光刻对准中干涉条纹相位解析研究

针对光刻对准中双光栅产生的具有多频率的干涉条纹,提出了一种基于二维解析小波变换进行条纹分析的方法。该方法首先通过二维小波变换的多尺度对条纹的多频率进行分析,并通过解析小波基函数将条纹的幅度与相位进行分离,最终通过二维小波脊方法提取出与偏移量相关的相位。在相位提取的同时通过二维小波脊所处点的角度分布来移除封闭条纹处理中常见的相位符号不确定性。数值模拟与实验验证了该方法的可行性并与传统的基于频域的相位分析方法进行了对比分析。结果表明,该方法能在获得所需相位信息的同时较好地滤除掉由光路抖动引起的噪声,具有很强的适应性。     

傅里叶变换轮廓术中频谱泄漏的讨论

讨论了频谱泄漏对傅里叶变换轮廓术测量精度的影响。由于用傅里叶变换轮廓术进行三维面形测量时 ,测得的变形光场是空间有限函数 ,故离散傅里叶变换时先要进行周期拓展 ,如果拓展周期选择不当 ,拓展后的条纹将不连续 ,对之进行傅里叶变换会产生频谱泄漏。文章从理论上推导了拓展周期与变形结构光场频谱泄漏之间的关系 ,给出了由泄漏引起的视场边缘误差的计算模型和定量分析。提出采用条纹外插以减小泄漏误差的方法 ,计算机模拟及初步实验证实了该方法的有效性。     

应用神经网络的复杂物体三维测量

将神经网络引入基于结构光投影的复杂物体三维面形测量。在测量过程中,利用神经网络强大的函数逼近能力,得到离散条纹图的连续逼近函数,从中解出物体的相位分布信息,获得物体的三维面形分布。应用神经网络方法,在结构光投影条件下,只需要获取一幅条纹图,便可以完成复杂物体的三维面形测量。该方法相比传统的傅里叶变换轮廓术,不存在滤波操作,不会在测量过程中丢失被测物体的高频分量,具有更高的空间带宽积和灵敏度,能准确测量出复杂物体的细节,更加适用于恢复复杂物体的三维面形。并且该方法在条纹图存在阴影的情况下与傅里叶变换轮廓术相比,能更好地提取出物体的相位信息,恢复物体的三维面形。模拟及实验均验证了该方法的可行性。     

Phase extraction using multi-directional moiré fringes for multi-lateral shearing interferometry

The multi-lateral shearing interferometers (multi-LSIs) are featured in the improved accuracy and noise resistance of wavefront reconstruction using phase differences in multiple directions. Nowadays the multidirectional phase differences are usually extracted from multi-LSIs’ interferogram using the fast Fourier transform (FFT) method, whose accuracy is limited by spectral leakage effect. To improve the measurement accuracy of multi-LSIs, a phase extraction method developed from moiré technique is proposed in this paper. Using virtual gratings with properly large carrier frequencies, the desired phase information in each of the multiple directions can be modulated into low-frequency domain of the corresponding moiré pattern with larger separations between unnecessary side lobes. In this way, low-pass filters with higher cut-off frequencies can be applied in moiré technique to reduce the inaccuracy induced by spectral leakage effect. Meanwhile, phase shifting method can be applied to extract phase information from a single fringe pattern with better noise resistance by easily introducing phase shifts in computer generated virtual gratings. Simulation results show that the proposed method has higher accuracy and better anti-noise performance than the FFT method when spectral leakage effect exists. To demonstrate accuracy of the proposed method, a null test experiment of the quadriwave LSI has been conducted and experimental results show that measurement accuracy of the quadriwave LSI can be significantly improved by substituting the FFT method with the proposed method in phase extraction process.     

一种基于希尔伯特变换实施相移的相位解调算法

相移法因其精度高、运算简单,所以被广泛应用于形貌检测中的相位解调。该方法的弱点是:不仅要采集多幅相移图像,而且不能克服相移器的移相误差。将小波分析与希尔伯特变换结合起来,采用小波分析去除直流背景成分,利用希尔伯特变换方法实现90°相移;利用相移法解调形貌相位,由于是采用软件来实现相移的,因此只需采集一幅变形栅线图。对该方法与传统相移技术进行了模拟比较实验,结果表明,该方法具有较高的精度。     

基于结构光投影的二维S变换轮廓术

S变换是一种集合了窗口傅里叶变换和小波变换优点的时频分析技术,目前一维S变换已成功应用于结构光投影的条纹相位解调中。由于二维S变换可以对图像在两个方向上进行时频分析,具有更优于一维S变换的分析和处理能力。为了完善S变换的条纹相位解调理论,将二维S变换方法引入到基于结构光投影的三维光学测量中,研究了二维S变换在条纹相位解调中的原理及应用,给出了详尽的理论分析,并同一维S变换结果进行了比较。模拟和实验都表明,在条纹图解相中,二维S变换比一维S变换提取的相位精度更高,即使在存在较严重噪声污染的情况下也表现出良好的可靠性,体现出二维S变换提取相位的优势。     

