Interferometric Length Measurements Research Articles

Thermally compensated common-path differential interferometer with reduced long-term zero-drifts

Abstract Laser interferometers have served as the workhorses in the metrology of length for several decades. Their broader application brings further challenges, especially for longer measurement time-frames or outside the laboratory environment with strictly controlled conditions. As a part of our team’s activities aiming at characterizing and eliminating the effects of unstable temperature on interferometric length measurements, we report on successfully remodelling a differential interferometer’s optical arrangement focused on increasing resilience against temperature changes. The experimental characterization under constant temperature and subsequently under thermal load proved a tenfold decrease in short-term fluctuations and reduced sensitivity to temperature changes by a factor of 100.

A GPS-Referenced Wavelength Standard for High-Precision Displacement Interferometry at λ = 633 nm.

Since the turn of the millennium, the development and commercial availability of optical frequency combs has led to a steadily increase of worldwide installed frequency combs and a growing interest in using them for industrial-related metrology applications. Especially, GPS-referenced frequency combs often serve as a "self-calibrating" length standard for laser wavelength calibration in many national metrology institutes with uncertainties better than u = 1 × 10-11. In this contribution, the application of a He-Ne laser source permanently disciplined to a GPS-referenced frequency comb for the interferometric measurements in a nanopositioning machine with a measuring volume of 200 mm × 200 mm × 25 mm (NPMM-200) is discussed. For this purpose, the frequency stability of the GPS-referenced comb is characterized by heterodyning with a diode laser referenced to an ultrastable cavity. Based on this comparison, an uncertainty of u = 9.2 × 10-12 (τ = 8 s, k = 2) for the GPS-referenced comb has been obtained. By stabilizing a tunable He-Ne source to a single comb line, the long-term frequency stability of the comb is transferred onto our gas lasers increasing their long-term stability by three orders of magnitude. Second, short-term fluctuations-related length measurement errors were reduced to a value that falls below the nominal resolving capabilities of our interferometers (ΔL/L = 2.9 × 10-11). Both measures make the influence of frequency distortions on the interferometric length measurement within the NPMM-200 negligible. Furthermore, this approach establishes a permanent link of interferometric length measurements to an atomic clock.

Comb-referenced metrology laser for interferometric length measurements in nanopositioning and nanomeasuring machines

Abstract In this article a new approach for the direct traceability of interferometric length measurements in nanopositioning- and measuring machines is presented. The concept is based on an optical frequency comb tied to a GPS disciplined oscillator. The frequency comb serves as a highly stable reference laser with traceable optical frequencies. By directly stabilizing the metrology lasers of a nanopositioning and -measuring machine to a single comb line a permanent link of the laser frequency to an atomic clock is created allowing direct traceability to the SI meter definition. The experimental conditions to provide traceability will be discussed. Furthermore, it is demonstrated how the long-term frequency stability of an individual comb line can be transferred onto the metrology lasers enhancing their stability by three orders of magnitude.

Interferometric bunch length measurements of 3 MeV picocoulomb electron beams

We report picosecond bunch length measurements using an interferometric method for a 3 MeV electron beam having bunch charge ranging from 1 to 14 pC. The method senses the single-cycle sub-terahertz (THz) pulse emitted by each electron bunch as coherent transition radiation which, in turn, is analyzed using a Michelson-type interferometer, forming an interferogram that is then processed to yield the nominal electron bunch length. This sub-THz coherent radiation intensity was measured using a quasi-optical detector (QOD) operated at room temperature. This experiment was quite challenging since the divergence angle of the sub-THz pulse emitted by the low-energy electron bunch exceeds ±10°, and its pulse energy at the entrance to the detector was as low as 100 pJ. When compared to a conventional helium-cooled silicon composite bolometer designed for frequencies above 0.5 THz, the QOD provided much better signal-to-noise ratio in the ∼80 GHz frequency range, which was critical for the successful measurement of the bunch length.

Heterodyne Standing-Wave Interferometer with Improved Phase Stability

This paper describes a standing-wave interferometer with two laser sources of different wavelengths, diametrically opposed and emitting towards each other. The resulting standing wave has an intensity profile which is moving with a constant velocity, and is directly detected inside the laser beam by two thin and transparent photo sensors. The first sensor is at a fixed position, serving as a phase reference for the second one which is moved along the optical axis, resulting in a frequency shift, proportional to the velocity. The phase difference between both sensors is evaluated for the purpose of interferometric length measurements.

