Color crosstalk compensation method for color phase-shifting fringe projection profilometry based on the phase correction matrix.

Color phase-shifting fringe projection profilometry is one of the single-shot three-dimensional shape measurement techniques. The color crosstalk of the projector-camera system yields undesired phase errors when using phase-shifting method. In this paper, a color crosstalk compensation method based on phase correction matrix is proposed. In this method, the phase correction matrix is established to compensate the deviations between the actual phase-shift values in the acquired fringes and the standard ones in the ideal fringes. Only two fringe patterns are utilized to obtain the phase correction matrix. The quadratic equations for calculating the actual phase-shift values of the fringes in the three color channels are derived. The actual phase-shift values and the corresponding standard ones are employed to form the equilibrium equations for computing the phase correction coefficients in the matrix. Experimental results demonstrate the feasibility of the proposed method and it can effectively reduce the induced overall phase error caused by the color crosstalk.

Two-dimensional angle measurement with sub-arcsecond precision and MHz update rate using heterodyne interferometry with optical frequency comb.

Heterodyne interferometry is a powerful tool for achieving high precision and fast measurement. We developed an angle measurement system based on heterodyne interferometry by combining discrete equal-spacing longitudinal modes of optical frequency comb with an acousto-optic modulator. Using a self-designed grating-corner-cube sensor, this method can achieve a two-dimensional angle measurement with sub-arcsecond accuracy and megahertz (MHz) update rate. We experimentally demonstrate a precision of 0.073 arcsec under a 3 MHz update rate, and comparison residuals are kept within 0.063 arcsec over 300 arcsec when compared to a piezo stage. In the dynamic measurement of a 40 Hz frequency, the continuous sinusoidal motion of 0.05 arcsec can be clearly distinguished and reconstructed.

Accurate calibration for fringe projection profilometry based on an improved subpixel mapping with local gray distribution.

Fringe projection profilometry is an efficient and accurate technique for three-dimensional (3D) measurement to calibrate a camera and projector setup. The feature centers of circles on a calibration board are extracted on the camera image plane and mapped to the projector image plane during the calibration procedure. The accuracy of the mapping between camera pixels and projector pixels is crucial to the calibration accuracy, which directly affects the measurement precision of the system. In this paper, we investigate an improved subpixel mapping with local gray distribution from the camera to the projector. The mapped pixels and their gray values are regarded as a set of 3D grayscale space points. The subpixel coordinates of the feature centers on the projector image plane are obtained by directly processing the 3D points. The entire procedure retains the subpixel precision. Calibration experiments were designed to verify the feasibility of our calibration method, which was compared to three existing methods. The reprojection errors and object-space errors were used to evaluate the calibration accuracy of the methods. Additionally, measurement experiments of displacement and in-plane distance were employed to verify the calibration results of the methods. Compared to the three existing methods, we believe our method can improve the calibration accuracy for fringe projection profilometry.

Mutual collimation self-calibration for dual-comb ranging-based multilateral coordinate measurement.

We propose a self-calibration method for multilateration based on dual-comb absolute distance measurement. By performing mutual collimation measurements between multilateral measurement bases, we could measure the system parameters in a multilateration system with high precision and efficiency. We demonstrated a multilateral coordinate measurement system based on the proposed self-calibration method. The system realized rapid coordinate measurement with micron-level precision in both tested directions.

Femtosecond-laser-based full-field three-dimensional imaging with phase compensation.

Coherence scanning interferometer (CSI) enables 3D imaging with nanoscale precision. However, the efficiency of such a system is limited because of the restriction imposed by the acquisition system. Herein, we propose a phase compensation method that reduces the interferometric fringe period of femtosecond-laser-based CSI, resulting in larger sampling intervals. We realize this method by synchronizing the heterodyne frequency with the repetition frequency of the femtosecond laser. The experimental results show that our method can keep the root-mean-square axial error down to 2 nm at a high scanning speed of 6.44 µm per frame, which enables fast nanoscale profilometry over a wide area.

Absolute angular position measurement by dual-comb spectroscopy of an autocollimation diffracted beam.

The dual-comb technique is a powerful tool in industrial inspection and scientific research and is capable of realizing ultrahigh-resolution and fast broadband spectral measurements. We propose an absolute angular-position measurement method based on dual-comb spectroscopy. With a simple layout, the absolute angular position can be naturally determined through the traceable and wide-amplitude spectra of the autocollimation diffracted beams of the target grating. We experimentally demonstrate that a precision of 0.12 arcsec in the dynamic range of approximately 6660 arcsec, along with a 1 kHz repetition rate difference, is achieved. Compared with a commercial autocollimator, over 1000 arcsec, the comparison residuals are kept within ±0.3 arcsec.