用于风场探测的非对称空间外差干涉数据处理方法研究

利用非对称空间外差光谱技术和多普勒效应,通过测量中高层大气气辉谱线的干涉图,采用傅里叶变换的方法求解相位,获得大气的风速信息。分析了干涉数据的处理方法,并针对干涉相位的求解进行推导。相比于传统观空间外差数据处理,不仅要考虑噪声和系统误差,而且要考虑用于光谱隔离的窗函数引入的相位误差。通过软件模拟了窗函数的类型和窗长度对干涉数据和风速误差曲线的影响;在此基础上选择合适的窗函数模拟了对干涉图添加噪声和平场因子情况下的风速反演误差。结果说明,虽然窗函数造成了干涉图和相位的畸变,但是使用汉宁窗在合适的光程差处能够使其引入的误差低于5%;同时,噪声的仿真说明,风速误差随着系统噪声的增加而增大,在实验过程中控制噪声以及实验数据预处理对于控制风速精度的必要性。数据处理方法的研究和相关的仿真,对于提高空间外差风速测量精度及系统设计提供了理论参考,具有一定的指导意义。     

利用合成谱在计算全息图中编码多个物体的方法

 提出在迂回位相傅里叶变换计算全息图中利用合成谱记录多个物体的方法。该方法利用多个物体合成的傅里叶频谱,代替传统的迂回位相型计算全息图中的单一频谱,在一幅计算全息图中完成多个物体的编码。再现时多个物体同时再现在同一衍射级的周围,并且再现像的形式可以多种多样。采用液晶空间光调制器(LC SLM)完成计算全息图的光学再现,实验验证了方法的有效性。结果表明：该方法可有效提高计算全息图的信息容量。     

Multiple information encryption by user-image-based gyrator transform hologram

A novel multiple information encryption by user-image-based gyrator transform hologram is proposed. In encryption process, each channel of the user image is phase encoded, modulated by random phase function and then gyrator transformed to get the gyrator spectrum of user image. Subsequently, each channel of the secret image is normalized, phase encoded, multiplied by modulated user image, and then gyrator transformed to obtain the gyrator spectrum of secret image. The encrypted digital hologram is recorded by the interference between the gyrator spectrum of user image and the spherical wave function. Similarly, the digital hologram for decryption is recorded by the interference between the gyrator spectrum of secret image and the spherical wave function. The multiple encrypted digital holograms are multiplexed into a final encoded hologram and the corresponding digital holograms for decryption are multiplexed into a final hologram for decryption. The wavelength and radius of the spherical wave function, and angle of gyrator transform are all essential keys for decryption. The proposed system has two main features. First, the encrypted hologram has no information about secret image. Second, the hologram for decryption used as identification key. Consequently the two marked security layers of information protection are achieved. The proposal can be realized by optoelectronic system. Numerical simulation results demonstrate the feasibility and security of the proposed technique.     

Neural network applied to reconstruction of complex objects based on fringe projection

The neural network has been introduced into the reconstruction of the complex object based on fringe projection. In this method, the neural network with powerful property of approximation is used to get the continuous approximate function of a discrete fringe pattern captured by an image frame grabber. The depth-related phase of the measured object modulated into the fringe pattern can be demodulated by dealing with the approximate function. Compared with the Fourier transform profilometry (FTP), in the network method, one deformed fringe pattern is needed to reconstruct the tested object, and a high spatial resolution is maintained for no filtering process. Therefore, this method performs better than FTP in the measurement of the complex object. Moreover, the network method is capable of demodulating more depth-related phase even in the case that the local shadow exists in the fringe pattern. Computer simulations and experiments validate the feasibility of this method.     

Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain

A position multiplexing method based on the modified Gerchberg-Saxton algorithm (MGSA) and a cascaded phase modulation scheme in the Fresnel transform domain is proposed in the multiple-image-encryption framework. First of all, each plain image is encoded into a complex function using the MGSA. The phase components of the created complex functions are then multiplexed with different position parameters, and summed. The phase part of the summation result is recorded in the first phase-only mask (POM). The MGSA is applied on the amplitude part of the summation result to determine another phase only function which is then recorded in the second POM. The simulation results show that the crosstalk between multiplexed images is significantly reduced compared with an existing similar method [20]. Therefore, the multiplexing capacity in encrypting multiple grayscale images can be increased accordingly.     

A matched filter echo summation technique for MRI

A technique is presented to increase the signal-to-noise ratio (SNR) in two-dimensional (2D), phase-encoded imaging at low SNR. The essence of this technique is to combine multiple echoes in the time domain. As analyzed in the paper, phase discrepancies exist among different echoes and may deteriorate the combined echo. In particular, extraneous phase shifts can be created if unshielded gradient coils are used. To overcome these phase discrepancies, a matched filter was derived from the k = 0 component of image. This matched filter has the same phase discrepancies among its echoes as the imaging signal and its magnitude decays with an average T₂. In the echo summation with the matched filter, the phase of the matched filter was subtracted from the imaging signal and the magnitude of the matched filter was used as the weighting function. We have shown that this matched filter echo summation technique has better SNR than the case of 2D, phase-encoded imaging in both simulation and experiment. The SNR improvement is up to 60% in a phantom experiment. This technique is mostly useful in low SNR imaging that requires long imaging time, such as spectroscopic imaging and ¹⁹F imaging.     

