Multi-wavelength Interferometry Research Articles

Multi-wavelength pinhole point diffraction interferometry for optics metrology with interferometric intensity based phase retrieval method

In this paper, we propose a multi-wavelength pinhole point diffraction interferometry (MPPDI) and a two-step phase extraction method based on the interferometric intensity information. MPPDI is mainly used to extend the dynamic measurement range of traditional pinhole point diffraction interferometry (PPDI) to realize the measurement of large-aperture and high-order aspheric surface. Spherical/aspherical optics will be test under three different wavelengths, and the corresponding interferograms are recoded by 3CMOS detector at the same moment. By combining different wavelengths, MPPDI can obtain a synthetic wavelength with a larger measuring range and greater flexibility. In interferometry, the choice of the wavelength of the light source has a great influence on the measurement range and accuracy. In MPPDI, we can choose different wavelength combinations to select the most suitable synthetic wavelength according to the asphericity of the tested mirror. To enhance efficiency and reduce the impact of air disturbances during phase shifts, we propose a new phase extraction method based on interferometric intensity to interpret the phase map of surface information. The background intensity of diffraction wavefront is firstly pre-recorded by 3CMOS, then phase-shift interferograms of test mirror is acquired with two-step piezoelectric ceramic driver (PZT) movement. From the analysis, it can be found that fringe modulation has tiny influence on the interferograms intensity. Therefore, based on global intensity distribution of fringe pattern and grayscale information, phase map can be retrieval using proposed two-step processing method (only single phase-shift). The two-step phase extraction method can reduce the number of phase shifts from 9 to 3, which improves the efficiency and reduces errors due to multiple phase shifts. MPPDI and two-step phase extraction we proposed have a larger measurement while reducing the number of phase shifts and avoiding error accumulation due to too many phase shifts. Suitable for large-aperture and high-order aspheric surface measurement.

Length measurement based on multi-wavelength interferometry using numerous stabilized frequency modes of an optical comb

Abstract The electro-optic comb (EO comb) with a relatively wide mode spacing of 25 GHz can be resolved into individual frequency modes with a commercially available high-resolution spectrometer. The EO comb has numerous discrete frequency modes, which can serve as a light source for a monochromatic laser interferometer to realize the meter. In this study, a method for measuring the absolute distances based on the multi-wavelength interferometer principle is proposed and demonstrated by simultaneously implementing 102 monochromatic laser interferometers using an EO comb. A phase shifting technique was used to determine the phase for each frequency mode by precisely translating a reference mirror with a constant interval. The phases of the interference signals for 102 stabilized individual frequency modes were measured by applying the model-based analysis on the phase-shifted interference signals. The absolute distance can be determined using phase values of a wavelength set corresponding to five to seven randomly selected frequency modes. In this study, the absolute distances for round-trip distances of 166 mm and 1316 mm were measured and the measurement uncertainty of each distance was evaluated. Through the uncertainty analysis of the distance measurement, the combined uncertainties of the measured distances in a short and long ranges were evaluated to be 30.1 nm and 211.1 nm, respectively. In addition, for each distance, the consistent measurement results of absolute distances were obtained through four different wavelength sets, which show the flexibility of wavelength selection in this work.

Sub-micron inline thickness measurement of cold-rolled metal strips by multi-wavelength interferometry and laser triangulation.

Thin metal foils of thicknesses below 100 µm are finding increasing use in high-tech applications. For such foils it is essential that production be controlled inline with sub-micron accuracy in highly challenging environments. An optical thickness gauge combining laser triangulation with multi-wavelength interferometry has now been developed for this purpose. Modulation-based 2f-3f-interferometry was used to realize a compact and robust sensor. A thorough measurement uncertainty analysis of the complete thickness measurement process yielded an expanded measurement uncertainty of U=(0.30μm)2+4π R a2, which is dependent on the roughness average Ra. The influence of oil remnants on measurement results is significantly weaker in the interference measurement than in geometric optical systems. Verification measurements against tactile reference measurements support the derived measurement uncertainty, and initial measurements in actual rolling mill environments have proven the real-world capability of this measurement technique over relevant process time scales at metal strip speeds of 200 m/min.

