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It is known that the periodic error of heterodyne interferometers limits the accuracy of measurement to nanometre order. It is mainly derived from frequency mixing in the interferometer optics and this can be resolved using the configuration with two spatially separated beams. However, there remains a periodic error associated with parasitic reflections. Recently, we have developed a differential single-path heterodyne interferometer with two spatially separated beams, which was constructed within a single small quasi-cubic optical unit to minimize the parasitic reflections. In this work, the residual periodic error of this interferometer was evaluated with two evaluation methods, ‘the amplitude method’ and ‘the subtraction method’, and their results were compared. By applying uncertainty estimation procedures to the results, these two methods were shown to be highly consistent, confirming the reliability of our evaluation results. The error in λ/2 period of this interferometer was 7.6 pm.

The fine-structured spectrum of a terahertz (THz) frequency comb has been observed using asynchronous-optical-sampling THz time-domain spectroscopy with an extended time window covering multiple THz pulses. Fourier transformation of 10 consecutive THz pulses enables us to obtain the spectrum of THz comb mode having a linewidth of 25 MHz at intervals of 250 MHz. Further expansion of time window up to 100 consecutive THz pulses reduces the linewidth of THz comb mode down to 2.5 MHz while conserving interval of 250 MHz. The observed THz comb mode can be used as a precise and accurate frequency marker for broadband THz spectroscopy because it is phase-locked to a microwave frequency standard by laser control. The spectroscopy of pharmaceutical tablets and low-pressure molecular gas is used to demonstrate the utility of this approach, indicating a spectral resolution of 250 MHz. The proposed method enables frequency calibration of the THz spectrometer based on a microwave frequency standard.

Two techniques for terahertz (THz) frequency metrology based on frequency comb, namely, a THz-comb-referenced spectrum analyzer and a continuously tunable, single-frequency continuous-wave (CW)-THz generator, are reviewed. Since the frequency comb enables to coherently link the frequency among microwave, optical, and THz regions, it is possible to establish the THz frequency metrology traceable to time of the SI base units. Using a THz-comb-referenced spectrum analyzer based on a stable THz comb generated in a photoconductive antenna for THz detection, the absolute frequency of CW test sources in the sub-THz and THz regions was determined at a precision of 10-11. Furthermore, a continuously tunable, single-frequency CW-THz generator was demonstrated around 120 GHz by photomixing of an accurately tunable CW laser and a tightly fixed CW laser in the optical frequency region, phase locked to two independent optical combs. The combination of the CW-THz generator with the THz-comb-referenced spectrum analyzer will open the door for establishment of frequency metrology in the THz region.

Previously, the authors have developed a subnanometre heterodyne interferometric system known as a three-mode heterodyne interferometer (TMHI). By converting the target displacement into twice the phase variation of a conventional interferometer, the TMHI has achieved position resolution of 0.044 nm even with a single-pass interferometer. However, the heterodyne beat frequency in TMHI is quite low, of the order of several hundred kilohertz, which limits the measurable target speed to several tens of millimetres per second. In this paper, we present a method to extend the measurable target speed of the TMHI without increasing the heterodyne beat frequency of a light source. Keeping the excellent position resolution of the TMHI, the proposed method provides sufficient response to high speed movement of the target. The system comprises a pair of TMHI and utilizes two conjugate signals generated by them selectively according to the direction of movement of the target. Possible errors in switching the two signals are analysed by introducing an error zone model. The switching function was demonstrated using the mechanical vibration of the interferometer and proved to be free from erroneous counts. It was also confirmed that the system can respond at a speed that exceeds that determined by the beat frequency.

Phase measurement of continuous-wave terahertz (CW-THz) radiation is a potential tool for direct distance and imaging measurement of optically rough objects due to its high robustness to optical rough surfaces. However, the 2π phase ambiguity in the phase measurement of single-frequency CW-THz radiation limits the dynamic range of the measured distance to the order of the wavelength used. In this article, phase-slope measurement of tunable CW-THz radiation with a THz frequency comb was effectively used to extend the dynamic range up to 1.834 m while maintaining an error of a few tens µm in the distance measurement of an optically rough object. Furthermore, a combination of phase-slope measurement of tunable CW-THz radiation and phase measurement of single-frequency CW-THz radiation enhanced the distance error to a few µm within the dynamic range of 1.834 m without any influence from the 2π phase ambiguity. The proposed method will be a powerful tool for the construction and maintenance of large-scale structures covered with optically rough surfaces.

