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In scanning probe microscopy laser interferometers are usually used for measuring the position of the probe tip with a metrological traceability. As the most of the AFM setups are designed to work under standard atmospheric conditions the changes of the refractive index of air have an influence to measured values of the length with 1.0e-4 relatively. In order to achieve better accuracies the refractive index of air has to be monitored continuously and its instantaneous value has to be used for compensating the lengths measured by all of the interferometric axes. In the presented work we developed a new concept of an electronic unit which is able to monitor the refractive index of air on basis of measurement of ambient atmospheric conditions: temperature, humidity, pressure of the air and the CO2 concentration. The data processing is based on Ciddor equation for calculating the refractive index of air. The important advantage of the unit is a very low power consumption of the electronics so the unit causes only negligible temperature effects to the measured environment. The accuracy of the indirect measuring method employed by the unit was verified. We tested the accuracy in comparison with a direct method of measuring refractive index of air based on an evacuatable cell placed at the measuring arm of a laser interferometer. An experimental setup used for verification is presented together with a set of measurements describing the performance. The resulting accuracy of the electronic unit falls to the 4.1e-7 relatively., Comment: 8 pages, 4 figures; SPIE Optical Metrology 2013, 2013, Munich, Germany

A passive optical resonator is a special sensor used for measurement of lengths on the nanometer and sub-nanometer scale. A stabilized optical frequency comb can provide an ultimate reference for measuring the wavelength of a tunable laser locked to the optical resonator. If we lock the repetition and offset frequencies of the comb to a high-grade radiofrequency (RF) oscillator its relative frequency stability is transferred from the RF to the optical frequency domain. Experiments in the field of precise length metrology of low-expansion materials are usually of long-term nature so it is required that the optical frequency comb stay in operation for an extended period of time. The optoelectronic closed-loop systems used for stabilization of combs are usually based on traditional analog electronic circuits processing signals from photodetectors. From an experimental point of view, these setups are very complicated and sensitive to ambient conditions, especially in the optical part, therefore maintaining long-time operation is not easy. The research presented in this paper deals with a novel approach based on digital signal processing and a software-defined radio. We describe digital signal processing algorithms intended for keeping the femtosecond optical comb in a long-time stable operation. This need arose during specialized experiments involving measurements of optical frequencies of tunable continuous-wave lasers. The resulting system is capable of keeping the comb in lock for an extensive period of time (8 days or more) with the relative stability better than 1.6 × 10

This research deals with preparation of an optical frequency references based on hollow-core photonic crystal fibers (HC-PCF). This fiber-based type of absorption cells represents a effiecient way how to replace classic bulky and fragile glass made tubes references with low-weight and low-volume optical fibers. This approach allows not only to increase possible interaction length between incident light and absorption media but it also carries a possibility of manufacturing of easy-operable reference which is set up just by plugging-in of optical connectors into the optical setup. We present the results of preparation, manufacturing and filling of a set of fiber-based cells intended for lasers frequency stabilization. The work deals with setting and optimalization of HC-PCF splicing processes, minimalization of optical losses between HC-PCF and SMF fiber transitions and finishing of HC-PCF spliced ends with special care for optimal closing of hollow-core structure needed for avoiding of absorption media leakage.

The absolute distance between the mirrors of a Fabry-Perot cavity with a spacer from an ultra low expansion material was measured by an ultra wide tunable laser diode. The DFB laser diode working at 1542 nm with 1.5 MHz linewidth and 2 nm tuning range has been suppressed with an unbalanced heterodyne fiber interferometer. The frequency noise of laser has been suppressed by 40 dB across the Fourier frequency range 30–300 Hz and by 20 dB up to 4 kHz and the linewidth of the laser below 300 kHz. The relative resolution of the measurement was 10 − 9 that corresponds to 0.3 nm (sub-nm) for 0.178 m long cavity with ability of displacement measurement of 0.5 mm.

In this paper, a novel principle of contactless gauge block calibration is presented. The principle of contactless gauge block calibration combines low-coherence interferometry and laser interferometry. An experimental setup combines Dowell interferometer and Michelson interferometer to ensure a gauge block length determination with direct traceability to the primary length standard. By monitoring both gauge block sides with a digital camera gauge block 3D surface measurements are possible too. The principle presented is protected by the Czech national patent No. 302948.

