Interference Fringe Systems Research Articles

In situ calibration of an interferometric velocity sensor for measuring small scale flow structures using a Talbot-pattern

Small scale flow phenomena play an important role across engineering, biological and chemical sciences. To gain deeper understanding of the influence of those flow phenomena involved, measurement techniques with high spatial resolution are often required, presuming a calibration of very low uncertainty. To enable such measurements, a method for the in situ calibration of an interferometric flow velocity profile sensor is presented. This sensor, with demonstrated spatial resolution better than 1 μm, allows for spatially-resolving measurements with low velocity uncertainty in flows with high velocity gradients, on condition that the spatial behavior of the interference fringe systems is well-known by calibration with low uncertainty, especially challenging to obtain at applications with geometries difficult to access. The calibration method described herein uses three interfering beams to form the interference fringe systems of the sensor, yielding Doppler burst signals exhibiting two peaks in the frequency domain whose amplitude ratio varies periodically along the measurement volume major z-axis, giving a further independent value of the axial tracer particle position that can be used to determine the calibration functions of the sensor during the flow measurement. A flow measurement in a microchannel experimentally validates that the presented approach allows for simultaneously estimating the calibration functions and the velocity profile, providing flow measurements with very low systematic measurement errors of the particle position of less than 400 nm (confidence interval 95%). In that way, the interferometric flow velocity profile sensor utilizing the in situ self-calibration method promises valuable insights on small scale flow phenomena, such as those given in shear and boundary layer flows, by featuring reliable flow measurements due to minimum systematic and statistical measurement errors.

Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres

We present an extension of the adaptive spatial carrier frequency method which is proposed for fast measuring optical properties of fibrous materials. The method can be considered as a two complementary steps. In the first step, the support of the adaptive filter shall be defined. In the second step, the angle between the sample under test and the interference fringe system generated by the utilized interferometer has to be determined. Thus, the support of the optical filter associated with the implementation of the adaptive spatial carrier frequency method is accordingly rotated. This method is experimentally verified by measuring optical properties of polypropylene (PP) fibre with the help of a Mach–Zehnder interferometer. The results show that errors resulting from rotating the fibre with respect to the interference fringes of the interferometer are reduced compared with the traditional band pass filter method. This conclusion was driven by comparing results of the mean refractive index of drown PP fibre at parallel polarization direction obtained from the new and adaptive spatial carrier frequency method.

Displacement, distance, and shape measurements of fast-rotating rough objects by two mutually tilted interference fringe systems

The precise distance measurement of fast-moving rough surfaces is important in several applications such as lathe monitoring. A nonincremental interferometer based on two mutually tilted interference fringe systems has been realized for this task. The distance is coded in the phase difference between the generated interference signals corresponding to the fringe systems. Large tilting angles between the interference fringe systems are necessary for a high sensitivity. However, due to the speckle effect at rough surfaces, different envelopes and phase jumps of the interference signals occur. At large tilting angles, these signals become dissimilar, resulting in a small correlation coefficient and a high measurement uncertainty. Based on a matching of illumination and receiving optics, the correlation coefficient and the phase difference estimation have been improved significantly. For axial displacement measurements of recurring rough surfaces, laterally moving with velocities of 5 m/s, an uncertainty of 110 nm has been attained. For nonrecurring surfaces, a distance measurement uncertainty of 830 nm has been achieved. Incorporating the additionally measured lateral velocity and the rotational speed, the two-dimensional shape of rotating objects results. Since the measurement uncertainty of the displacement, distance, and shape is nearly independent of the lateral surface velocity, this technique is predestined for fast-rotating objects, such as crankshafts, camshafts, vacuum pump shafts, or turning parts of lathes.

Distance measurement technique using tilted interference fringe systems and receiving optic matching

The precise measurement of the distance of fast laterally moving rough surfaces is important in several applications such as lathe monitoring. A nonincremental interferometer based on two tilted interference fringe systems and a precise phase-difference estimation has been realized for this task. However, due to the speckle effect, the two scattered light signals exhibit different phase jumps and random envelopes causing small correlation coefficients and high uncertainties of the phase difference as well as the distance. In this Letter we present for the first time a method to enhance the signal correlation coefficient significantly. The interference signals are generated by scattered light of a rough surface from two different directions. A matching of illumination and receiving optic is performed. By this novel method, distance measurements with an uncertainty down to 1.2 μm at about 10 m/s lateral moving velocity have been achieved. Together with the simultaneously measured lateral velocity, the shape of rotating objects can be precisely determined.

