Digital holography with microcombs

. Optical microresonators are attractive comb sources due to their small form factor and stable broad optical spectra. We report on the first demonstration of microcomb-based digital holography. The large line spacing of microcombs promises an unprecedented combination of precision, fast update rate and ambiguity ranges on the scale of a few mm. Using a pulse-driven lithium niobate microcomb of 100 GHz line spacing and a scanning Michelson interferometer, we generate spectral hypercubes of holograms. Our first experimental results show that the amplitude and phase information of the object can be recovered for more than 100 comb lines.


Introduction
Digital holography is a well-established tool for threedimensional imaging and surface metrology [1].By recording the spatial interference pattern between light scattered by the sample and a reference beam, the phase front of the object beam can be numerically reconstructed with high accuracy.However, as an interferometric technique, the phase retrieval is restricted to an ambiguity range of λ/2.
One approach to overcome this limitation has been the use of several holograms recorded at different wavelengths.A hierarchical phase retrieval algorithm allows the unwrapping of the phase by utilizing synthetic wavelengths [2].One possible multi-frequency source for such experiments is a frequency comb.As first demonstrated in [3], a frequency comb can be used to provide holograms at multiple optical frequencies.Using dual-comb interferometry, the interference signal of all comb lines is recorded on a detector matrix.However, the slow acquisition rate of commercially available infrared camera sensors limits the number of comb lines that can be efficiently used.In order to obtain a large spectral bandwidth with a small number of lines, a large comb spacing is beneficial.
Recently, microcombs generated in optical microresonators have gained a lot of attention.They promise to be a compact, broad-band, and stable frequency comb source.Due to their small cavity length their repetition rate is usually on the order of tens of GHz up to THz, which makes them perfectly suited for our application in frequency comb digital holography, providing fast measurement times and a possible phase ambiguity range on the order of several millimeters.

Comb generation
We use a thin-film lithium niobate microresonator with a radius of 200 µm and a free spectral range of 100 GHz.The resonator has a loaded Q-factor of around 10 6 and features anomalous dispersion with  2 = −0.0174ps 2 /m.It is pulse-pumped using an electrooptic (EO) comb with a repetition rate of 20 GHz.Fig. 1 shows a schematic of the experimental setup and comb generation process.The EO comb is generated by seeding two intensity modulators and one phase modulator with a 1555 nm tunable continuous-wave (cw) laser.The generated pulse is compressed to a width of about 2 ps using 200 m of single-mode fiber.The spectrum of the EO comb is shown as inset in Fig. 2. Subsequently, the EO comb is amplified in an erbium-doped fiber amplifier to an average power of 25 dBm.By tuning the center frequency of the EO comb into the resonance of the microresonator, a stable microcomb spanning around 200 nm can be generated.Apart from an increased conversion efficiency [4], one feature of the pulsepumping approach is that the repetition rate of the microcomb is locked to that of the EO comb [5], which is well controlled.

Scanning Michelson interferometer
The holography setup is implemented in a scanning Michelson interferometer (SMI).After the generation of the microcomb, the light is collected with a lensed fiber.A notch filter with a bandwidth of 10 nm, centered at 1555 nm is used to filter out the driving pulse, such that only the microcomb is sent to the SMI.The scanning arm introduces a Doppler shift of the comb line frequencies in the reference beam, and the wave scattered by the object interferes with that of the Doppler-shifted comb at the detector matrix.The slight frequency difference between the lines of the two combs leads to the generation of beat notes, which form a third comb in the in the audio domain [6] which can be detected by the detector matrix.The time domain interference is recorded on an infrared camera sensor with 320x256 pixels at a sampling rate of 192 Hz.We note that, with a stepped Michelson interferometer, a different approach to holography for low temporal coherence multi-level optical sectioning had been reported with a frequency comb of 5 GHz line spacing [7].

Results
For each pixel, the complex spectrum of the object beam can be recovered by Fourier transforming the timedomain interferogram.By considering all pixels at one comb line, a complex hologram for this optical frequency is obtained, which can be numerically reconstructed using the well-known angular-spectrum method [1].The blue trace in Fig. 2 shows the optical spectrum of the microcomb.It was recovered by Fourier-transforming the time domain signal of a single pixel.The spectrum exhibits 105 lines above the noise level which can be used for hologram reconstruction.The envelope of the spectrum shows excellent agreement with the spectrum as measured on an optical spectrum analyzer, which is shown as the dashed line in Fig. 2.
After reconstructing the spectrum for each pixel, by taking the complex value of all pixels for one optical frequency a complex hologram is obtained.The phase and amplitude of a reflecting object can be reconstructed by backpropagation of the light field into the focal plane.The sample under investigation is a reflective 1951 USAF resolution target.The hologram and reconstructed amplitude for one comb line are exemplarily shown in Fig. 3.

Conclusion
We have introduced the new concept of microcomb digital holography.We have experimentally illustrated the use of a frequency comb generated in a pulse-pumped lithium niobate microresonator for digital holography.Using a scanning Michelson interferometer, we are able to recover the microcomb spectrum with high accuracy.The good signal-to-noise ratio of the spectrum allows the reconstruction of holograms for more than 100 lines.By implementing the hierarchical phase retrieval, we will be able to reconstruct phase images with high axial precision.

Fig. 1 .
Fig. 1.Experimental setup.An electro-optic comb is amplified in an erbium-doped fiber amplifier.It is coupled into the microresonator using lensed fibers.Part of the generated light is sent to an optical spectrum analyzer.Only the microcomb is then sent to the scanning Michelson interferometer.

Fig. 2 .
Fig. 2. Microcomb spectrum.The blue trace shows the spectrum recovered from the time domain interferogram of a single pixel.The dashed line shows the microcomb spectrum as measured on an optical spectrum analyzer (OSA).The inset shows the spectrum of the electro-optic pump pulse.

Fig. 3 .
Fig. 3. a) Magnitude of the complex hologram recovered for a single comb line.b) Reconstructed amplitude image of the resolution target in the focal plane.