In this contribution we propose a scheme for a generation of precise displacements through conversion of relative stability of components of a femtosecond laser into the length of a Fabry-Perot cavity. The spacing of mirrors of a Fabry-Perot interferometer represents a mechanical length standard referenced to stable optical frequency of a femtosecond mode-locked laser. With the help of a highly selective optical filter, it is possible to get only a few discrete spectral components. By tuning and locking the Fabry-Perot cavity to a selected single component it is possible to get a mechanical length standard with the uncertainty of the repetition frequency of the femtosecond laser. To verify the method, an auxiliary single-frequency laser is locked to the resonance mode of the cavity and simultaneously it is optically mixed with an independent optical frequency standard He-Ne-I2. The stability of the beat-frequency between these 2 lasers represents the stability of the Fabry-Perot cavity length. The stability recording evaluated through Allan variances for one hour of operation is presented. The pilot experimental setup is able to generate the length standard in the order of 0.01 nm for 20 min of integration time.

Semiconductor lasers found a foothold in many fields of human activities, mainly thanks to its small size, low cost and high energy efficiency. Recent methods for accurate distance measurement in industrial practice use principles of laser interferometry, which are based on lasers operating in the visible spectrum. When the laser beam is visible the alignment of the industrial interferometer makes the measuring process easier. Traditional lasers for these purposes for many decades - HeNe gas laser - have superb coherence properties but small tunable range. On the other hand laser diodes are very useful lasers but only if the active layer of the semiconductor equips with a passive selective element that will increase the quality of their own resonator and also prevents the structure of its higher longitudinal modes. The main aim of the work is a design of the laser source based on a new commercial available laser diode with Distributed Bragg Reflector structure, butterfly package and fibre coupled output. The ultra-low noise injection current source, stable temperature controller and supply electronic equipment were developed with us and experimentally tested with this laser for the best performances required of the industrial interferometry field. The work also performs a setup for frequency noise properties investigation with an unbalanced fibre based Mach-Zehnder interferometer and 10 m long fibre spool inserted in the reference arm. The work presents the way to developing the narrow-linewidth operation the DBR laser with the wide tunable range up to more than 1 nm of the operation wavelength at the same time. Both capabilities predetermine this complex setup for the industrial interferometry application as they are the long distance surveying or absolute scale interferometry.

This work is oriented towards our research in the field of splicing and ending of optical frequency references based on hollow core photonics crystal fibers (HC-PCF). This type of references is very promising optical element to replacing classic bulky absorption cells for laser frequency stabilization. We prepared and present methods of splicing HC-PCF to standard telecommunication fiber by a fiber splicer. A special care was taken to optimize the splicer setting and to find and obtain a splice with minimal optical losses between HC-PCF and SMF. The manufactured fiber cell was closed at one side by connecting to SMF and second fiber end was prepared for placing into the vacuum chamber with the help of vacuum-tightened connection to be used as a optical frequency reference based on the acetylene gas for frequency stabilization of the laser standards.

The development of absolute distance measurement methods have been enabled by new kind of lasers, special digital signal processing electronics, algorithms and new materials for optics. The phenomenon of the mode-lock of the femtosecond pulse laser increased a number of potential applications with distance surveying where that stable generator of very short and periodically repeated coherent pulses can be used. The main aim of the work is a description of precise measuring method with absolute scale which is able to determine the length of unknown distance with direct traceability to a time standard. The principle of the method is based on a passive optical cavity with mirrors keeping measured distance, in our case a piezoelectric actuator. Time spacing of short femtosecond pulses generated by mode-locked laser is optically phase locked to the cavity free spectral range. A value of the repetition frequency of the laser determines the measured distance. The exact value of the frequency/period of the femtosecond pulse train is detected by a frequency counter. The counting gate of the counter is synchronized with a highly stable oscillator disciplined by H-maser or GPS received signal from atomic clocks. The work shows methods how to overcome problems with dispersive optics in the passive cavity and a way of phase lock of the femtosecond laser repetition rate to free spectral range of the cavity. This measuring technique is demonstrated on length characterization of the piezoelectric transducer which belongs to ultra-precise positioning actuators.

We present a method of noise suppression of laser diodes by an unbalanced Michelson fiber interferometer. The unstabilized laser source is represented by compact planar waveguide external cavity laser module, ORIONTM (Redfern Integrated Optics, Inc.), working at 1540.57 nm with a 1.5-kHz linewidth. We built up the unbalanced Michelson interferometer with a 2.09 km-long arm based on the standard telecommunication single-mode fiber (SMF-28) spool to suppress the frequency noise by the servo-loop control by 20 dB to 40 dB within the Fourier frequency range, remaining the tuning range of the laser frequency.

