Two-wavelength Interferometry Research Articles

Phase space analysis of two-wavelength interferometry.

Multiple wavelength phase shifting interferometry is widely used to extend the unambiguous range (UR) beyond that of a single wavelength. Towards this end, many algorithms have been developed to calculate the optical path difference (OPD) from the phase measurements of multiple wavelengths. These algorithms fail when phase error exceeds a specific threshold. In this paper, we examine this failure condition. We introduce a "phase-space" view of multi-wavelength algorithms and demonstrate how this view may be used to understand an algorithm's robustness to phase measurement error. In particular, we show that the robustness of the synthetic wavelength algorithm deteriorates near the edges of its UR. We show that the robustness of de Groot's extended range algorithm [Appl. Opt.33, 5948 (1994)APOPAI0003-693510.1364/AO.33.005948] depends on both wavelength and OPD in a non-trivial manner. Further, we demonstrate that the algorithm developed by Houairi and Cassaing (HC) [J. Opt. Soc. Am. A26, 2503 (2009)JOAOD60740-323210.1364/JOSAA.26.002503] results in uniform robustness across the entire UR. Finally, we explore the effect that wavelength error has on the robustness of the HC algorithm.

Two-wavelength interferometry for measurement of transonic airflow in a compressor blade cascade

This paper presents high-speed two wavelength interferometry for measuring fast phenomena, which allows to extend the dynamic range of measurement using two different wavelengths at the same time. The method was applied to measure transonic airflow through a blade cascade

Noise-resistant two-wavelength interferometry for single-shot measurement of high-gradient flows

This paper presents a new robust approach to measuring dynamic phenomena with high gradients using two-wavelength high-speed interferometry. A multiplexed interferogram with two different wavelengths and spatial-carrier frequencies is captured by a single high-speed camera shot. Quantitative processing of the interferogram is based on Fourier analysis, which is followed by a robust procedure to retrieve the unwrapped phase map with single-wavelength accuracy but with an extended range of unambiguity. This method is significantly more noise-resistant than the standard two-wavelength technique, which is sensitive to noise and synthetic phase distortion. The method was successfully applied to studying shock waves in a transonic compressor blade cascade in an industrial aerodynamic laboratory, where single-wavelength and standard two-wavelength approaches fail.

Digital holographic system for layer-by-layer control of additively manufactured component quality

Subject of study. A digital holographic system for layer-by-layer control of component quality in additive manufacturing able to determine the size and depth of defects on the surface of each layer was investigated. Method. The digital holographic system for layer-by-layer control of component quality in additive manufacturing operates based on a two-wavelength holographic interferometry method. The digital holographic system is based on a Michelson interferometer. The considered method involves recording holograms of the surface of each component layer at two adjacent wavelengths. As a result of hologram reconstruction, the complex amplitudes of the object wave in the reconstruction plane are determined, which, in turn, define the phases of the waves and their difference. The wave phase difference allows the depth of the defect on the component layer surface to be determined. A tunable diode laser and camera based on a CCD matrix are used as the radiation source and detector, respectively. Main results. The results of the investigation of the surfaces of additively manufactured components using the two-wavelength holographic interferometry method are presented. The recognition of large irregularities is possible through expansion of the phase pattern. The detection of surface defects with the size of 25 µm is demonstrated. The reconstructed surface of a component manufactured by laser sintering of successive layers using the M250 additive setup for selective laser sintering and the reconstructed surface of a millimeter-scale macroscopic object are presented. Practical significance. The possible use of the digital holographic system for component quality control in industrial settings, including those applying additive technologies, is demonstrated. The component quality criterion is the absence of defects (cavities or protrusions) with size larger than 25 µm.