Multiple-surface interference fringes analysis basing on wavelength-modulated phase shifting interferometry

Phase-shifting interferometry is widely used for high-precision surface measurements, but has difficulty in dealing with parallel optical plates. In this paper, an advanced method is proposed to simultaneously measure surface distributions of parallel optical plates from multiple surface interference fringes. The basic theory behind the technique is by applying wavelength-modulated phase shifting interferometry (WMPSI) to get enough frames of multiple surface interference fringes. In the procession of wavelength-modulated phase shifting, the phase variation for one point of the surface is traced and is processed by Fourier transform, and then the frequency spectrum of every surface can be separated from each other. Therefore, it allows extraction of front surface, back surface and thickness variation from multiple surface interference fringes with high precision.     

Real-time optical reconstruction of the diffused 3D object using phase information calculated by Continuous Wavelet Transform

We propose the real time optical reconstruction of a three-dimensional (3D) object from a digitally recorded hologram. Phase distribution of the recorded hologram is numerically calculated by 1-dimensional Continuous Wavelet Transform (1D-CWT) for digital reconstruction with phase only information. Also, the phase distribution of 1D-CWT transferred to the spatial light modulator (SLM) is used to obtain optically reconstructed image. It is observed that an efficient real-time analysis can be achieved, if phase of 1D-CWT is used. In the same time, optically reconstructed 3D objects obtained by only phase information are about three times brighter than bleached hologram intensity's. So the minimum power loss can be obtained. Numerical and experimental results are presented.     

非均匀采样的功率谱反演大气湍流相位屏的快速模拟

对大气湍流功率谱非均匀采样可以有效改善传统功率谱反演法低频采样严重不足的缺陷, 实现高精度的大气湍流相位屏的模拟. 但采用的直接求和运算计算复杂度高, 相位屏的模拟速度极慢. 将非均匀快速傅里叶变换(NUFFT)引入到大气湍流相位屏的模拟, 可以实现相位屏的快速模拟. 从随机过程的谱分解出发, 将大气湍流相位随机过程表示为有限谐波分量叠加和的均方极限. 通过一个高斯核函数的卷积, 将非均匀分布的谐波复振幅映射到均匀网格空间, 进而利用快速傅里叶变换, 降低计算复杂度, 加快大气湍流相位屏的模拟速度. 以大气湍流的Kolmogorov 谱为例, 利用NUFFT仿真得到大气湍流相位屏, 并对相位屏的模拟精度、模拟速度和误差进行统计分析. 结果表明, NUFFT的引入可以实现快速、高精度的大气湍流相位屏的模拟.     

光学空间滤波过程的计算机仿真

提出了一种利用MATLAB软件并通过计算机仿真光学空间滤波实验过程的新方法.其特点是:既可以随意改变所设计滤波器的参量,又可以对输入图象进行振幅、相位或复合滤波,并且可实现傅里叶变换频谱中相位信息的提取、存储和利用,因而能够完成一般光学实验中往往难以实现的某些操作.并分别给出了网格滤波、低通、高通及相位滤波等仿真实验结果.这种仿真实验给光学滤波器的设计和图象处理带来很大方便,同时也为相关器件的设计提供了一条新的途径.     

A Combined Phase Type Optical Element for Realizing Multiple Images

In this paper we introduce a new phase type combined optical element. The element is combined with Dammann grating and Fresnel zone plate in the same substrate by microelectronics technique, hence it has splitting functions of the Dammann grating and self-focusing function of the Fresnel plate. It can produce uniform multiple images by itself. We experimentally designed and fabricated an 9x9 multiple image element, and results show that the element can realize the multiple images we require and the intensity of each image is the same. Relative error is less than 5%.     

Kinoform sampling filter

We present a new phase element which has the same optical properties as those of the amplitude sampling filter but it can use theoretically all the incident light for multiple image formation. The paper discusses a design method of the element and a diffraction efficiency of its structure obtained in a lithographic process. Then the quality and imaging ability of a phase element, fabricated according to the described design, are verified in an optical set-up.     

Mie理论递推公式计算散射相位函数

在激光雷达探测中,关于多次散射雷达回波的研究,散射相位函数是个非常重要的物理量。本文利用Mie理论的递推公式,对单一粒径介质的散射相位函数进行了计算,计算结果与散射理论中前、后向散射峰值大小随粒子半径的增大而增大相一致。同时,对非单一粒径介质的散射相位函数进行了计算,可用于大气、雾和云等气溶胶多次散射的研究。