Twyman-Green Interferometer Research Articles

Development of novel interferometric system for short and long gauge block calibration

Abstract This paper presents the development of a novel multiwavelength Twyman–Green interferometer for gauge block (GB) calibration. In this work, a novel gauge block interferometer (GBI) for both short- and long-gauge block calibration at the SASO-NMCC was designed, built, tested, and described. The interferometer features an optomechanical modulation-based proprietary evaluation system, and the final length value was determined by applying Edlén’s equation to the refractive index of air. The developed interferometric system comprises two setups: one for short GB calibration, and the other for long GB calibration. The first short (GBI) setup utilizes two stabilized lasers, green and red, in vertical-mode operation. Another long GBI utilizes three stabilized lasers in the horizontal mode of operation. The primary characteristics of the interferometric system are explained. An uncertainty analysis with a careful study of the main components, such as wavelength standards, fringe fraction, temperature corrections, refractive index correction, obliquity correction, phase correction, block geometry correction, wavefront correction, and wringing correction, is presented. With interferometry, measurement method (ISO 3650 and ASME B89.1), using our described highly-precision horizontal mode system (GBI), we could achieve uncertainty level of ‘Q[49;0,28 l]nm l (mm)’ (k = 2) in the measurement range ‘125–1000 (mm)’. For the other system(GBI) for short gauge blocks, the associated uncertainty is ‘Q[30;0,27 l]nm l(mm)’ (k = 2) in the range of ‘0.5–100 (mm)’.

Large-range high-precision macroscopic common phase detection of segmented mirrors based on white light dynamic Twyman-Green interferometer

Segmented mirrors (SMs) provide a solution for the construction of the next generation of extremely large telescopes. The large-range, high-precision detection of piston error between mirror segments is a must-be solved problem in the application of SMs. This paper proposes a large-range high-precision macroscopic co-phase detection method of SMs based on white light dynamic Twyman-Green interferometer. By adopting a white light interferometry in the macroscopic co-phase detection, the probability of the occurring of the 2π ambiguity anomalies can be reduced. A piston error calculation model for SMs was established through Zernike fitting analysis, which improved the detection accuracy. A white light Twyman-Green interferometer with Kohler illumination was experimentally constructed. Based on the scanning of the reference mirror, an efficient detection of the piston error was achieved simultaneously with large range and high precision. Through the new method, the piston error of two planar mirrors was compensated from 38.9344 μm in coarse co-phase stage to 3.6 nm in fine co-phase stage. The method shows great potential for efficient co-phase adjustment of large primary segmented mirrors.

Temperature-Dependent Residual Stresses and Thermal Expansion Coefficient of VO2 Thin Films

This study aims to investigate the thermomechanical properties of vanadium dioxide (VO2) thin films. A VO2 thin film was simultaneously deposited on B270 and H-K9L glass substrates by electron-beam evaporation with ion-assisted deposition. Based on optical interferometric methods, the thermal–mechanical behavior of and thermal stresses in VO2 films can be determined. An improved Twyman–Green interferometer was used to measure the temperature-dependent residual stress variations of VO2 thin films at different temperatures. This study found that the substrate has a great impact on thermal stress, which is mainly caused by the mismatch in the coefficient of thermal expansion (CTE) of the film and the substrate. By using the dual-substrate method, thermal stresses in VO2 thin films from room temperature to 120 °C can be evaluated. The thermal expansion coefficient is 3.21 × 10−5 °C−1, and the biaxial modulus is 517 GPa.

Measuring the radius of curvature of spherical surfaces with actively tunable Fizeau and Twyman-Green interferometers

Accurate and repeatable measurement of the radius of curvature (RoC) of spherical sample surfaces is of great importance in optics. This importance lies in the ubiquitous use of spherical optical elements such as curved mirrors and lenses. Due to a high measurement sensitivity, interferometric techniques are often deployed for accurate characterization of the sample surface RoC. One method by which a typical commercial Fizeau or Twyman-Green (TG) interferometer measures surface RoC is via scanning between two principal retroreflective optical configurations—namely, the confocal and catseye configurations. Switching between these two configurations is typically achieved by moving an optical head along the axis of the propagating laser beam and the RoC is estimated by measuring the magnitude of mechanical motion to switch between the two principal configurations. In this paper, we propose a motion-free catseye/confocal-imaging-based sample RoC measurement system. The necessity of bulk motion to switch between the two configurations is circumvented via the use of an actively controlled varifocal lens. We demonstrate the usefulness of the proposed innovation in RoC measurements with either the TG or the Fizeau interferometer. Furthermore, we convert a commercial motion-based Zygo RoC measurement system into a motion-free one by introducing a tunable lens inside the apparatus and using it to accurately characterize the RoC of different test samples. We also compute the wavefront aberrations for all spherical sample surfaces from the recorded measurement data.

