基于变焦快速里埃变换的实时测量二维精度级别
Haijin Fu1,2, Zheng Wang1,2, Xionglei Lin1,2
1Ultra-Precision Optoelectronic Instrument Engineering Center, School of Instrument Science and Engineering, Harbin Institute of Technology, Harbin 150080, China.
Micromachines
|November 25, 2023
概括
这项研究引入了一种新的二维精度水平,利用变焦快速里叶变换 (FFT) 算法进行高分辨率的实时角度测量. 该方法显著提高了角度分辨率和精度,性能优于商业自动聚合器.
科学领域:
- 计量学 计量学 计量学
- 光学工程是指光学工程.
- 信号处理 信号处理
背景情况:
- 传统的角度测量系统在实现高分辨率和实时测量能力方面存在局限性.
- 现有的方法难以平衡测量速度和角度精度之间的权衡.
- 精密工程中需要先进的计量工具需要创新的解决方案.
研究的目的:
- 开发一种能够实时高分辨率角度测量的二维精度水平.
- 为了解决高分辨率和高测量速度在角度测量系统中的内在矛盾.
- 为了提高精密平衡仪器的角度分辨率和精度.
主要方法:
- 实现基于快速变焦的富里埃变换 (FFT) 的解算法,集成到可现场编程的网关阵列 (FPGA).
- 使用油表面作为角度敏感接口,结合同质干扰原理.
- 干扰边缘频率的分析,以确定角度变化和提高频率分辨率.
主要成果:
- 拟议的zoom FFT算法显著提高了干扰边缘的频率分辨率,改善了角度分辨率.
- 通过将角度解过程移植到FPGA板上来实现实时角度测量.
- 原型测试表明,角度分辨率从9弧秒提高到大约0.1弧秒,可重复度为±0.2弧秒,精度为±0.6弧秒.
结论:
- 基于zoom FFT的脱算法有效地克服了角度测量中的分辨率速度权衡.
- 与现有方法相比,开发的二维精度水平提供了更高的角度分辨率和精度.
- 该系统的实时测量能力和高精度验证了其在高级计量应用中的有效性.
相关概念视频
Fast Fourier Transform
340
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
The computational efficiency of the FFT becomes...
340
Relation of DFT to z-Transform
396
The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the...
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the...
396
Discrete Fourier Transform
295
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
295
Linear Approximation in Frequency Domain
92
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
92
Continuous -time Fourier Transform
318
The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
318
Confocal Fluorescence Microscopy
13.3K
Confocal microscopy is an advanced microscopic technique. The prime advantage of the confocal microscope over other microscopy techniques is its ability to block the out-of-focus light from the illuminated samples using pinholes. It is widely used with fluorescence optics to obtain high-resolution, sharp contrast images. Unlike optical microscopes, confocal microscopes use a focused beam of light laser to scan the entire sample surface at different z-planes. These microscopes are, therefore,...
13.3K