Two-wavelength digital holographic interferometry for unambiguous range extended measurements in fluid mechanics

Non-contact optical methods such as digital holographic interferometry are highly suitable in measurements where the phenomena is fast, performed in transparent or semi-transparent environment and mustn’t be obstructed as when applying local contact techniques. Such specific application can be studying dynamic events during transonic and supersonic blade flutter. Fast, sensitive and rather easy access to the phase information make these techniques very attractive in the study of phase objects/phenomena. However, since light’s phase is bounded to a repetitive cycle of 2π radians, the range of measurement is limited to one cycle of the phase, limiting applications to small gradient phenomena. This paper presents a new interesting way of by-passing this limitation, while still keeping noise values low, by introducing a second laser with a close value wavelength, giving rise to a new interferometric pattern with an extended unambiguous range of measurement. Image acquisition is done simultaneously for both wavelengths and all reconstructions are digitally performed. The principle and preliminary results are included in this paper.

Full-field heterodyne phase shifting two-wavelength interferometry surface testing technologies

Full-field heterodyne phase shifting two-wavelength interferometry surface testing technologies

Correction of periodic displacement non-linearities by two-wavelength interferometry

Non-linearities in interferometric displacement measurements commonly affect both homodyne and heterodyne optical interferometers. Unwanted back reflections (ghost reflections) or polarisation leakage introduce non-linearity terms at harmonics of the illuminating wavelength that cannot be fully corrected for with standard non-linearity correction techniques. A two-wavelength interferometric approach, operating at 632.8 and 785 nm, is presented here that is capable of correcting such non-linearities. Non-linearities are separated from the difference between two displacement measurements made at differing wavelengths with a Fourier approach. Compared to a standard Heydemann ellipse fitting correction, the proposed approach reduces estimated residual non-linearities from 84 to 11 pm in the case of a linear displacement profile. In particular this approach is applicable to the correction of higher order non-linearities that are caused by multiple reflections, and that are therefore very sensitive to alignment conditions.

High-dynamic range segmented mirror metrology by two-wavelength PISTIL interferometry: demonstration and performance.

The PISTIL interferometry has been recently developed for the wavefront sensing of phase delays (pistons) and tilts of segmented surfaces, used in many domains such as astronomy, high-power lasers or ophthalmology. In this paper, we propose a two-wavelength version of this interferometer developed to bypass the dynamic range limitation of the ambiguous 2π phase wrapping. Principle of the technique is presented, along with experimental results obtained with a demonstration deformable mirror PTT-111 from Iris AO. Above wavelength pistons are measured with a precision and accuracy below λ/100, making the two-wavelength PISTIL interferometry a high-dynamic range technique. To prove these performances, we successfully compare the results in terms of precision and accuracy with those of a reference phase-shifting Interferometer, from a blind experimentation.

Single-Shot Imaging of Two-Wavelength Spatial Phase-Shifting Interferometry.

In this investigation, we propose an effective method to measure 3D surface profiles of specimens with single-shot imaging. Based on the two-wavelength interferometric principle and spatial phase-shifting technique using a polarization pixelated camera, the proposed system can not only rapidly measure the phase, but also overcome the 2π-ambiguity problem of typical phase-shifting interferometry. The rough surface profile can be calculated by the visibility of the interference fringe and can compensate for the height discontinuity by phase jumps occurring in a fine height map. An inclined plane mirror and a step height specimen with 9 μm were used for the validation of capability of measuring continuously smooth surface and large step heights. The measurement results were in good agreement with the results of typical two-wavelength interferometry.

Radial Hilbert transform for phase retrieval using two-wavelength three-frame phase-shifting interferometry

Dual-wavelength interferometry (DWI) without phase unwrapping is widely applied in optical measurement and imaging. For improving measurement efficiency and increasing the range of applications, a method of retrieving a phase using fewer interferograms and shorter calculating time is proposed in this study. The proposed method requires only three multiplexed and phase-shifted interferograms. By subtracting the other two interferograms from the first frame image and using the Hilbert transform (HT), we first obtained the phase at each wavelength and then calculated the continuous phase at the synthetic wavelength. The method is applicable to open-loop fringes obtained in an off-axis interferometric system and closed-loop fringes obtained in an on-axis system. We used a combination of the radial HT and coordinate conversion method to solve the problem of having to use the conventional HT for closed-loop fringes. The feasibility and applicability of the method are verified using simulation and experimental results.

Optical Acceleration Measurement Method with Large Non-ambiguity Range and High Resolution via Synthetic Wavelength and Single Wavelength Superheterodyne Interferometry.