Laser Velocimetry for the In Situ Sensing of Deep-Sea Hydrothermal Flow Velocity.

Laser Doppler velocimetry (LDV) based on a differential laser Doppler system has been widely used in fluid mechanics to measure particle velocity. However, the two outgoing lights must intersect strictly at the measurement position. In cross-interface applications, due to interface effects, two beams of light become easily disjointed. To address the issue, we present a laser velocimeter in a coaxial arrangement consisting of the following components: a single-frequency laser (wavelength λ = 532 nm) and a Twyman-Green interferometer. In contrast to previous LDV systems, a laser velocimeter based on the Twyman-Green interferometer has the advantage of realizing cross-interface measurement. At the same time, the sensitive direction of the instrument can be changed according to the direction of the measured speed. We have developed a 4000 m level laser hydrothermal flow velocity measurement prototype suitable for deep-sea in situ measurement. The system underwent a withstand voltage test at the Qingdao Deep Sea Base, and the signal obtained was normal under a high pressure of 40 MPa. The velocity contrast measurement was carried out at the China Institute of Water Resources and Hydropower Research. The maximum relative error of the measurement was 8.82% when compared with the acoustic Doppler velocimeter at the low-speed range of 0.1-1 m/s. The maximum relative error of the measurement was 1.98% when compared with the nozzle standard velocity system at the high-speed range of 1-7 m/s. Finally, the prototype system was successfully evaluated in the shallow sea in Lingshui, Hainan, with it demonstrating great potential for the in situ measurement of fluid velocity at marine hydrothermal vents.

Simultaneous thickness and phase index measurements with a motion-free actively tunable Twyman-Green interferometer.

In this paper, we present a scheme to simultaneously measure the thickness and refractive index of parallel plate samples, involving no bulk mechanical motion, by deploying an electronically tunable Twyman-Green interferometer configuration. The active electronic control with no bulk mechanical motion is realized via the introduction of a tunable focus lens within the classical motion-based Twyman-Green interferometer configuration. The resulting interferometer is repeatable and delivers accurate estimates of the thickness and refractive index of a sample under test. Elimination of bulk motion also promises a potential for miniaturization. We develop a theoretical model for estimating sample thickness and index values using this reconfigurable interferometer setup and present detailed experimental results that demonstrate the working principle of the proposed interferometer.

Robust, motion-free optical characterization of samples using actively-tunable Twyman–Green interferometry

Optical interferometry-based techniques are ubiquitous in various measurement, imaging, calibration, metrological, and astronomical applications. Repeatability, simplicity, and reliability of measurements have ensured that interferometry in its various forms remains popular—and in fact continues to grow—in almost every branch of measurement science. In this paper, we propose a novel actively-controlled optical interferometer in the Twyman–Green configuration. The active beam control within the interferometer is a result of using an actively-controlled tunable focus lens in the sample arm of the interferometer. This innovation allows us to characterize transparent samples cut in the cubical geometry without the need for bulk mechanical motion within the interferometer. Unlike thickness/refractive index measurements with conventional Twyman–Green interferometers, the actively-tunable interferometer enables bulk-motion free thickness or refractive index sample measurements. With experimental demonstrations, we show excellent results for various samples that we characterized. The elimination of bulk motion from the measurement process promises to enable miniaturization of actively-tunable Twyman–Green interferometers for various applications.

Vibration measurement by projection of phase-modulated and amplitude-modulated structured light

Most of the whole-field optical methods for vibration measurement have low sensitivity when the points of the studied surface vibrate with the same amplitude. Those techniques also usually require complex and/or expensive solutions which are difficult to implement in engineering processes when the vibration amplitudes are relatively high. In order to overcome those limitations we propose a method for out-of-plane vibration measurement which uses structured light projection. The vibrating surface is obliquely illuminated by straight and parallel interference fringes produced by a Twyman-Green interferometer with a 532-nm laser as light source. In order to enable fringe visualization two techniques were employed, namely, the phase modulation of the fringe pattern by using a vibrating mirror in the interferometer, and a stroboscopic illumination by using a Fabry-Perot etalon amplitude modulator. We demonstrated the technique by measuring the vibration amplitudes of small objects in the millimeter and submillimeter range.

