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Abstract
Single-shot measurement of surface defects of mirrors is vital for monitoring the operating states of high power lasers systems. While conventional methods suffer from low speed and small dynamic range. Here, we demonstrate a method for high speed two-dimensional (2D) surface amplitude-type defects measurement based on ultrafast single-pixel imaging assisted by a virtually imaged phased-array. Together with an optical grating, 2D wavelength to space mapping is achieved based on Fraunhofer far field diffraction, and the uniform broad spectrum of a home-made dissipative soliton is uniformly dispersed into the targeted mirror with one-to-one wavelength-to-space mapping. The surface amplitude-type defects are modulated into the intensity variation of the reflected spectrum. Then, we build a dispersive Fourier transform module for wavelength to time mapping, through which modulated spectral information is time stretched into the temporal domain, and recorded by a high speed photodetector together with a real time oscilloscope. Finally, to diminish the distortions induced by nonlinear dispersion during the wavelength-time mapping, we utilize the interpolation, and reconstruct the 2D surface with a frame rate of 7.6 MHz. A two-dimensional image with widths of 1.5 × 2 mm can be obtained within 10 ns, with a y direction spatial resolution of 180 µm and a x direction spatial resolution of 140 µm. This ultrafast 2D surface defects measurement scheme is promising for real-time monitoring of surface defects mirrors with large aperture, which are widely utilized in various high power laser systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High power laser systems are vital in fields of high energy physics, laser nuclear fusion, free electron laser [1,2]. While their on-site health monitoring technique are relatively less developed. Numerous precision optical devices with large apertures, such as mirrors, lens, prisms, are equipped within these laser systems. To handle the extremely high peak power, these expensive devices are coated with fine films, either for antireflecting or high-reflecting. While, when the laser energy is high enough, the undesirable Joule heat absorbed by mirrors results into high temperature across the surface, and localized thermal expansion [3–5]. Other defects may come from fabrication imperfections, environmental contaminations, which would bring great damages to the mirrors [3]. Additionally, the nonlinear mode coupling induced localized heat accumulation, and nonlinear effects, such as SPM, stimulated Raman and Brillouin scattering, and four-wave-mixing, damage the reflective optical surfaces [6]. Therefore, monitoring the quality of the mirrors make it possible to inspect and maintain the long term performance of the laser systems, and preventing the potentially catastrophic damage in downstream applications.
Due to the urgent demands, great efforts have been devoted to monitor the surface qualities of mirrors on site. For example, the interferometers and Hartmann methods [8–10]. Both methods permit large-scale measurement as they converge the light spot on the charge-coupled device image plane by beam shrinking. Yet, they are limited by the relative slow response speed of the camera, so still unable to achieve high speed online detection. To ensure the healthy operation of large high-energy laser devices, the on-line damage detection technology based on side illumination dark field imaging is used to monitor the state of optical components. Thompson et al proposed the final optics damage inspection (FODI) system with active laser illumination, and achieve 600 µm accuracy [7]. Yet, it is hard to accurately distinguish which optical element the damage in the FODI image belongs to, due to crosstalk from adjacent optical elements. After that, Conder et al achieved the 192 images acquisition within 2 hours by using dark field time-sharing independent side illumination [11]. Meanwhile, the spatial filtering is utilized to improve the image quality, and the total internal reflection or machine vision are also used for online measurement. However, limited by their intrinsic mechanism, their detection time are still too long, and are only suitable for static surface damages. For those defects detection systems, one core constraint is the utilization of two-dimensional (2D) detectors, such as, charge-coupled device and complementary metal-oxide-semiconductor. The relative low readout speed results in large response time, which is insufficient to record the transient and non-repetitive damaging process of mirrors within high power laser systems, ranging with a duration of microsecond or even to picosecond time scale.