Simultaneous Phase Detection of Multi-Wavelength Interferometry Based on Frequency Division Multiplexing

Simultaneous phases detection in multi-wavelength interferometry (MWLI) is essential for high-accuracy dynamic absolute distance measurement in high-end equipment manufacturing. To address this problem, a simultaneous phase detection scheme based on frequency-division multiplexing (FDM) technique is proposed in this paper. High-frequency sinusoidal phase modulation with non-overlapping frequencies were applied to multiple lasers individually using electro-optic modulators (EOMs), and interference phases of multiple wavelengths were extracted in parallel using phase generated carrier (PGC) demodulation technique from the FDM interference signal. Principles of FDM multi-wavelength interferometry and simultaneous phase detection scheme were illustrated. A FDM dual-wavelength interferometer was constructed to verify the performance of the proposed phase detection scheme by simulation analysis and experiments. Results of simulations show that the resolution, accuracy and nonlinear error of the two demodulated phases are all better than 0.01°. Experiments of nanometer displacement measurement further verified the good performance of the phase detection scheme and its feasibility in dynamic measurement.

Statistical analysis of phase values for the determination of step heights in multi-wavelength interferometry

Abstract To determine step heights between a few nanometers and several micrometers, we present a statistical evaluation procedure which overcomes the limitations of the unambiguity range of conventional multi-wavelength interferometry. The experimental setup consists of a shear interferometer with two different wavelengths to measure the phase difference between light reflected from an object with regions of two different heights. The statistical averaging over a large area of both regions of the object for both wavelengths generates a pair of phase difference values. A diagram of the space of phase values converts the pair of phase difference values into a step height. This statistical method enables the determination of step heights greater than the synthetic wavelength with an accuracy of a few nanometers even with small tilts of the object.

Exploiting Wavelength Diversity for High Resolution Time-of-Flight 3D Imaging

The poor lateral and depth resolution of state-of-the-art 3D sensors based on the time-of-flight (ToF) principle has limited widespread adoption to a few niche applications. In this work, we introduce a novel sensor concept that provides ToF-based 3D measurements of real world objects and surfaces with depth precision up to 35m and point cloud densities commensurate with the native sensor resolution of standard CMOS/CCD detectors (up to several megapixels). Such capabilities are realized by combining the best attributes of continuous wave ToF sensing, multi-wavelength interferometry, and heterodyne interferometry into a single approach. We describe multiple embodiments of the approach, each featuring a different sensing modality and associated tradeoffs.

Absolute distance measurement using laser interferometric wavelength leverage with a dynamic-sideband-locked synthetic wavelength generation.

Absolute distance measurement with laser interferometry has the advantages of high precision and traceability to the definition of meter but its accuracy is primarily limited by the phase demodulation. Among kinds of absolute distance interferometric measurements, the multi-wavelength interferometry is widely used but seriously limited by the generation of suitable synthetic wavelength and the stability of adopted synthetic wavelength. Inspired by the mechanical lever, we hereby establish a principle of laser interferometric wavelength leverage (LIWL) for absolute distance measurement. By keeping the phase difference in two single wavelengths constant, LIWL achieves the measurement of large distance with respect to synthetic wavelengths by detecting nanometer displacement with respect to a single wavelength. The merit of LIWL is eliminating the influence of phase demodulation error. And a dynamic-sideband locking method based on a high-frequency electro-optic modulator is proposed, which can flexibly and quickly generate variable synthetic wavelengths from tens of kilometer to millimeter with high stability. Experimental setup was constructed and absolute distance measurements were performed. Experimental results show that a measurement range of 100 m with residual error of less than 15 µm has been achieved by comparing the LIWL system and an incremental laser interferometer.