Dual-comb ranging method for simultaneously measuring the refractive index and surface spacing in a multi-lens system.

Precise determination of the refractive index and surface spacing in multi-lens system is essential for ultra-precision system performance, such as lithography objectives with strict requirements for each lens fabrication and assembly position. Generally, the nominal value of the refractive index at a given wavelength must be known before resolving the geometric thickness of multi-lens using conventional methods, which leads to inaccurate and inconvenient measurements. We propose a method to simultaneously measure the refractive index and surface spacing in multi-lens system based on dual-comb ranging method. The precision of the thickness measurement is better than 0.18 µm, and the refractive index is better than 1.6 × 10-4. This study provides a potential solution for realizing the real-time, fast, and precise measurement of the geometric thickness and assembly position of multi-lens in lithography objectives.

Fast measurement of the thickness and group refractive index distribution of solid plates by line-field dispersive interferometry.

Real-time measurement of the thickness and group refractive index is crucial for semiconductor devices. In this paper, we proposed a fast synchronous method for measuring the thickness and group refractive index distribution of solid plates based on line-field dispersive interferometry. The proposed method measured the line-field distribution in an illuminated region through a single step. A low-cost spectrometer calibration method using an eight-channel dense wavelength division multiplexer was developed for verification. The line-field distribution of a three-step silicon wafer was successfully measured within 3.3 ms. The combined uncertainties for the geometrical thickness and group refractive index were <50 nm and 4 × 10-4, respectively.

Theoretical investigation and experimental support for the cavitation bubble dynamics near a spherical particle based on Weiss theorem and Kelvin impulse.

In the present paper, the laser-induced cavitation bubble dynamics near a fixed spherical particle is comprehensively investigated based on the Weiss theorem, the Kelvin impulse theory and the high-speed photography experiment. Firstly, the applicability range of the theoretical model in the time and the space is statistically obtained based on sufficient experimental results. Then, the in-depth theoretical analysis is carried out in terms of the liquid flow field and the bubble Kelvin impulse with the corresponding experimental results as the reasonable support. In addition, the theoretical prediction model of the bubble movement is established and experimentally fitted from the analytic expression of the Kelvin impulse. Through our research, it is found that: (1) the applicability range of the Kelvin impulse theory for the bubble near the spherical particle is approximately the dimensionless distance between the bubble and particle (γ) greater than 0.50. (2) The effect of the particle on the liquid velocity between the bubble and the particle is mainly manifested in the form of the image bubble, which always causes the liquid velocity in this region to be significantly lower than other surrounding regions. (3) The average movement velocity of the bubble centroid can be reasonably predicted by establishing a directly proportional function between the Kelvin impulse and the velocity with the relationship constant (α) equal to 3.57×10-6 ± 1.63×10-7 kg.

Dynamic ellipsometry measurement based on a simplified phase-stable dual-comb system.

Spectroscopic ellipsometry is a powerful tool for characterizing thin film, polarization optics, semiconductors, and others. Conventional approaches are subject to restrictions of mechanical instability and measurement speed. The complex locking scheme of previous dual-comb spectroscopic ellipsometry belies its practicability. We present and demonstrate here dynamic spectroscopic ellipsometry based on a simplified phase-stable dual-comb system, which could realize the online dynamic measurement of optical properties of materials. A precision of 1.31 nm and a combined uncertainty of 13.80 nm (k = 2) in the thickness measurement of thin-film samples has been achieved. Moreover, the dynamic performance of the system is investigated under a high data acquisition rate (1 kHz) with a dynamic resolution of ellipsometric parameter better than 0.1 rad.

Three-dimensional morphology measurement of underwater objects based on the photoacoustic effect.

Complexities of the underwater environment can seriously affect many underwater detection means, especially the influence of light scattering by water. To solve this problem, a three-dimensional (3D) morphology measurement method is proposed based on the photoacoustic effect. In this method, a measurement object is irradiated with pulsed laser light to produce ultrasonic waves via the photoacoustic effect. A probe collects the ultrasonic signal and subsequent data processing can yield complete object detection. This approach can make full use of the advantages of high precision and good directivity of laser ranging and completely avoid the influence on the laser of backscattering from water. The results yield a displacement measurement accuracy of less than 0.5 mm and an average error of 3D reconstruction of 0.21 mm, demonstrating great application potential.