Dynamic range expansion of spatial light modulators based on a module-nπ method.

It is known that the cumbersome 2π correction is needed in the traditional module-2π method (i.e.,the phase wrapping method) due to the 2π deviation of the phase modulation depth of spatial light modulators (SLMs). To avoid the cumbersome 2π correction in the module-2π method, this paper proposes a module-n π method, and it can directly utilize any full-field phase modulation depth. First, for a Gaussian phase with a phase depth of 30rad, wrapped by the module-3.6π, it is reconstructed with the root-mean-square (RMS) values of its phase response are 0.1006λ (for the Twyman-Green interferometer) and 0.1101λ (for the Shack-Hartmann wavefront sensor method), respectively, which proves that the monitoring accuracy is relatively consistent. Subsequently, some comparative experiments based on the traditional module-2π are performed. The experimental results show that the RMS values of its phase response are 0.8886λ (for a modulation depth of 11.3rad) and 0.2261λ (for a modulation depth of 6.28rad), respectively. All the results have proved that the SLM with a phase modulation depth exceeding 2π (e.g.,11.3rad) has more prominent advantages. More specifically, increasing the SLM's phase modulation depth can effectively reduce the fringe orders of the wrapped patterns generated by the module-n π method. With the further reduction of the fringe orders, the influence of the fly-back zone error on the wavefront phase modulation is reduced, that is, the modulation accuracy is improved (the RMS values are reduced from 0.2261λ to 0.1006λ). Different from the traditional module-2π method, there is no need to consider the problems of the SLMs' over modulation or the insufficient modulation in the module-n π method. Furthermore, it avoids the cumbersome 2π correction process, which will make the use of the SLM more convenient.

Vibration amplitude mapping by stroboscopic structured light projection

In this work a method to evaluate the distribution of vibration amplitudes of objects was demonstrated, combining for the first time oblique structured light projection, stroboscopic illumination and fringe evaluation. The light pattern was formed by straight and parallel fringes produced by a slightly misaligned Twyman–Green interferometer illuminated by a 40-mW, 650-nm diode laser. Stroboscopic illumination was achieved by driving the laser with a PWM signal with the same frequency than that of the vibrating object. By evaluating the fringes with phase stepping and phase unwrapping procedures, the amplitude mapping of a formica bar and circular rubber membranes was performed. By averaging the fringe position over the light pulse duration a correction ratio between the actual phase and the measured phase was obtained as a function of the pulse duty cycle, and the dependence of the fringe visibility on the duty cycle was studied. The experiments showed that relatively large amplitudes in a range from tens of millimeters up to few millimeters can be measured.

Phase response measurement of spatial light modulators based on a Shack-Hartmann wavefront sensor.

It is known that the phase response of spatial light modulators (SLMs) measured by double-beam interferometers is sensitive to mechanical and environmental disturbances. This paper proposes a Shack-Hartmann wavefront sensor (SHWS) method to measure the phase response characteristics of the SLM. The results show that the phase modulation depth measured by the proposed method is 1.7581λ, and 1.7993λ by the Twyman-Green interferometer method. The difference in the phase modulation depth between the two methods is only 0.0412λ, and its relative error rate is 2.29%. It proves that the phase modulation accuracy obtained by the SHWS with lenslets of 73*73 used in this paper is equivalent to that of the Twyman-Green interferometer. Compared with the interferometer method, the SHWS method is simple, compact, and robust, has good real-time performance, and is relatively vibration insensitive. In the future, the SHWS method will play a more important role in the detection of the SLM's phase response.

