RESUMEN

Spectrally resolved interferometry utilizing a femtosecond laser is widely employed for absolute distance measurement. However, deviations in the output time pulse of the conventional algorithm through inverse Fourier transform are inevitable. Herein, an improved data processing algorithm employing a time-shifting parameter is proposed to improve the accuracy of spectrally resolved interferometry. The principle of the proposed time-shifting algorithm is analyzed theoretically after clarifying the deviation source of the conventional algorithm. Simulation and experimental work were conducted to indicate the improvement in the accuracy of the output absolute distance. The results demonstrated that the proposed algorithm could reduce the deviation of output distances towards the reference values, reaching 0.58 µm by half compared to the conventional algorithm. Furthermore, the measurement uncertainty was evaluated using the Guide to the Expression of Uncertainty in Measurement (GUM), resulting in an expanded uncertainty of 0.71 µm with a 95% confidence.

RESUMEN

Dispersive interferometry based on a femtosecond laser is extensively utilized for achieving absolute distance measurements with high accuracy. However, this method cannot measure arbitrary distances without encountering a dead zone, and deviations in its output results are inevitable due to inherent theory limitations. Therefore, two enhanced data-processing algorithms are proposed to improve the accuracy and reduce the dead zone of dispersive interferometry. The principles of the two proposed algorithms, namely the truncated-spectrum algorithm and the high-order-angle algorithm, are proposed after explaining the limitations of conventional methods. A series of simulations were conducted on these algorithms to show the improved accuracy of measurement results and the elimination of the dead zone. Furthermore, an experimental setup based on a dispersive interferometer was established for the application of these proposed algorithms to the experimental interference spectral signals. The results demonstrated that compared with the conventional algorithm, the proposed truncated-spectrum algorithm could reduce the output distance deviations derived from direct inverse Fourier transforming by eight times to reach as low as 1.3 µm. Moreover, the unmeasurable dead zone close to the zero position of the conventional algorithm, i.e., the minimum working distance of a dispersive interferometer, could be shortened to 22 µm with the implementation of the proposed high-order-angle algorithm.

RESUMEN

Differing from the conventional peak-to-peak method using two neighboring spectral peaks in the frequency-domain fringe spectrum of the spectral response of a Fabry-Perot etalon to a femtosecond laser, which contains N spectral peaks equally spaced with a spacing of the etalon free spectral range (FSR), the proposed method employs a pair of spectral peaks with a spacing of an integer multiple k (k ≫ 1) of FSR for measurement of the etalon cavity length d with a reduced measurement error. Under the constrain of the total N spectral peaks obtainable in the finite spectral range of the femtosecond laser, the optimized k is identified to be N∕2 in consideration of an averaging operation using N - k samples of d to achieve the minimum measurement error. The feasibility of the proposed method is demonstrated by experimental results with an uncertainty analysis based on "Guides to the Expression of Uncertainty in Measurement".

RESUMEN

Two algorithms of data processing are proposed to shorten the unmeasurable dead-zone close to the zero-position of measurement, i.e., the minimum working distance of a dispersive interferometer using a femtosecond laser, which is a critical issue in millimeter-order short-range absolute distance measurement. After demonstrating the limitation of the conventional data processing algorithm, the principles of the proposed algorithms, namely the spectral fringe algorithm and the combined algorithm that combines the spectral fringe algorithm with the excess fraction method, are presented, together with simulation results for demonstrating the possibility of the proposed algorithms for shortening the dead-zone with high accuracy. An experimental setup of a dispersive interferometer is also constructed for implementing the proposed data processing algorithms over spectral interference signals. Experimental results demonstrate that the dead-zone using the proposed algorithms can be as small as half of that of the conventional algorithm while measurement accuracy can be further improved using the combined algorithm.

RESUMEN

A measurement method based on a confocal probe on the second harmonic generation that can measure linear and angular displacements in the focusing point is proposed. In the proposed method, a pinhole or an optical fiber placed in front of the detector in conventional confocal probes is replaced by a nonlinear optical crystal, which is utilized as a medium generating second harmonic wave whose light intensity changes by the linear and angular displacements of a target under measurement. The feasibility of the proposed method is verified by theoretical calculations and experiments with the newly designed optical setup. Experimental results have demonstrated that the developed confocal probe has a resolution of 20 nm and 5 arc-seconds for measurement of linear and angular displacements, respectively.