Dual-wavelength interferogram decoupling method for three-frame generalized dual-wavelength phase-shifting interferometry based on deep learning

In dual-wavelength interferometry, the key issue is how to efficiently retrieve the phases at each wavelength using the minimum number of wavelength-multiplexed interferograms. To address this problem, a new dual-wavelength interferogram decoupling method with the help of deep learning is proposed in this study. This method requires only three randomly phase-shifted dual-wavelength interferograms. With a well-trained deep neural network, one can obtain three interferograms with arbitrary phase shifts at each wavelength. Using these interferograms, the wrapped phases of a single wavelength can be extracted, respectively, via an iterative phase retrieval algorithm, and then the phases at different synthetic beat wavelengths can be calculated. The feasibility and applicability of the proposed method are demonstrated by simulation experiments of the spherical cap and red blood cell, respectively. This method will provide a solution for the problem of phase retrieval in multiwavelength interferometry.

Choosing wavelengths and assessing blunder risk for the method of exact fractions

We revisit the problem of choosing combinations of sources for multi-wavelength interferometry, using the risk of assigning the wrong integer interference order to a measured phase as a quantitative criterion. We model this risk, explicitly accounting for the experimenter’s ability to reject implausible measurement results. We present a general reliability limit for the method of exact fractions, which can be used as a benchmark when evaluating wavelength combinations, as well as performance estimates for several promising combinations.

Wavelength-Demultiplexed Laser Interferometry for Metrology

Non-contact, cost-efficient, and long-range precision metrology is essential for applications in diverse areas, from 3D sensing and robotics to automated manufacturing, and multiwavelength interferometry is a compelling candidate. Here, we present a new arithmetic approach for multiwavelength phase unwrapping, with the maximum theoretical range and tolerance to measurement noise in phase. We supplement our formulation with a simultaneous phase shifting interferometry setup with a low measured standard deviation of phase, σφ = 2π/1325. We unwrap the interferometric phases of experiments performed through wavelengths with a greatest common divisor of 25 nm, demonstrate a range equal to their lowest-common-multiple with the precision of a single wavelength interferometer, and reconstruct three-dimensional scenes based on a single-pixel 3D imaging system.

Real-time absolute distance measurement by multi-wavelength interferometry synchronously multi-channel phase-locked to frequency comb and analysis for the potential non-ambiguity range

Real-time absolute distance measurement by multi-wavelength interferometry synchronously multi-channel phase-locked to frequency comb and analysis for the potential non-ambiguity range

A method for simultaneously measuring 6DOF geometric motion errors of a precision rotary stage based on absolute position-distance measurement

In this paper, an absolute position-distance measurement based method for simultaneous measurement of six-degree-of-freedom (6DOF) errors of a precision rotary stage is proposed. This method uses the multi-wavelength phase-shifting interferometry technology and high-speed CCD camera to measure the instantaneous absolute spatial posture of the specially designed micro structure feature following the movement of a measured rotary stage. By analyzing the spatial posture of a series of instantaneous micro structure features, the 6DOF errors of the precision rotary stage are separated. The simultaneous, high precision and dynamically continuous measurement of 6DOF errors of the precision rotary stage is achieved. To improve the accuracy of error analysis, a model of 6DOF errors of the precision rotary stage is established to determine the mapping relationship between the 6DOF errors and the spatial posture of the micro structure feature. A test platform for 6DOF geometric motion errors of the precision rotary stage is built. The measurement results demonstrate the effectiveness and accuracy of the proposed method.

Unambiguous measurement range and error tolerance in dual-wavelength interferometry.

In dual or multiwavelength interferometry, the traditional equivalent wavelength method is widely used for phase recovery to enlarge the unambiguous measurement range (UMR). In fact, however, this method ignores information of size and sign (positive or negative) of single wavelength wrapped phases, and the extension of the UMR is not sufficient. For the reflective measurement, the largest UMR of the dual or multiwavelength interferometry is half of the least-common multiple (LCM) of single wavelengths, called the LCM effective wavelength, which is often several times the equivalent wavelength. But why do we often use the equivalent wavelength and seldom use the larger UMR in practice? Existing research reveals that the actual UMR is related to the measurement error of single-wavelength-wrapped phases, and half of the LCM effective wavelength is only the theoretical value. But how do errors affect the UMR? We think the quantitative analysis and description are lacking. In this paper, we continue to study this problem, analyze it in a graphical method, and give quantitative descriptions. The simulation experiments are carried out and verify our analysis.

