Computer-generated line holograms using an xy plotter

A new method is presented for constructing a computer-generated Fourier-transformed line hologram using an xy plotter. Phase and amplitude of the complex amplitude in the hologram plane are represented by varying, respectively, the position and height of triangles formed in the cells composing the hologram. An image reconstructed optically from the hologram can be moved arbitrarily from the optical axis since the hologram contains information about the phase and amplitude of the complex amplitude in the hologram plane. A three-dimensional hologram from which an image was successfully reconstructed is also presented.     

基于液晶空间光调制器的全息显示

在传统的纯相位全息显示系统中, 一般基于快速傅里叶变换(FFT)算法来计算相位全息图, 在FFT的计算中需要遵循Nyquist采样定理, 因此, 重建图像的尺寸往往受限于空间光调制器的固定采样率. 这个限制可以通过卷积算法或者两步菲涅耳衍射算法来解决, 但是需要使用多个FFT的计算, 导致计算量增大. 鉴于此, 提出了一种基于透镜的纯相位全息图计算方法. 在全息图的计算中, 通过透镜的成像原理建立一个采样率可变的虚拟全息面, 通过调节相应的距离参数使得在全息图的计算中可以任意调节原始图像的采样率, 摆脱了传统方法中液晶空间光调制器带宽积对重建图像尺寸的限制, 并且这种算法只需使用一次FFT就能达到变采样率的衍射计算, 大幅提高了全息图的计算速度. 数值模拟及光学实验结果证明了此方法可以在全息显示光学系统中清晰地重建不同尺寸的图像. 同时该系统可以有效地消除由空间光调制器的像素化结构带来的零级衍射.     

Spatial Filtering of Lateral-Shear Interferograms in the Case of Double-Exposure Recording of a Lens Fourier Hologram of a Mat Screen. II

Distortions of lateral-shear interferograms in fringes of infinite width due to hologram aberrations are analyzed in a third approximation for a complex field amplitude. The interferometer sensitivity range in the field is shown to increase in the case where a Fourier hologram of a mat screen is recorded using a negative lens, two identical subjective speckles of two exposures are superimposed in the hologram plane, and errors of control are eliminated.     

Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: Modeling and simulation

A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms.     

Lateral-shear interferograms registered with double-exposure recording of a gabor lens hologram

An analysis is made of the results of a double-exposure recording based on superposing the subjective speckle fields of a Gabor hologram with a negative lens located in the plane of the amplitude scatterer. It is shown that when the hologram is reconstructed a lateral-shear interferogram is formed in this plane and on the optic axis if the diffraction field is spatially filtered, and an interference pattern having twice the interferometer sensitivity for a fixed lateral shear is localized in the plane of the hologram. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–54, March, 1998.     

Confocal microscopy with a volume holographic filter

We describe a modified confocal microscope in which depth discrimination results from matched filtering by a volume hologram instead of a pinhole filter. The depth resolution depends on the numerical aperture of the objective lens and the thickness of the hologram, and the dynamic range is determined by the diffraction efficiency. We calculate the depth response of the volume holographic confocal microscope, verify it experimentally, and present the scanned image of a silicon wafer with microfabricated surface structures.     

余弦二值编码纯相位全息图的数字微镜器件显示

分析了采用错误减算法的迭代过程,在已知物波函数傅里叶谱的振幅和物波函数振幅的情况下恢复出纯相位的物波函数,最大限度地保留物波的振幅及相位信息.提出采用余弦二值编码生成二值全息图,即全息图的透射率函数取0或1.二值全息图通过数字微镜器件全息显示系统进行了重构显示,重构效果很好.理论分析了数字微镜器件的衍射效率,表明其最大衍射效率仅和微镜之间的间隔尺寸与微镜边长之比有关.余弦二值编码方法从理论上消除了零级衍射,可以制作像素较多的全息图.     