Design and Fabrication of a Cost-Effective Optical Notch Filter for Improving Visual Quality

This study presents a multilayer design and fabrication of an optical notch filter for enhancing visual quality. A cost-effective multilayer design of notch filter with low surface roughness and low residual stress is proposed. A 9-layer notch filter composed of SiO2 and Nb2O5 with a central wavelength of 480 nm is prepared by electron beam evaporation combined with ion-assisted deposition. The optical transmittance, residual stress, and surface morphology are measured by a UV/VIS/NIR spectrophotometer, Twyman-Green interferometer and field emission scanning electron microscopy (FE-SEM). The transmittance of the notch filter at the central wavelength is above 15%, and the average transmittance of the transmission band is about 80%. The residual stress of the notch filter is −0.235 GPa, and the root mean square surface roughness is 1.85 nm. For improving the visual quality, a good image contrast can be obtained by observing the microscopic image using the proposed notch filter.

Design and Fabrication of Laser Protective Lenses Based on Multilayered Notch Filter with Low Residual Stress and Low Surface Roughness

We present a new laser protective lens based on a multilayered notch filter design with low residual stress and low surface roughness. An18-layer notch filter was prepared by electron beam evaporation with an ion-assisted deposition technique, which was composed of SiO2 and Nb2O5 with a center wavelength of 532 nm. The optical transmittance, residual stress, surface roughness, and surface morphology were measured by a UV/VIS/NIR spectrophotometer, Twyman–Green interferometer, scanning probe microscope, Linnik microscopic interferometer, and field-emission scanning electron microscopy (FE-SEM). The transmittance of the notch filters at center wavelength is 0.2%, and the average transmittance of the transmission band is about 70%. The residual stress of the notch filter is −0.298 GPa, and the root mean square surface roughness is 1.88 nm. The experimental results show that the optical transmittance meets the design requirements.

The measurement of ocular axial length in normal human eyes based on an improved Twyman-Green interferometer.

In order to meet the demands of myopia prevention, as well as the increasing needs of measurement for refractive and cataract operations in China, a new axial length (AL) measurement system combining an improved Twyman-Green interferometer with digital signal processing has been established. The ALs of 33 eyes of different optical refractive subjects (-8.50 ~ 0.50 D) were measured with the New AL and intraocular lens (IOL) master. The repeatability of measurements with the New AL was assessed using coefficient of variation (CoV) and intra-group correlation coefficient (ICC). Comparison, correlation, linear regression and agreement of AL between devices were analyzed. There was good repeatability (CoV=0.0617%, ICC=0.9999) with the New AL and great agreement has been obtained with both devices. These show that the New AL is capable of providing precise AL values over the normal AL range compared to the IOL master, and indicate that the New AL developed can be used for routine clinical AL measurements.

Phase Compensation of the Non-Uniformity of the Liquid Crystal on Silicon Spatial Light Modulator at Pixel Level.

Phase compensation is a critical step for the optical measuring system using spatial light modulator (SLM). The wavefront distortion from SLM is mainly caused by the phase modulation non-linearity and non-uniformity of SLM’s physical structure and environmental conditions. A phase modulation characteristic calibration and compensation method for liquid crystal on silicon spatial light modulator (LCoS-SLM) with a Twyman-Green interferometer is illustrated in this study. A method using two sequences of phase maps is proposed to calibrate the non-uniformity character over the whole aperture of LCoS-SLM at pixel level. A phase compensation matrix is calculated to correct the actual phase modulation of the LCoS-SLM and ensure that the designed wavefront could be achieved. Compared with previously known compensation methods, the proposed method could obtain the phase modulation characteristic curve of each pixel on the LCoS-SLM, rather than a mono look-up table (LUT) curve or multi-LUT curves corresponding to an array of blocks over the whole aperture of the LCoS-SLM. The experiment results show that the phase compensation precision could reach a peak-valley value of 0.061λ in wavefront and this method can be applied in generating freeform wave front for precise optical performance.

Out-of-Plane Thermal Expansion Coefficient and Biaxial Young’s Modulus of Sputtered ITO Thin Films

This paper proposes a measuring apparatus and method for simultaneous determination of the thermal expansion coefficient and biaxial Young’s modulus of indium tin oxide (ITO) thin films. ITO thin films simultaneously coated on N-BK7 and S-TIM35 glass substrates were prepared by direct current (DC) magnetron sputtering deposition. The thermo-mechanical parameters of ITO thin films were investigated experimentally. Thermal stress in sputtered ITO films was evaluated by an improved Twyman–Green interferometer associated with wavelet transform at different temperatures. When the heating temperature increased from 30 °C to 100 °C, the tensile thermal stress of ITO thin films increased. The increase in substrate temperature led to the decrease of total residual stress deposited on two glass substrates. A linear relationship between the thermal stress and substrate heating temperature was found. The thermal expansion coefficient and biaxial Young’s modulus of the films were measured by the double substrate method. The results show that the out of plane thermal expansion coefficient and biaxial Young’s modulus of the ITO film were 5.81 × 10−6 °C−1 and 475 GPa.