Interferometric optomechanical accelerometers provide superior resolution, but the application is limited due to the non-ambiguity range that is always less than half of the wavelength, which corresponds to the order of mg. This paper proposes a novel acceleration measurement method based on synthetic wavelength and single wavelength superheterodyne interferometry to address this issue. Two acousto-optical modulators and several polarizers are introduced to the two-wavelength interferometry to create four beams with different frequencies and polarization states, and two ultra-narrow bandwidth filters are used to realize the single wavelength measurement simultaneously. This technique offers the possibility to expand the non-ambiguity range without compromising the high resolution. Also, the superheterodyne phase measurement and the corresponding processing algorithm are given to enable real-time measurement. A prototype is built and the preliminary experimental results are compared with the simulation results, showing good agreement. The results prove an estimated acceleration measurement resolution of around 10 μg and a non-ambiguity range of larger than 200 mg, which is more than 100 times that of the single wavelength-based optical accelerometer.

Study of density distribution of electrical exploding tungsten wire in air

The density distribution is important information in the investigation of electrical exploding wires in the air. In this study, the density profiles of the electrons, tungsten atoms, and air at different instants were reconstructed based on a two-wavelength interferometry method. The experiment was carried out on a 1 kA, 0.1 kA/ns pulsed current generator, with a fine tungsten wire (10 μm in diameter). The laser probing images of the exploding products showed a two-layer structure, exhibiting a shunting discharge scenario. The fitted expanding trajectory of the dense core indicates that the expansion of the wire starts at the instant of the voltage drop. The reconstructed densities show the distribution of particles in the expansion process of the exploding wire. It is found that the wire core has a tube-like structure, and the plasma channel is located around the core boundary.

Multi-object investigation using two-wavelength phase-shift interferometry guided by an optical frequency comb

Two-wavelength phase-shift interferometry guided by optical frequency combs is presented. We demonstrate the operation of the setup with a large step sample simultaneously with a resolution test target with a negative pattern. The technique can investigate multi-objects simultaneously with high precision. Using this technique, several important applications in metrology that require high speed and precision are demonstrated.

Measurement of transient gas temperature with two-wavelength laser interferometry

Measurement of transient gas temperature with two-wavelength laser interferometry

Development of dual-wavelength fiber ring laser and its application to step-height measurement using self-mixing interferometry.

A dual-wavelength erbium-doped fiber (EDF) ring laser was developed and its application to step-height measurement using two-wavelength self-mixing interferometry (SMI) was demonstrated. The fiber laser can emit two different wavelengths without any laser mode competition. It is composed of two EDF laser cavities and employs fiber Bragg gratings to determine which wavelengths are emitted. The step heights can be measured using SMI of the two wavelengths, and the maximum height that can be measured is half the synthetic wavelength of the two wavelengths. A step height of 1mm was constructed using two gauge blocks and then measured using the laser. The measurement was repeated ten times, and the standard deviation of the measurements was 2.4nm.

The Image Processing Algorithm of Surface Topography Based on Laser Interference Measurement

In the measurement methods of microcosmic surface topography, laser interference microscopy with high precision and non-contact advantages, has been widely used. Based on the current processing algorithms of interference image, this paper studies principally the processing algorithms of single-wavelength laser interferometry and analyses the image processing algorithm of two-wavelength laser interferometry. On the basis of the original measurement precision, the two-wavelength measurement method can extend the depth measurement range and restore effectively the tested surface topography.

Improved and expanded measurements of transition probabilities in UV Ar ii spectral lines