Full Color Computer-Generated Rainbow Hologram with Enlarged Viewing Angle

The viewing angle of a computer-generated hologram (CGH) can be expanded by lens-less Fourier configuration. However, a laser is required to illuminate the CGH for reconstruction. We proposed earlier making a second hologram for white-light reconstruction; here, we propose a method to calculate CGH for a full-color rainbow hologram with enlarged viewing angle. First, we calculate the master hologram with three virtual slits whose positions correspond to red, green and blue wavelength. The transfer hologram can be made from the master CGH with a single exposure. In the experimental result, we obtain a full-color computer-generated rainbow hologram with 17° of viewing angle and 3.0mm × 2.5 mm image size.     

Diffraction patterns for a transmission volume hologram under Bragg mismatch

We have presented simulations and experiments for 2-dimensional diffraction distributions of a transmission volume hologram. We sample the input pattern with a few elementary points and calculate the diffraction of the corresponding elementary grating. The simulations can describe well the diffraction pattern obtained in the experiment and can be used to predict the tolerance for angular deviation of the reading beam. The tolerance for angular deviation depends on its direction. It is affected by the Bragg degeneracy. The simulation results provide a clear picture of the spatial tolerance for reading a transmission volume hologram.     

Image reconstruction from a dielectric volume hologram

The phenomenon of image reconstruction from an absorptionless volume hologram is analyzed using coupled-wave diffraction theory. Reconstruction efficiency formulas are derived, which apply when the hologram intermodulation component is negligible and when no extraneous diffracted orders of significant amplitude are generated. Both transmission and reflection holograms are considered, and the analysis is developed for diffraction geometries in which polarization effects are appreciable.     

Characterization of axially tilted fibres utilizing a single-shot interference pattern

We proposed a method to solve the problem of extracting meaningful phase information for a single-shot interference pattern taken for an axially tilted fibre sample. Conventionally such interference patterns can be not evaluated with appropriate accuracy. Here, such an interference pattern is considered to be a special hologram since it contains information about light propagated through a laterally fixed sample located at different axial planes. Thus, part of the test object in such a hologram is in focus and the other parts are out of focus. The proposed method can be considered as two complementary steps. In the first step the complex amplitude across the hologram plane is recovered using an adaptive spatial carrier frequency method. This is followed by the second step where the complex amplitude is numerically propagated within a given volume. Thus, planes where the test object is in focus are defined. Consequently, the phase distributions corresponding to all of these planes are together stitched. Thus a complete focus phase map for the fiber sample under test is obtained. From the obtained phase map the two dimensions refractive and the two dimensions birefringence of isotactic polypropylene fibre were calculated.     

Holographic image projection using fractional Fourier transformation

A new method of image projection based on fractional Fourier transformation is presented. This method can project an image at any distance after a lens plane. We use a modified Gerschberg–Saxton (GS) iteration algorithm to compute a phase-only hologram. The amplitude distributions both on the hologram plane and image plane are restricted while allowing their phase distributions to drift into an optimum value. The quality of the image projected by fractional Fourier hologram is close to the image projected by Fourier hologram. The RMS error between the projected image and the constrained image is computed in our experiment. A comparison in flexibility of the two projection methods is also discussed.     

Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field

The theoretical analysis of unstationary holographic recording in photorefractive crystals under an external alternating electric field is presented. In particular, a step-like ac field resulting in a shifted phase hologram with an amplitude exceeding that of a hologram recorded under an external dc field is shown to be most efficient. The experimental curves for the gain factor Γ obtained in Bi₁₂TiO₂₀ (λ = 0.63μm) under an ac step-like field illustrate the field and spatial frequency dependencies of the hologram amplitude characteristics of the unstationary mechanisms of holographic recording.     