Estimation of an uncertainty budget and performance measurement for a dual-wavelength Twyman-Green interferometer.

In this paper, the uncertainty budget from 10 sources we claim they have direct impact on measurement is estimated. The measurement has been applied to nominal step heights of 1.34 and 1.50 μm using a dual-wavelength Twyman-Green interferometer. Experimental results show that the measured step heights match with their nominal values with expanded uncertainty in the range of 5% from the object being measured. The performance of the measurement process over time has been estimated at different confidence levels and the obtained results show that the process is maintained in a state of statistical control. To the best of our knowledge, this is the first report for estimation of uncertainty budget from a synthetic wavelength.

Evaluation of electrical resistivity, residual stress and surface roughness of sputtering indium tin oxide films with different thicknesses

This paper investigates the influence of film thickness on the electrical and mechanical properties of transparent indium tin oxide (ITO) thin films. Two groups of ITO thin films deposited on unheated substrates were prepared by the radio-frequency magnetron sputtering technique. The biaxial residual stress and surface roughness for two groups of ITO thin films were measured by a Twyman–Green interferometer and a Linnik microscopic interferometer, respectively. The electrical resistivity of the ITO films was measured by a four-point probe apparatus, the thickness was determined mechanically with a profilometer. The measurement results show that the average resistivity of ITO thin films decreases with increasing the deposited thickness. The compressive residual stress in the ITO thin films decreases with increasing the deposited thickness. We also find that an anisotropic stress in the two groups of ITO films is more compressive in a certain direction. The RMS surface roughness in the two groups of ITO films is less than 1 nm.

Accurate prediction of multilayered residual stress in fabricating a mid-infrared long-wave pass filter with interfacial stress measurements.

We present an accurate approach to predict the residual stress in a multilayered mid-infrared long-wave pass filter (MIR-LWPF) by using interfacial stress measurements. Magnesium fluoride (MgF2) and zinc sulfide (ZnS) thin films were used to fabricate 7-layer (MgF2/ZnS)3/MgF2 MIR-LWPF devices by electron-beam evaporation with ion-assisted deposition technique. The interfacial stress between the high-index of ZnS and low-index of MgF2 thin film materials was obtained from the residual stress measurements based on Twyman-Green interferometer and fast Fourier transformation (FFT) method. The modified Ennos formula was used to estimate the residual stress in the (MgF2/ZnS)3/MgF2 multilayered thin films. The difference between the predicted stress value and the measured value is 28 MPa by the proposed method. In the MIR-LWPF design of (MgF2/ZnS)3/MgF2 multilayer structure, the optical transmittance at a near-infrared wavelength of 1.0 µm to 2.5 µm is less than 10%, and the transmittance at a mid-infrared wavelength of 2.5 µm to 7.5 µm is greater than 93%. The proposed method can accurately evaluate and predict residual stress in fabricating mid-infrared long-wave pass filter device which possesses low residual stress as well as lower surface roughness.

Simulation and experimental study of laser-induced thermal deformation of spectral beam combination grating.

The multilayer dielectric (MLD) grating is a critical device for combining multiple laser beams into a single beam in a spectral beam combining (SBC) system. We established a theoretical thermal deformation model of the laser-irradiated MLD grating. Thermal deformation on the surface of the grating is simulated according to a series of parameters including the laser irradiation time, laser power density, and substrate size. To verify the model, we exposed a 960 l/mm, 50×50×1.5 mm3 grating to a laser power density of 3.61 kW/cm2 and observed the temperature change. We used a Twyman-Green interferometer to measure the interference fringes on the grating surface. Based on the Fourier-transform method and a Zernike polynomial fitting method, the real-time grating surface profile is reconstructed. The results show that substrate thickness increase or area decrease can reduce thermal deformation, the average decreases are 18.3% and 19.9%, respectively. The discussion and analysis of the grating thermal deformation are potentially valuable for designing grating to decrease the thermal deformation and improve the combined beam quality of a SBC system.