Improved technique for measuring small angles

Integrated Optical Deformation Measurement with TIR Prism Rods

In this paper, a novel optical measurement principle for deformation, especially torsion, is presented. A laser beam is guided via total internal reflection (TIR) in a prism rod. Every single reflection causes an increasing change in the beam path, which can be measured by its effect on the outcoupling position of the laser. With a diameter of the prism rod of 10 mm and a length of 120 mm, the system achieves torsion sensitivities between 350 µm/° and more than 7000 µm/°, depending on the actual torsion angle φ. A decency level of sensitivity is defined for comparison, which is exceeded by a factor of ~55 at φ=0. The presented principle of TIR prism rods can be adapted to measure different load cases. Using two laser beams, bending and torsion can be distinguished and combined load cases analyzed. The resulting system can be integrated into machine elements, such as screws, to perform condition monitoring on mechanically loaded components.

High-precision rotation angle measurement method based on a lensless digital holographic microscope

To accurately measure ultrasmall rotation angles, a robust and effective method based on lensless digital holographic microscopy is proposed in this paper. The method combines holographic microscopy, solid geometry, and 3D measurement, including holographic measurement and angle measurement processes. We can calculate the 3D shape by the angular spectrum algorithm and the least-squares phase-unwrapping algorithm in the holographic process. According to the relationship between the surface shape and rotation angles, the real-time rotation angles can be calculated. To validate the feasibility and practicability of the proposed approach, numerical noise simulations and experiments were performed. The measurement precision of rotation angle can reach 0.5″ in the range of 1000″ in this paper's experiments. The holographic method has high measurement precision and good stability. In addition, the compact small volume has great potential in small-angle sensor applications.

Small-angle measurement with highly sensitive total-internal-reflection heterodyne interferometer

In this paper, a high-sensitivity total-internal-reflection (TIR) heterodyne interferometer is proposed for measuring small angles. In the proposed interferometer, a half-wave plate and two quarter-wave plates that exhibit specific optic-axis azimuths are combined to form a phase shifter. When a rhomboid prism is placed between the phase shifter and an analyzer that exhibits suitable transmission-axis azimuth, it shifts and enhances the phase difference of the s- and p-polarization states at double TIR. The enhanced phase difference is dependent on the incident angle; thus small angles can be easily and accurately measured by estimating the phase difference. The experimental results demonstrate the feasibility of this method. Angular resolution and sensitivity levels superior to 1.2×10⁻⁴ deg (2.1×10⁻⁶ rad) and 100 (deg/deg), respectively, were attainable in a dynamic range of 0.5 deg.

Littrow angle based autocollimation method for precision online monitoring three-dimensional angular drifts of chirped-pulse compression-gratings

A simple optical method for online precisely monitoring three-dimensional (3D) angular drifts of chirped-pulse compression-gratings in chirped-pulse amplification (CPA) lasers is proposed. Monitoring objects include all dimensional angular drifts of a grating, especially the grating groove in-plane-rotation. Monitoring contents contain direction and amount. And monitoring results are obtained by detecting the direction and the amount of 2D relative offsets of three focal spots formed by a ternary monitoring beam line. The theoretical model of the proposed method is set up using a matrix ray-tracing method, and a simplified monitoring equation is concluded based on numerical simulations. And the validity of this method is verified by a simple demonstration experiment. Besides, monitoring error and reliability discussion of the method are presented, as well.

Angular probe based on using Fabry-Perot etalon and scanning technique

A novel angular probe using the Fabry-Perot etalon and angular scanning technique is proposed for absolute angular displacement determinations in this paper. The measurement theory is first derived, a setup constructed to implement the angular probe is then introduced and analyzed, and the experimental results from the uses of the setup are finally presented. The setup analyses reveal that the probe is with high measurement resolution and sensitivity. The experimental results not only confirm the validity, stability, accuracy, and repeatability, but also show an application of the angular probe.

Determination of the refractive index and the chiral parameter of a chiral solution based on chiral reflection equations and heterodyne interferometry

This study develops a method for determining the chiral parameter and the refractive index of an isotropic chiral medium using chiral reflection equations and critical angle phenomena. Linearly polarized light propagates back and forth in a parallelogram prism between two parallel compartments with chiral solutions. A beam splitter then divides the light that emerges from the prism into a reflected light beam and a transmitted light beam. The two beams pass through a compensator and an analyzer, respectively, to cause phase compensation and interference of s and p polarizations. The phase difference between the two interference signals are initially optimized by a suitable optical arrangement and subsequently measured by heterodyne interferometry. Additionally, the refractive index of the solution is determined from the critical angle that occurred at the discontinuity of the phase difference between the two interference signals. These results are substituted into derived equations to calculate the chiral parameter. The approach has the merits of both common-path interferometry and heterodyne interferometry.

Optical fiber sensor for small angle and infinite angle detection

An optical fiber angle sensor that consists of a cam, linear displacement attenuators, and a sensitive Fabry-Perot cavity (FPC), is demonstrated to simultaneously measure small angle and infinite angle with high resolution. When the cam is driven to rotate by a fixed rotary shaft, a linear displacement transformed from an angle will be further attenuated by linear displacement attenuators and will subsequently modulate the FPC, which causes the reflected interference intensity of FPC to vary. By using the method of interferometric fringe counting, we can measure an infinite angle accurately and continuously. Moreover, a small angle measurement can be performed in a locally linear region. Experimental results show that two resolutions of 0.5 and 1.5 s in the angle range of 0.1944 degrees and 3.5496 degrees are achieved, respectively.

