A multi-gigahertz frequency comb (MGFC)-based interferometer was developed for profilometry and tomography using a frequency variable supercontinuum (SC). The comparatively flattened and broadened SC light source with variable multi-gigahertz interval frequency was developed using an optical pulse synthesizer and highly nonlinear dispersion flattened fiber. The generated SC provided a stable interference output with a full width half maximum of 19 μm during interval frequency sweeping of over 400 MHz. We experimentally confirmed that the interference signal exhibited an envelope-only waveform without fringes, which enabled the drastic reduction of the sampling points resulting in high speed measurement. A full-field 3-D image with 320 × 256 × 300 pixels was acquired with a measurement time of only 10 seconds. It was demonstrated that the MGFC-based interferometer with the novel SC light source has the potential for application in a high speed full-field 3-D metrology.
© 2012 OSA
Monochromatic laser interferometers using a phase shift  or sinusoidal phase modulating method  ensue high accuracy for a precise profilometer. However, these interferometers suffer from measurements of longer displacement than the wavelength due to 2π ambiguities of the measured interference phase. A variety of light sources such as white-light sources, wavelength tunable laser, and short pulse lasers have been used for optical interferometry, and been extensively developed for distance measurements, surface profilometry, and tomography. The femtosecond laser exhibits a frequency comb spectrum with a mode frequency (i.e. interval frequency) in the MHz band and a bandwidth of several tens of nano-meters. The femtosecond pulse laser can generate a much broader frequency comb called a supercontinuum (SC) in a highly nonlinear fiber (HNLF) . The SC has an extremely large broadband spectrum over several hundreds of nanometers with an interval frequency of the order of 10 MHz; therefore, it has been regarded as a white-light source with a semi-continuous spectrum, and has been applied to white-light interferometry with an ultra-high resolution [4–6].
For several years, a variety of metrology techniques based on frequency combs have been developed to replace white-light interferometers. The femtosecond laser has been utilized for precise distance measurements using the phase difference of the beat signal  and for metrology using the carrier envelope offset frequency . The synthesis of the coherence function as a quasi-frequency comb has been utilized for fiber stress tests . The frequency comb generator with a monolithic modulator has been applied to ultrahigh-speed tomography based on the vernier effects of the two slightly different repetition frequencies . The surface profilometeries have been demonstrated using a Fizeau interferometer with multiple frequencies produced by a Fabry–Pérot cavity [11,12].The quasi-monochromatic optical coherence metrology using a spatial frequency comb has been proposed for dispersion-free depth sensing . More recently, short temporal coherence digital holography using the frequency comb has been proposed . As noted above, the requirements for various metrology techniques based on frequency combs has been increasing recently.
We have already proposed a laser frequency comb (LFC)-based interferometer without mechanical scanning for surface profilometry and tomography [15, 16]. This technology has the potential for full electro-optic and a high speed measurement for a full-field 3-D profilometry. It requires a multi-gigaherz frequency comb (MGFC) light source with a variable interval frequency. However, it is not easy to produce a variable and multi-gigaherz interval frequency.
In the previous study, we proposed a novel SC generation technology employing the optical pulse synthesizer (OPS) [17,18] and highly nonlinear dispersion shifted fiber (HN-DSF), and proved its feasibility for the MGFC-based interferometer . The generated SC provided a variable interval frequency of 12.5 and 25 GHz, respectively, with a scan range of a few hundreds MHz. The MGFC-based interferometer exhibited a poor depth axial resolution due to the small SC bandwidth of 30 nm. As a result, it was difficult to evidently observe the 3-D profile.