Multi-wavelength phase-shifting interferometry based on a two-step phase-shifting phase retrieval algorithm with a color CMOS

By combining the advantages of multi-wavelength phase-shifting interferometry and two-step phase-shifting phase retrieval algorithm, a measured phase with high precision and a large measuring range can be retrieved rapidly from three multi-wavelength interferograms with unknown phase shifts, recorded by a single-chip color CMOS. Firstly, two normalized differential interferograms without backgrounds are obtained by means of subtraction followed by normalization between the three color interferograms. Next, the wrapped phases of a single wavelength are retrieved via the Gram–Schmidt orthonormalization approach. Finally, the unambiguous phase of the three synthetic wavelengths can be achieved by subtraction between the wrapped phases of corresponding wavelengths. To reduce the phase noise amplification introduced by the magnification of wavelengths, the phase unwrapping algorithm of reducing the noise of the three- synthetic wavelength to the level of a two-synthetic long wavelength, a single-wavelength, and a two-synthetic short wavelength are implemented in turn. Compared with conventional multi-wavelength phase shifting interferometry, only three interferograms with unknown phase shifts are needed to reconstruct the actual phase of the measured object to a high degree of measurement resolution, and with a large measurement range; this approach would be useful in dynamic phase measurement. Both simulation and experimental results validate the performance of the proposed method.

Combining Harmonic Laser Beams by Fiber Components for Refractivity–Compensating Two-Color Interferometry

A perfect spatial overlap with multiple beams of different wavelengths is a prerequisite for multi–wavelength interferometry. Beam combination with the help of fibers seems to be an interesting method for this. We investigated three different types of fiber components, multi–mode wavelength division multiplexers (MM–WDMs), single–mode wavelength division multiplexers (SM–WDMs), and endlessly single–mode polarization maintaining photonic crystal fibers (PM–PCFs). All three seem potential candidates for a perfect spatial overlap of laser beams separated by an octave, i.e. fundamental and harmonic beams. We performed an experimental study on the impact of these components on polarization, wavefront, and coherence. These properties are essential for high–accuracy interferometry. As a test system, we used the fundamental and second harmonic beam of a Nd:YAG laser system at 1064 and 532 nm as a popular system in two–color interferometry for intrinsic refractive index compensation. The experimental results show the potential of PM–PCFs for this challenging application.

Distance Measurements Using Mode-Locked Lasers: A Review

We present a progress review on the advance of distance measurements made at KAIST by making use of mode-locked lasers as the light source to meet ever-growing industrial demands on the measurement precision and functionality. Diverse principles exploited for the progress are described in this review with focus on four attributes: first, the optical spectrum of a mode-locked laser, distinctively called the frequency comb, permits multi-wavelength interferometry to be realized for absolute distance measurement up to several meters without losing the nanometer precision of well-established laser-based phase-measuring displacement measurement. Second, the frequency comb enables spectrally resolved interferometry for absolute distance measurement to be conducted with a nanometer resolution by Fourier transform analysis of the dispersive interference data captured using a spectrometer. Third, the mode-locked laser in the time domain appears as a train of ultrashort pulses, of which the time-of-flight is measured with a picosecond resolution by control of the pulse repetition rate with reference to the radio-frequency atomic clock. Fourth, the pulse-to-pulse cross-correlation occurring in the optical frequency domain is down-converted to the radio-frequency domain to achieve femtosecond pulse timing precision by means of dual-comb interference. All these principles based on unique spectral and temporal characteristics of ultrashort mode-locked lasers are anticipated to make contributions to the advance of nanotechnology particularly in manufacturing and metrology.

Sinusoidal phase modulating absolute distance measurement interferometer combining frequency-sweeping and multi-wavelength interferometry.