Aperiodic interferometer for six degrees of freedom position measurement

We present a new class of interferometer system that is capable of simultaneous measurement of absolute position and rotation in all six degrees of freedom (DOF) with nanometer precision. This novel capability is due to the employment of a system of interference fringes that is not periodic. One of the key strengths offered by this new approach is that the absolute position of the system can be determined with a single measurement, rather than by counting fringes during displacement from a known location. The availability of a simultaneous measurement of all six DOF eliminates many problems associated with conventional interferometry.

Brewster fringes from a single plate

An autocollimation system with an illuminated circular entrance aperture located in the front focal plane of a lens L is considered. In the middle between S0′ and L, a transparent plate a few millimeters thick is placed at an angle of i0 = 45° to the axis of the system, and, near the rear focal plane of the lens L, a plane reflecting mirror is placed. The plate divides the primary beam into parts during its propagation both forward and backward (after the reflection from the mirror). This ensures the formation of derivative beams that propagate toward an ocular and that are overlapped in the region of spatially separated images S0, S1, and S2. The possibility of formation of a high-contrast system of first-order two-beam interference fringes in the region of S2 is discussed. Conditions for achieving this result are also discussed.

Non-incremental interferometric displacement measurement using a laser Doppler sensor with phase coding

The inspection of fast rotating objects with rough surfaces is an important task in the emerging field of process control. However, this is challenging since fast and non-contact inspection techniques with a measurement uncertainty in the nanometer range are often required. We present a novel optical sensor allowing non-incremental interferometric displacement measurement of moving solid state objects with rough surfaces. It features three wavelength coded interference fringe systems which are superposed slightly tilted. The displacement is determined by evaluating the phase shift between the resulting scattered light signals. Experimentally, a measurement uncertainty of 660 nm was obtained. This displacement uncertainty is independent of the lateral object velocity in principle. Due to this unique feature, the sensor can be utilized advantageously for precise displacement and vibration measurements of high speed objects as demonstrated by vibration measurements at a turbo pump shaft rotating with 48 000 rpm.

Laser Doppler distance sensor using phase evaluation

This paper presents a novel optical sensor which allows simultaneous measurements of axial position and tangential velocity of moving solid state objects. An extended laser Doppler velocimeter setup is used with two slightly tilted interference fringe systems. The distance to a solid state surface can be determined via a phase evaluation. The phase laser Doppler distance sensor offers a distance resolution of 150 nm and a total position uncertainty below 1 microm. Compared to conventional measurement techniques, such as triangulation, the distance resolution is independent of the lateral surface velocity. This advantage enables precise distance and shape measurements of fast rotating surfaces.

Laser Doppler sensor employing a single fan-shaped interference fringe system for distance and shape measurement of laterally moving objects

For monitoring the position and shape of fast moving and, especially, rotating objects such as turbo machine rotors, contactless and compact sensors with a high measurement rate as well as high precision are required. We present for the first time, to the best of our knowledge, a novel laser Doppler sensor employing a single fan-shaped interference fringe system, which allows measuring for the position and shape of fast moving solid bodies with known tangential velocity. It is shown theoretically as well as experimentally that this sensor offers concurrently high position resolution and high temporal resolution in contrast to conventional measurement techniques, since its measurement uncertainty is, in principle, independent of the object velocity. Moreover, it can be built very compact, because it features low complexity. To prove its operational capability and its potential for practical applications, radial and axial shape measurements of rotating bodies are demonstrated in comparison with triangulation. An average position resolution of about 2 microm could be achieved.

Precise flow rate measurements of natural gas under high pressure with a laser Doppler velocity profile sensor

This paper reports about the first application of a laser Doppler velocity profile sensor for precise flow rate measurements of natural gas under high pressure. The profile sensor overcomes the limitations of conventional laser Doppler anemometry (LDA) namely the effect of spatial averaging and the effect of fringe spacing variation (virtual turbulence). It uses two superposed, fan-like interference fringe systems to determine the axial position of a tracer particle inside the LDA’s measurement volume. Consequently, a spatial resolution of about 1 μm can be achieved and the effect of virtual turbulence is nearly eliminated. These features predestine the profile sensor for flow rate measurements with high precision. Velocity profile measurements were performed at the German national standard for natural gas, one of the world′s leading test facilities for precision flow rate measurements. As a result, the velocity profile of the nozzle flow could be resolved more precisely than with a conventional LDA. Moreover, the measured turbulence intensity of the core flow was of 0.14% mean value and 0.07% minimum value, which is significantly lower than reference measurements with a conventional LDA. The paper describes the performed measurements, gives a discussion and shows possibilities for improvements. As the main result, the goal of 0.1% flow rate uncertainty seems possible by an application of the profile sensor.