In this paper, we show the improvement of the SC bandwidth and spatial resolution of the interference waveform by introducing the highly nonlinear dispersion flattened fiber (HN-DFF). The comparatively flattened and broadened SC was generated by replacing the previous HN-DSF with the HN-DFF. We constructed the MGFC based-interferometer with the improved SC for 3-D profilometry. We demonstrated that both the SC comb spectrum and its interference waveform were kept near constant during the interval frequency sweeping. We also confirmed that the interference waveform produced by the interval frequency sweeping of the MGFC-based interferometer exhibits only the intensity peak envelope without fringes, in contrast with conventional interferometers, which exhibit the interference waveform with fringes. It was experimentally proved that these advantages, including no mechanical scan and envelope-only interference waveforms enabled the high-speed full-field 3-D measurement.
2. Principle of MGFC-based interferometer using SC light source
Figure 1 shows the configuration for the MGFC-based interferometer using the SC light source with a variable MGFC. This system consists of an SC light source and a microscopic interferometer. The SC light source consists of a seed comb generator, the OPS, a high-power erbium doped fiber amplifier (EDFA), and a highly nonlinear fiber. The initial seed comb was generated by an optical modulator and a laser diode (LD). The comb interval frequency was determined at 12.5 GHz by a modulation frequency applied to the optical modulator. The OPS synthesizes picosecond pump pulses with a repetition frequency of 12.5 GHz from the initial seed comb. The pump pulse peak power was amplified by the EDFA to achieve a sufficient nonlinear effect in the HNLF. The interval frequency of the generated SC was varied by several hundred MHz by sweeping the modulation frequency applied to the optical modulator. The generated SC entered the microscopic interferometer, in which the high order interference was produced by reflection beams from a sample and a reference mirror.
The N-th order interference waveform SN detected on the detector can be approximately written byEq. (1), the following expression
The phase term of cos(2πL/λc) in the SN is fixed at a constant value because the OPD and the λc are fixed while the νi is swept. Figure 2 shows schematics of the interference waveform obtained by varying νi (i.e., interval frequency) and L (i.e., OPD), respectively for the interference order of N. Note that this phase term characterizes a unique interference output which is different from the one in the conventional time-domain interferometer. In the time-domain interferometer, the interference waveform is rewritten asEq. (4) is varied by a mechanical scan of L, the interference fringe with a period of the wavelength λc is observed.
For this interference characteristic wherein only the intensity envelope is directly obtained, the number of measurement points can be greatly reduced to less than 1/8 relative to a conventional interferometry as shown in Fig. 2. In addition, a full-field 3-D profile can be measured using a 2-D CCD image sensor without x-y axial scanning because the high output power and coherence of the SC permits the illumination of the entire field of the sample surface. For example, as a sampling interval longer than the wavelength can sufficiently fix the interference waveform, a 3-D profile with a measurement range of 1 mm requires only approximately 500 points. A high-speed CCD image sensor with a frame rate of a few KHz enables a measurement time of within one second to obtain the 3-D volume data. Therefore, a high speed and stable full-field measurement can be performed by the MGFC-based interferometry.
3. Pump pulse synthesis and SC generation
Figure 3 shows the actual experimental setup for the SC light source. The light source was a distributed feedback LD with a center wavelength in the 1550 nm region. The initial seed comb with an interval frequency of 12.5 GHz was produced as approximately 30 sidebands using the single Lithium Niobate phase modulator driven by an RF signal generator (SG). By varying the RF, we investigated the stability of seed comb spectrum for an interval frequency sweep. As a result it was determined that the spectral intensity fluctuation in the comb spectrum was negligible even for an interval frequency sweeping of several hundred MHz.
The OPS consisted of an arrayed waveguide grating (AWG) with 30 output waveguides. Each output waveguide has an intensity and phase modulator. They are integrated on a single chip fabricated by silica-based planar waveguide technology. The AWG spectrally separates the input comb into the waveguides with 12.5-GHz spacing. The interval frequency sweeping range is unlimited within the channel bandwidth of the AWG. The modulators precisely manipulate the intensity and phase of each frequency component. The pulse waveform was synthesized as follows. First, we defined the target intensity spectrum, which was calculated by the Fourier transform of the desired pulse shapes. Next, the power spectrum of the optical frequency combs was reshaped with the intensity modulators by monitoring the power spectrum with an optical spectrum analyzer. Finally, the phase spectrum was adjusted using the feedback control of the phase modulators to obtain target-shaped pulses. We employed genetic algorithm to precisely manipulate the phase spectrum. We used the differences between the pulse waveform measured by an autocorrelator and the target waveform as a fitness function.