Optical frequency combs are innovative tools for broadband spectroscopy because a series of comb modes can serve as frequency markers that are traceable to a microwave frequency standard. However, a mode distribution that is too discrete limits the spectral sampling interval to the mode frequency spacing even though individual mode linewidth is sufficiently narrow. Here, using a combination of a spectral interleaving and dual-comb spectroscopy in the terahertz (THz) region, we achieved a spectral sampling interval equal to the mode linewidth rather than the mode spacing. The spectrally interleaved THz comb was realized by sweeping the laser repetition frequency and interleaving additional frequency marks. In low-pressure gas spectroscopy, we achieved an improved spectral sampling density of 2.5 MHz and enhanced spectral accuracy of 8.39 × 10(-7) in the THz region. The proposed method is a powerful tool for simultaneously achieving high resolution, high accuracy, and broad spectral coverage in THz spectroscopy.

We present a high-resolution heterodyne interferometric system using a high-output-power, three-longitudinal-mode He-Ne laser. In this system, an interferometric wavelength of λ/2 is synthesized with the super-heterodyne detection of the three modes, resulting in twice the sensitivity for the target displacement in comparison with the conventional two-frequency interferometer. In the experiment, the achievement of subnanometre resolution has been confirmed.

We present here a new method for real-time absolute-distance measurement. It is based on a two-wavelength superheterodyne interferometer. It is performed by simultaneous measurement of its synthetic wavelength and one of two wavelengths. The phase of one of two wavelengths is electrically separated from the synthetic one, thus maintaining the resolution of a one-wavelength heterodyne interferometer. Two He-Ne lasers operating at 1 = 633 nm and 2 = 612 nm are incorporated into the measuring system, as two wavelength sources, resulting in the synthetic wavelength of s = 18.4 µm. Thus, the proposed system has a range of 9.2 µm with nanometre resolution.

A simple frequency stabilization method for frequency-doubled output (532 nm) of an Nd:YAG laser is described. The frequency shift caused by an acousto-optic modulator is effectively applied to stabilize the laser frequency. For the frequency stabilization, there are two kinds of error signal: (1) the first-derivative of absorption of iodine molecules and (2) the first-derivative of dispersion were extracted to examine which signal is suitable for the actual stabilization of the laser frequency. Based on this examination, the stabilization was executed utilizing the error signal (1), resulting in a frequency instability of .

Frequency of a 532 nm emission line of a diode-laser-pumped Nd:YAG laser is stabilized by lock of the output line to the linear absorption line of iodine molecules. The stabilization method is very simple utilizing the frequency shift caused with an acousto-optic modulator. The laser frequency was stabilized at the zero-crossing point of the second-derivative of the dispersion curve. Instability obtained by the error signal is affected by the phase-characteristics of detectors, which results in 3*10-8.

We demonstrated a frequency measurement of CW-THz wave referring to THz frequency comb. Effectiveness of the proposed method is demonstrated by measurement of sub-THz test sources. The achieved precision of frequency measurement was 2.0*10-11.

Undesirable phase delay in avalanche photodiode (APD) between input light and output current is noticeable when modulation frequency of the incident light is over several hundreds of MHz. The degree of the delay increases with a decrease of the incident intensity. To clarify this phenomenon, relationships among the phase delay, output current, and the multiplication factor (current gain) of APD have been investigated. From this investigation, we found that the multiplication factor of APD increased with a decrease of the incident intensity, resulting in a decrease of the cutoff frequency of the APD. Supposing that the cutoff frequency defines the signal delay, the amount of the phase delay has been quantified with respect to the multiplication factor. Such a phase delay can be eliminated by superimposing a bias light on the modulation light so that the total intensity remains constant. To confirm this, a servo control system using an intensity modulated laser diode and unmodulated laser diodes (LDs) was c...

We improved the spectral accuracy in asynchronous-optical-sampling THz time-domain spectroscopy (ASOPS-THz-TDS) by sweeping the mode-locked frequency in dual fiber lasers. We confirmed from THz spectroscopy of low-pressure water vapor that the achieved spectral accuracy largely exceeds the spectral resolution in ASOPS-THz-TDS.

