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Following describes experimental setup of frequency-comb-referenced multi-wavelength interferometry. We exploited the frequency comb as the wavelength ruler to precisely calibrate multiple wavelengths sources simultaneously. The uncertainty of the generated wavelengths was 10-12 at 10 s averaging time. Home-made multi-channel optical frequency generator (OFG) generates four wavelengths simultaneously for real-time absolute distance measurement. Four wavelengths were selected with optimized process of extension of non-ambiguity range and generated simultaneously. Four wavelengths were combined through FBG array and split into two beams. One beam is send to the target retro-reflector and the other beam is frequency shifted to 40 kHz with a pair of AOMs. The absolute distance interferometer was designed to minimize cyclic error caused by imperfection of polarization optics. In the multi-wavelength interferometry, the absolute distance L is determined by following equation,
L =λi / 2* (mi + ei) (i =1,2, … N)
where λi is i-th air wavelength, mi is a positive integer, and ei is a fractional phase (0 < ei < 1). Phases of four wavelengths were simultaneously detected by home-made phase meter with phase resolution of 2π/2500 rad. Environment parameters such as the temperature, relative humidity, pressure and CO2 contents were also measured for compensation of fluctuation of air refractive index using the modified Edlen’s formula. For comparison, a conventional He-Ne laser interferometer is installed on the translation stage. With multi-channel phases and environmental parameters, the absolute distance is determined by MWI algorithm based on excess fraction method.
(1) High precision absolute distance measurement using optical frequency comb of femtosecond laser
In today’s precision engineering, laser interferometers based on heterodyne or homodyne phase-measuring techniques are widely used to measure the position of a machine axis with sub-wavelength resolutions over extensive ranges up to tens of meters. These interferometers basically measure displacement, not distance, since the non-ambiguity range for a single phase measurement is restricted to the half of a wavelength. Subsequently, the position of a machine axis is determined by accumulating the displacement continuously monitored at a high update rate. On the other hand, the attempt of absolute distance measurement (ADM) seeks to determine distance directly by a single measurement over a large range, thereby enabling distance measurement instantly even with the measurement laser beam being interrupted in between. In the past, ADM was realized with various principles but the measurement performance was not comparable particularly in terms of precision, i.e., the ratio of the measurement resolution to the measured distance, compared to displacement-measuring interferometers. In recent years, femtosecond pulse lasers began to offer breakthroughs in ADM through their superior characteristics in both the temporal and spectral terms. First of all, the frequency comb of a femtosecond laser allows the wavelength of the continuous-wave laser used for distance measurement to be calibrated precisely with direct traceability to the well-defined atomic clock of frequency standard. In addition, the femtosecond laser itself can be used as a light source directly for distance measurements as demonstrated in the synthetic radio-frequency wavelength interferometer, Fourier-transform-based dispersive interferometer, multi-heterodyne interferometer using a pair of femtosecond lasers of different pulse repetition rates and incoherent time-of-flight (TOF) measurement using balanced optical detection. These newly established techniques share the aim of achieving sub-wavelength precision at long ranges for high-precision ADM applications by exploiting the unique temporal and spectral characteristics of ultrashort light pulses which are absent in conventional lasers.
Following figure shows an experimental result of absolute distance measurement. The performance of the frequency-comb-referenced multi-wavelength interferometry was evaluated along the stage with 3-m of movement. A conventional He-Ne laser interferometer offered the reference distance measurement with resolution of 1 nm. The measurement precision is estimated to be less than a hundred nm in peak-to-valley compared to conventional He-Ne laser interferometer along distance of 3 m with an update rate of 100 Hz. Our absolute distance measurement system could be potentially available in scientific and industrial applications through its high precision, high speed, long range, and direct traceability to the rf time standard such as the atomic clock.
The conventional time-of-flight measurements are capable of measuring long distance but precision is limited to several hundreds of micrometer due to the low timing resolution of photo detectors. We improved the precision of the time-of-flight measurement to nanometer regime by timing femtosecond laser pulses through phase-locking control of repetition rate of femtosecond pulses using the optical cross-correlation technique. Following figure shows the experimental setup of TOF measurement. The measurement technique is based on the balanced optical cross-correlation technique which converts the timing difference between two pulses into an optical signal without losing the femtosecond timing resolution. The error signal generated by the balanced optical cross-correlator gives a feedback to the PZT actuator to vary the cavity length. The repetition rate of femtosecond laser was simultaneously counted and converted to absolute distance by following equation.
D = mc/(2frN)
where D is the measured distance, m is an integer, c is the speed of light, fr is the repetition rate of femtosecond laser, and N is the group refractive index of air. A target distance of 0.7 km was measured for evaluation of proposed ADM system. The target mirror was located on a separate building to form a round-trip path of 1.4 km. The repetition rate of femtosecond laser was super-heterodyned to 400 kHz in order to attain more significant digits and a higher update rate.