A sinusoidal phase modulating absolute distance measurement (ADM) interferometer combining frequency-sweeping interferometry (FSI) and multi-wavelength interferometry (MWI) is proposed in this paper. The swept frequency in FSI and the wavelengths for MWI are calibrated by an optical frequency comb, so the distance measurement can be directly traced back to the SI definition of a meter. With a simple optical structure, an ADM interferometer consisting of a measurement interferometer and a monitor interferometer is constructed without polarization optics. A near-infrared external cavity diode laser (ECDL) calibrated by an optical frequency comb is used as a work source of the measurement interferometer for frequency sweeping and hopping. The monitor interferometer using a He-Ne laser runs parallel to the measurement interferometer to monitor the fluctuation of the measured distance during the measurement. Experiments for absolute distance measurements in a range of 8.25 m were carried out to verify the feasibility of the proposed ADM interferometer. The experimental results show that the maximum measurement error is less than 1 μm compared with an incremental-type laser interferometer.

Real-Time and Meter-Scale Absolute Distance Measurement by Frequency-Comb-Referenced Multi-Wavelength Interferometry.

We report on a frequency-comb-referenced absolute interferometer which instantly measures long distance by integrating multi-wavelength interferometry with direct synthetic wavelength interferometry. The reported interferometer utilizes four different wavelengths, simultaneously calibrated to the frequency comb of a femtosecond laser, to implement subwavelength distance measurement, while direct synthetic wavelength interferometry is elaborately introduced by launching a fifth wavelength to extend a non-ambiguous range for meter-scale measurement. A linearity test performed comparatively with a He–Ne laser interferometer shows a residual error of less than 70.8 nm in peak-to-valley over a 3 m distance, and a 10 h distance comparison is demonstrated to gain fractional deviations of ~3 × 10−8 versus 3 m distance. Test results reveal that the presented absolute interferometer enables precise, stable, and long-term distance measurements and facilitates absolute positioning applications such as large-scale manufacturing and space missions.

Long distance measurement up to 1.2 km by electro-optic dual-comb interferometry

We perform a long distance measurement up to 1.2 km on the outdoor baseline by electro-optic dual-comb interferometry. A frequency comb pair is developed by phase modulating a continuous laser with a narrow linewidth, and the slightly different repetition frequencies are synchronized to the Rb clock via the signal generators. A RF electrical comb can be generated by multi-wavelength heterodyne interferometry, and thus, a series of synthetic wavelengths can be obtained, whose phases can be used to determine the distances. Compared with the reference values, the experimental results show an agreement within 379 μm in the 1180 m range. In the long-time experiments, the Allan deviation can be below 20 μm with an averaging time of 10 s, and can be further improved to be less than 600 nm when the averaging time is above 350 s at 435 m and 1180 m, respectively.

High-accuracy long distance measurements with a mode-filtered frequency comb

Homodyne interferometry with a frequency comb as multi-wavelength source is a powerful method to measure long distances with high accuracy. The measurement principle requires that individual comb modes are spectrally resolved, making hundreds or thousands of accurately known wavelengths available for interferometry. For this reason the method cannot be applied directly to frequency combs with a low repetition rate (e.g. 100 MHz), since the modes are too close to be resolved. In this paper we use cavity mode filtering to increasing the pulse repetition rate of a comb and we apply the filtered comb for mode-resolved absolute distance measurement. Mode-filtering takes place with a single Fabry-Perot cavity in a Vernier configuration, allowing to set mode spacings ranging from 10s of GHz to more than 100 GHz. Large mode-spacings significantly reduce the requirements on the resolution of the spectrometer. We demonstrate absolute long distance measurement with a mode-filtered frequency comb using a simple array spectrometer for mode-resolved detection. Here a 1 GHz comb is used, that is converted into a 56 GHz comb by mode-filtering. A trade-o between non-ambiguity range and spectral resolution needs to be made when choosing a filter ratio. The pulse-to-pulse distance after filtering is 5.3 mm in this case, so to overcome ambiguity a rough measurement with an accuracy of about 2.5 mm is required. We show that in comparison to a conventional counting interferometer an agreement within 0.5 µm for distances up to 50 m is found. The presented method may enable the field application of low-repetition rate frequency comb lasers, like fiber lasers, for multi-wavelength homodyne interferometry. It relaxes the requirements on the spectral resolution, allowing for simple grating spectrometers as detector.