Turbo machine tip clearance and vibration measurements using a fibre optic laser Doppler position sensor

This paper presents a novel fibre optic laser Doppler position sensor for single blade tip clearance and vibration measurements at turbo machines, which offers high temporal resolution and high position resolution simultaneously. The sensor principle is based on the generation of a measurement volume consisting of two superposed fan-like interference fringe systems with contrary fringe spacing gradients using wavelength division multiplexing. A flexible and robust measurement system with an all-passive fibre coupled measurement head has been realized employing diffractive and refractive optics. Measurements of tip clearance and rotor vibrations at a transonic centrifugal compressor performed during operation at up to 50 000 rpm (833 Hz) corresponding to 21.7 kHz blade frequency and 586 m s−1 blade tip velocity are presented. The results are in excellent agreement with those of capacitive probes. The mean uncertainty of the position measurement was around 20 µm and, thus, considerably better than for conventional tip clearance probes. Consequently, this sensor is capable of fulfilling the requirements for future active clearance control systems and has great potential for in situ and online tip clearance and vibration measurements at metallic and non-metallic turbine blades with high precision.

Fiber-optic laser Doppler turbine tip clearance probe

A laser Doppler based method for in situ single blade tip clearance measurements of turbomachines with high precision is presented for what we believe is the first time. The sensor is based on two superposed fanlike interference fringe systems generated by two laser wavelengths from a fiber-coupled, passive, and therefore compact measurement head employing diffractive optics. Tip clearance measurements at a transonic centrifugal compressor performed during operation at 50,000 rpm (833 Hz, 586 m/s tip speed) are reported. At these speeds the measured uncertainty of the tip position was less than 20 microm, a factor of 2 more accurate than that of capacitive probes. The sensor offers great potential for in situ and online high-precision tip clearance measurements of metallic and nonmetallic turbine blades.

Determination of the axial velocity component by a laser-Doppler velocity profile sensor

We report about the determination of the axial velocity component by a laser Doppler velocity profile sensor that is based on two superposed fanlike interference fringe systems. Evaluation of the ratio of the Doppler frequencies obtained from each fringe system yields the lateral velocity component and the axial position inside the fringe system. Inclined particle trajectories result in chirped burst signals, where the change of the Doppler frequency in one burst signal is directly related to the axial velocity component. For one single tracer particle it is possible to determine (i) the lateral velocity component, (ii) the axial velocity component including the direction, and (iii) the axial position of the tracer trajectory. In this paper we present the measurement principle and report about results from simulation and experiments. An uncertainty of the axial velocity component of about 3% and a spatial resolution in the micrometer range were achieved. Possible applications of the sensor lie in three-component velocity measurements of flow fields where only one optical access is available.

Investigation of the influence of spatial coherence of a broad-area laser diode on the interference fringe system of a Mach–Zehnder interferometer for highly spatially resolved velocity measurements

Laser Doppler anemometry is a method for absolute velocity measurements that is based on a Mach-Zehnder interferometer arrangement and usually employs transverse fundamental-mode lasers. We employed inexpensive and powerful broad-area laser diodes and investigated ways in which an interference fringe system is influenced by the spatial coherence properties of a multimode beam. It was demonstrated that, owing to poor spatial coherence of the beam, interference is suppressed in the marginal regions of the intersection volume. Based on these results, a sensor for highly spatially resolved velocity measurements can be built. The inherent astigmatism of the broad-area diode is corrected by an arrangement of two crossed cylindrical lenses. An interference fringe system of length 200 microm and a relative variation in fringe-spacing of only 0.22% were demonstrated with light emitted from a broad-area laser diode with a 100 microm x 1 microm emitter size. Based on this principle a powerful, simple, and robust laser Doppler sensor has been achieved. Highly spatially resolved measurements of a boundary layer flow are presented.

