Commercial Interferometer Research Articles

On bench evaluation of intraocular lenses: performance of a commercial interferometer

NIMO-TEMPO is a metrology device that measures all types of intraocular lenses available in the ophthalmic market. Its technology, based on interferometry, captures the wavefront of the lens to compute optical results essential to evaluate its quality and understand its characteristics. This study aims to demonstrate the reliability of this device and its associated software, TEMPO-MENTOR, in measuring intraocular lenses. The analysis is based on comparing the theoretical results of the optical design and data computed by the device algorithm. Results provided with NIMO-TEMPO are also validated using another metrology device.

Precision straightness and displacement measurement based on phase-modulated interferometric scheme with different modulation depths

In this study, a novel straightness and displacement measurement method using a Wollaston prism-sensing phase-modulated interferometer (WPHI) is proposed to accurately measure straightness errors and the position of linear stages. In the proposed WPHI, a Wollaston prism assembly along with a semi-reflector serves as a sensing element to generate two straightness and one displacement measuring beams. By using an electro-optic phase modulator to modulate the linearly polarized laser beam at 45° to its optic axis, different modulation depths are introduced into the straightness and displacement measuring beams to obtain phase-modulated interference signals. Thus, the straightness error can be directly obtained from the change in the optical path difference between the two measuring beams, thereby avoiding any additional errors introduced by separately measuring the changes in the optical path of each beam. Moreover, a 2 × 2 array photodetector is used to simultaneously measure the displacement and rotational angles of stage to compensate for the influence of rotational errors on the displacement result. The experimental results showed that within a range of 4 m, the standard deviations of the straightness error and displacement measurements between the proposed WPHI and a commercial interferometer were 0.50 and 0.59 μm, respectively. Thus, the proposed WPHI has substantial applications in the fields of ultraprecision machine-tool control, precision motion stage testing, and displacement sensor calibration.

Development of fixed-point two-degree-of-freedom positioning errors measurement system with precision improvement function

A two-degree-of-freedom (2-DOF) error measurement system is proposed for assessing the positioning errors of a rotary stage. Additionally, this study introduces a compensation method for addressing four-degree-of-freedom (4-DOF) laser drift errors and presents a refined approach for correcting the decoupling matrix. Initially, passive compensation is utilized to address the 4-DOF laser drift errors, and the impact of laser drifts is minimized through an averaging technique. Subsequently, the identified laser drift errors are analyzed using a mathematical model to effectively compensate for these errors and enhance the overall accuracy of the measurement system. Concerning the correction of the decoupling matrix, a more precise method is employed in contrast to traditional approaches. Experimental data obtained from commercial interferometers are subjected to linear fitting using the least squares method, facilitating a more accurate refinement of the decoupling matrix. This method enables a better alignment of the decoupling matrix with the experimental conditions.

A three-degrees-of-freedom motion error measurement system based on Mach–Zehnder interferometry

This paper proposes a three-degree-of-freedom motion error measurement system based on Mach–Zehnder interferometry. The system consisted of an optical flat, beam-splitting prisms, and a reflector. When the stage was moving, the straightness error of the linear guides changed the optical path difference, which in turn caused a phase shift in the interferogram. This phase shift could be calculated by utilizing an image processing algorithm that was also developed during this study. The 3-DOF straightness errors, which included one linear error and two angular errors could be calculated. A commercial laser interferometer and a chromatic confocal sensor were used as reference sensors. The experimental results showed that the linear and angular measurement errors of the system were within ± 0.05 μm and ± 0.3″, respectively over measurement ranges of 100 mm and 60″. The repeatability, which was expressed by the standard deviation, was within 40 nm and 0.3″ for the linear and angular measurements, respectively. The proposed Mach-Zehnder interferometer has been successfully applied in a high-accuracy 3D surface topographic measurement system. It was able to effectively compensate the motion error and improve the accuracy for surface profiling.