Aliasing-free dual-comb ranging system based on free-running fiber lasers.

A dual-comb ranging (DCR) system without spectral aliasing based on free-running fiber lasers was proposed. By monitoring the repetition frequency over time, we compensate for the instability of the optical pulse train from the free-running fiber lasers. We demonstrated a double-channel filtering structure that eliminates the aliasing between multiheterodyne beats in radio frequency interferograms. Without any frequency locking, the DCR system implements stable running for at least 60 min. The system realizes a 6-µm repetition precision without averaging and shows good consistency with a commercial interferometer.

Multi-color method for the self-correction of the air refractive index.

We propose a multi-color method for the self-correction of the air refractive index based on the dispersive interferometry of an optical frequency comb. This method can be applied to correct the air refractive index for long-distance measurements in moist air. Optical lengths of multiple wavelengths were obtained simultaneously by the dispersive interferometry of an optical frequency comb. Interferometric measurement results and calculations from the empirical equation of air refractive indices were similar, with a standard deviation of 2.0×10-9 throughout the 2 h continuous measurement period. By applying the multi-color method, correction of the air refractive index with an uncertainty of 3.5×10-7 was achieved.

Two-channel six degrees of freedom grating-encoder for precision-positioning of sub-components in synthetic-aperture optics.

We investigate a novel two-channel grating encoder that can perform simultaneous measurements of six-degree-of-freedom (DOF) motions of two adjacent sub-components of synthetic-aperture optics such as pulse-compression gratings(PCGs) and telescope-primary mirrors. The grating encoder consists of a reading head and two separate gratings, which are attached to the back of the sub-components, respectively. The reading head is constructed such that there two identical optical probes can share the same optical components. The two probes are guided to hit each of the two gratings and can detect six-DOF motions simultaneously and independently. For each probe, the incident beam propagates through both a three-axes grating interferometry module and a three-axes diffraction integrated autocollimator-module, which detects translational and rotational movement, respectively. By combining the two modules it is possible to perform six-DOF measurement for a single point. The common-path configuration of the two probes enable identical responses to environmental variation, which ensures high accuracy.

Compression-coding-based surface measurement using a digital micromirror device and heterodyne interferometry of an optical frequency comb.

We propose a compression-coding-based surface measurement method that combines single-pixel imaging and heterodyne interference using an optical frequency comb. The real and imaginary parts of the heterodyne interference signals are used to obtain the depth information rapidly. By optimizing the ordering of the Hadamard measurement basis, we reconstruct a three-step sample with heights of approximately 10, 20, and 30 µm without an iterative operation in 6 ms, with a precision of 5 nm. Compared with the uncompressed measurement, the sampling times reduced to 20%, and the measurement time reduced by five times without measurement accuracy loss. The proposed method is effective for rapid measurements, particularly for objects with a simple surface topography.

Grating-Corner-Cube-Based Roll Angle Sensor.

This paper presents a specifically designed grating-corner-cube sensor for precise roll angle measurements. Owing to the diffraction characteristics of the transmission grating and reflection characteristics of the corner cube, two spatially separated parallel beams are naturally constructed. Through differential detection of the positions of two parallel beams, we experimentally demonstrate the possibility of a precise roll angle measurement at a high refresh rate. A performance evaluation of the proposed technique indicates a stability of 0.46 arcsec over 5 min. Compared with a commercial autocollimator over a range of 500 arcsec, the residuals are maintained within ±2 arcsec with a standard deviation of 1.37 arcsec. Furthermore, a resolution of 0.8 arcsec can be achieved using the proposed method. The developed compact roll angle sensor has potential applications in academic and industrial fields.

Large-field step-structure surface measurement using a femtosecond laser.

We present a femtosecond laser-based interferometry for step-structure surface measurement with a large field of view. A height axial scanning range of 348 µm is achieved by using the method of repetition frequency scanning with reference to the Rb atomic clock and the optical path length difference design for 21 times of the pulse interval. A combined method, which includes the envelope peak positioning method for rough measurement, synthetic-wavelength interferometry for connection, and carrier wave interferometry for fine measurement, is proposed to reconstruct the surface. A three-step specimen with heights of approximately 20, 50, and 70 µm was successfully measured with a height precision of 7 nm, and the accuracy was verified by a commercial white light interferometer. The diameter of the field of view that was demonstrated was 17.3 mm, which could be much larger owing to the high spatial coherence of the femtosecond laser. The results show that the femtosecond laser system combines the step-structure measurement performance of white light interferometry and the high-precision large-field performance of phase shifting interferometry, indicating its potential for widespread use in ultra-precision manufacturing of micro/nano-devices, such as semiconductor chips, integrated circuits, and micro-electro-mechanical systems.