Transition probabilities have a significant interest in the astrophysical field. The aim of this experiment is to extend the present data base of measured Ar II transition probabilities to the ultraviolet (UV) region and to improve the quality of some of the already existing data. Despite all the efforts made to assemble an accurate set of transition probabilities (Aki), some of the data recommended by the National Institute of Standards and Technology (NIST) for Ar II spectral lines in the UV region have uncertainties around 50percent. We measured relative intensities of spectral lines emitted from a low-pressure-pulsed discharge lamp which generates an argon plasma. Excitation temperatures of 19 000–22 000 K are determined from the Boltzmann-plot of 11 Ar II spectral lines for which accurate Aki data are available from the literature. The transition probabilities of these 11 spectral lines were used for calculating new Aki-values. Electron densities (Ne) of 3.5–9.0 × 10 22 m −3 are determined by two-wavelength interferometry method. The measurements yield to a collection of 43 atomic transition probabilities of Ar II lines in the spectral region of 294–386 nm, 11 of which are new, at least up to the authors knowledge, and 22 improved Aki-values for which the existing data in the literaturehaveuncertaintiesaround50percent.Comparisonwithprevious datashowshowour measurements have good agreement with the most accurate Aki-values from the bibliography, whereas some of the values recommended by NIST present a significant disagreement.

Divertor Erosion Monitoring in ITER Using Two-Wavelength Speckle Interferometry

ITER will operate long-time discharges (400 s) at high performances ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(Q=10\) </tex-math></inline-formula> ) and will have to satisfy strong safety and operational limits in term of tritium and dust inventory. This implies to control the erosion of the plasma facing components. Erosion monitoring diagnostic based on speckle interferometry and an optical design with its implementation in ITER are presented.

Correction of quadratic phase error in two-wavelength digital holographic interferometry using laser diodes

We present the correction of a quadratic phase error in two-wavelength digital holographic interferometry using laser diodes. This phase error arises from numerical reconstructions of wavefronts from digital holograms based on the Fresnel diffraction integral. To correct the quadratic phase error, it is numerically produced by computer on the basis of the theoretical prediction and is subtracted from the phase difference map in two-wavelength digital holographic interferometry. Experimental results show that the method of correction in this paper is useful for two-wavelength digital holographic interferometry using laser diodes.

Multispectral phase shifting interferometry algorithm

Standard phase shifting interferometry (PSI) algorithms are used to obtain phase map from fringe patterns. Their spectral properties can by analyzed using frequency transform function (FTF). In this paper new multispectral phase shifting interferometry algorithm (mPSI) has been proposed. It is combination of two simpler PSI algorithms and enables filtering out unwanted high frequency fringes from the image. It can be used to increase measurement range of standard interferometry by analyzing fringe pattern created by multiplication of two other fringe patterns recorded with the use two different wavelength. Numerical simulations of mPSI algorithm and results from real setup are shown in the paper. Full Text: PDF References J. Schmit, K. Creath,"Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry", Appl. Opt. 34 No. 19 3610 (1995) [CrossRef] J. Schmit, K. Creath,"Window function influence on phase error in phase-shifting algorithms", Appl. Opt. 35 No. 28 5642 (1996) [CrossRef] B. S. Lee,T. C. Strand,"Profilometry with a coherence scanning microscope", Appl. Opt. 29 No. 26 3784 (1990) [CrossRef] P. Hariharan, M. Roy,"White-light Phase-stepping Interferometry for Surface Profiling", J. Mod. Opt. 41 No 11 2197 (1994) [CrossRef] H. van Brug H, R. G., "On the effective wavelength in two-wavelength interferometry", Pure Applied. Opt. 7 1465 (1998) J. C. Wyant Optical Testing: Extended Range Two-Wavelength Interferometry (Optical Sciences Center University of Arizona) J. Schmit, P. Hariharan,"Two-wavelength interferometric profilometry with a phase-step error-compensating algorithm", Opt. Eng. 45, 115602 (2006) [CrossRef] Y. Cheng, J. C. Wyant,"Two-wavelength phase shifting interferometry", Appl. Opt. 23, No 24 4539 (1984) [CrossRef] P. de Groot,"Measurement of Transparent Plates with Wavelength-Tuned Phase-Shifting Interferometry", Appl. Opt. 39, No 16 2658 (2000) [CrossRef] M. Servin, J. C. Estrada, J. A. Quiroga, "The general theory of phase shifting algorithms", Opt. Exp. 17 No 24, 21867 (2009) M. Wengierow, L. Sałbut, Z. Ramotowski,"Interferometric multiwavelength system for long gauge blocks measurements", Proc. SPIE 8082, 80822R (2011) [CrossRef]