Optical image amplification in dual-comb microscopy by use of optical-fiber-amplified interferogram

Dual-comb microscopy (DCM), based on a combination of dual-comb spectroscopy (DCS) with two-dimensional spectral encoding (2D-SE), is a promising method for scan-less confocal laser microscopy giving an amplitude and phase image contrast with the confocality. However, signal loss in a 2D-SE optical system hampers increase in image acquisition rate due to decreased signa-to-noise ratio. In this article, we demonstrated optical image amplification in DCM with an erbium-doped fiber amplifier (EDFA). Combined use of image-encoded DCS interferogram and EDFA benefits from not only the batch amplification of amplitude and phase images but also significant rejection of amplified spontaneous emission (ASE) background. Effectiveness of the optical-image-amplified DCM is highlighted in the single-shot quantitative nanometer-order surface topography and the real-time movie of polystyrene beads dynamics under water convection. The proposed method will be a powerful tool for real-time observation of surface topography and fast dynamic phenomena.


Introduction
An optical frequency comb (OFC) [1][2][3] has a unique optical spectrum composed of a vast number of discrete, regularly spaced optical frequency modes, and the optical frequency and phase of all OFC modes are secured to a frequency standard by active laser control of carrier-envelope-offset frequency fceo and a frequency spacing or repetition frequency frep. Dual-comb spectroscopy (DCS) [4][5][6][7] has appeared as a new mode to make full use of OFC as an optical frequency ruler for broadband high-precision spectroscopy. Use of two OFCs with slightly different frequency spacings (signal OFC, frep1; local OFC, frep2 = frep1 + ∆frep) enables us to make a replica of the signal OFC in radio-frequency (RF) region based on a frequency scale of 1:(frep1/∆frep), typically 1:10 5 .
Recently, a new door of application has opened for DCS: dual-comb imaging (DCI) [17][18][19][20][21][22][23]. In this case, OFC is regarded as an optical carrier of amplitude and phase with a vast number of discrete frequency channels in place of optical frequency ruler. Then, image pixels to be measured is spectrally encoded into OFC modes by space-to-wavelength conversion or spectral encoding (SE). Finally, image is decoded all at once from the mode-resolved spectrum of the image-encoded OFC acquired by DCS, based on one-to-one correspondence between images pixels and OFC modes. Due to the scan-less imaging capability in DCI and the simultaneous acquisition capability of amplitude and phase spectra in DCS, combination of DCI with confocal laser microscopy enables the scan-less confocal one-dimensional (1D) [17,[19][20][21]23] or two-dimensional (2D) [18,22] imaging of amplitude and phase. Such dual-comb microscopy (DCM) has been effectively applied for the surface topography of a nanometer-scale step-structured sample and the nonstaining imaging of standing culture fixed cells [18].
DCM has a potential to boost the image acquisition rate up to ∆frep (typically, a few kHz). While such kHz imaging rate will expand application fields of DCM into observation of fast dynamic phenomena, the largely reduced time of image acquisition leads to poor signal-to-noise ratio (SNR).
Also, signal loss in a 2D-SE optical system is another reason that hampers increase in the image acquisition rate. Although increase of incident optical power is a straightforward way from the viewpoint of light source, it often causes photodamage in a sample. On the other hand, from the viewpoint of detector, acquisition of DCS interferogram under strong non-interferometric background light makes it difficult to use a highly sensitive photodetector. One interesting approach to enhance SNR in rapid imaging is optical amplification of image-encoded optical signal.
For example, the fiber-amplifier-based image amplification was effectively applied for real-time observation of fast dynamic phenomena in serial time-encoded amplified microscopy (STEAM) [24,25].
In this article, we adopted the optical image amplification for DCM to enhance imaging performance in rapid data acquisition or weak signal acquisition. The SNR and contrast in confocal amplitude and phase images were significantly enhanced without influence of incoherent background light of amplified spontaneous emission (ASE) by coherent amplification of imageencoded OFC interferogram in erbium-doped fiber amplifier (EDFA). Figure 1 shows an experimental setup of the optical-image-amplified DCM system. Since the detail of DCM without the optical image amplification is described in the previous paper [18], we here give a brief description of it. We used a pair of homemade femtosecond Er-fiber OFC lasers for a signal OFC (center wavelength = 1560 nm, spectral range = 1545~1575 nm, mean output power = 125 mW, fceo1 = 21.4 MHz, frep1 = 100,388,730 Hz) and a local OFC (center wavelength = 1560 nm, spectral range = 1545~1575 nm, mean output power = 15 mW, fceo2 = 21.4 MHz, frep2 = 100,389,709 Hz, ∆frep = frep2 -frep1 = 979 Hz) in DCM. fceo1, frep1, fceo2, and frep2 were all phaselocked to a rubidium frequency standard (not shown, Stanford Research Systems, Inc., Sunnyvale, CA, USA, FS725, frequency = 10 MHz, accuracy = 5 × 10 -11 , instability = 2 × 10 -11 at 1 s) via a laser control system. The signal OFC beam (mean power = 65 mW) was separated into a reference arm for a reference signal OFC beam and a signal arm for an imaged-encoded signal OFC beam by a 50:50 beam splitter (BS), respectively. The reference signal OFC beam in the reference arm was reflected by a gold plane mirror and was combined with the imaged-encoded signal OFC beam by BS. To separate an interferogram of the reference signal OFC from that of the imaged-encoded signal OFC temporally, we adjusted difference of optical path length between the reference arm and the signal one. In the signal arm, the signal OFC beam was fed into a 2D-SE optical system, composed of a virtually imaged phased array (VIPA, Light Machinery, Inc., Nepean, Ontario, Canada, OP-6721-6743-8, free spectral range = 15.1 GHz, finesse = 110), a diffraction grating (Spectrogon AB, Täby, Sweden, PC 1200 30 × 30 × 6, groove density = 1200 grooves/mm, efficiency = 90 %), and a lens (L1, focal length = 150 mm). The 2D-SE optical system forms 2D spectrograph of signal OFC modes at an optical Fourier plane. The 2D spectrograph was relayed and focused as 2D focal spot array of signal OFC modes onto a sample by a combination of a lens (L2, focal length = 150 mm) with a dry-type objective lens (OL, Nikon Corp., Tokyo, Japan, Plan Apo Lambda 40XC, numerical aperture = 0.95, working distance = 160~250 µm). Reflection, absorption, scattering, and/or phase change of the signal OFC beam in the sample encode the image contrast onto the amplitude and phase spectra of 2D spectrograph. As the image-encoded 2D spectrograph of the signal OFC passed through the same optical system in the opposite direction, each wavelength component of the spectrograph was spatially overlapped with each other again as an image-encoded signal OFC. Typical power of the image-encoded signal OFC was decreased down to several tens to a few hundreds µW mainly due to VIPA passage in the return path. After being spatially overlapped with the reference signal OFC beam by BS, the image-encoded signal OFC beam was fed into the experimental setup of the DCS.

