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The air refractive index is an important parameter in interferometric length measurements, since it substantially affects the measurement accuracy. We present a refractive index of air measurement method based on monitoring the phase difference between the ambient air and vacuum inside a permanently evacuated double-spaced cell. The cell is placed in one arm of the Michelson interferometer equipped with two light sources—red LED and HeNe laser, while the low-coherence and laser interference signals are measured separately. Both phase and group refractive indices of air can be calculated from the measured signals. The method was experimentally verified by comparing the obtained refractive index values with two different techniques.

This paper presents a method implemented in a system for automatic contactless calibration of gauge blocks designed at ISI ASCR. The system combines low-coherence interferometry and laser interferometry, where the first identifies the gauge block sides position and the second one measures the gauge block length itself. A crucial part of the system is the algorithm for gauge block alignment to the measuring beam which is able to compensate the gauge block lateral and longitudinal tilt up to 0.141 mrad. The algorithm is also important for the gauge block position monitoring during its length measurement.

This paper presents a contactless method for gauge blocks calibration combining laser interferometry and low-coherence interferometry. In the presented system, the contactless measurement of the absolute gauge block length is done as a single-step operation without any change in optical setup during measurement, giving complete information about the gauge block length. The paper also presents a set of optimization steps which have been done in order to transform the original experimental setup into the automatic system which meets legal length metrology requirements. To prove the measurement traceability, we conducted a set of gauge block length measurement comparing data from the optimized system and the established reference systems TESA NPL A.G.I. 300 and TESA–UPC operated in Czech Metrology Institute laboratory.

We present an interferometric technique based on a differential interferometry setup for measurement under atmospheric conditions. The key limiting factor in any interferometric dimensional measurement are fluctuations of the refractive index of air representing a dominating source of uncertainty when evaluated indirectly from the physical parameters of the atmosphere. Our proposal is based on the concept of an over-determined interferometric setup where a reference length is derived from a mechanical frame made from a material with a very low thermal coefficient. The technique allows one to track the variations of the refractive index of air on-line directly in the line of the measuring beam and to compensate for the fluctuations. The optical setup consists of three interferometers sharing the same beam path where two measure differentially the displacement while the third evaluates the changes in the measuring range, acting as a tracking refractometer. The principle is demonstrated in an experimental setup.

The influence of the refractive index of air has proven to be a major problem on the road to improvement of the uncertainty in interferometric displacement measurements. We propose an approach with two counter-measuring interferometers acting as a combination of tracking refractometer and a displacement interferometer referencing the wavelength of the laser source to a mechanical standard made of a material with ultra-low thermal expansion. This technique combines length measurement within a specified range with measurement of the refractive index fluctuations in one axis. Errors caused by different position of the interferometer laser beam and air sensors are thus eliminated. The method has been experimentally tested in comparison with the indirect measurement of the refractive index of air in a thermal controlled environment. Over a 1 K temperature range an agreement on the level of 5 × 10(-8) has been achieved.

We propose to extend the principle of compensation of the fluctuations of the refractive index of air through monitoring the optical length within the measuring range of the displacement measuring interferometer. The concept is derived form a tracking refractometry evaluating the refractive index of air in the beam axis coinciding with the positioning interferometer. Application of this approach in multi-axis positioning and measurement mans to compromise the principle of spatial unity of the displacement measuring laser beam and the beam of the tracking refractometer. In this contribution we evaluate the level of uncertainty associated with the spatial shift of these two beams. Consequently the nature of the fluctuations of the refractive index of air in laser interferometry is investigated and discussed with the focus on potential applications in coordinate measuring systems and long-range metrological scanning probe microscopy systems.

This paper presents a method for active angular alignment of gauge block implemented in a system for automatic contactless calibration of gauge blocks designed at ISI ASCR. The system combines low-coherence interferometry and laser interferometry, where the first identifies the gauge block sides position and the second one measures the gauge block length itself. A crucial part of the system is the algorithm for gauge block alignment to the measuring beam which is able to compensate the gauge block lateral and longitudinal tilt up to 0.141 mrad. The algorithm is also important for the gauge block position monitoring during its length measurement.

We present an interferometric technique based on differential interferometry setup for measurement in the subnanometer scale in atmospheric conditions. One of the important limiting factors in any optical measurement are fluctuations of the refractive index of air representing a source of uncertainty traditionally compensated when the index is evaluated indirectly from the physical parameters of the atmosphere. Our proposal is based on the concept of overdetermined interferometric setup where a reference length is derived from a mechanical frame made from a material with very low thermal coefficient on the 10− 8 level. The technique allows to track the variations of the refractive index of air on-line directly in the line of the measuring beam and to compensate for the fluctuations.