A phase measurement distance meter has been devised using a frequency‐stabilized intermode optical beat generated from a two‐mode He‐Ne laser (14‐cm‐long cavity) and a conventional phase meter. The beat frequency (1096 MHz) is stabilized to within 1 kHz fluctuation by a feedback control system. This frequency was converted to an electrical signal and reduced to 6 MHz by a rf‐heterodyne technique in order to match the best frequency response range of the phase meter. Experimental results show that the total distance error of the optical distance meter due to the frequency fluctuation of the laser and the performance of the phase meter is 1 and 19 μm, respectively, for a mirror target located 1 m away from the laser source. Further improvement in the resolution is possible if a better phase meter is used.

A high‐power, frequency‐stabilized laser source is required for an atomic force microscope which uses interferometric techniques to obtain distance measurements with picometer resolution. For this purpose, the oscillation frequency of a 10 mW multimode He‐Ne laser was stabilized using a new technique. Optical interaction between the longitudinal modes synthesizes intermode beats. Frequency of the intermode beat signal changes periodically with respect to cavity thermal expansion. This phenomenon is explained by the concept of ‘‘frequency pulling.’’ The secondary beats synthesized by the interaction between the intermode beat signals also change due to frequency pulling. The relation between the secondary beat of an intermode beat frequency and the laser cavity length is utilized for the stabilization of laser frequency. The change in the frequency of the secondary intermode beat is employed as the feedback signal to control the length of the cavity of the laser. To detect the frequency change in the secon...

A frequency-stabilized two-mode He-Ne laser has been developed. The intermode beat frequency of the experimental laser was approximately 600 MHz for a 25-cm cavity. The laser frequency in which the mode stands is pulled to the center of the gain curve (frequency pulling). The degree of pulling depends on where the longitudinal modes stand in the broadened gain curve. Beat frequency is thereby changed periodically of the order of hundreds of kilohertz with respect to cavity expansion. The frequency pulling was effectively used for frequency stabilization of the laser. The standing position of the longitudinal mode lights was locked in the gain curve by controlling the change of intermode beat frequency. A microwave mixer was applied to extract the frequency change of the intermode beat. Excellent frequency stability (10(10) for the laser oscillation and 10(6) for the beat frequency) was attained. The polarization orthogonality of the proposed laser was superior to that of Zeeman lasers.

We proposed a method to determine the absolute distance of a distant target using asynchronous-optical-sampling terahertz impulse radar. The determined distance was good agreement with the actual distance measured by a scale.

We propose a fiber-based, terahertz-comb-referenced spectrum analyzer which has the advantages of being a portable, alignment-free, robust, and flexible apparatus suitable for practical use. To this end, we constructed a 1550-nm mode-locked Er-doped fiber laser whose mode-locked frequency was stabilized precisely by referring to a rubidium frequency standard, and used it to generate a highly stable terahertz (THz) frequency comb in a photoconductive antenna or an electro-optic crystal. By standardizing the THz comb, we determined the frequency accuracy of an active-frequency-multiplier-chain (AFMC) source to be 2.4 x 10(-11). Furthermore, the potential of the THz spectrum analyzer was effectively demonstrated by real-time monitoring of the spectral behavior of the AFMC source and a photomixing source of two free-running CW lasers at adjacent wavelengths.

We demonstrate the phase measurement of a tunable CW-THz radiation at multiple frequencies. The error of the phase measurement with is less than 1 degree at each frequency under correction of the cyclic error. We further applied this method for the absolute distance measurement of a target.

We propose real-time THz impulse radar based on time-of-flight measurement of a pulsed THz wave. Combined use of the THz impulse radar with asynchronous optical sampling technique can achieve a real-time distance measurement of a moving and/or distant object because it requires no mechanical stages for time delay. The achieved precision of the THz impulse radar was 550 mum to an object at a distance of 1 m.

We proposed a new method of THz frequency measurement referring to as THz frequency comb. Effectiveness of the proposed method is demonstrated by measurement of a 100-GHz test source. The achieved precision and signal-to-noise ratio of frequency measurement were 2.85times10-11 and 46.2 dB, respectively.