RESUMEN

An angle sensor based on multiple beam interference of a Fabry-Pérot etalon employing a mode-locked femtosecond laser as the measurement beam is proposed. Output angles are evaluated by using estimated local maxima within a measurement bandwidth of an output fringe spectrum detected by an optical spectrum analyzer. In the proposed method, fringe spectra produced by beams from transmittance and a reflectance side of the Fabry-Pérot etalon are detected individually, and intensities of two spectra are divided to increase the visibility by narrowing a spectrum width. Confirmation of an increase in the visibility is conducted by comparing full width half maximum values of spectra obtained by a constructed optical setup, and evaluation accuracies were compared by repeating measurements for 100 times. The output angle using estimated local maxima of the divided spectra is then evaluated to verify the feasibility of the proposed method. As a result, it is confirmed that the proposed method improves the accuracy of angle determination by one order of magnitude.

RESUMEN

A new method based on the interferometric pseudo-lateral-shearing method is proposed to evaluate the pitch variation of a large-scale planar variable-line-spacing (VLS) grating. In the method, wavefronts of the first-order diffracted beams from a planar VLS grating are measured by a commercial Fizeau form interferometer. By utilizing the differential wavefront of the first-order diffracted beam before and after the small lateral shift of the VLS grating, the pitch variation of the VLS grating can be evaluated. Meanwhile, additional positioning errors of the grating in the lateral shifting process could degrade the measurement accuracy of the pitch variation. To address the issue, the technique referred to as the reference plane technique is also introduced, where the least squares planes in the wavefronts of the first-order diffracted beams are employed to reduce the influences of the additional positioning errors of the VLS grating. The proposed method can also reduce the influence of the out-of-flatness of the reference flat in the Fizeau interferometer by taking the difference between the measured positive and negative diffracted wavefronts; namely, self-calibration can be accomplished. After the theoretical analysis and simulations, experiments are carried out with a large-scale VLS grating to verify the feasibility of the proposed methods. Furthermore, the evaluated VLS parameters are verified by comparing them with the readout signal of an absolute surface encoder employing the evaluated VLS grating as the scale for measurement.

Asunto(s)

RESUMEN

A modified two-axis surface encoder is proposed to separately measure both the in-plane displacement and the Z-directional out-of-plane displacement with minor crosstalk errors. The surface encoder is composed of a scale grating and a small-sized sensor head. In the modified surface encoder, the measurement laser beam from the sensor head is designed to be projected onto the scale grating at a right angle. For measurement of the X- and Y-directional in-plane scale displacement, the positive and negative first-order diffracted beams from the scale grating are superimposed on each other in the sensor head, producing interference signals. On the other hand, the Z-directional out-of-plane scale displacement is measured based on the principle of a Michelson-type interferometer. To avoid the influence of reflection from the middle area of the transparent grating, which causes periodic crosstalk errors in the previous research, a specially fabricated transparent grating with a hole in the middle is employed in the newly designed optical system. A prototype sensor head is constructed, and basic performances of the modified surface encoder are tested by experiments.

Asunto(s)

RESUMEN

This paper proposes a new optical configuration for a two-axis surface encoder that can measure the in-plane (X-axis) and out-of-plane (Z-axis) displacements of a positioning stage. The two-axis surface encoder is composed of a scale grating and a sensor head. A transparent grating is employed in the sensor head for measurement of the Z-directional displacement of the scale grating based on the Fizeau-type measurement method; a reference beam reflected from the transparent grating and the zeroth-order diffracted beam from the scale grating are superimposed to generate an interference signal. A pair of prisms and a beam splitter are also employed in the sensor head, so that the positive and negative first-order diffracted beams can be superimposed over a long working distance to generate an interference signal for measurement of the X-directional displacement of the scale grating. Focusing on the new, extended Z-directional measurement mechanism, proof-of-principle experiments were carried out to verify the feasibility of the proposed optical configuration for the surface encoder that can measure the uni-directional displacements of a scale grating along the X- and Z-axis. Experimental results from the developed optical configuration demonstrated the achievement of a Z-directional measuring range of ±1.5 mm.