Basic performance of EDFA for optical image amplification
We first evaluated the static performance of EDFA using a continuous-wave extended cavity laser diode (ECLD) (Redfern Integrated Optics, Inc., Santa Clara, CA, USA, RIO PLANEX, center wavelength = 1650 nm, FWHM < 2.0 kHz). Figure 2(a) shows a relationship between an optical input power and an optical output power at 1650 nm when a LD pumping current of EDFA was set to 280 mA. A liner relationship was confirmed between them without the saturation, and an optical amplification factor of 13 was achieved from the slope coefficient between them. We used this amplification factor in the following experiments by considering sublinear increase of amplified light, linear increase of ASE, and saturation of the photodetector. Figure 2(b) shows the optical amplification factor with respect to wavelength within the range of OFC spectrum. Such no wavelength dependence will lead to flat amplification of optical image because OFC modes has a one-to-one correspondence with 2D image pixels.
We next evaluate the time-domain performance of EDFA using an interferogram between the signal OFC and the local one. A plane gold mirror was used for a sample.  Fine structure of red plot in Fig. 2(e) reflects the 2D image information of the test chart although

Imaging performance of optically-image-amplified DCM
To evaluate the effectiveness of the optical image amplification in DCM, we first acquired the confocal amplitude image of the test chart with and without the optical image amplification.   To evaluate the quantitativity of the rapid confocal phase imaging, we calculated surface unevenness H(x, y) of the silver-thin-film-coated test chart by (1) where l is a typical wavelength of OFC modes (= 1550 nm), and f(x, y) is the phase image. We

Confocal amplitude and phase movie of moving sample
To highlight the rapid imaging capability of the optical-image-amplified DCM, we demonstrated confocal amplitude and phase imaging of a moving sample. We prepared an aggregation of polystyrene beads with two different diameters (= 10 µm and 20 µm), and put it into water H x, y

Discussion
We demonstrated effectiveness of optical image amplification in DCM for enhanced quality of confocal amplitude and phase images in the rapid acquisition rate or weak signal acquisition. We here discuss comparison of optical image amplification between DCM and STEAM [24,25]. One important difference between them is in property of optical spectrum: discrete spectrum of OFC in DCM and continuous spectrum of broadband light in STEAM. Although 2D images pixels are superimposed on the optical spectrum by 2D spatial disperser and are amplified by fiber amplifiers in both DCM and STEAM, discrete optical spectrum of OFC in DCM is more robust to the pixel cross-talk in the optical image amplification than continuous spectrum in STEAM.
Another important difference between DCM and STEAM is in property of optical detection: coherent interferometric detection in DCM and incoherent non-interferometric detection in STEAM. Although the coherent interferometric detection contributes ASE rejection capability to DCM demonstrated above, incoherent non-interferometric detection makes it difficult to reject ASE because both signal light and ASE are incoherent. Also, such the coherent interferometric detection enables us to maintain the phase image contrast after optical amplification because the phase non-linearity or phase noise in optical amplification is common between the image-encoded signal OFC and the local OFC due to simultaneous process of optical amplification, leading to cancellation of the phase non-linearity or phase noise in the optical amplification process.
The final important difference between DCM and STEAM is in existence of background light.
The non-interferometric detection in STEAM enables the background-free measurement and benefits from the high gain in the optical amplification if ASE is negligible. On the other hand, the background light always accompanies as non-interferometric light with the interferogram in interferometric detection in DCM, and both are optically amplified by EDFA. The amplified non-interferometric light significantly limits the dynamic range of the photodetector. As a result, the amplification ratio of EDFA was remained at 13. Such negative contribution of noninterferometric light to the photodetector dynamic range is common problem in DCS.

Conclusion
Optical image amplification was successfully introduced in DCM for confocal amplitude and