Study on measurement method of mirror reflection laser tracking interferometric length measurement

Study on measurement method of mirror reflection laser tracking interferometric length measurement

FREQUENCY COMB-COUPLED METROLOGY LASERS FOR NANOPOSITIONING AND NANO MEASURING MACHINES

This article shows how a direct readout of the interferometric length measurement in nanopositioning machines can be transferred by connecting the metrology laser to a frequency comb line. The approach is based on a GPS-referenced frequency comb with which the stability of the timer (atomic clock via GPS) is transferred to the metrology laser of the nanopositioning and nano measuring machine NPMM-200. The necessary prerequisites for ensuring traceability are discussed. It is demonstrated that with this approach an improvement in the long-term stability of the metrology laser by three orders of magnitude can be achieved.

Sphere diameter interferometry with nanometer uncertainty

In this paper we present both the design details and uncertainty budget for a National Institute of Standards and Technology (NIST)-developed high-accuracy Fizeau-type interferometer specifically adapted to measurement sphere diameter. To do this, we provide some historic details of the instrument’s origins, an explanation of the clever accuracy-improving enhancements integrated into the design over the past several decades, and a detailed discussion of the role automation has played in achieving its current world-class accuracy. With utmost attention to the dominating components of a detailed uncertainty budget, we methodically improved a rather dated instrument design into a high-accuracy state-of-the-art system for sphere diameter measurement with an expanded uncertainty, U(k = 2), of less than ±10 nm for spheres with nominal diameters of between 0.4 mm and 26 mm. We conclude with a brief description of a novel application of this instrument for determining the phase-change upon reflection correction for both gauge blocks and gauge block platens. Applying corrections for phase-change upon reflection differences between different surfaces, gauge block and platen, is critically important for high-accuracy interferometric gauge block length measurements.

Heterodyne standing-wave interferometer / Heterodynes Stehende-Welle-Interferometer

Abstract This manuscript describes a novel standingwave arrangement with two laser sources of different wavelengths, emitting towards each other. The resulting standing wave has a continuously moving intensity profile, a thin, transparent photo sensor is inserted into. When the sensor is moved along the optical axis a frequency shift, proportional to the velocity, occurs. This frequency shift can be evaluated for the purpose of interferometric length measurements.

Control chart analysis for interferometric length measurement

INTI is the national metrology institute of Argentina and the responsible for maintenance and the dissemination of the national length standard. The practical realization of this reference is performed according to the optical wavelength standards established and published by the International Committee of Weights and Measures (CIPM). The length unit is materialized by artefacts known as gauge blocks which length is measured by optical interferometric methods. For this purpose INTI has a commercial interferometer based on a Twyman-Green configuration. By this system INTI provides length traceability to national calibration laboratories and others national metrology institutes of the region. Even though the equipment that forms the interferometric system is calibrated periodically, it is convenient to establish quality control procedures for monitoring not only the system as a whole but also the calibration process. We report on a 5-year study of two control steel gauge block sets, the statistical techniques applied on control chart and its selection criteria. The pool of data allows long term stability analysis of these standards as well as the operating examination of the interferometer.

Measurement of the refractive index of air in a low-pressure regime and the applicability of traditional empirical formulae

The refractive index of air is a major limiting factor in length measurements by interferometry, which are mostly performed under atmospheric conditions. Therefore, especially in the last century, measurement and description of the air refractive index was a key point in order to achieve accuracy in the realisation of the length by interferometry. Nevertheless, interferometric length measurements performed in vacuum are much more accurate since the wavelength of the light is not affected by the air refractive index. However, compared with thermal conditions in air, in high vacuum heat conduction is missing. In such a situation, dependent on the radiative thermal equilibrium, a temperature distribution can be very inhomogeneous. Using a so-called contact gas instead of high vacuum is a very effective way to enable heat conduction on nearly the same level as under atmospheric pressure conditions whereby keeping the effect of the air refractive index on a small level. As physics predicts, and as we have demonstrated previously, helium seems like the optimal contact gas because of its large heat conduction and its refractive index that can be calculated from precisely known parameters. On the other hand, helium gas situated in a vacuum chamber could easily be contaminated, e.g. by air leakage from outside. Above the boiling point of oxygen (−183 °C) it is therefore beneficial to use dry air as a contact gas. In such an approach, the air refractive index could be calculated based on measured quantities for pressure and temperature. However, existing formulas for the air refractive index are not valid in the low-pressure regime. Although it seems reasonable that the refractivity (n − 1) of dry air simply downscales with the pressure, to our knowledge there is no experimental evidence for the applicability of any empirical formula. This evidence is given in the present paper which reports on highly accurate measurements of the air refractive index for the wavelengths 532 nm, 633 nm and 780 nm in the low-pressure regime from 0 Pa to 1300 Pa. In our approach, using a vacuum cell, n − 1 is obtained from the comparison of optical path lengths in vacuum and air along the same path by imaging interferometry. These measured values are compared with the ones obtained from Bönsch’s formula. An agreement of ±10−9 is found in the low-pressure regime. Accordingly, this formula could be applied for the accurate determination of the refractive index of dry air even at low pressures, provided that the pressure is measured with high accuracy.