基于离散Fourier变换的内源全息图重构计算方法

对基于离散Fourier变换的内源全息图重构计算方法作了深入系统的分析，讨论了如何计算整个球面全息图对原子重构像的贡献，克服了以往该方法只能计算半个球面全息图的不足，并运用采样定理知识，分析了全息图的采样率、重构像的空间范围和分辨率等问题. 关键词： 内源全息术 离散Fourier变换 采样定理 同步辐射     

Revealing the target structure information encoded in strong-field photoelectron hologram

By numerically solving the two-dimensional time-dependent Schrödinger equation, we investigate the strong-field photoelectron holography (SFPH) for different atomic and molecular targets. The results show that the photoelectron hologram is capable of providing structural information-the phase of scattering amplitude. In our calculations, the holographic pattern shifts with the target, indicating the phase difference between various targets. However, for the near-forward scattering, the phases of scattering amplitude for different targets are similar and thus no structural information has been retrieved in the previous works on near-forward scattering hologram. We suggest to use the backward scattering photoelectron hologram to extract this type of structural information. This paves a significant step towards time-resolved imaging of molecular structure and dynamics with the concept of SFPH.     

On the properties of a ‘finite beam’, reflection-type volume hologram

The properties of a volume-phase hologram of the reflection type are studied in the case when the reference and object waves are beams of finite width. Numerical results are obtained by considering a sufficiently large number of terms in a previously derived infinite series solution. The results reproduce Kogelnik's one-dimensional theory [1] when the thickness of the hologram is small in comparison with the widths of the beams but otherwise the finiteness of the recording beams leads to significant variations in the amplitude of the reconstructed beam.     

Multiple images encryption based on Fourier transform hologram

A new optical encryption method is proposed in this paper to achieve multiple images encryption. We introduce reference waves with different incident angles and random amplitude masks into a Fourier transform hologram configuration to encrypt multiple images. In the encryption procedure, different random amplitude masks (RAMs) which are placed into the reference arm vertically admit the multiplexing capability. When decrypting one of the original images, reference wave with the same incident angle as encrypting the target image is used to illuminate the encrypted hologram with the insertion of random amplitude mask whose transmissivity is reciprocal of that of the encrypting random amplitude mask in the reference arm. We also simulate and analyze the influence of partly wrong decrypting key on the decrypted results. Numerical simulation proves that the proposed encryption method is valid and of high security level.     

Correction of aberration for a high-resolution electron hologram by means of the amplitude contrast criterion of image wave

In order to further improve the resolution for a high-resolution electron hologram, the aberration working on the hologram must be corrected. Since it is rather difficult to precisely control aberration coefficients in the experimental stage, we proposed an amplitude contrast D criterion of imaging wave to determine the working aberration from the hologram itself. In the determination or correction of the aberration, we assume a symmetrical aberration function is parameterized only by a spherical aberration coefficient and a defocus value. First, D is calculated from a holographically reconstructed imaging wave of YBa(2)Cu(3)O(7-x) for each combination of these parameters. The working aberration on the imaging wave is determined from the combination of the parameters by noting the maximum or minimum D of the imaging wave at some specifically chosen thickness regions. The theoretical validity for the D criterion is then proved with three-beam dynamical diffraction formula. Finally, the 'experimental' examination for the D criterion is successfully performed on the reconstructed image wave for the Sigma=9 interface structure of a wedge-shaped silicon sample.     

A general solution for two-dimensional volume holograms

We inv estigate the problem in which a volume hologram is produced by two waves of arbitrary amplitude and phase distribution (the only restriction being that they must obey the rules of geometrical optics), and the developed hologram is illuminated by one of the waves having the same phase distribution but not necessarily the same amplitude distribution. Coupled partial differential equations are derived and solved in the form of an infinite series valid for both transmission and reflection holograms. For transmission holograms a simple approximate solution is given for the amplitude of the reconstructed wave in the immediate vicinity of the input surface.     

Single-shot phase-shifting digital holography with a photon-sieve-filtering telescope

A method of single-shot phase-shifting digital holography with a photon-sieve-filtering telescope is proposed. Three copy images with different phases are first generated by use of a monofocal photon-sieve filter in Kepler telescope, and then interfere with the reference plane wave by a beam combiner. The hologram is captured by a charge-coupled device(CCD)in one single exposure. The complex-valued amplitude of the test object can be reconstructed by three-step phase-shifting interferometry through three frames of extracted sub-interferograms from the single-exposure hologram. The principle and simulation experiments are carried out and verified the validity of our proposed method. This method can be applied for snapshot imaging and three-dimensional object construction.