Following figure shows an Allan deviation of absolute distance measurement versus averaging time. For large distance of more than several meters, measured distance is fluctuated by refractive index change due to air-borne disturbances. This disturbance could be negligible in the vacuum and the intrinsic system noise such as the optical and electrical noise could be achieved at the zero distance. The ultimate precision of proposed time-of-flight measurement could achieve 8.7 nm at an averaging time of 10 ms, 2.7 nm at 100 ms, and 1.1 nm at 1 s in vacuum. Our absolute distance measurement system is suitable to precision engineering and future space mission such as formation flying through its high precision, long range and real-time measurement.
(2) Femtosecond laser based precision surface metrology
Recently, many applications such as surface metrology, distance metrology, and spectroscopy prefer to apply the ultrafast mode-locked lasers to their systems. With femtosecond pulsed laser as a light source for interferometry, it is possible to measure target surface with a large field of view(FOV) owing to its good spatial coherence. Also, data can be acquired without any parasite fringe and 2π-ambiguity from repeated pulses with good time coherence. As for unbalanced-arm interferometry, by using repetition rate tunable oscillator, coherence signal can be rapidly obtained without mechanical scanning part in the interferometry system. Therefore, many advantageous characteristics of femtosecond laser are expected to open a new vista in the field of precision surface metrology and play an important role in achieving unprecedented performance in low-coherence 3-D profiling of various surfaces.
Low-coherence scanning interferometry using femtosecond laser pulses is possible to demonstrate a fast and precise profiling method of various stepstructures. An unequal-path, non-symmetric interferometer system is configured such that the optical path difference(OPD) between the reference and measurement arms are varied by scanning the repetition rate of femtosecond pulses. The scale of OPD variation is readily extended by adjusting the unbalanced length of the interferometer for a given scanning range of the pulse repetition rate. Furthermore, the high spatial coherence of femtosecond pulses provides higher visibility over a wide FOV. In preceding research, we achieved a fast OPD scanning speed of 100 m/s for a 120 μm range using an electro-optic modulator (EOM) with the scanning precision being traceable to the Rb atomic clock. The lateral FOV of a single measurement was also extended to a 14.5 mm without significant wavefront errors due to the high spatial coherence of the femtosecond laser. As a result, fast and precise 3-D profiling is possible by using low-coherence scanning interferometers with unbalanced-arm. All these measurement capabilities offered by using femtosecond pulses are suited for fast 3-D profiling of large step-structures such as semiconductor packaging, flat panel displays and photovoltaic devices.
The proposed system configuration of the fiber oscillator having a wide repetition rate tuning range is shown in the figure above. Mode-locking can be achieved by integrating two schemes: nonlinear polarization evolution (NPE) and saturable absorption (SA). The repetition rate scanning part composed of paired CFBGs and one circulator is installed between NPE unit and SA unit. The total group delay(GD) of CFBG part is near zero because paired CFBGs in opposite direction cancels out the GD of each CFBG. For repetition rate scanning, the length of one CFBG is fixed and the other CFBG will be stretched with a PZT flexure. The length change of the CFBG can make the GD shift of the mode-locked pulse while the group delay dispersion remains as constant. In this method, this GD works to amplify the repetition rate change by several tens of times in the mode-locked oscillator. As a result, we expect wider scanning range and fast scanning speed when this oscillator is applied to the unbalanced interferometry.
(3) Frequency-comb-referenced multi-wavelength profilometry for largely stepped surfaces
3-D profiles of discontinuous surfaces patterned with high step structures are measured using four wavelengths generated by phase-locking to the frequency comb of an Er-doped fiber femtosecond laser stabilized to the Rb atomic clock. This frequency-comb-referenced method of multiwavelength interferometry permits extending the phase non-ambiguity range by a factor of 64,500 while maintaining the sub-wavelength measurement precision of single-wavelength interferometry. Experimental results show a repeatability of 3.13 nm (one-sigma) in measuring step heights of 1800, 500, and 70 μm. The proposed method is accurate enough for the standard calibration of gauge blocks and also fast to be suited for the industrial inspection of microelectronics products.
The proposed method of frequency-comb-referenced multi-wavelength interferometry enabled fast, precise absolute measurement of largely stepped surfaces without phase ambiguity. With reference to the frequency comb of an Er-doped femtosecond laser stabilized to the Rb atomic clock, four wavelengths were generated using DFB lasers with an uncertainty of 3.44 × 10−12 at a 10 s averaging time. Then, the generated wavelengths were converted from the NIR to visible range by second harmonic generation, so that the resulting interferogram were observed using a conventional Si CCD camera. The measurement repeatability (one-sigma) was found 3.13 nm, being direcltly tractable to the time standard. The measurement time was 400 ms. The proposed method is well suited for fast, precise inspection of large industrial specimens such as semiconductor wafers, printed circuit boards, and flat panel displays.
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