We report on the length measuring instrument with the absolute scale that was based on the combination of an optical frequency comb and a passive optical cavity. The time spacing of short femtosecond pulses, generated by the optical frequency comb, is optically phase locked onto the cavity free spectral range with a derivative spectroscopy technique so that the value of the repetition frequency of the femtosecond laser is tied to and determines the measured displacement. The instantaneous value of the femtosecond pulse train frequency is counted by a frequency counter. This counted value corresponds to the length given by the spacing between the two mirrors of the passive cavity. The phase lock between the femtosecond pulsed beam and the passive cavity is possible due to the low-dispersion of the cavity mirrors, where the silver coating on the mirrors was used to provide the low dispersion for the broadband radiation of the comb. Every reflection on the output mirror feeds a portion of the beam back to the cavity so that the output beam is a result of multiple interfering components. The parameters of the output beam are given not only by the parameters of the mirrors but mainly by the absolute distance between the mirror surfaces. Thus, one cavity mirror can be considered as the reference starting point of the distance to be measured and the other mirror is the measuring probe surveying the unknown distance. The measuring mirror of the experimental setup of the low-dispersion cavity is mounted on a piezoelectric actuator which provides small changes in the cavity length we used to test the length measurement method. For the verification of the measurement accuracy a reference incremental interferometer was integrated into our system so that the displacement of the piezoelectric actuator could be obtained with both measuring methods simultaneously.
This paper presents the progress in the development of two Fabry-Pérot filter cavities for repetition rate multiplication of two femtosecond frequency combs. The optical design of both setups consists of mode matching optics and a resonant cavity for the repetition rate multiplication. In one case, the cavity consists of two dielectric mirrors with near-zero group velocity dispersion and in the other of two silver coated mirrors. We demonstrate multiplication of a 1 GHz repetition rate to 10 GHz for a Ti:Sa femtosecond frequency comb with central wavelength around 820 nm and of 250 MHz repetition rate to 1 GHz for a Er-doped fiber femtosecond frequency comb with central wavelength around 1560 nm.
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 the field of precise measurement of optical frequencies, laser spectroscopy and interferometric distance surveying the
optical frequency synthesizers (femtosecond combs) are used as optical frequency references. They generate thousands
of narrow-linewidth coherent optical frequencies at the same time. The spacing of generated components equals to the
repetition frequency of femtosecond pulses of the laser. The position of the comb spectrum has a frequency offset that is
derived from carrier to envelope frequency difference. The repetition frequency and mentioned frequency offset belong
to main controlled parameters of the optical frequency comb. If these frequencies are electronically locked an ultrastable
frequency standard (i.e. H-maser, Cs- or Rb- clock), its relative stability is transferred to the optical frequency
domain. We present a complete digitally controlled signal processing chain for phase-locked loop (PLL) control of the
offset frequency. The setup is able to overcome some dropouts caused by the femtosecond laser non-stabilities
(temperature drifts, ripple noise and electricity spikes). It is designed as a two-stage control loop, where controlled offset
frequency is permanently monitored by digital signal processing. In case of dropouts of PLL, the frequency-locked loop
keeps the controlled frequency in the required limits. The presented work gives the possibility of long-time operation of
femtosecond combs which is necessary when the optical frequency stability measurement of ultra-stable lasers is
required. The detailed description of the modern solution of the PLL with remote management is presented.
KEYWORDS: Frequency combs, Signal processing, Digital signal processing, Radio optics, Femtosecond phenomena, Semiconductor lasers, Continuous wave operation, Analog electronics, Computing systems, Oscillators
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 (frep) and offset frequency (fceo) 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.
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 1.0exp(-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 4.1 exp(-7) relatively.
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.
KEYWORDS: Digital signal processing, Frequency combs, Laser sources, Continuous wave operation, Femtosecond phenomena, Signal processing, Optical signal processing, Demodulation, Semiconductor lasers, Nonlinear optics
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 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.
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.
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.