Comparison of full fiber coupled interferometer systems under vacuum conditions

Abstract The PTB built a comparator setup for testing length measuring systems under vacuum conditions. The setup is equipped with a linear stage which is operated in a closed loop using the feedback of a 1.5D encoder system with three encoder heads for length and vertical rotation angle and exhibits a movement range of 150 mm. The main measurement system is a heterodyne interferometer with periodic nonlinearities with amplitudes below 10 pm. The comparator setup was characterized using a mirror mounted on the stage reflecting the measurement as well as the reference beams. By these means, the resolution, the stability of the setup as well as the influence of guiding errors on position-dependent measurement deviations of the fully fiber coupled interferometer were investigated. A position-depending error was observed which was resulting from the variation of the performance of the coupling into the multi-mode fibers used to transfer the superposed beams to the photoreceivers. The measured deviations were 1.5 nm or 0.2 nm over 70 mm travel range depending on the core diameter of the multi-mode fibers of 50 µm and 200 µm, respectively. Three different commercial fiber interferometer systems were analysed under vacuum conditions with the comparator setup. All tested systems are working with light sources with a wavelength of approximately 1535 nm but differ in the amplitude of their periodic nonlinearities in the range between 10 pm and 29 nm. The tests of their resolution and stability were limited by vibrations in the comparator setup and the lack of adequate synchronization capabilities of the data acquisition of these systems.

Error Analysis of an Economical On-Site Calibration System for Linear Optical Encoders

A calibration system was designed to evaluate the accuracy of linear optical encoders at the micron level in a fast and economical manner. The system uses a commercial interferometer and motor stage as the calibrator and moving platform. Error analysis is necessary to prove the effectiveness and identify areas for optimization. A fixture was designed for the scale and interferometer target to meet the Abbe principle. A five-degree-of-freedom manual stage was utilized to adjust the reading head in optimal or suboptimal working conditions, such as working distance, offset, and angular misalignment. The results indicate that the calibration system has an accuracy of ±2.2 μm. The geometric errors of the calibration system, including mounting errors and non-ideal motions, are analyzed in detail. The system could be an inexpensive solution for encoder manufacturers and customers to calibrate a linear optical encoder or test its performance.

Analysis of phase calculation error introduced by the extinction ratio in instantaneous phase shifting interference.

Instantaneous phase shifting interferometry technology, the core component of which is the pixel micropolarizer camera, has been widely used in commercial interferometers. This technology has the superiority of single-frame acquisition, vibration insensitivity, and no need for phase shifting devices. However, due to manufacturing defects and accuracy limitations, the extinction ratios (ER) of the micropolarizer array are different and fairly small, directly affecting the phase calculation accuracy. This paper initially derives a theoretical expression for the phase calculation error introduced by the extinction ratio (ER) and proposes the error correction model to reduce phase calculation errors caused by the extinction ratio. The theoretical analysis can serve as an important basis for accurately assessing the polarization characteristics of a pixel micropolarizer camera. Quantifying the impact of the extinction ratios provides significant support for the selection of polarization equipment. In addition, the paper proposes a calibration model to improve measurement accuracy, which can serve as an effective means to reduce the impact of the extinction ratio (ER). The innovative research content revealed the influence of extinction ratio (ER), serving as a valuable complement to the existing analysis and research on extinction ratio (ER).

Phase retrieval for single-frame interferogram with an irregular-shaped aperture based on deep learning.

This paper proposes a high-precision phase retrieval method based on deep learning to extract the Zernike coefficients from a single-frame interferogram with an irregular-shaped aperture. Once the Zernike coefficients are obtained, the phase distribution can be retrieved directly using the Zernike polynomials. For many apertures, the root mean square (RMS) of the residual wavefront between the true and estimated wavefronts reached the order of 10-3 λ. Simulations were conducted under different noise conditions, indicating that the proposed method has high measurement accuracy and robustness. Experiments demonstrated that the accuracy achieved by this method was comparable to that of commercial phase-shifting interferometers. We believe that this method is useful for measuring optical surfaces with irregular apertures.

