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A reliable calibration method for the investigation of the quasi-static performances for nano-positioning stage is proposed and the corresponding system is developed, which consists of an optical system based on a differential plane mirror interferometer with double-pass configuration from NPL[14], an NPL-developed FPGA-based interferometric data acquisition and decoding system, and mechanical system.
By means of the different plane mirror interferometer, the movement displacement of the ultra-fine positioning stage can be transmitted to the phases of the photoelectric signals. The variation of the signals is acquired by the data acquisition and decoding system, and the displacement is calculated successfully. On the base, the method and its system can be used to calibrate and trace the metrological characteristics of nano-positioning stages effectively and creatively.
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The optical configuration of the NPL Jamin Differential Plane Mirror interferometer is shown as Fig.1. The interferometer based on a common-path optical configuration is regarded as a standard. The laser beam (λ=632.991 nm) coming from a frequency-stabilized He-Ne laser (Thorlabs, intensity stabilization of ±0.2%) is firstly coupled into a polarization-maintaining single-mode (PM) fiber through Faraday optical isolator and aperture, and then delivered to the integrated interferometric calibration system, thereby separating the heat generated by the laser from the experimental devices. This optical fiber delivery system has also effectively decoupled the laser source from the calibration setup, and therefore offered flexibility for the following calibration work.
The decoupled laser beam enters the Jamin interferometer after it is collimated by an aspheric lens, and forms the linearly reference and measurement laser beams. Then they are reflected back from the U-shaped reference and measurement mirror respectively to produce an interference pattern incident.
Owing to the phase quadrature coatings at the corresponding positions on the Jamin beamsplitter, two phase-quadrature interference signals (sin and cos, in Fig.1) are generated and captured by the photo detectors, given as the optimum signal-to-noise conditions for fringe counting and subdividing.
While the moving measurement mirror travels attached to an ultra-fine stage which is driven by a piezoelectric actuator, its relative displacement can be expressed in Eq.(1):
$$L = N \cdot \frac{\lambda }{4}$$ (1) where N is the number of the interferometric fringe, and λ is the wavelength of the frequency-stabilized He-Ne laser beam.
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A mechanical system of the calibration setup has been fabricated correctly to be in accordance with the design and configuration of the NPL interferometer. The interferometer block together with its U-shaped reference mirror is supported by three evenly-distributed columns made of invar. Two micrometers located on the V-groove of the invar columns (not shown in Fig.1) are used to align the measurement beams with the measurement mirror, which is fixed onto the stage under calibration. Three additional micrometers are utilized for fine adjustment of the U-shaped reference mirror. Care has been taken to make sure that (1) the reference mirror is vertical to the reference beams, (2) the optical path difference between the reference and the measurement beams is close to zero, and (3) the calibrated setup should be let stand still for 72 h after the adjustment and tight fixation.
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The phase quadrature interference signals (sin and cos, shown in Fig.1) together with the reference signal are firstly transmitted into a NPL-developed preamplifier for current-to-voltage conversion, amplification and denoising. The signals are then processed using a NPL-developed signal optimizing unit to remove the direct current (DC) offset of the signals, compensate for the potential laser intensity fluctuation, and amplify the analog signals in such a way that they can match with the full dynamic range of the analog to digital converters (ADCs) on the field-programmable gate array (FPGA) card. The magnified quadrature interference signals ix(t) and iy(t), acquired from the signal conditioning unit have nearly zero-offset, and a magnitude of about ±9 V. And they are converted into a displacement through fringe counting and subdividing.
The two signals ix(t) and iy(t) can be expressed in Eq.(2):
$$\left\{ {\begin{array}{*{20}{c}} {{i_x}(t) = {i_{x0}} + {C_x}\cos \varphi (t)\begin{array}{*{20}{c}} {}&{} \end{array}} \\ {{i_y}(t) = {i_{y0}} + {C_y}\sin [\varphi (t) + {\varphi _0}]} \end{array}} \right.$$ (2) where ix0 and iy0 are the DC offsets; Cx and Cy are the different AC amplitudes for the signal, and φ0 is the phase-quadrature error between the two signals.
In the case of zero-path difference, the displacement ∆L of the measurement mirror is proportional to the phase shift ∆φ in interference signals during the period of [t0, t1], which can be expressed in Equation (5):
$$\Delta L = \frac{{\Delta \varphi }}{{8\pi }} \times \lambda = \frac{{\varphi ({t_1}) - \varphi ({t_0})}}{{8\pi }}\lambda $$ (3) where λ is the laser wavelength.
Subsequently, a FPGA-based DAQ system (NI PCIe-7842R) is used to acquire the optimized interference signals ix(t) and iy(t). This multifunction reconfigurable DAQ system features a sampling rate of 200 kS/s with a user programmable FPGA for high-performance onboard signal processing and direct control over I/O signals. This DAQ system is also capable of A/D conversion per channel (16 bit single-ended) for independent timing and triggering. It is therefore especially suitable for high-speed acquisition of phase-quadrature interference signals without introduction of additional phase shifts or retardation between the two signals ix(t) and iy(t).
