Hilbert transform and mirror-image optical correlators

An optical correlator, believed to be novel, adds an x-y mirror image to the input and filter images to perform convolution involving amplitude and phase. The resulting real Fourier transform filters can be loaded into a liquid-crystal device (LCD). In contrast, a complex filter would require high-resolution film. A Hilbert transform and a point source are applied at the filter plane to reduce filter storage and LCD loading time by a factor of 2. An optional spatial filter removes an offset intensity and squares the result. Filters have only twice the number of pixels of the images. Analysis is verified by computer simulation, and performance is discussed.     

Investigation of ultrafast time gating by spatial filtering

With a spatial-filtering method of gating, we explore image formation through scattering media using first-arriving light. Gating times of a few femtoseconds and less are produced, and the resolution at these extremely short gating times is investigated.     

Isotropic and anisotropic dipeptide films based on gas phase deposition

We demonstrated the fabrication and application of well-ordered and vertically aligned dipeptide nanostructures based on a simple gas phase deposition. Deposited nanostructures exhibited the superhydrophobic property with a very low sliding angle. Highly reproducible SERS data have also been obtained after combining deposited films with a thin layer of gold. In addition to these, directional peptide films were, for the first time, successfully fabricated based on the oblique angle deposition technique. We believe that such bio-inspired materials would have a great impact in several technological applications involving catalysis, tissue engineering and biosensors.     

Realization of time gating by use of spatial filtering

A method for simulating conventional time gating in low-coherence optical imaging processes in highly scattering media is given. The method uses monochromatic instead of broadband light, and spatial filtering is substituted for time gating. The process enables the study of imaging techniques in scattering media to be carried out in an easy and highly controllable way. Experimental results are given.     

复分析Hilbert变换计算理论及非线性检测准则

在众多非线性检测方法中,基于Hilbert变换的方法理论明确可靠,且有完成非线性识别后续全部流程的能力,因此受到广泛关注。但是,若通过数值积分方法直接计算Hilbert变换,将引入明显的截断误差,进而影响基于Hilbert变换的非线性检测,以及后续进行的非线性描述、参数识别的结果。结合复分析计算理论和有理逼近理论进行的Hilbert变换运算可有效避免截断误差,因此本文提出利用留数理论推导复分析Hilbert变换的计算理论,在原方法基础上补充讨论了实轴存在极点这一特殊情况;同时,重新推导了基于Hilbert变换的非线性检测方法,并澄清了其在Hilbert变换定义上的误用;最后通过建立新的推导格式,使复分析Hilbert变换计算理论与Hilbert变换非线性检测方法协调统一,定义了新的Hilbert变换非线性检测准则。数值算例和试验研究涵盖了单自由度和多自由度系统,线性和非线性情况,连续和不连续非线性类型,充分证明了本文发展的复分析Hilbert变换计算理论的准确性,以及本文定义的Hilbert变换非线性检测准则的可靠性。     

Programmable spatial filtering with bacteriorhodopsin

We describe a programmable spatial-filtering system using bacteriorhodopsin (BR) film as a programmable, optically addressed spatial light modulator illuminated by a single wavelength of light. We use a computer-controlled mirror scanning system to write time-varying filter functions to the BR film and present proof-of-principle experimental results that demonstrate several elementary filtering operations.     

应用Hilbert变换和ZFFT提取变速器齿轮故障特征

变速器故障齿轮振动信号,调幅现象和调频现象同时存在,其频谱中包括啮合频率及其谐波、调制产生的耦合频率。Hilbert变换无法提供足够高的频率分辨率解调低频调制信号,为此提出复调制细化谱分析方法。通过变速器齿轮故障模拟实验,采集齿轮正常、轻微磨损和严重磨损时的稳态振动信号,对其进行Hilbert变换得到信号的包络,对包络信号进行复调制细化谱分析,得到齿轮轴转频基波及其谐波幅值。随着齿轮磨损程度的增加,齿轮轴转频基波及其谐波幅值明显增大,可作为齿轮磨损故障特征参数。     

Optical symmetry filtering by use of anisotropic self-diffraction in BaTiO3 crystals

We propose what we believe to be a novel and simple method for optical symmetry filtering, using anisotropic self-diffraction in BaTiO(3) crystals. This method allows us to distinguish a centrosymmetric pattern from a noncentrosymmetric pattern easily with scale invariance. It is self-referential; no extra reference element is required. Both the theory and the experiment are demonstrated.     