Recently, we propose a high speed surface defects detection method of mirrors based on ultrafast single-pixel imaging [12]. Ultrafast single-pixel imaging, sometimes named as serial time-encoded imaging [13], make it possible to recorded an image with ultrahigh frame rate [14–16]. It has been utilized in applications, including surface vibrometer and surface defect detection [17]. As a proof-of-concept, we build a spatial Fourier optical module for frequency-space mapping through an optical grating, and a dispersive Fourier transform (DFT) module for wavelength-time mapping, through which the surface amplitude-type defects coded spectral information is mapped into the temporal domain. However, the 1D mapping for the grating only permits a line imaging with a high frame rate. Further 2D imaging needs mechanically electric scanning, reducing the effective frame rate into kHz. To monitor the transient surface defects, a genuine single-shot 2D imaging system rather than one dimensional line imaging is needed.
In this manuscript, we demonstrate a single-shot 2D imaging system for mirrors amplitude-type surface defects detection based on ultrafast single-pixel imaging. Different from our previous scheme, a virtually imaged phased-array (VIPA) is utilized to mapping the uniform spectrum of a home-made dissipative soliton point-by-point into a 2D spatial plane through far field approximation, where the surface mirror is inspected. By adopting the DFT module for wavelength to time mapping, the modulated continuous spectra can be obtained in real time. To reconstruct the targeted 2D image, we find that the spatial resolutions are distorted by the dispersion nonlinearity. An interpolation algorithm is proposed to diminish the nonlinear dispersion. In our experiment, a lateral and longitudinal resolution of 140 µm and 180 µm are obtained, respectively. The obtained effective 2D imaging frame rate is 7.6 MHz. Such a measurement system breaks the limitations of low speed, permits transient amplitude-type surface defects measurement with high speed.
2. Main principle and experimental setup
Figure 1 (a) depicts the experimental setup for the 2D imaging of surface defects for refractive mirror. It mainly consists a home-made dissipative soliton (DS) as optical source, a 2D spectral shower based on VIPA, a DFT module for wavelength-time mapping, then the modulated optical signals are detected and recorded by the high optoelectronic system. In our experiment, the DS laser source is generated by passively mode-locked by single-wall carbon nanotubes within a ring fiber cavity with net normal dispersion [17]. Its repetition rate is 7.6 MHz. The optical spectrum is rectangle-shaped with a bandwidth of 8 nm (Fig. 1 (c)), and the center wavelength is about 1567 nm. Such a rectangle shape makes it attractive for ultrafast imaging with high uniformity. By controlling the fiber length in laser cavity, we can obtain DS with different bandwidths. In fact, such a kind of laser has been used in our previous works in Ref. 12, whose repetition rate, center wavelength, and optical bandwidth are 8.4 MHz, 1561 nm, and 13 nm, respectively. Besides, as DS here is highly chirped, its large pulse duration of 35 ps make it possible to be amplified without pulse breaking. Figure 1 (c) show the optical spectra before and after amplified by a commercial erbium-doped fiber amplifier (EDFA), through which the average power is amplified from 0.2 mW into 70 mW.
Fig. 1. (a) Schematic of the mirror surface defects detection system. (b) Experimental setup of the 2D spectral shower. (c) Optical spectra of DS before and after amplification, and stretching.
After the amplification, the optical spectrum is mapped by the 2D spectral shower into the focal plane, where the target mirror is placed. The 2D spectral shower consists of a VIPA together with an optical grating with 600 lines/mm. To be more specifically, the collimated light with a beam waist of 2 mm from the optical fiber is coupled into the VIPA along y direction, while the output dispersed light from VIPA is injected into the grating, whose grooves are along the x direction. Therefore, the amplified DS is dispersed by two orthogonal dispersions, then it is collimated by a plane convex lens with a focal length f equals 200 mm. The mirror to be tested is placed in the focal plane. Though such a 2D spectral shower, the uniform wavelengths of the DS is mapped into a 2D plane, and the surface defects of the target mirror can be reflected by the modulation of optical spectrum of DS. After the illumination of the mirror, the reflected beam is separated into two paths by an optical coupler (OC). The spectrum for one path is detected by a conventional optical spectrum analyzer (OSA). The single-shot spectra for the other path is detected by a DFT module via dispersive Fourier transformation. The DFT module consists of a section of dispersion compensation fiber (DCF), which would not disturb the spectrum measurement of OSA. Together with a high-speed photodiode (PD) with a bandwidth of 12 GHz and a real-time oscilloscope (OSC) with a bandwidth of 20 GHz, the single-shot spectra can be recorded by the DFT system. The DFT module permits a spectral-to-temporal mapping coefficient of 1.3 ns/nm. Through the DFT module, once the consecutive spectra can be detected real-timely, any transient surface amplitude-type defects can be revealed by demodulating the corresponding spectra through a computer. The detection speed is just determined by the repetition rate, here, 7.6 MHz.