KEYWORDS: Digital signal processing, Laser sources, Femtosecond phenomena, Continuous wave operation, Signal processing, Frequency combs, Demodulation, Radio optics, Signal detection, Analog electronics
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.
In construction of highly mechanically stable measuring devices like AFM microscopes or nano-comparators the use of low expansion materials is very necessary. We can find Zerodur ceramics or ULE glasses used as a frame or basement of these devices. The expansion coefficient of such low-expansion materials is lower than 0.01 x 10-6 m•K-1. For example in case of a frame or basement 20 cm long it leads to a dilatation approximately 4 nm per 1 K. For calculation of the total uncertainty of the mentioned measuring devices the knowledge of the thermal expansion coefficient of the frame or basement is necessary. In this work we present a method, where small distance changes are transformed into rf-frequency signal. The frequency of this signal is detected by a counter which measures the value of the frequency with respect to an ultra-stable time-base. This method uses a Fabry-Perot cavity as a distance measuring tool. The spacer of the optical resonator is made from the investigated low-expansion material. It is placed into a vacuum chamber where the inside temperature is controlled. A selected mode of the femtosecond frequency of the femtosecond comb which represent the distance changes of the optical resonator. The frequency is measured by the rf-counter which is synchronized by a time-base signal from an atomic clock. The first results show the resolution of the method in the 0.1 nm order. Therefore the method has a potential in characterisation of materials in the nanoworld.
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.
In this contribution we propose a scheme of Fabry-Perot interferometer measuring the absolute distance in
atmosferic conditions using a femtosecond laser comb. The spacing of mirrors of the Fabry-Perot interferometer
represents the length standard 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. By tuning
and locking of 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. If the interferometer measures
distance in atmospheric conditions, the absolute value of the laser wavelength fluctuates with a refractive index
of air. Compairing the measurement in evacuated chamber with measurement in ambient air leads to enhanced
precision in measurement of refrective index of air.
Need of precise definition of the calibrated length is of great importance in industrial application in these days.
The Fabry-Perot interferometer or etalon with very high stable laser produces length etalon sensitive in nanometer
scale with linear response to its change. Fabry-Perot interferometer (etalon) with length L represents a set of
equidistant frequencies that could be transmitted through the length etalon. Each frequency could be described
as multiple of free spectral range of Fabry-Perot etalon which depends inversely to the mirror spacing. Tuning
DFB diode covering the tuning frequency range of hundreds of GHz is used as laser source for detection of
transmitted light. Found DFB diode laser wavelength transmitted through the Fabry-Perot etalon is measured
by wavelengthmeter. Train of femtosecond laser pulses produces an optical frequency spectrum (optical comb)
of separate equidistant frequencies with an offset frequency. Stabilized optical comb generates a very precise
frequency rule. Frequency beat between DFB laser source and the closest femtosecond laser line is detected to
find the exact frequency. This procedure is done in whole DFB laser diode tuning range. Such method produce
about hundred of reproductive and well defined measured points in DFB laser diode tuning range. Measured
points are treated by computer algorithm. Moreover the Fabry-Perot mirror distance changes could be precisely
analyzed by this method.
Interferometric methods are used for definition of length by distance translation to one of the interferometric arms. The
Fabry-Perot interferometer or etalon with very high stable laser produces length etalon sensitive in nanometer scale with
linear response to its change. We present in our work improvements of such method by removing the very high stable
laser by the femtosecond stabilized optical frequency comb. Train of femtosecond laser pulses produces an optical
frequency spectrum separated by equidistant frequency frep with frequency offset fceo called frequency comb. Stabilized
frequency comb generates a very precise frequency rule. Locking the scanning Fabry-Perot interferometer to one of
the frequency components could perform length etalon. The Fabry-Perot etalon in simple geometry transmits only the
frequencies with integer multiple of fcav which depends inversely to the mirror spacing. The principle of the first method
is based on the direct relation between the repetition frequency of the comb and the etalon length. Fabry-Perot etalon
transmits only the optical frequencies of the comb for those fceo equal to zero and fcav is an integer multiple of frep. The
detected scanning spectrum is characterized by interferogram. The center of the gravity fulfills the condition for direct
length transfer between the Fabry-Perot mirror distance length and frep of the femtosecond frequency synthesizer.