The authors proposed a novel method of phase measurement of terahertz intermode beat in optical frequency comb, to enhance the dynamic-range of distance meter. Utilizing nonlinear optical process, distance measurement with 130 GHz equivalent frequency was realized.

We developed a stabilized laser source for high-precision, asynchronous optical sampling terahertz time-domain spectroscopy, in which individual mode-locked frequencies in the two lasers and the frequency difference between them are stabilized by two independent laser-control systems. We further applied it for THz spectroscopy of water vapor.

We report a terahertz frequency-comb technique for high-accuracy, high-resolution terahertz spectroscopy by combination of two mode-locked-frequency-stabilized femtosecond lasers and multi-frequency-heterodyning photo conductive detection.

Fourier transform spectroscopy (FTS) has been widely used in a variety of fields due to its high signal-to-noise ratio, simultaneous acquisition of a broad spectrum, and versatility for different radiation sources. Further improvement of the spectroscopic performance will widen its scope of applications. Here, we demonstrate improved spectral resolution by overcoming the time-window size limitation using a mode-locked terahertz (THz) pulse train as precisely periodic pulsed radiation in discrete Fourier transform spectroscopy (dFTS). Since infinitesimal resolution can be achieved at harmonic components of its repetition frequency 1/T when the time-window size is exactly matched to the repetition period T, a combination of dFTS with a spectral interleaving technique achieves a spectral resolution limited only by the spectral interleaving interval. Linewidths narrower than 1/(50T) are fully resolved by THz-dFTS, allowing rotational-transition absorption lines of low-pressure molecular gases to be attributed within a 1.25 MHz band.

We propose a terahertz (THz) frequency-comb technique for high-accuracy, high-resolution THz spectroscopy, based on multi-frequency-heterodyning (MFH) photoconductive detection using two femtosecond optical frequency combs with slightly mismatched frequency spacing.

In the measurement using conventional heterodyne interferometer, `high-speed' and `high-resolution' were methodologically contradictory problems. Previously, authors have solved this contradiction by using two conjugate beat signals. In this work, we realized highly sensitive measurement without speed limit of the target using a three- mode laser. The synthetic wavelength of (lambda) /2 generated by three-mode laser enabled to increase the measurement sensitivity twice. The three-mode laser also has an advantage of higher output power.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A new method of high-resolution two-wavelength interferometry was proposed for real-time and absolute measurement of micron-order distance or step-shapes in the depth. Simultaneous phase measurement of synthetic wavelength and one of two wavelengths was executed to measure the distance in the range of synthetic wavelength with interferometric resolution. A heterodyne light source constructed of two longitudinal modes was also proposed. The intermode beat of two modes was used as heterodyne career. Experiments were done with He-Ne lasers of 633 nm and 544/612 nm to measure 3 - 18 micrometers range.

We report on a real-time terahertz (THz) impulse ranging (IPR) system based on a combination of time-of-flight measurement of pulsed THz radiation and the asynchronous-optical-sampling (ASOPS) technique. The insensitivity of THz radiation to optical scattering enables the detection of various objects having optically rough surfaces. The temporal magnification capability unique to ASOPS achieves precise distance measurements of a stationary target at an accuracy of -551 μm and a resolution of 113 μm. Furthermore, ASOPS THz IPR is effectively applied to real-time distance measurements of a moving target at a scan rate of 10 Hz. Finally, we demonstrate the application of ASOPS THz IPR to a shape measurement of an optically rough surface and a thickness measurement of a paint film, showing the promise of further expanding the application scope of ASOPS THz IPR. The reported method will become a powerful tool for nondestructive inspection of large-scale structures.

We propose a distance meter that utilizes an intermode beat of terahertz frequency in an optical frequency comb to perform high resolution and high dynamic range absolute distance measurements. The proposed system is based on a novel method, called multiheterodyne cross-correlation detection, in which intermode beat frequencies are scaled down to radio frequencies by optical mixing of two detuned optical frequency combs with a nonlinear optical crystal. Using this method, we obtained a 1.056 THz intermode beat and achieved a distance resolution of 0.820 microm from its phase measurement. Absolute distance measurement using 1.056 THz and 8.187 GHz intermode beats was also demonstrated in the range of 10 mm, resulting in a precision of 0.688 microm.