Bubble materials characterization using spatial filtering

A technique for bubble materials characterization is described which utilizes spatial filtering. This method of characterization is amenable to automation and the resolution actually improves as the bubble diameter is decreased from 4μm to 1μm. The technique of spatial filtering is then applied to the problem of magnetic defect detection to produce instant defect maps of large areas.     

相关Hilbert差值时延估计方法误差分析

被动探测的关键技术之一就是通过有效的信号处理方法提取出多接收器的时间差,而确定时差最基本的方法是进行信号相关以获得估计信息,相关算法虽然计算过程简单,但是算法对信号和噪声频谱特性要求比较高。基于希尔伯特变换的时延估计是广义相关时延估计方法的拓展,把相关函数的对称性由偶函数转化成奇函数,将相关法中对峰值的检测转化为对过零点的检测。通过对两种算法的误差比较分析,信号的截至频率越高,希尔伯特变换法的均方误差与基本相关法的均方误差相差越明显,估计误差越理想,证明Hilbert算法的优越性。     

Median-prior tomography reconstruction combined with nonlinear anisotropic diffusion filtering

Positron emission tomography (PET) is becoming increasingly important in the fields of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation for image reconstruction in emission tomography place conditions on which types of images are accepted as solutions. The recently introduced median root prior (MRP) favors locally monotonic images. MRP can preserve sharp edges, but a steplike streaking effect and much noise are still observed in the reconstructed image, both of which are undesirable. An MRP tomography reconstruction combined with nonlinear anisotropic diffusion interfiltering is proposed for removing noise and preserving edges. Analysis shows that the proposed algorithm is capable of producing better reconstructed images compared with those reconstructed by conventional maximum-likelihood expectation maximization (MLEM), MAP, and MRP-based algorithms in PET image reconstruction.     

基于小波变换和改进Hilbert变换对科氏质量流量计信号处理

针对工程应用中现有算法处理科式质量流量计两路时变信号相位差计算准确度不高的问题,采用一种基于小波变换和改进Hilbert算法结合的方法,对其两路时变信号进行分析处理,从而快速、准确计算出两路输出信号相位差。该算法首先采用基于小波变换重构的方法对信号进行逐层滤波,滤除现场环境中各种干扰信号并保持检测正弦信号滤波后相位不变,最后应用改进Hilbert算法计算出所测两路信号实时相位差。通过实验可知:该算法可行有效,实时性强,测量准确度高,能够实现科式质量流量计的高准确度测量。     

Optical implementation of the fractional Hilbert transform for two-dimensional objects

The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is pi-phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.     

Saturable-absorber-based spatial filtering of high-power laser beams

A saturable-absorber-based technique for spatial filtering of high-average-power laser beams is described. For a focused, radially symmetric beam having its highest intensity at the center, this saturable absorber behaves like a soft aperture with gradually increasing attenuation toward the beam edges, thus selectively transmitting the low divergence components that are confined close to the central axis of the propagating laser beam. This technique has been successfully used to reduce the divergence of a high-power, high-repetition-rate, tunable, narrowband, pulsed dye laser. Our results demonstrate how a judicious choice of operating parameters allows spatial filtering to be achieved with the introduction of a minimum absorption loss of the laser beam in the saturable absorber. Following a time-dependent analysis of a rate equation model describing the propagation and interaction of the laser beam with the saturable absorber, we have also obtained theoretical estimates for the extent of spatial filtering. Our theoretical estimates have been found to be in good agreement with our experimental observations.     

Notch spatial filtering with an acousto-optic modulator

The role of acousto-optic (AO) modulators in programmable real-time image processing has recently been demonstrated. For fully investigating the image-processing capabilities of the AO modulator, general techniques to derive spatial transfer functions are needed for a variety of physical situations. We develop a technique to determine the spatial transfer functions numerically for various cases of beam incidence on an AO modulator. Normal incidence and incidence at twice the Bragg angle are investigated as examples for which double-sided and single-sided notch spatial filtering, respectively, are achieved. The observed spatial-filtering characteristics are reconciled with simple intuitive physical arguments.     

Self-aligned spatial filtering using laser optical tweezers

We present an optical spatial filtering device that has been integrated into a microfluidic system and whose motion and alignment is controlled using a laser optical tweezer. The lithographically patterned micro-optical spatial filter device filters out higher frequency additive noise components by automatically aligning itself in three dimensions to the focus of the laser beam. This self-alignment capability is achieved through the attachment of a refractive optical element directly over the circular aperture or pinhole of the spatial filter. A discussion of two different spatial filter designs is presented along with experimental results that demonstrate the effectiveness of the self-aligned micro-optic spatial filter.