Interferometric focal length measurement of positive and negative lenses using a lateral-shearing cyclic path optical configuration setup and polarization phase-shifting interferometry.

We present a simple interferometric focal length measurement technique for measuring the focal length of positive and negative lenses using a lateral-shearing cyclic path optical configuration (CPOC) setup and polarization phase-shifting interferometry (PPSI). The technique requires an auxiliary lens, whose focal length need not be known accurately, for generating a focused point source at its focal plane. The focal point of the test lens is adjusted to be in the vicinity of the focus of the auxiliary lens. The radii of the resulting spherical wave fronts emerging from the test lens, due to the defocus, for two different longitudinal shifted positions of the test lens are measured using the lateral-shearing CPOC setup and PPSI. Focal length of the test lens is determined from the known longitudinal shift and from the measured radii of the spherical wave fronts. Results obtained for 200.0mm convex and 100.0mm concave test lenses are presented.

Phase topography-based characterization of thermal effects on materials and joining techniques.

There are growing demands to characterize the stability of assemblies of optical components for ultrahigh-precision instruments. In this paper we demonstrate how absolute length measurements by interferometry can be applied to measure the thermal and dimensional stability of connections. In order to enable investigation of common joining techniques, including wringing, screwing, and gluing, as well as specialized, inorganic joining techniques such as silicatic bonding, thin-film soldering, and solderjet bumping, representative connections were fabricated. By using gage blocks or prismatic bodies as joining parts, parallelism and flatness were provided which are needed for precision interferometric length measurements. The stability of connection elements used in ultrahigh-precision instruments was investigated longitudinally and laterally to the connection interface, and also mutual tilting of the parts was detected by analysis of the phase topographies. The measurements have an accuracy level of about 1 nm, and the traditional wringing method was also considered as a reference joining technique. The long-term behavior was studied within a period of about 1 year under constant temperature. Further, the thermal dilatation and the reaction of connections to thermal stress were measured. Results show that screwed connections do not exhibit a significant drift of length or orientation. They also did not show response to temperature variations of ±10°C. This is different for adhesive connections, where dimensional changes of up to 100 nm were observed. The specimens produced by using thin-film soldering as well as silicatic bonding revealed stability of length better than 5 nm per year and angular stability within ±0.1 arcsec. Furthermore, these specimens were shown to be insensitive to a temporary temperature variation in a range from 10°C to 40°C. This situation is slightly different for the sample connections produced by solderjet bumping, which show a positive length change of ∼25 nm and a tilt of ∼1 arcsec. These observations can be explained by creeping of the relatively large solder bumps that bridge a gap of about 100 μm between the connected mirror plates. The thermal expansion of the connections shows a strong correlation with the "layer thickness."

High-precision diode-laser-based temperature measurement for air refractive index compensation

We present a laser-based system to measure the refractive index of air over a long path length. In optical distance measurements, it is essential to know the refractive index of air with high accuracy. Commonly, the refractive index of air is calculated from the properties of the ambient air using either Ciddor or Edlén equations, where the dominant uncertainty component is in most cases the air temperature. The method developed in this work utilizes direct absorption spectroscopy of oxygen to measure the average temperature of air and of water vapor to measure relative humidity. The method allows measurement of temperature and humidity over the same beam path as in optical distance measurement, providing spatially well-matching data. Indoor and outdoor measurements demonstrate the effectiveness of the method. In particular, we demonstrate an effective compensation of the refractive index of air in an interferometric length measurement at a time-variant and spatially nonhomogeneous temperature over a long time period. Further, we were able to demonstrate 7 mK RMS noise over a 67 m path length using a 120 s sample time. To our knowledge, this is the best temperature precision reported for a spectroscopic temperature measurement.