The digitized interference signals read by this DAQ system are firstly normalized using the Heydemann correction to compensate for the five parameters such as offsets, gains, and signal phase [ix0, iy0,Cx, Cy, φ][15], those tend to be time-varying. Thus, the nonlinear error within this homodyne interferometer will be eliminated as much as possible. This nonlinearity correction and thereafter interferometric decoding is realized by a NPL-developed LabView® program. The DAQ system is also used to provide the analog signals for the controller of nano positioning stages and acquire their displacement sensor signals by a user LabView interface software.
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The interferometric calibration setup is mounted on an optical vibration isolation platform, and works under nearly open-air conditions, as shown in Fig.2. More care is taken that a plastic cover is used to isolate the heat generated by the laser from the experimental devices or other heat source so as to eliminate the influence to the calibrated ultra-fine stage.
Figrue 3(a) shows the mid-term stability and drift of the interferometer within 50 s, which is a typical duration for one nanoindentation process including loading, holding and unloading procedures, respectively.
Figure 3. Experimental investigation of the quasi-static performance of the interferometric calibration setup
The corresponding noise spectrum density, obtained by using short-time Fourier transform with Hanning window, is illustrated in Fig.3(b). The vertical and horizontal coordinates in this figure are of logarithmic forms. It can be seen from Fig.3 that the calibration setup has a drift smaller than 200 pm within the period of 50 s, and a noise floor lower than 10
${\rm{pm/}}\sqrt {{\rm{Hz}}} $ . So, the system measurement accuracy and stabilization can meet the requirement during calibration.To evaluate the relative position and orientation between the optical axis of the interferometer and the measurement mirror mounted onto the z axis of the piezostage within the z-axis motion range, an experiment was carried out under nearly open-air conditions. The z-axis motion deviations of the interferometric calibration setup are measured, and a polynomial fitting is done using least square estimation, as shown in Fig.4.
Figure 4. Experimental investigation of the z-axis motion performance of the interferometric calibration setup
Seen from Fig.4, the interferometric measurement errors are of non-linear with the displacement over the range, and obviously there exists angular variation between the optical axis of the interferometer and the measurement mirror due to possible temperature fluctuation. They may be also caused by other reasons such as the near heat, surface shape error of the mirror, the interference intensity, and so on. Here, the relative position and orientation between the interferometer and the piezostage is adjusted again till there exists less angular error between the optical axis and the measurement mirror. So, it can be evaluated that the performance of the interferometric calibration setup can be further improved when the setup is located in a well air-conditioned measurement box with additional heatproof and vibration isolation.
Traceable analysis of the performance of an ultra-fine positioning stage using a differential plane mirror interferometer
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摘要: 超精密纳米位移台常用于扫描探针显微镜、光学显微镜等高精度分析仪器中,其纳米机械性能的精密计量和校准对显微测量系统的性能起着关键作用。基于一种双通道结构差动式平面镜干涉测量与校准方法(英国国家物理实验室),文中对一种超精密位移台的关键计量特性进行了定量研究。构建了基于现场可编程门阵列(FPGA)和LabView的高精度稳频激光干涉数据采集和数据解码系统,使其可溯源超精密纳米位移台的准静态校准计量特性。进一步地,利用该干涉测量系统对超精密位移台的计量特性进行了校准和分析。测试结果显示,该激光干涉校准系统在准开放环境中的背景噪声低于10
${\rm{pm/}}\sqrt {{\rm{Hz}}} $ ;该超精密位移台具有优良的纳米机械性能,其线性度低于1.2×10−4,分辨率达40 pm,重复性和稳定性较好。上述对校准设备准静态性能和对纳米位移台计量特性的测试结果表明,所提出的方法和系统能够对纳米位移台进行计量,从而用于小于几皮米的皮米级压痕测量以及原子尺度上的大范围测量。Abstract: Ultra-fine positioning stages are the indispensable components in many areas of nanotechnology and advanced material analysis, and are always integrated into analytical devices such as Scanning Probe Microscope (SPM), optical microscope. The mechanical properties of the microscopic measurement system were strongly influenced by the nano-mechanical performance of an ultra-fine positioning stage. A traceable calibration setup for investigating the quasi-static performance of nano-positioning stage was developed, which utilized a differential plane mirror interferometer with double-pass configuration from the National Physical Laboratory (NPL). Based on an NPL-developed FPGA and LabView, the laser interferometric data acquisition (DAQ) and data decoding system with high precision and stable frequency was built up to enable traceable quasi-static calibration of ultra-fine nano positioning stages. Furtherly, the proposed system was used to calibrate and analyze the metrological characteristics of nano-positioning stages. The experimental results have proven that the calibration setup can achieve a noise floor lower than 10${\rm{pm/}}\sqrt {{\rm{Hz}}} $ under nearly open-air conditions. The calibrated pico-positioning stage has an excellent nano-mechanical performances, such as the linearity of being lower than 1.2×10−6, the resolution of being up to 40 picometer, good repeatability and stabilization. The results indicate that the proposed method and system can be used to measure the performances of the ultra-fine positioning stages, and furtherly be used for pico-indentation with indentation depths down to a few picometers and the large-scope measurement at the atomic scale.-
Key words:
- nanometrology /
- laser interferometry /
- ultra-fine positioning stages /
- traceability
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