Dynamic gravitational excitation of structural resonances in the hertz regime using two rotating bars

With the planning of new ambitious gravitational wave observatories, fully controlled laboratory experiments on dynamic gravitation become more and more important. Such experiments can provide new insights in potential dynamic effects such as gravitational shielding or energy flow and might contribute to bringing light into the mystery still surrounding gravity. Here we present a laboratory-based transmitter-detector experiment using two rotating bars as transmitter and a 42 Hz, high-Q bending beam resonator as detector. Using a precise phase control to synchronize the rotating bars, a dynamic gravitational field emerges that excites the bending motion with amplitudes up to 100 nm/s or 370 pm, which is a factor of 500 above the thermal noise. The two-bar design enables the investigation of different transmitter configurations. The detector movement is measured optically, using three commercial interferometers. Acoustical, mechanical, and electrical isolation, a temperature-stable environment, and lock-in detection are central elements of the setup. The moving load response of the detector is numerically calculated based on Newton’s law of gravitation via discrete volume integration, showing excellent agreement between measurement and theory both in amplitude and phase. The near field gravitational energy transfer is 1025 times larger than the one of the propagating gravitational wave component.

Comparison of fiber interferometric sensor with a commercial interferometer for a Kibble balance velocity calibration

This article presents a fiber interferometric sensor (FIS) for measuring the velocity amplitude of an oscillatory vibrating object, with a focus on velocity mode measurement in applications using the Kibble balance principle. The sensor uses the range-resolved interferometry method to measure the displacement of the moving object and employs a multi-harmonic sine-fit algorithm to estimate the displacement amplitude and frequency, thereby determining the velocity amplitude. This article provides a comprehensive explanation of the experimental setup and the measurement techniques employed, as well as a detailed analysis of the uncertainty budget, with the performance validation of the FIS benchmarked against a commercial interferometer within a Kibble balance setup. The velocity amplitude of a coil of the Kibble balance, oscillating with an approx. amplitude of 20 μm and a frequency of 0.25 Hz, was measured using the sensor and found to be 31.282 31 μm s−1 with a relative deviation of −1.9 ppm compared to a commercial interferometer. The high performance of the FIS, especially with regard to non-linearity errors, and the small size of the measuring head enable universality of integration into a wide variety of measurement systems, also including the use as general-purpose vibration and displacement sensor.

Development of a precision vertical planar stage as a programmable planar artefact

Planar artefacts play the role of calibration references for areal measuring instruments. Due to the need of high accuracy, they are fabricated by high precision processes. There are various artefacts for different measuring systems. If those planar artefacts can be generated by respective computer programs and performed through a common platform, it could be a versatile and time-saving tool. The goal of this work is to build up a precision vertical planar stage to provide programmable planar artefacts for field accuracy calibration of areal sensors. In order to improve the real-time motion accuracy of the planar stage, its spatial positional errors are modeled, measured, and compensated. The Vector Transfer (VT) method is used to derive the planar positional error model based on Abbe principle and Bryan principle. A new six-degree-of-freedom (6-DOF) measurement system is proposed for simultaneously measuring all geometric errors of the linear stage. Experimental verification by comparing the positioning accuracy of two diagonals of the constructed plane with the commercial laser interferometer has confirmed that the maximum spatial positioning error of the developed vertical stage was reduced from −124.0 μm to 13.5 μm after the positional error compensation, achieving 89.1% accuracy improvement. This vertical planar stage can generate any shape of programmed trajectory for the accuracy calibration of industrial areal sensors.

On-chip digital holographic interferometry for measuring wavefront deformation in transparent samples.

This paper describes on-chip digital holographic interferometry for measuring the wavefront deformation of transparent samples. The interferometer is based on a Mach-Zehnder arrangement with a waveguide in the reference arm, which allows for a compact on-chip arrangement. The method thus exploits the sensitivity of digital holographic interferometry and the advantages of the on-chip approach, which provides high spatial resolution over a large area, simplicity, and compactness of the system. The method's performance is demonstrated by measuring a model glass sample fabricated by depositing SiO2 layers of different thicknesses on a planar glass substrate and visualizing the domain structure in periodically poled lithium niobate. Finally, the results of the measurement made with the on-chip digital holographic interferometer were compared with those made with a conventional Mach-Zehnder type digital holographic interferometer with lens and with a commercial white light interferometer. The comparison of the obtained results indicates that the on-chip digital holographic interferometer provides accuracy comparable to conventional methods while offering the benefits of a large field of view and simplicity.