We present a method of noise suppression of laser diodes by unbalanced Michelson fiber interferometer. The unstabilized laser source is represented by compact planar waveguide external cavity laser module ORION (Redfern Integrated Optics, Inc.) working at 1040.57 nm with < 3 kHz linewidth. We built Michelson interferometer with 1 km long arm based on SMF-28 fiber spool to suppress the frequency noise by fast PI servo-loop up to 33 kHz of laser injection current modulation. We were able to decrease the noise level by −60 dBc/Hz up to 1.5 kHz noise frequency of the laser.

In cases when it is necessary to lock optical frequencies generated by an optical frequency comb to a precise radio frequency (RF) standard (GPS-disciplined oscillator, H-maser, etc.) the usual practice is to implement phase and frequency-locked loops. Such system takes the signal generated by the RF standard (usually 10 MHz or 100 MHz) as a reference and stabilizes the repetition and offset frequencies of the comb contained in the RF output of the f-2f interferometer. These control loops are usually built around analog electronic circuits processing the output signals from photo detectors. This results in transferring the stability of the standard from RF to optical frequency domain. The presented work describes a different approach based on digital signal processing and software-defined radio algorithms used for processing the f-2f and beat-note signals. Several applications of digital phase and frequency locks to a RF standard are demonstrated: the repetition (f rep ) and offset frequency (f ceo ) of the comb, and the frequency of the beat note between a CW laser source and a single component of the optical frequency comb spectrum.

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 1*E-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. 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 on an experimental setup and a set of measurements describing the performance is presented.

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 presented work is focused on digital processing of beat note signals from a femtosecond optical frequency comb. The levels of mixing products of single spectral components of the comb with CW laser sources are usually very low compared to products of mixing all the comb components together. RF counters are more likely to measure the frequency of the strongest spectral component rather than a weak beat note. Proposed experimental digital signal processing system solves this problem by analyzing the whole spectrum of the output RF signal and using software defined radio (SDR) algorithms. Our efforts concentrate in two main areas: Firstly, using digital servo-loop techniques for locking free running continuous laser sources on single components of the fs comb spectrum. Secondly, we are experimenting with digital signal processing of the RF beat note spectrum produced by f–2f 1 technique used for assessing the offset and repetition frequencies of the comb, resulting in digital servo-loop stabilization of the fs comb. Software capable of computing and analyzing the beat-note RF spectrums using FFT and peak detection was developed. A SDR algorithm performing phase demodulation on the f– 2f signal is used as a regulation error signal source for a digital phase-locked loop stabilizing the offset frequency of the fs comb.

The work presents a measurement of lengths by an optical measuring 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. For the testing of the method the special combination of the optical resonator and Michelson interferometer was put together. This system combines the cavity length of the optical resonator with the measuring arm of the Michelson laser interferometer. The one mirror of the system is common for both laser interferometers and it is driven by piezoelectric transducer. The testing range is limited by the range of tuneability of the used laser and it covers 1000 nm of the length measurement.

The presented work is focused on digital processing of beat note signals from a femtosecond optical frequency comb. The levels of mixing products of single spectral components of the comb with CW laser sources are usually very low compared to products of mixing all the comb components together. RF counters are more likely to measure the frequency of the strongest spectral component rather than a weak beat note. Proposed experimental digital signal processing system solves this problem by analyzing the whole spectrum of the output RF signal and using software defined radio (SDR) algorithms. Our efforts concentrate in two main areas: Firstly, we are experimenting with digital signal processing of the RF beat note spectrum produced by f–2f 1 technique and with fully digital servo-loop stabilization of the fs comb. Secondly, we are using digital servo-loop techniques for locking free running continuous laser sources on single components of the fs comb spectrum. Software capable of computing and analyzing the beat-note RF spectrums using FFT and peak detection was developed. A SDR algorithm performing phase demodulation on the f– 2f signal is used as a regulation error signal source for a digital phase-locked loop stabilizing the offset and repetition frequencies of the fs comb.

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.

This paper describes 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. Hereafter, a concept of the light source for the low-coherence interferometry based on high-luminescent LED and single mode optical fibres is presented.The design comes out form a requirement to have an output beam combining a white-light beam and a laser beam. In the case of coaxial white-light and laser beam, the white-light interferometer is precisely combined with an incremental laser interferometer. This combination allows doing online surface diagnostics with high precision. 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.