Figure 4(a) shows autocorrelation waveforms of the synthesized sech2 pulse used to vary the repetition frequency, which was varied by the comb interval frequency νi. The time-bandwidth product was 0.351 with a full width half maximum (FWHM) of 3.4 ps when the repetition frequency was 12.5 GHz. Marginal variation in the pulse waveform was observed when sweeping the repetition frequency from 12.3 to 12.7 GHz. Figure 4(b) shows FWHM of the pulses as a function of the repetition frequency. The change in the FWHM of the synthesized pulse was within ± 0.3 ps for the interval frequency sweep in the range of 400 MHz.
The synthesized sech2 pulse was amplified by a high power EDFA and propagated in the HNLF. We investigated the SC characteristics of HN-DSF and HN-DFF for a length of 1km. The HN-DSF has a zero-dispersion wavelength of 1571 nm with a dispersion slope of + 0.019 ps/nm2/km. The group velocity dispersion (GVD) at 1550 nm was −0.37 ps/nm/km with a nonlinear coefficient of 30 /W/km. On the other hand, the HN-DFF has a flattened dispersion slope, which is + 0.003 ps/nm2/km less than that of HN-DSF. It exhbits a GVD of −0.02 ps/nm/km and a nonlinear coefficient of 7 /W/km at 1550 nm. Both parameters are much smaller than those of HN-DSF.
Figure 5(a) and 5(b) show the generated SC spectra as a function of the pulse peak power input into the HN-DSF and HN-DFF, respectively. The pulse peak power was amplified by the EDFA from approximately 4 to 41 W. The SC spectrum broadening in the HN-DSF was suppressed for the wavelength range of 1520−1570 nm, even if the peak power was increased, as shown in Fig. 5(a). This was due to the modulation instability in the anomalous dispersion regime of the HN-DSF. On the other hand, the SC spectrum in the HN-DFF was broadened more effectively by the SPM effects in the normal dispersion region over the range of 1520−1600 nm. The bandwidth in terms of −20dB became approximately 90 nm when the pump pulse was amplified by 41 W.
We investigated the effect on the SC spectrum of the sweep of the pulse repetition frequency when it was applied to the MGFC-based interferometer. Figure 6(a) shows the variation of the SC spectral envelope as a function of the repetition frequency when the input pulse peak power was 41 W. Figure 6(b) shows the −20 dB-bandwidth fluctuation as a function of the repetition frequency. Marginal variation was observed in the SC spectrum when the repetition frequency was swept. In Fig. 6(b), the red square plot shows the simulated interference peak widths calculated using the inverse Fourier transform from the spectral envelopes shown in Fig. 6(a). The maximum fluctuation of the spectrum bandwidth was approximately 6 nm when the repetition frequency was swept in a range of over 400 MHz. This resulted in a very small change that was less than 1 μm of the interference peak width (i.e., axial resolution) for the repetition frequency sweep.
5. MGFC-based interferometer and its demonstration
We constructed a microscopic MGFC-based interferometer with a frequency-variable SC light source, as shown in Fig. 7 . The light beam output from the SC light source through an SMF was collimated with a beam diameter of 2 mm. The input average power was attenuated less than approximately 1 mW by using a tunable fiber attenuator placed before the collimator to avoid the damage of a CCD image sensor. The collimated beam was divided into two paths by a non-polarization beam splitter (BS) with a ratio of 50:50 over the wavelength range of 1500−1600 nm. The transmitted beam was reflected by a gold-coated reference mirror that produced a reference wave. The reflected beam was directed toward the object. The illuminated area was magnified to 10 times using an objective lens with a working range of 10 mm. The OPD was set to 72 mm to observe the 6-th interference order with an interval frequency of approximately 12.5 GHz. The interference image recombined by the BS was formed by an optical configuration with the objective and projection lenses on a detection plane of a photo detector or a 2-D CCD image sensor (ALPHA NIR, 30 frame/s). The sensitivity of noise equivalent irradiation of the CCD was approximately 1 nW/cm2 at the wavelength of 1550 nm.