Differential confocal measurement of microstructure surface topography based on centering error optimization and wavelet threshold denoising

This paper proposes a precise differential confocal measurement method based on centering error optimization and wavelet threshold denoising (DCM-COWD), which can realize non-contact measurement of microstructure surface topography with high precision and efficiency. Firstly, the influence of pinhole diaphragm size and offset on axial response curve is analyzed through multiple experiments to obtain the optimal pinhole diaphragm diameter and offset of the differential confocal measurement system. Secondly, a probe centering method based on grating rotation successive approximation is designed, in order to reduce the centering error of 3D topography measurement during the spiral scanning process. Thirdly, a translation invariant (TI) wavelet threshold denoising algorithm based on median filtering and whale optimization (WOA) is proposed, which can improve the signal-to-noise ratio (SNR) and reduce the root mean square error (RMSE), and effectively suppress the Pseudo-Gibbs phenomenon of discontinuous points. Finally, the surface topography of a standard sample is measured based on DCM-COWD system. The measurement results show that the center error is within 0.75 μm and the maximum deviation is within 1.45 %. The measurement results show high accordance with the commercial white light interferometer, and the processing speed is improved by 4.17 times. The proposed method has great application potential for the precise and efficient measurement of 3D surface topography.

Self-calibrated free-running dual-comb ranging using subsampled repetition frequency information

Dual-comb ranging (DCR) is an emerging absolute distance measurement method with rapid speed, high precision, and wide ambiguity range. DCR has important applications in remote sensing, large-scale manufacturing, and aerospace exploration. However, the typical DCR system requires cumbersome phase-locking electronics for frequency stabilization and distance calibration, which hinders the practical application of DCR. In this paper, we demonstrate a free-running DCR scheme based on two free-running mode-locked fiber lasers. Two fiber lasers are environment-shared to improve the anti-aliasing capability. We then introduce a self-calibration technique that can directly extract the subsampled repetition frequency information from the interferograms (IGMs). By using this technique, real-time calibration of measured distance can be achieved without extra repetition frequency detection module and frequency counter. The system realizes a 5.3 µm precision for ∼1 m stand-off distance at ∼1 kHz acquisition speed. With averaging, the measurement precision drops to ∼101 nm at the averaging time of 3 s. The ambiguity range of our DCR system is ∼2.6 m due to the relatively small repetition frequency. For dynamic distance measurement, it shows good consistency with a commercial heterodyne interferometer. Our method provides a cost-effective scheme for high-performance absolute distance measurement, and it is promising for promoting DCR system out of the laboratory and realizing field-deployed applications.

Self-Calibration of a Large-Scale Variable-Line-Spacing Grating for an Absolute Optical Encoder by Differencing Spatially Shifted Phase Maps from a Fizeau Interferometer

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.

Six-degree-of-freedom geometrical errors measurement system with compensation of laser beam drifts and installation errors for linear stage

In this paper, an optical measurement system is proposed to measure the six-degree-of-freedom (6DOF) geometrical errors of a linear stage, and the errors are analyzed by the interferometric method and the geometrical optics method. Among them, the interferometric method is mainly used for the position error analysis. This method can solve the problem that geometrical optics is limited by the size of the sensor in our previous system, and improve the measurement accuracy of the position error. The geometrical optics method is used for the error analysis of the remaining 5DOF geometrical errors to simplify the data acquisition time and calculation amount. In addition, this paper also proposes a methodology to compensate for laser beam drifts and installation errors of optical components. We use two sensors to measure the 4DOF laser beam drifts and add them into the proposed mathematical model to solve these errors. We also use sensitivity analysis to analyze the influence of each installation error of optical components and find out the installation errors that need to be considered. Then we bring them into the mathematical model and solved them with least square methods. Finally, we verify the feasibility of the proposed measurement system through repeated experiments and comparisons with a commercial interferometer and an electronic level.