High-sensitivity small-angle sensor based on surface plasmon resonance technology and heterodyne interferometry

A high-sensitivity small-angle sensor based on surface plasmon resonance technology and heterodyne interferometry is proposed that uses a new technique with two right-angle prisms. Interestingly, the technique provides a novel method for designing small-angle sensors with high sensitivity and high resolution. Its theoretical resolution can reach 1.2x10(-7) rad over the measurement range of -0.15 degrees < or =theta< or =0.15 degrees . The method has some merits, e.g., a simple optical setup, easy operation, high resolution, high sensitivity, and rapid measurement. Its feasibility is demonstrated.

Optical approach to angular displacement measurement based on attenuated total reflection

An optical approach for angular displacement measurement (ADM) based on the attenuated total reflection technique is presented. As a laser beam is incident upon a planar optical waveguide, an m line is obtained by scanning the incident angle. Theoretical analysis shows that the m line sharply shifts with a tiny variation of the thickness of the waveguided layer. And the specific schemes for ADM, which are based on the angular interrogation and the intensity measurement, are analyzed. The calculated result of sensitivity demonstrates that the intensity measurement is more efficient than the angular interrogation. Furthermore, small incident angles indicate higher sensitivity to the angular displacement than relatively large incident angles for the intensity measurement.

Instrument for measuring small angles by use of multiple total internal reflections in heterodyne interferometry

A new instrument for measuring small angles by use of multiple total internal reflections in heterodyne interferometry is presented. With this instrument we can achieve a small rotation angle only by measuring the variation in phase difference between s- and p-polarization states. To improve its sensitivity we increase the number of total internal reflections by using two parallelogram prisms instead of two right-angle prisms. The angular resolution of the new instrument is better than 2.2 x 10(-6) rad over the measurement range -2.12 degrees < or = theta < or = 2.12 degrees for 20 total-internal reflections. The experimental results and the theoretical curve are in good agreement.

Total internal reflection for precision small-angle measurement

A method for precision small-angle measurement is proposed. This method is based on the total-internal-reflection effect of a light beam at a pair of glass prisms. Angular displacement of the light beam is measured when the intensity change of the reflected beam is detected as a result of the relative phase shift between the s- and the p-polarized beams. An initial phase shift between the s- and the p-polarized components is introduced to increase measurement sensitivity. For increased measurement linearity and reduced effect of laser power fluctuation on the output, a differential method is used in which the light beam is split equally into two beams, each reflected at a prism and detected by a photodiode. The output is obtained as the difference of the two detected intensities divided by their sum. A prototype device was built, which demonstrated a nonlinearity error of 1.3% in a measurement range of ?0.6 degrees or 0.4% in ?0.3 degrees . The peak-to-peak noise level was found to be at approximately 0.5 arc sec. This noise level can be reduced further and resolution increased by a reduction of the measurement range.

Small-angle measurement based on surface-plasmon resonance and the use of magneto-optical modulation

A new, to our knowledge, optical method for small-angle measurement based on surface-plasmon resonance (SPR) is presented. In this method the high sensitivity of the phase of SPR to the angle of incidence is employed to improve the resolution of the measurement of the angle. Small-angle measurement is performed by the monitoring of the phase shift resulting from the minute change of the angle of incidence with the use of magneto-optical modulation. The validity of this method is demonstrated, and a measurement resolution of 0.2 arc sec is achieved experimentally.

Use of thin films for high-sensitivity angle measurement

We propose to use thin films to provide a drastic improvement of measurement sensitivity in the recently developed small-angle measurement method, namely, angle measurement based on the internal-reflection effect. By designing the thin films (single layer or multiple layers) so that they provide an antireflection effect in the vicinity of the critical angle, we show that the sensitivity of angle measurement can be increased exponentially with the increase of the number of thin-film layers. This method provides a new means of designing angle sensors with increased sensitivities without having to increase the number of reflections and therefore the physical size and the required fabrication accuracy of the reflection prisms. We describe the design of the thin films for this particular application and the analysis of measurement sensitivity and range as determined by the material and the number of layers of the thin films. Selection of the optimal initial angle for high linearity performance is also discussed.

Improved angle interferometer based on total internal reflection

We describe an improved interferometer for angle measurement based on the internal reflection effect. The improvement is achieved by eliminating the influence of wave-plate rotation on the measurement. In the proposed angle interferometer the wave plate is fixed and placed between a rhomb assembly and a retroreflector. This scheme not only allows the angle interferometer to keep the optical configuration compact but also doubles the resolution and can measure the pitch and yaw of moving objects. Both a theoretical analysis and an experimental verification have been conducted on the interferometer. The results indicate that the performance of the modified angle interferometer is greatly improved, especially when the rotation angle is large. The nonlinearity error of the measurement equation is also addressed.

Interferometer for small-angle measurement based on total internal reflection

We describe a new method for angle measurement based on the internal-reflection effect and heterodyne interferometry. A novel prism assembly is designed that can always parallel retroreflect the incoming light beams so the optical configuration is compact. As a differential common-path optical configuration is integrated into the design, the linearity of the method is greatly improved. Details of theoretical analysis of the method and experimental verification of the principle are presented. The resolution can be better than 0.3 arc sec. The experimental results and further improvements of the proposed method are also addressed.