLM is proposed and analyzed based on the physical and numerical principles of the FINCH system. The field-of-view of imaging system is improved by increasing the effective diameter of SLM through moving the center of the dual-lens optical axis mounted on the SLM to the edge in different directions respectively. An optical setup of reflection mode is constructed to verify the theoretical analysis of this study, and the sub-holograms in different field-of-views are obtained by CCD through changing the masks displayed on the SLM sequentially. Then, the complex holograms in different field-of-views are obtained by using the three-step phase-shifting method, and the reconstructed images are acquired respectively through the angular spectrum method (ASM) by using a computer. Finally, the large field-of-view image is obtained by stitching the reconstructed images in each field-of-view by utilizing the matlab program. The experimental results show that the efficient recording field-of-view of SLM can be increased by 2.77 times with our proposed method. Accordingly, the recording field-of-view of the system is improved significantly. The recording field-of-view of the FINCH system will increase further if the center of the dual-lens optical axis continues to move toward the edge. Therefore, this study provides an important support for the further application of high resolution microscopic imaging with large field-of-view.

菲涅耳非相干相关全息相移技术

菲涅耳非相干相关全息相移技术

Optical sectioning using compressive Fresnel holography with dictionary learning

Optical sectioning through the numerical reconstruction of digital holographic data with low diffraction noise is the key process for understanding the structure of a recorded three-dimensional object. Recently, this has been enabled by compressive holography, by virtue of sparse signal processing. However, interpretation of the object signal domain has been limited to predefined domains, such as spatial, discrete cosine transform, and wavelet transform domains. We propose a reconstruction technique of compressive Fresnel holographic data using an overcomplete dictionary learned from natural images to enhance the axial resolution of the sectional images. The redundant (overcomplete) dictionary gives sparser and more flexible solutions for representing the two-dimensional images compared to predefined transforms. We provide simulation results to verify the feasibility of our proposed method.

Holographic near-eye displays for virtual and augmented reality

We present novel designs for virtual and augmented reality near-eye displays based on phase-only holographic projection. Our approach is built on the principles of Fresnel holography and double phase amplitude encoding with additional hardware, phase correction factors, and spatial light modulator encodings to achieve full color, high contrast and low noise holograms with high resolution and true per-pixel focal control. We provide a GPU-accelerated implementation of all holographic computation that integrates with the standard graphics pipeline and enables real-time (≥90 Hz) calculation directly or through eye tracked approximations. A unified focus, aberration correction, and vision correction model, along with a user calibration process, accounts for any optical defects between the light source and retina. We use this optical correction ability not only to fix minor aberrations but to enable truly compact, eyeglasses-like displays with wide fields of view (80°) that would be inaccessible through conventional means. All functionality is evaluated across a series of hardware prototypes; we discuss remaining challenges to incorporate all features into a single device.

Reduction of speckle noise in holographic images using spatial jittering in numerical reconstructions.

This Letter presents an easy, fast, and efficient single-shot method to reduce speckle noise in digital Fresnel holography. In this method, several images from a single hologram are reconstructed by introducing spatial displacements in the Fresnel kernel. Spatial jitters produce images with different speckle positions. Averaging the set of numerically produced images leads to a strong reduction of speckle noise in both amplitude and phase difference images. The experimental results show the suitability of the proposed approach and confirm its applicability to digital holographic interferometry.

Refocus criterion based on maximization of the coherence factor in digital three-wavelength holographic interferometry.

This Letter presents an alternative approach for image refocusing in digital Fresnel holography. In the literature, a large majority of reported focus detection criteria is based on amplitude contrast or phase contrast. We propose a focus detection criterion based on the speckle phase coherence factor. This factor reaches its maximum value at the best focus distance. At any reconstruction distance, estimation of the coherence factor is based on robust noise estimation from anisotropic diffusion. We propose a theoretical relation to estimate the coherence factor from the measured standard deviation. Experimental results for the case of three-color holographic imaging and interferometry are provided. Experimental results show the suitability of the proposed approach for image plane refocusing.

Comparative simulations of Fresnel holography methods for atomic waveguides

We have simulated the optical properties of micro-fabricated Fresnel zone plates (FZPs) as an alternative to spatial light modulators for producing non-trivial light potentials to trap atoms within a lensless Fresnel arrangement. We show that binary (1 bit) FZPs with wavelength (1 μm) spatial resolution consistently outperform kinoforms of spatial and phase resolution comparable to commercial SLMs in root mean square error comparisons, with FZP kinoforms demonstrating increasing improvement for complex target intensity distributions. Moreover, as sub-wavelength resolution microfabrication is possible, FZPs provide an exciting possibility for the creation of static cold-atom trapping potentials useful to atomtronics, interferometry, and the study of fundamental physics.

Parallel-mode scanning optical sectioning using digital Fresnel holography with three-wave interference phase-shifting.

The Fresnel incoherent correlation holography (FINCH) method is applicable to various techniques of imaging, including fluorescence microscopy. Recently, a FINCH configuration capable of optical sectioning, using a scanning phase pinhole, has been suggested [Optica 1, 70 (2014)]. This capability is highly important in situations that demand the suppression of out-of-focus information from the hologram reconstruction of a specific plane of interest, such as the imaging of thick samples in biology. In this study, parallel-mode scanning using multiple phase pinholes is suggested as a means to shorten the acquisition time in an optical sectioning FINCH configuration. The parallel-mode scanning is enabled through a phase-shifting procedure that extracts the mixed term of two out of three interfering beams.

X-ray interferometric Fresnel holography

The X-ray interferometric Fresnel holography was proposed and theoretically investigated. It was shown that under definite conditions the recorded interference pattern formed at the output surface ofthe analyzer crystal (the third block of interferometer) is the X-ray interferometric hologram (generally the Fresnel one) of the object under investigation. Further reconstruction of an image is performed with the help of visible light or a numerical method. As an example the recording of a Fresnel hologram of the simplest case of one-dimensional object, a narrow slit, and the reconstruction of an image by means of visible light were considered. This method may be used in X-ray microscopy and realized using synchrotron sources ofX-ray radiation, as well as X-ray free electron lasers.