Universal phase-shifting algorithm (UPSA) for nonuniform phase-step demodulation and null-testing criterion for phase accuracy gauging

We propose a non-iterative, universal phase-shifting algorithm (UPSA) for phase-demodulation regardless if the phase steps are linear, nonuniform, or even unknown. Nonlinear phase-step algorithms are important because those steps are not “floating-point” linear due to thermal drift, mechanical instabilities, or aging, even for commercial laser interferometers. Additionally, we propose a null-testing criterion to gauge the accuracy of the demodulated phase. Usually, novel PSAs are tested using simulations where we can compute the difference between the demodulated phase and the ideal one. This seems a vicious trap: usually, experimental phase gauging accuracy is unreachable having no prior access to the measuring phase. Here we offer a way to escape from this vicious circle by proposing a null-test that proves that the phase from experimental fringes is error-free. This null-test can be used for testing the phase quality of any PSA. In brief, we are proposing two interferometry tasks: 1) the UPSA for phase demodulation, and 2) a null-testing criterion which verify that the estimated phase is error-free.

Challenges in double-beam laser interferometry measurements of fully released piezoelectric films

When utilizing double-beam laser interferometry to assess the piezoelectric coefficient of a film on a substrate, probing both top and bottom sample surfaces is expected to correct the erroneous bending contribution by canceling the additional path length from the sample height change. However, when the bending deformation becomes extensive and uncontrolled, as in the case of membranes or fully released piezoelectric films, the double-beam setup can no longer account for the artifacts, thus resulting in inflated film displacement data and implausibly large piezoelectric coefficient values. This work serves to identify these challenges by demonstrating d33,f measurements of fully released PZT films using a commercial double-beam laser interferometer. For a 1 μm thick randomly oriented PZT film on a 10 μm thick polyimide substrate, a large apparent d33,f of 9500 pm/V was measured. The source of error was presumably a distorted interference pattern due to the erroneous phase shift of the measurement laser beam caused by extensive deformation of the released sample structure. This effect has unfortunately been mistaken as enhanced piezoelectric responses by some reports in the literature. Finite element models demonstrate that bending, laser beam alignment, and the offset between the support structure and the electrode under test have a strong influence on the apparent film d33,f.

Development of low-cost heterodyne interferometer with virtual electronic phasemeter

Commercial laser interferometers are conventionally used to measure the positioning error of a long linear stage in multiaxis computer numerical control machine tools. However, commercial laser interferometers are costly and difficult to use. Therefore, a low-cost photodetector-based heterodyne interferometer combined with an electronic phasemeter module was proposed for precise measurement of the positioning error of a long linear stage. The proposed heterodyne interferometer was combined with a virtual electronic phasemeter that employs a self-developed signal-processing technique. Our core algorithm and proposed photoelectric-signal-processing technique were developed using the LabVIEW human–machine interface. Moreover, to verify the performance of the proposed heterodyne interferometer, a laboratory-built prototype was constructed and used to measure the positioning error of a long linear stage. The experimental results indicated that the positioning accuracy of the proposed interferometer was ±4.5 μm for a linear stage with a displacement of 250 mm; the results obtained were comparable to those obtained with a commercially available laser interferometer. The proposed heterodyne interferometer can thus be used in other applications related to precision engineering.

Absolute distance measurement to coaxial multi-targets based on optical balanced cross-correlation using a single femtosecond laser.

We describe a high-precision ranging method based on an optical balanced cross-correlation system with a scanning repetition rate using a single femtosecond laser. By scanning the repetition rate of a laser, measuring pulses can be overlapped with reference pulses. It is an effective method to make reference pulses overlap with coaxial multiple target pulses without additional mechanical devices. The overlapped pulses are launched to the optical balanced cross-correlation system, which improves the time resolution measurement to the attosecond level. Two nominal distances are measured, and an additional commercial laser interferometer is used as a comparison to evaluate the accuracy of our measurement system. Moreover, the thickness of three stacked glasses is measured by our measurement system to verify that this system can measure coaxial multiple targets more quickly than conventional optical balanced cross-correlation systems using a single optical frequency comb.