Near-field diffraction of irregular phase gratings with multiple phase-shifts

A phase-step in a phase mask is not copied into the substrate but is split into two half-amplitude phase-shifts in the near-field because of the presence of an additional interference fringe system of the two beams diffracted from the two grating sections separated by the phase-step. In the case of multiple phase-shifts, the split phase-shifts from two adjacent phase-steps can crossover in the propagation without interfere. This paper contributes to understanding the near-field diffraction of irregular phase gratings with multiple phase-shifts, and provides a theoretical base for designing multiple phase-shifted phase masks for high channel-count phase-only sampled fiber Bragg gratings [1,2].

Method for Determining Material Constants of Nematic Liquid Crystals by Use of Wedge Cells

A wedge cell of the wedge angle of order of few milliradians was used to measure the phase shift between ordinary and extraordinary rays of transmitted light, for the Fréedericksz transition induced by a magnetic or an electric field. A nematic liquid crystal, PCB, filling the cell, was of the planar alignment enforced by the treatment of the flat boundary plates. A polyimide, MK8–poly (amic acid), was used as aligning substance. A system of interference fringes appeared in the cell placed in normally incident light between the analyser and the polariser crossed. In the neighbourhood of each fringe the cell can be considered as a flat-parallel one and hence it is equivalent to a system of flat cells of different precisely determined thickness. The dependence of the phase shift on applied external fields was measured for several interference fringes. The nematic liquid crystal material parameters (the splay and bend elastic constants, the anisotropy of diamagnetic susceptibility and the boundary tilt angle as a function of the torque) were determined by fitting the calculated characteristics to the measured ones.

Spatial resolving laser Doppler velocity profile sensor using slightly tilted fringe systemsand phase evaluation

In this paper we report on a differential laser Doppler velocimeter which offersspatially resolved measurements in the probe volume. For the first time, twolaser wavelengths are employed to generate two interference fringe systems withidentical fringe spacing which are slightly tilted towards each other. The relativephase shift varies linearly with the position along the optical axis, thus allowingspatially resolved measurements. In the centre of the measurement volume a spatialresolution in the nanometre range is achieved. The sensor was applied in a windtunnel for the determination of the wall shear stress of a laminar flat-plate flowwithout mechanical traversing. Spatially resolved measurements of the Blasiusvelocity profile are presented. All results agree well with the theoretical prediction.

Measurement of diffusion coefficient of transparent liquid solutions using Michelson interferometer

The study of diffusivity is important for the design of chemical equipment and its knowledge is needed for mass transfer studies and is the most fundamental property of any chemical system in which the chemical engineers are interested. Here, we report a new interferometric technique to determine the diffusion coefficient of transparent liquid solutions using Michelson interferometer geometry. The experimental cell containing the diffusing solution was kept in one of the arms of Michelson Interferometer. The liquids of differing concentrations were introduced in the cell. Two separate circular interference fringe systems were formed due to the two solutions and they were recorded on a PC using a CCD camera. The time variation of these interferograms yields the diffusion coefficient. The obtained diffusivity values matched very well with the existing experimental results. Detailed theoretical and experimental analysis is given in the paper.

Passive directional discrimination in laser-Doppler anemometry by the two-wavelength quadrature homodyne technique.

We report a method for passive optical directional discrimination in laser-Doppler anemometers. For this purpose frequency-shift elements such as acousto-optic modulators, which are bulky and difficult to align during assembly, have traditionally been employed. We propose to use a quadrature homodyne technique to achieve directional discrimination of the fluid flow without any frequency-shift elements. It is based on the employment of two laser wavelengths, which generate two interference fringe systems with a phase shift of a quarter of the common fringe spacing. Measurement signal pairs with a direction-dependent phase shift of +/- pi/2 are generated. As a robust signal-processing technique, the cross-correlation technique is used. The principles of quadrature homodyne laser-Doppler anemometry are investigated. A setup that provides a constant phase shift of pi/2 throughout the entire measurement volume was achieved with both single-mode and multimode radiation. The directional discrimination was successfully verified with wind tunnel measurements. The complete passive technique offers the potential of building miniaturized measurement heads that can be integrated, e.g., into wind tunnel models.

Kinetics of photoinduced gratings by a moving grating technique

A moving grating technique is used to monitor the kinetics of the amplitudes and phases of the modulations of refractive index and absorption coefficients induced in a photosensitive material by exposure to a system of interference fringes. The analysis is performed here, in the case of thick materials including the slanted geometry, useful for polymeric photorefractive materials. It is illustrated in the case of a photochromic photorefractive crystal. A detailed error analysis is presented for a photochromic DR1 film and a SBN photorefractive crystal.