Considering the mapping structure of the 2D spectral shower in Fig. 1 (b), the resolution in y direction is determined by the FSR of VIPA. Figure 2 depicts main structure of the commercially available VIPA (OP-6721-X, LightMachinery). It has a squared shape with a dimension of 18 mm, and the finesse is 82. The free spectral range (FSR) is 0.54 nm. Fundamentally, it is a tilted etalon, or a cavity made of two plates [18–22]. The reflectivity of one plate is near 100%, while that for the other is 95%. Therefore, when the collimated beam is focused into the VIPA cavity with angle of θ, only 5% of the energy will be outputted due to refraction, and most of it will be reflected multiples times. Multiple beam interference will occur when the phase matching is satisfied, and the multiple virtual images are obtained. The constructive interference determines the output wavelengths in y direction by the following equation
In our experiment, the effective resolutions are also determined by the optical resolution of the wavelength to time module based on DFT. Similar to the far field approximation of Fraunhofer diffraction, for an optical pulse propagates through a dispersive medium with large dispersion, its optical spectrum can be approximated by its time-domain intensity through wavelength to time coefficient [24,25]:
where, Δλ, and $\Delta \tau $ are optical bandwidth and temporal pulse width, respectively. D is the dispersion coefficient in ps⋅km−1⋅nm−1. Here, to compare the dispersion’s influence, we utilize two kinds of DCFs. A kind of 2 km DCF has a dispersion coefficient of -215 ps⋅km−1⋅nm−1, corresponding to a spectral-to-temporal coefficient of 0.43 ns/nm, and it has strong dispersion nonlinearity, namely, third order dispersion. The dispersion coefficient for the other kind of DCF is 1.3 ns/nm, with rectified nonlinear dispersion.3. Results and discussion
3.1 Testing of the 2D spectral shower
To test the 2D wavelength to space mapping of the 2D spectral shower, we record the reflected averaged spectrum by the OSA. The surface of the target mirror has been written manually with numbers of 0, 1, and 2. The numbers written by mark pen would change the reflection of the mirror, of which can be used to mimic the static amplitude-type surface defects. Then we reconstructed the 2D images. The optical resolution of the OSA is 0.05 nm. Figures 3 (a)-(c) show the original images, and the reconstructed images are denoted by Figs. 3 (d)-(f). Amplitude decrease is observed on the vertical direction (y axis), which is mainly is induced by the nonuniformity of the spectrum after optical amplification as indicted by the Fig. 1 (c). However, high consistency can still be found between those two kinds of images, revealing that our 2D spectral shower can mapping the spectrum into two dimensions. While, as the conventional OSA is based on mechanically scanning, its detection speed is low enough (> 1 ms), therefore, it is not possible to record the single-shot spectrum. To perform the surface defects with high speed, we need to use the DFT module for real time spectrum caption.
Fig. 3. (a)-(c) Numbers written on the surface of mirror. (d)-(f) reconstructed images from averaged spectrum obtained by OSA.
3.2 Influence of the dispersion nonlinearity
For capturing the transient surface amplitude-type defects, we record the single-shot spectrum by the DFT module. The large memory depth of the oscilloscope permits us recording the events occurring within a wide time duration. Here, we use the 2 km DCF for time stretching. The spectral-to-temporal coefficient of 0.43 ns/nm, and the effective optical resolution is about 0.4 nm. Besides, the strong dispersion slope of 9 ps/nm2/km makes the wavelength to time mapping rather tricky. For example, when we want to record the transient events within a wide time range, the FSR becomes larger and larger, and the reconstructed images will be distorted. The influence induced by dispersion nonlinearity can be cleared shown in Fig. 4, where the FSR is no longer fixed to the specific parameters of VIPA, but changes gradually.
Fig. 4. Temporal signals recorded after DFT module for number 1, where the FSR is not fixed to the VIPA, but increases when time changes.