Measuring value correction and uncertainty analysis for homodyne interferometers

The Nanopositioning and Nanomeasuring Machine (NMM-1) developed at the Ilmenau University of Technology is equipped with three homodyne plane-mirror miniature interferometers for the measurement of the displacement of a movable corner mirror. The object being measured is placed on the corner mirror, which is positioned by a three-axis drive system. The uncertainty of interferometric length measurements is dependent on several factors. Starting with an improved equation for calculating length, this paper describes a part of the determination of the measurement uncertainty for a displacement measurement using two positions of the measuring mirror. The new approach separates the correlated influencing factors for three positions of the measuring mirror: for the position where the interferometer counter is reset to zero and the other two positions of two measured points. Additionally, the work takes into account the influence of the dead path length and its determination.

Precise interferometric length measurement using real-time fringe fitting

We created a simple device for the measurement of nanoscale displacements consisting in a Twyman–Green interferometer with one mirror having a slight offset in the horizontal plane with respect to the direction perpendicular to the incoming beam and one mobile mirror, a CCD array camera that captures frames of fringes (interferograms) generated by the interferometer and a software that acquires the interferograms captured by the camera and fits the fringes in order to determine the initial spatial phase of the series of fringes and, consequently, to monitor the movement of the mobile arm of the interferometer. Because the interferograms were acquired and analyzed sequentially, the algorithm could be parallelized easily on a multiprocessor/multicore platform. The device can work in real-time in which case the maximum speed of the mobile arm of the interferometer for which we can obtain unambiguous results is 30 λ/8/s, which is, assuming a He–Ne laser as the light source, almost 2.5 μm/s. In real-time conditions, the precision and accuracy of the measurement are low. In stationary conditions, however, the precision was determined to be below 1 nm.

Limitations of precision length measurements based on interferometers

The most important principles, the basis and operation of heterodyne and homodyne interferometers are discussed. Their benefits and limitations are covered based on a metrological analysis. The resolution of interferometers can be determined by calculating the smallest resolvable distance increment. Also, it is shown here how the Abbe comparator principle can be fulfilled in all three measuring dimensions by using interferometers. Other factors in addition to the Abbe errors are discussed which affect the measurement uncertainty of interferometric length measurements. The Abbe-error-free design is explained using the example of a nanopositioning and nanomeasuring machine developed at the Institute of Process Measurement and Sensor Technology (Ilmenau University of Technology) and manufactured at the SIOS Meßtechnik GmbH Ilmenau, Germany.

Implementation of armlocking with a delay of 1 second in the presence of Doppler shifts

LISA relies on several techniques to reduce the initial laser frequency noise in order to achieve an interferometric length measurement with an accuracy of ≈ 10pm/. LISA will use ultra-stable reference cavities as a first step to reduce the laser frequency noise. In a second step the frequency will be stabilized to the LISA arms which provide a better reference in the frequency band of interest. We present experimental results demonstrating Arm locking with LISA-like light travel times and Doppler shifts. We also integrated this system with a LISA-like pre-stabilization system using our ultra-stable cavities. The addition of realistic Doppler shifts led to further refinements of the arm locking controllers compared to the controller architecture discussed in the past. A first experimental result of the new controller is also presented.

Highest-accuracy interferometer alignment by retroreflection scanning

One important prerequisite for interferometric length measurements of high accuracy is autocollimation adjustment. This guarantees that the direction of the length scale represented by light waves is parallel to the length direction of the object investigated. First we describe the conventional visual autocollimation adjustment method used at Physikalisch-Technische Bundesanstalt since the beginning of interferometric length measurements. Then a new autocollimation method based on scanning the retroreflection from the interferometer is described. Check measurements are performed in order to investigate the quality of the adjustment. As a result of the method applied the uncertainty contribution originating from the cosine error could be reduced drastically for the interferometer used.

Acoustic method for determination of the effective temperature and refractive index of air in accurate length interferometry

An acoustic method for the measurement of the effective temperature and refractive index of air for precision length interferometry is described. The method can be used to improve the accuracy of interferometric length measurements outside the best laboratory conditions and also in industrial conditions. The method is based on the measurement of speed of 50-kHz ultrasound over the same distance measured with a laser interferometer. The measured speed of ultrasound is used to define the effective temperature or the refractive index of air along the laser beam path using the equations presented. The measured speed of sound, Cramer equation, dispersion correction, and Edlén equations are used in the fitting of new equations for the effective air temperature and refractive index of air as a function of speed of 50-kHz ultrasound. The standard uncertainties of the effective temperature and the refractive index of air equations are 15 mK and 1.7×10–8, respectively. The uncertainties of the effective temperature and refractive index of air measured with the test setup for distances of about 5 m are 25 mK and 2.6×10–8, respectively.