Precision frequency measurements of terahertz (THz) waves are required to establish metrology in the THz spectral region. However, frequency measurement techniques in this region are immature. We propose a THz spectrum analyzer to measure the absolute frequency and spectral shape of continuous-wave THz waves. Based on a stable frequency comb generated in a photoconductive antenna, the absolute frequency of a sub- THz test source was determined at a precision of 2.8 x 10(-11). Furthermore, the spectral bandwidth of the THz spectrum analyzer can be extended over 1 THz, as demonstrated by measurement of a THz test source. This spectrum analyzer has the potential to become a powerful tool for THz frequency metrology.

In conventional heterodyne interferometer it Is necessary to provide a high-beat frequency laser when measurement for a high-speed target Is required1 . But use of the high-beat frequency laser makes the " nanometerdivisions" difficult. We have developed a novel interferometer system that has a sufficient response to high-speed movement of the target without Increase of the laser beat frequency. In this work a two frequency laser light passes through the same optical path of the interferometer so that two conjugate beat signals are obtained. By processing the multiple beat signals with a newly developed signal processor the above methodological contradiction is solved. l. OPTICS FOR LINEAR DISTANCE MEASUREMENT Optical system of the interferometer Is shown In Flg. l in which two frequency lights Fl and F2 (freq. f and f2) of orthogonally linear-polarized components of a two mode laser are used. A reference beat signal R (freq. r ) is generated from Fl and F2. Fl and F2 are passed through exactly the same path of the interferometer. A half power of Fl and F2 Is reflected and the rest Is transmitted In the beam splitter ( BS ). Polarization direction of the reflected beam is rotated for ir/2 after passing the X/4 plate twice. The transmitted beam Is reflected by a moving mirror (MM) mounted on the moving target so that frequency of the reflected beam Is shifted by Doppler

We report a terahertz spectroscopy technique based on a stable terahertz frequency comb from a photoconductive terahertz emitter driven by a stabilized femtosecond laser. To this end, a photocurrent frequency comb is induced in a photoconductive terahertz detector by instantaneous photogating with another detuned femtosecond laser and is applied to read out the terahertz frequency comb. The detailed structure of the terahertz frequency comb was clearly observed with frequency accuracy of 2.5×10−7 and resolution of 81.8MHz using multifrequency-heterodyning photoconductive detection, which in turn is caused by the slightly mismatched frequency spacing between terahertz and photocurrent frequency combs.

The output characteristics of an avalanche photodiode show an unwanted dependence on incident light intensity. For intensity modulated inputs, the corresponding signal delay in the diode output increases with decrease in the incident intensity. This characteristic leads to errors in distance measurements where the optical modulation method is employed. Such phase delay errors can be corrected by applying an optical dc bias into the modulated optical input. When the bias intensity is adjusted to make the mean diode output current constant at all times, the resultant phase value becomes independent of the intensity of modulated input.

Rapid THz impulse radar was achieved by combination of time-of-flight measurement of THz pulse and asynchronous optical sampling technique. The precision of 354 µm was achieved in the displacement measurement.

We fully interpolated frequency gaps between THz-comb modes by their incremental sweeping at intervals of their linewidth, showing the possibility of enhancing the spectral resolution in THz spectroscopy to the linewidth of THz comb mode.

We demonstrated gapless THz comb spectroscopy for high-resolution THz spectroscopy. Frequency sweeping of THz comb mode enables us to enhance the spectral resolution in THz spectroscopy down to the linewidth of THz comb mode.

We demonstrated combination of spectrally interleaved terahertz (THz) frequency comb with dual-comb spectroscopy, enabling us to achieve the spectral sampling equal to linewidth of the comb tooth in the low-pressure gas spectroscopy in THz region.

We demonstrate phase-slope measurement of tunable CW-THz radiation by photoconductive heterodyne detection with a photocarrier THz comb. Distance of optically rough object is determined from the measured phase-slope within accuracy of 100 μm.

We observed detailed spectrum of THz frequency comb by extending the measured time window of the pulsed THz electric field up to ten pulse periods with asynchronous-optical-sampling THz-TDS (ASOPS-THz-TDS). Observed spectrum of THz comb mode has a linewidth of 5.6 MHz and a frequency interval of 56 MHz.