Although the laser interferometry represents the most precise class of techniques in the field of precise measurement of geometrical quantities, its wide use in measurement systems is still accompanied by many unresolved challenges. One of these challenges is the complexity of underlying optical systems. We present a novel approach to the interference phase detection - fringe subdivision - in the homodyne laser interferometry that aims at reduction of the optical complexity while the resolution is preserved. Our method employs a series of computational steps to infer a pair of signals in quadrature that allows to determine the interference phase with a sub-nanometre resolution from an interference signal from a non-polarising interferometer sampled by a single photodetector. The complexity trade-off is the use of laser beam with frequency modulation capability. The method was experimentally evaluated on a Michelson interferometer-based free-space setup and its performance has been compared to a traditional homodyne detection method. The results indicate the method is a feasible al­ ternative for the traditional homodyne detection since it performs with comparable accuracy (< 0.5nm standard deviation), especially where the optical setup complexity is principal issue and the modulation of laser beam is not a heavy burden, for instance in multi-axis measurement systems or laser diode based systems.

The work presents a method where the change of the length of the measuring arm of the Michelson interferometer is monitored by the cavity length of the optical resonator. The resonator works as distance-to-optical frequency converter with ultimate linearity. It has locked a tunable laser to certain cavity mode. The optical frequency of the laser is heterodyned with immediate “tooth” of the femtosecond comb spectrum. The results of measured scale linearity of the homodyne interferometer for corrected and non-corrected scale are presented for measuring range of the homodyne interferometer in order of one micrometer and more.

This paper presents a novel principle for contactless gauge block measurement using a combination of low-coherence interferometry and laser interferometry. The experimental setup combines a Dowell interferometer and a Michelson interferometer to ensure a gauge block length determination with direct traceability to the primary length standard. This setup was designed for contactless complex gauge block analysis providing information about gauge block length, gauge block faces surface profile (e.g., indication of scratches) and by analysis of the interference fringes shape, also about the gauge block edge flatness distortion. The designed setup is supplemented by an automatic handling system designed for a set of 126 gauge blocks (0.5 mm to 100 mm) to allow the automatic contactless calibration of the complex gauge block set without a human operator.

We present a concept of suppression of the influence of variations of the refractive index of air in displacement measuring interferometry. The principle is based on referencing of wavelength of the coherent laser source in atmospheric conditions instead of traditional stabilization of the optical frequency and indirect evaluation of the refractive index of air. The key advantage is in identical beam paths of the position measuring interferometers and the interferometer used for the wavelength stabilization. Design of the optical arrangement presented here to verify the concept is suitable for real interferometric position sensing in technical practice especially where a high resolution measurement within some limited range in atmospheric conditions is needed, e.g. in nanometrology.

We present a concept combining traditional displacement incremental interferometry with a tracking refractometer following the fluctuations of the refractive index of air. This concept is represented by an interferometric system of three Michelson-type interferometers where two are arranged in a counter-measuring configuration and the third one is set to measure the changes of the fixed length, here the measuring range of the overall displacement. In this configuration the two counter-measuring interferometers have identical beam paths with proportional parts of the overall one. The fixed interferometer with its geometrical length of the measuring beam linked to a mechanical reference made of a high thermal-stability material (Zerodur) operates as a tracking refractometer monitoring the atmospheric refractive index directly in the beam path of the displacement measuring interferometers. This principle has been demonstrated experimentally through a set of measurements in a temperature controlled environment under slowly changing refractive index of air in comparison with its indirect measurement through Edlen formula. With locking of the laser optical frequency to fixed value of the overall optical length the concept can operate as an interferometric system with compensation of the fluctuations of the refractive index of air.

Determination of the interference phase, i.e. the mutual phase shift between interfering waves is a principal issue in the interferometric measurement, especially on the nanometre scale. Our goal was to develop a novel interference phase detection technique that employs a computational approach and a frequency modulation of the laser source to achieve comparable performance with a homodyne detection with an optical phase shift generation. We have used a Michelson setup with polarizing optics that allowed to compare both the homodyne detection method and our novel method side by side while both methods shared the optical setup. Our method also comprises error compensation that deals e.g. with residual amplitude modulation and the scale non-linearities. The experiments revealed that the novel method achieves a periodic error less than 0.16 angular degrees and a standard deviation of less than 1.5 degrees, compared against the reference. The operational distance was 600mm. The method had proven it is suitable replacement for traditional homodyne detection techniques since it has comparable performance and significantly lower demands on the optical setup.

This paper presents a novel principle for contactless gauge block measurement using a combination of low-coherence interferometry and laser interferometry. The experimental setup combines a Dowell interferometer and a Michelson interferometer to ensure a gauge block length determination with direct traceability to the primary length standard. This setup was designed for contactless complex gauge block analysis providing information about gauge block length, gauge block faces surface profile (e.g., indication of scratches) and by analysis of the interference fringes shape, also about the gauge block edge flatness distortion. The designed setup is supplemented by an automatic handling system designed for a set of 126 gauge blocks (0.5 mm to 100 mm) to allow the automatic contactless calibration of the complex gauge block set without a human operator.

