Ondřej Číp

Problems regarding linearity of data of a laser interferometer with a single-frequency laser

In this paper, the main causes of scale nonlinearity of a laser interferometer with a single-frequency laser and a quadrature fringe detection system are described. The primary causes of scale nonlinearity are quadrature phase shift error and imperfect optical elements in the interferometer and detection unit. A method for measuring this nonlinearity with an optical compensator is described. Nonlinearities arising from quadrature phase shift error, unequal amplitudes, and electronic offsets in the detection unit can be compensated by means of a PC program as described herein. By using a differential interferometer with a resolution of 0.3 nm, the nonlinearity compensation was experimentally verified, and by averaging the measured values for 20 s, a linearity better than ±0.5 nm was achieved.

Multidimensional interferometric tool for the local probe microscopy nanometrology

This work reports on the measurement at the nanoscale using local probe microscopy techniques, primarily atomic force microscopy. Recent applications using the atomic force microscope as a nanometrology tool require that not only the positioning of the tip has to be based on precise measurements but also the traceability of the measuring technique has to be ensured up to the primary standard. Thus, in our experimental work, laser interferometric measuring methods were employed. In this paper, a new design of the six-axis-dimensional interferometric measurement tool for local probe microscopy stage nanopositioning is presented.

Absolute frequency shifts of iodine cells for laser stabilization

We present an investigation of iodine cell purity and influence of contaminations upon frequency shifts of iodine-stabilized frequency-doubled Nd : YAG lasers. The study combines measurements of laser-induced fluorescence and evaluation through the Stern–Volmer formula, with direct measurement of frequency shifts referenced by means of an optical comb to a radiofrequency clock etalon. These indirect and direct approaches are compared and provide feedback on the cell manufacturing procedure. Significant improvement of the apparatus for the measurement of induced fluorescence is reported, leading to better repeatability of the results. The ultimate precision that can be achieved in measurements of the absolute frequency of a stabilized laser is discussed in terms of the cell quality. (Some figures in this article are in colour only in the electronic version)

Suppression of Air Refractive Index Variations in High-Resolution Interferometry

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.

Refractive Index Compensation in Over-Determined Interferometric Systems

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.

Displacement interferometry with stabilization of wavelength in air

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.

Local probe microscopy with interferometric monitoring of the stage nanopositioning

We present a system of positioning and interferometric monitoring of a sample position for measurements and calibration in the nanoscale in metrology. The positioning is based on a three-axis stage which allows replacing scanning by the probe of an atomic force microscope with a system with full interferometric displacement measurement. A stage with 200 µm × 200 µm of horizontal travel extends also the microscope range. The stage allows positioning with sub-nanometer resolution in all three axes under a closed loop control with position detection via capacitive sensors. Interferometric system monitoring all six degrees of freedom of the stage ensures full metrological traceability of the positioning to the fundamental etalon of length and improves resolution and overall precision of the displacement monitoring.

Frequency Noise Properties of Lasers for Interferometry in Nanometrology

In this contribution we focus on laser frequency noise properties and their influence on the interferometric displacement measurements. A setup for measurement of laser frequency noise is proposed and tested together with simultaneous measurement of fluctuations in displacement in the Michelson interferometer. Several laser sources, including traditional He-Ne and solid-state lasers, and their noise properties are evaluated and compared. The contribution of the laser frequency noise to the displacement measurement is discussed in the context of other sources of uncertainty associated with the interferometric setup, such as, mechanics, resolution of analog-to-digital conversion, frequency bandwidth of the detection chain, and variations of the refractive index of air.

Small displacement measurements with subatomic resolution by beat frequency measurements

In this paper a novel method for high-resolution measurement of displacements with sub-atomic resolution is described. With this method, a length change of an optical resonator is directly transformed to a radio-frequency signal. A tunable He?Ne laser is locked to a mode of the resonator using a digital signal processing technique. Heterodyne mixing of this locked laser with an iodine-stabilized He?Ne laser converts the frequency of the laser locked to the cavity into the radio-frequency region. A HF counter measures the beat frequency from which the displacement can be derived directly. This method delivers inherent linearity and sub-nanometre resolution of the displacement over a range of several micrometres. An example of the capabilities of this system is given in this paper, where it is used for checking periodic deviations of a laser interferometer system. Emphasis is put on the construction of the optical resonator, on how its narrow resonance line-width is achieved, and how the required mechanical stability is achieved. The measurement range and the scale linearity are discussed in detail. Possible applications of this method are the calibration of nano-position systems based on PZT transducers, as well as inductive and capacitive sensors.

White-light fringe detection based on a novel light source and colour CCD camera

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 the white-light spectra, the 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 parts 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.