Electro-optic frequency combs for multi-wavelength digital holography with high dynamic range

Abstract

Multi-wavelength digital holography enables surface-shape measurements with an exceptional dynamic range by combining interferometric resolution with synthetic wavelengths spanning multiple length scales. Although the concept promises measurement ranges of many orders of magnitude, its practical implementation is limited by the lack of light sources that allow fast, reliable, and calibration-free switching between synthetic wavelengths over a wide frequency range. Here, we present a synthetic-wavelength generator based on an electro-optic frequency comb with electronically tunable modulation frequency and a set of switchable band-pass filters. By combining discrete selection of comb-lines with continuous radio-frequency tuning, the proposed scheme merges the advantages of single-sideband modulation and filter-based comb extraction. Using only off-the-shelf components, the system provides synthetic frequencies from 0.1-220GHz, corresponding to synthetic wavelengths from meters down to millimeters in the visible. The generator achieves MHz-level frequency accuracy, side-mode suppression exceeding 40dB, and switching times below 25ms, even without active stabilization. We characterize the spectral purity and frequency agility of the source and demonstrate rapid tuning of synthetic wavelengths over 3 orders of magnitude. We apply the light source to multi-wavelength digital holography and reconstruct the surface of an industrially machined metal part featuring height variations from 0.1-100mm. The measurements achieve ten-mum-level precision using 7 single wavelengths covering synthetic wavelengths from 1.36mm to 1.874m within an acquisition time < 2s. The presented architecture combines high dynamic measurement range of 50dB, fast electronic reconfigurability, and intrinsic frequency calibration, making it a promising light source for high-speed interferometric surface metrology.

Figures (10)

• Figure 1: a)-c): Different schemes for modulated light sources with their available control parameters of the modulation frequency $f$ and or the sideband order N. EOCG, electro-optic comb-generator; TBPF, tunable bandpass filter; BPF, bandpass filter. d): Overview of the available synthetic wavelength based on the presented schemes.
• Figure 2: Temporally varying frequencies of the components of an electro-optic frequency comb pumped at the optical carrier frequency $\nu_0$ and modulated at the radio-frequency values $f_{1,2}$, in combination with two switchable band-pass filters. Shown are three consecutive acquisition cycles consisting of alternating switching and measurement intervals where every but the selected component are sketched in gray. During the switching times $T_\mathrm{s1,2,3}$, either the modulation frequency $f$ or the selected filter is changed to address a different comb component at the order $N$. The intervals $T_\mathrm{m1,2,3}$ denote the time windows during which interferograms are recorded while a nominal comb component is selected. Due to the laser-frequency drift $\Delta\nu$ and the short-term frequency fluctuations $\delta\nu$ ( both not to scale), the actual optical frequency during the measurement intervals can significantly differ from the target values (dashed lines).
• Figure 3: Normalized power of selected frequency-comb components at the optical frequencies $\nu_{-3\ldots 3}$ and normalized transmission of the optical band-pass filter as a function of frequency. PB denotes the 3 dB passband of the filter. SB indicates the stopband regions, characterized by the stopband suppression $\Delta T$, while TB marks the transition bands between passband and stopband.
• Figure 4: Experimental setup for generating synthetic wavelengths and its characterization: NIR, near-infrared; VOA, voltage-controlled optical attenuator; RF radio frequency; PM, phase modulator; FS, fiber switch; ONBP, optical narrow bandpass filter; OWBP, optical wide bandpass filter; EDFA, erbium doped fiber amplifier; SHG second harmonic generation; SOA semiconductor optical amplifier; VIS, visible light.
• Figure 5: Near-infrared optical spectra of the frequency comb (gray traces in a, b and c) and of the light at the output of the filter bank (yellow and blue traces in d, e and f). The yellow traces indicate the output at $N=-1$ transmitted by the optical wide-band filter (OWBF), while the blue one indicates the output at $N=2$ transmitted by the optical narrow-band filter (ONBF). The modulation frequency is set to 30 GHz (a and d), to 35 GHz (b and e) and to 40 GHz (c and f).