Discrete value of length etalons is obtained. The improvement of the method is based on separation of few optical
frequency lines (narrowing the frequency spectrum) from the wide frequency range of the optical frequency synthesizer.
It suppresses the presence of the interferogram which has very high demands on the further computer analysis.
Widening the scanning Fabry-Perot free spectral range as much as possible enable us to observe each frequency line
(line of the comb) only once. The detected scanning spectrum better characterizes the frequency output of the optical
frequency synthesizer. This feature enable us to lock the Fabry-Perot intermode distance to one of the detected comb
line. Moreover the mirror distance in the Fabry-Perot is arbitrary. We verified the experiment by the fiber based
femtosecond stabilized optical frequency synthesizer working at central wavelength 1560 nm and with frep 100 MHz.
Two He-Ne stabilized lasers for coarse Fabry-Perot mirror spacing length adjustment were separated by different optical
polarization. Dielectric multilayer mirror coatings were wavelength dependent. DFB laser diode working on the 1542 nm
were added into the set-up. Intermode beat between the frequency comb component and the DFB diode well defines
the exact frequency position on which the etalon is locked. Comparison between different Fabry-Perot etalon has been
made.
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.
We present in recent work release of very precise length standard based on laser frequency comb. Each frequency comb
produces a frequency spectrum with equidistant modes frep with frequency offset fceo. Stabilized frequency comb produce a very precise frequency rule. Fabry-Perot cavity is frequently used as interferometer using a scanning mirror position.
Depending on mirror coatings and reflectivity of mirrors one could obtain a spectrum of any laser adjusted to the
Fabry-Perot cavity. Two methods of length stabilization using the
Fabry-Perot cavity are presented and compared. One method
uses the cavity of mirror distance defined by νcav as an integer multiple of frep. The second is based on selection of narrow part of the spectrum and very wide inter-mode frequency νcav. Two continuous working He-Ne stabilized lasers for coarse Fabry-Perot mirror spacing length adjustment were separated by different optical polarization and one
stabilized frequency comb separated from both lasers operated at different central wavelength.
We present an improved technique for detection of trace impurities in iodine-filled absorption cells for laser frequency
stabilization. The results of purity investigation are compared to frequency shifts measured with a set of two iodine
stabilized Nd:YAG lasers. The setup for direct fluorescence measurement with an Argon-ion laser operating at 502 nm
wavelength is equipped with compensation for laser power and spectral instabilities.
The progress in the field of optical frequency standards is oriented to femtosecond mode-locked lasers stabilized by
technique of the optical frequency synthesis. Such a laser produces a supercontinuum light, which is composed of a
cluster of coherent frequency components in certain interval of wavelengths. A value of the repetition rate of
femtosecond pulses determines (in the frequency domain) spacing of these coherent components. If we control the mode-locked
laser by means of i.e. atomic clocks we ensure frequency of these components very stable. With respect to
definition of SI unit "one meter" on basis of speed of light the stabilized mode-locked laser can be used for
implementation of this definition by non-traditional way. In the work we present our proposal of a system, which
converts excellent frequency stability of components generated by the mode-locked laser to a net of discrete absolute
lengths represented by a distance of two mirrors of an optical resonator. On basis of theory, the optical resonator with a
cavity length has a periodic frequency spectrum Similarly the frequency of i-th comb component could be written as: fi =
fceo + i frep, where fceo is the comb offset frequency and frep is the repetition rate. For the simplicity we presume the offset
frequency fceo equals to zero. If the supercontinuum beam of the mode-locked laser illuminates the resonator and at the
same time the cavity length L is adjusted to length Lp = c / (2 p frep ) then both spectra fit. The symbol 'p' is an integer
value. It produces intensity maximum in the output of the cavity, which is detected by a photodetector and locked in the
servo-loop. For absolute discrete values of cavity lengths Lp that well satisfy the condition above we obtain precise
etalons of length.
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.
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