To reconstruct the 2D image from the distortion, we propose the idea of interpolation process. Namely, we take the maximum period of sampling points as the standard, and interpolate and supplement the periods for fewer sampling points, which is equivalent to improving the sampling rate and aligning each FSR peak value. Figure 5 denotes the comparation between the images with and without interpolation. It is clear that the positions of the selected peak values are aligned, and the distortion in Fig. 5 (b) is corrected.
Fig. 5. (a) Selected region of number 1. Reconstructed 2D images without interpolation (b), and with interpolation (c). Location of peak values without (d) and with interpolation (e)
3.3 Influence of the dispersion value
In addition to the dispersion nonlinearity, the absolute dispersion value also influences the overall spatial resolution. In fact, a better optical resolution of the DFT module results to better spatial resolution of the ultrafast 2D imaging. Here, we use the DCF with rectified dispersion nonlinearity. The dispersion coefficient for this kind of DCF module is 1.3 ns/nm, responding to an effective optical resolution of 0.13 nm. The optimized optical parameters would expected improved resolutions in the fast imaging. Figure 6 (a) and (b) denotes the original data obtained by conventional OSA, and DFT module. As the numbers are written on the surface of mirrors, the reflected light through smooth surface has been subtracted by those through objects. The surface defects are more clearly shown in the inset of Fig. 6 (b).
Fig. 6. (a) Experimental spectra obtained from conventional OSA for number 2. (b) Experimental spectra obtained from DFT. The inset shows the subtracted single-shot spectrum without backgrounds.
Figure 7 (a) denotes the comparison of the background-free data, where high consistency is shown between those from OSA and DFT. The reconstructed 2D images in Fig. 7 (c) and 7 (d). During reconstruction, the values below zero are redefined as zero, of which would not influence the image qualities. Those two images exhibit similar amplitude decreasing on the vertical direction, which is also induced by nonuniformity of amplified DS. We can see a slight deviation, which is mainly attributed to the relative worse spectral resolution. Here, the effective spatial resolutions for x and y directions for the measurement system are 140 µm, and 180 µm, respectively. Those spatial resolutions are relatively low, when compared to conventional methods. However, they can be optimized via decreasing the grating period and focal length, or increasing the beam radius. The field of view here is 1.5 mm×2 mm. It is mainly determined by the optical width of the DS, and the FSR of the VIPA. Further, a broader coherent pulsed laser may help to enlarge the field of view.
Fig. 7. (a) Comparison between subtracted spectrum obtained from OSA and DFT. (b) Image of number 2. (c) Reconstructed image from data obtained from OSA. (d) Reconstructed image from data obtained from DFT.
Although such an imaging system is still suffering with undesired resolution and field of view, it permits measurement of transient surface amplitude-type defects of mirrors by demodulating the consecutive single-shot spectra. The results in Fig. 3 show that the measurement is successful in detecting the static defects, based on the spectra obtained by OSA with low speed. The ability for monitoring the transient laser-induced defects are demonstrated by the images in Figs. 5(b) and 5(c), and 7(d) that reconstructed by the single-shot spectra with a frame rate of 7.6 MHz. Therefore, the proposed measurement system is able to monitor transient laser-induced amplitude-type defects, via two-dimensional imaging with high frame rate. Such a imaging frame rate is just determined by the repetition rate of the pulsed laser we used, which could be extended to GHz.
4. Conclusion
We have demonstrated an ultrafast two-dimensional imaging for surface amplitude-type defects measurement of mirrors based on a VIPA. A 2D spectral shower is built by the VIPA together with an optical grating. The two orthogonally placed dispersers permit the mapping from spectrum into two-dimensional plane. Besides, a DFT mapping module are employed to record the reflected beam from the target mirror. The manually written numbers are tested as surface defects on the mirrors. We rectified the distortions induced by nonlinear dispersion by interpolation, and reconstruct the 2D surface defects images with a frame rate of 7.6 MHz, with a y direction spatial resolution of 180 µm and a x direction spatial resolution of 140 µm. The measurement time can be less than 10 ns. Such an 2D ultrafast imaging system may find potential applications in monitoring the transient surface defects of mirrors, and also is promising for monitor of high power laser systems.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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