RESUMEN

An interferometric self-calibration method for the evaluation of the pitch deviation of scale grating has been extended to evaluate the pitch deviation of the long-range type linear scale by utilizing the stitching interferometry technique. Following the previous work, in which the interferometric self-calibration method was proposed to assess the pitch deviation of the scale grating by combing the first-order diffracted beams from the grating, a stitching calibration method is proposed to enlarge the measurement range. Theoretical analysis is performed to realize the X-directional pitch deviation calibration of the long-range linear scale while reducing the second-order accumulation effect by canceling the influence of the reference flat error in the sub-apertures' measurements. In this paper, the stitching interferometry theory is briefly reviewed, and theoretical equations of the X-directional pitch deviation stitching are derived for evaluation of the pitch deviation of the long-range linear scale. Followed by the simulation verification, some experiments with a linear scale of 105 mm length from a commercial interferential scanning-type optical encoder are conducted to verify the feasibility of the self-calibration stitching method for the calibration of the X-directional pitch deviation of the linear scale over its whole area.

RESUMEN

This paper proposes a new optical angle measurement method in the optical frequency domain based on second harmonic generation with a mode-locked femtosecond laser source by making use of the unique characteristic of the high peak power and wide spectral range of the femtosecond laser pulses. To get a wide measurable range of angle measurement, a theoretical calculation for several nonlinear optical crystals is performed. As a result, LiNbO3 crystal is employed in the proposed method. In the experiment, the validity of the use of a parabolic mirror is also demonstrated, where the chromatic aberration of the focusing beam caused the localization of second harmonic generation in our previous research. Moreover, an experimental demonstration is also carried out for the proposed angle measurement method. The measurable range of 10,000 arc-seconds is achieved.

RESUMEN

In dimensional metrology it is necessary to carry out multi-axis angle and displacement measurement for high-precision positioning. Although the state-of-the-art linear displacement sensors have sub-nanometric measurement resolution, it is not easy to suppress the increase of measurement uncertainty when being applied for multi-axis angle and displacement measurement due to the Abbe errors and the influences of sensor misalignment. In this review article, the state-of-the-art multi-axis optical sensors, such as the three-axis autocollimator, the three-axis planar encoder, and the six-degree-of-freedom planar encoder based on a planar scale grating are introduced. With the employment of grating reflectors, measurement of multi-axis translational and angular displacement can be carried out while employing a single laser beam. Fabrication methods of a large-area planar scale grating based on a single-point diamond cutting with the fast tool servo technique and the interference lithography are also presented, followed by the description of the evaluation method of the large-area planar scale grating based on the Fizeau interferometer.

RESUMEN

We demonstrate the first actively Q-switched fiber laser operating in the 3.5 µm regime. The dual-wavelength pumped system makes use of an Er3+ doped ZBLAN fiber and a germanium acousto-optic modulator. Robust Q-switching saw a pulse energy of 7.8 µJ achieved at a repetition rate of 15 kHz, corresponding to a peak power of 14.5 W.

RESUMEN

In this paper a new concept of a liquid-surface-based three-axis inclination sensor for evaluation of angular error motion of a precision linear slide, which is often used in the field of precision engineering such as ultra-precision machine tools, coordinate measuring machines (CMMs) and so on, is proposed. In the liquid-surface-based three-axis inclination sensor, a reference float mounting a line scale grating having periodic line grating structures is made to float over a liquid surface, while its three-axis angular motion is measured by using an optical sensor head based on the three-axis laser autocollimation capable of measuring three-axis angular motion of the scale grating. As the first step of research, in this paper, theoretical analysis on the angular motion of the reference float about each axis has been carried out based on simplified kinematic models to evaluate the possibility of realizing the proposed concept of a three-axis inclination sensor. In addition, based on the theoretical analyses results, a prototype three-axis inclination sensor has been designed and developed. Through some basic experiments with the prototype, the possibility of simultaneous three-axis inclination measurement by the proposed concept has been verified.

RESUMEN

We report the femtosecond laser inscription of fiber Bragg gratings (FBGs) in an Er-doped fluoride glass fiber used for lasing at a mid-infrared wavelength of 2.8 µm. The lasing evolution is discussed in terms of the FBG reflectivity, wavelength transition to the Bragg wavelength, and output power of the mid-infrared fiber laser. A first-order and short (2.5-mm-long) Bragg grating showed a reflectivity of 97%, because of a laser-induced index modulation of 1.1 × 10-3. This modulation was sufficient to saturate this system's output power. The laser oscillator is designed to lase in the atmospheric window of 2799-2800 nm slope. Further, this oscillator's efficiency is as high as 29.1% for the launched pump power over the range of 0.4-4.6 W and at a lasing wavelength of 2799.7 nm. This oscillator also exhibited a FWHM bandwidth of 0.12 nm.