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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.

Improvement of the linewidth and the mode-hop free tuning range of the Vertical Cavity Surface Emitting Laser (VCSEL) diode is the main goal of our upcoming Fiber Bragg Gratings (FBGs). The VCSEL with the fiber grating will be very suitable laser source for new generation of the absolute and the incremental laser interferometers based on our published VCSEL interferometer. The linewidth of the emission spectrum and the mode-hop free tuning range of the wavelength are critical in laser interferometry. The full width in half maximum (FWHM) linewidth of VCSEL at 760 nm wavelength is 100 MHz approximately. Tuning range up to 1 nm was measured by a highly precise commercial lambdameter with 0.1 pm resolution. To improve such a characteristic a high precise FBG must be selected. On the basis of our simulations and measurements of the commercially available fiber gratings we designed a special 100 mm long fiber Bragg grating with apodization. We expect the application of the FBG to improvement of the linewidth and mode-hop free tuning range of VCSEL at the wavelength 760 nm to increase resolution of laser interferometer based on VCSEL diode.

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 simulated chirped and apodized fiber Bragg gratings (fiber gratings with modulation of the amplitude and with modulation of the spacing) the same as uniform fiber gratings. Results of our simulations are presented. Apodization of fiber Bragg gratings (FBG) has many advantages in comparison to other types of FBGs. Main improvement is suppressing of the side lobes in the grating spectral properties. The difference of side lobes suppression for uniform and Gaussian apodized grating is more than 110dB. On the basis of these results we designed a special fiber Bragg grating with apodization especially for using to stabilize semiconductor lasers for high precision laser applications with central wavelength 760nm. We present application of methods for calculation of parameters of apodized fiber Bragg gratings (FBG). We used combination of methods based on layered dielectric media (LDM) and the transfer matrix. On the contrary to the other calculation techniques the LDM method is based on sequence of thin films of dielectric media assembled in the direction of wave propagation. The combination of the LDM method and the transfer matrix method can be used to the calculation of arbitrary fiber gratings with high precision. For this designed apodized FBG we calculated the phase mask to manufacture by interference patterns. The phase mask and the fixation bottom of the fiber were made by e-beam lithography to achieve highly precise stability during manufacturing. We present the set-up of this system for writing FBG by pulsed UV laser with wavelength 266nm. Measurement of commercially available FBG with comparison to our calculated FBG is presented.

Mechanical construction of the fiber absolute laser interferometer is presented in this article. The unique system is based on the VCSEL laser diode (wavelength 760 nm) and uses single-mode fibers. Optical setup consists of new E2000/APC connectors and fiber optic isolator to minimize the back-reflection to the laser diode. The whole system is placed on the massive duralumin plate to minimize mechanical influences. Base plate is placed on the rack with control electronics to create compact unit. The whole system is developed for industrial applications.

The work is oriented to development of methods for the absolute laser interferometry. The difference between absolute and incremental measurement is described. In the field of the absolute laser interferometry, the linewidth of the laser source limits the maximum measurable distance and the interval of mode-hop free tuning range determines the resolution of the distance measurement. Then, is work is oriented to selection of the primary laser source for the absolute laser interferometry and to determination of its characteristics. Methods of measurements and calculation of basic parameters of the tunable lasers are well described. The method of the absolute laser interferometry with wavelength-scanning interferometry technique improved by an amplitude division of interference fringe was designed and it is described. The Fabry-Perot etalon was designed and it is used to measure the tuning range ofthe laser source.

This paper discusses methods for calculation properties of apodized fiber Bragg gratings (FBGs). These are one of the most enveloping optical devices in telecommunications and sensor systems. Work is aimed to simulation of FBGs, with utilization especially in sensor systems and laser interferometry for semiconductor laser stabilization at wavelength about 760nm. Program for FBG properties calculation was written in Matlab software. At first, FBG is divided into several uniform sections. To calculate properties of each uniform section is used coupled-mode theory. Coupled-mode theory is ordinary used for electromagnetic field specification in waveguides with periodic perturbations in the propagation direction. Next the transfer matrix method is used for overall properties calculation. The main point of simulation is reflectivity spectrum calculation in dependence of fiber dimensions and material properties. These FBGs have wide range of use in optical systems as band filters, in-fiber sensors or fiber grating lasers and amplifiers for their unique properties.