Before taking the 3-D measurements for some samples, we first observed the interference waveform for both the interval frequency sweep and the mechanical scan. The observation was performed using the microscopic interferometer shown in Fig. 7 with a photo detector instead of the CCD. Figure 8(a) shows the envelope−only interference waveform without fringes, as observed by the interval frequency sweep. On the other hand, in the case of the mechanical scan of the reference mirror for the fixed frequency comb, an interference waveform with fringes was observed as shown in Fig. 8(b). These results agree with the principle (e.g. Figure 2). There is a difference factor of greater than 10 between the sampling points of these two methods. The FWHM of both intensity peaks were approximately 19 μm, and the resulting interference waveforms exhibited small ripples which may disturb the S/N ratio. The spectral shaping of the SC in the vicinity of the pump wavelength using a proper frequency filter is required for further improvement.
Figure 9 shows the one-dimensional tomographic measurement of a glass plate with a thickness of approximately 0.15 mm. The interference signal was obtained by the interval frequency sweep ranging from 12.45 to 12.55 GHz with a 0.1 MHz step. This sweeping range corresponded to an approximately 500 μm scan range with a 0.6 μm sampling interval. Even such a coarse sampling interval enables us to fix the interference peak, and results in a high-speed measurement. The average depth axial resolution was approximately 19 μm, which was maintained during measurement with the interval frequency sweep. The measured optical thickness including the refractive index was 219 μm, which agreed well with the known value that was measured by a caliper. The standard deviation of the thicknesses from nine measurements was 0.6 μm.
The advantages of the MGFC-based interferometry demonstrated in previous experiments led to the full-field 3-D profilometry and tomography. Figure 10 shows an example of the 3-D measurement of a Japanese 10-yen coin. Interference signals with a size of 320 by 256 pixels covering the measurement region of 0.96 by 0.76 mm2 were captured by the CCD synchronized with the SG. The interval frequency was swept from 12.49 to 12.52 GHz with 100 kHz steps, corresponding to a sampling interval of approximately 0.57 μm and a depth scanning range of 172 μm for the 6-th interference order. The axial resolution for the surface measurement can be defined by 1/10 of the FWHM of the interference peak . Thus the actual axial resolution was estimated to be 1.9 μm. The acquisition time for a 3-D volume reconstructed from 300 interference images was approximately 10 seconds with a frame rate of 30 Hz. The measurement speed was limited mainly by the frame rate. Hence, the acquisition time for a 3-D volume could be within one second if we introduce a CCD with a faster frame rate.
The MGFC-based interferometer was developed for surface profile and tomographic measurement using a frequency-variable SC. The comparatively flattened and broadened SC light source with a variable multi-gigahertz interval frequency was developed using an optical pulse synthesizer and HN-DFF. The generated SC provided stable interference output with a FWHM of 19 μm during interval frequency sweeping of over 400 MHz. We experimentally confirmed that the interference signal exhibited an envelope-only waveform without fringes, which enabled the drastic reduction of the sampling points resulting in high speed measurement. The cross-section of the glass plate was measured with a repeatability of 0.6 μm. We acquired the full-field 3-D 320 × 256 × 300 pixel image of the surface profile of a 10-yen coin with a measurement time of only 10 seconds. It was demonstrated that the MGFC-based interferometer with the novel SC light source has the potential for an application in a high-speed full-field 3-D metrology.
Part of this work was supported by Grant-in-Aid of JSPS No. 23360029. The authors appreciate the contributions of Naoyuki Tamura and Hiroyuki Ishizu. Samuel Choi thanks Osami Sasaki for his helpful discussions and encouragement.
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