An FPGA Platform for Next-Generation Grating Encoders.

Among various nanometer-level displacement measurement methods, grating interferometry-based linear encoders are widely used due to their high robustness, relatively low cost, and compactness. One trend of grating encoders is multi-axis measurement capability for simultaneous precision positioning and small order error motion measurement. However, due to both lack of suitable hardware data processing platform and of a real-time displacement calculation system, meeting the requirements of real-time data processing while maintaining the nanometer order resolutions on all these axes is a challenge. To solve above-mentioned problem, in this paper we introduce a design and experimental validation of a field programmable gate array (FPGA)-cored real-time data processing platform for grating encoders. This platform includes the following functions. First, a front-end photodetector and I/V conversion analog circuit are used to realize basic analog signal filtering, while an eight-channel parallel, 16-bit precision, 200 kSPS maximum acquisition rate Analog-to-digital (ADC) is used to obtain digital signals that are easy to process. Then, an FPGA-based digital signal processing platform is implemented, which can calculate the displacement values corresponding to the phase subdivision signals in parallel and in real time at high speed. Finally, the displacement result is transferred by USB2.0 to the PC in real time through an Universal Asynchronous Receiver/Transmitter (UART) serial port to form a complete real-time displacement calculation system. The experimental results show that the system achieves real-time data processing and displacement result display while meeting the high accuracy of traditional offline data solution methods, which demonstrates the industrial potential and practicality of our absolute two-dimensional grating scale displacement measurement system.

Patterning nanoscale crossed grating with high uniformity by using two-axis Lloyd's mirrors based interference lithography.

A two-axis Lloyd's mirrors interferometer based optical fabrication system was theoretically investigated and constructed for patterning high-uniformity nanoscale crossed grating structures over a large area with a high throughput. The current interferometer was configured with two reflected mirrors and a grating holder, which are placed edge by edge and orthogonal with each other. In such a manner, the two beams reflected from the two mirrors interfere with the incident beam, respectively, forming a crossed grating patterns with only one exposure. Differing from the conventional solution for elimination of unexpected interference between the two reflected beams, a systematical analysis, that is based on the proposed index indicating the non-orthogonality between the two beams at different incident angles, was conducted by using a spatial full polarization tracing method. Without polarization modulation to eliminate the additional interference, an optimal exposure condition with small non-orthogonality between reflected beams was found at a certain incident angle range, while the two required interferences to construct cross grating still remain high. A pattern period of ∼1 µm-level crossed grating structure could be obtained through balancing the structure area and the non-orthogonality. Finally, the exposure setup with orthogonal two-axis Lloyd's mirrors interferometer is established, and the crossed grating structure with the periods of 1076 nm along X-direction and 1091 nm along Y-direction was successfully fabricated on a silicon substrate via microfabrication technology over a large area of 400 mm2. The uniformity of crossed grating array over the whole area was evaluated by an atomic force microscope, and the standard deviations of structure periods along X- and Y-directions smaller than 0.3% are achieved. It is demonstrated that the orthogonal two-axis Lloyd's mirrors interferometer based on single-beam single-exposure scheme with non-orthogonality systematic analysis is an effective approach to fabricate crossed grating patterns of 1 µm-level period with high uniformity over a large area.

Multi-pulse sampling dual-comb ranging method.

A multi-pulse sampling dual-comb ranging (MS-DCR) method is proposed in this paper. Four sampling pulses and two signal pulses separated in the time domain are generated in a repetition period by fiber delay. Through multi-pulse linear optical sampling, eight cross-correlation interferograms (IGMs) are generated in an updating period. The proposed method realizes the multiplication of IGMs so that additional ranging results can be obtained. The experimental results demonstrate that we suppress any random noise by averaging the ranging results and improve the precision of the time-of-flight (TOF) method and carrier-wave interferometric (CWI) method simultaneously. The precision of TOF is improved from 3.85 µm to 1.39 µm without time averaging and that of CWI is improved from 25 nm to 11 nm. The TOF result can link to the interferometric phase with 15 ms averaging, and a precision of 0.48 nm is reached with 0.5 s averaging. The proposed technique overcomes the limitations of linear optical sampling in conventional dual-comb interferometers and achieves faster and higher precision distance measurements without decreasing the unambiguity range.