The work presents measurements of the length stability of Zerodur glass ceramic with temperature change. Measurement of this thermal characteristic is necessary for determination of the optimal temperature at which the Zerodur glass ceramic has a coefficient of thermal expansion close to zero. The principle of the measurement is to monitor the length changes using an optical resonator with a cavity mirror spacer made from the Zerodur material to be studied. The resonator is placed inside a vacuum chamber with a temperature control. A tunable laser diode is locked to a certain optical mode of the resonator to monitor the optical frequency of this mode. A beat-note signal from optical mixing between the laser and a stabilized femtosecond frequency comb is detected and processed. The temperature dependence of the glass ceramics was determined and analyzed. The resolution of the length measurement of the experimental set-up is on the order of 0.1 nm.

We describe in this paper a pilot experiment of optimization of a white-light source for a low-coherence interferometry. The white-light source combines the light beams generated with colour LEDs. By modelling of the white light spectra, a contrast of a white light interference fringe could be changed and set to the maximal value. The second part of this paper is a description of a white-light fringe analysis ensured with a low-cost colour CCD camera. The used detection technique employs a phase-crossing algorithm which identifies a zero optical path difference as the point where the phase difference between the red, green and blue part of the white-light interference fringe becomes equal to zero. The optimized white light source is designed to be a crucial part of an experimental setup for the surface diagnostics and automatic calibration of gauge blocks.

The use of an ultra low expansion cavity plays a crucial role in laser stabilization, and in atomic or ion clocks. We propose an easy method of precise monitoring of optical path distance in Fabry-Perot interferometer. The spacing of mirrors of the Fabry-Perot interferometer in ambient air represents the optical path distance referenced to stable optical frequency of the femtosecond mode-locked laser. With the help of highly selective optical filter it is possible to get only a few of separate spectral components of laser comb. Optical path distance is transfered to optical frequency of the comb component and through the repetition frequency of the laser to the radio-frequency domain. Repetition frequency of the laser can be monitored with the uncertainty referenced to the any local oscillator or through the GPS to the atomic clock standard. By using this mehod we are able to measure and lock the Fabry-Perot cavity to a selected single component of optical frequency comb an to measure the optical path distance directly in rf domain.

We describe in this paper a pilot experiment of a white-light fringe analysis with a low-cost color CCD camera. The used detection technique employs the phase-crossing algorithm which identifies the zero optical path difference as the point where the phase difference between the red, green and blue part of the white-light interference fringe becomes equal to zero. An experimental arrangement is based on superluminescent LED diode. The experimental setup is designed to be a crucial part of the complex system for automatic contactless diagnostic and calibration of gauge blocks.

In metrology applications of laser interferometers like a scale calibration of capacitive or inductive sensors, strictly linear positioning of the measuring mirror of the interferometer is necessary. It is maintained usually by a stage, which is based on principle of linear guide ways with ball carrier bearings. But possible imperfection of guides of the travel stage can cause deviations of the mirror plane from the right angle to the axis of traveling. Mentioned angle deviations lead to distortion of interference fringes in the output of the interferometer and by other words it causes non-linearity of the interferometer scale. Because the phenomenon is very random for this type of the travel stage the uncertainty of calibration of sensors is higher. In the work we present a method, which eliminates this usual problem by two ways. The first of them utilizes a special configuration of the laser interferometer where possible angle deviation of the mirror plane is compensated by second pass of the laser beam in the measuring arm of the interferometer. The next way is based on continual monitoring of spatial position of laser beams in the interferometer when the measuring mirror is positioned. It works with condition that the mirror can be slightly tilted by piezoelectric actuators in servo-loop mode with respect to detected spatial position.

Laser interferometers are even more precise distance measurement devices with resolution up to sub-nanometer region. If the measurements are carry out under atmospheric conditions (usual situation in an industry), the interferometers measure optical path length of an unknown distance instead of its true geometrical value. It is caused by an index of refraction of air that introduces a multiplicative constant to measured results. If we want correct values of the distance measurement the knowledge of the instantaneous value of the index is necessary. In the work, we present design and the first experimental results of method of the direct measurement of the index, where a Fabry-Perot (F.-P) interferometer is used as a detection system. The method employs a differential setup of two F.-P interferometers, where the cavity of the first is permanently evacuated and the other is on the air. The ultimate resolution of the measurement and the operating regime without need of a vacuum pump stay the method very advantage. The work includes comparison of the method with conventional refractometer where evacuatable cell is inserted into the measuring arm of Michelson interferometer. The comparison of the method with indirect measurement of the index with using Edlen formula is presented too.

We present a new interferometric method for shape measurement of hollow cylindrical tubes. We propose a simple and robust self-referenced interferometer where the reference and object waves are represented by the central and peripheral parts, respectively, of the conical wave generated by a single axicon lens. The interferogram detected by a digital camera is characterized by a closed-fringe pattern with a circular carrier. The interference phase is demodulated using spatial synchronous detection. The capabilities of the interferometer are experimentally tested for various hollow cylindrical tubes with lengths up to 600 mm.