Phase distortion correction of fringe patterns in spaceborne Doppler asymmetric spatial heterodyne interferometry
doi: 10.37188/CO.EN-2024-0007
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Abstract:
As an advanced device for observing atmospheric winds, the spaceborne Doppler Asymmetric Spatial Heterodyne (DASH) interferometer also encounters challenges associated with phase distortion, particularly in limb sounding scenarios. This paper discusses interferogram modeling and phase distortion correction techniques for spaceborne DASH interferometers. The modeling of phase distortion interferograms with and without Doppler shift for limb observation was conducted, and the effectiveness of the analytical expression was verified through numerical simulation. The simulation results indicate that errors propagate layer by layer while using the onion-peeling inversion algorithm to handle phase-distorted interferograms. In contrast, the phase distortion correction algorithm can achieve effective correction. This phase correction method can be successfully applied to correct phase distortions in the interferograms of the spaceborne DASH interferometer, providing a feasible solution to enhance its measurement accuracy.
摘要:作为观测大气风的先进设备，星载多普勒非对称空间外差（DASH）干涉仪也面临着与相位畸变相关的挑战，特别是在临边探测场景中。本文讨论了星载DASH干涉仪的干涉图建模和相位畸变校正技术。对临边观测中有与无多普勒频移的相位畸变干涉图进行了建模，并通过数值模拟验证了解析表达式的有效性。仿真结果表明，在使用洋葱皮反演算法处理相位失真干涉图时，误差会逐层传播。相比之下，相位畸变校正算法可以实现有效的校正。该相位校正方法可成功应用于星载DASH干涉仪干涉图中的相位畸变校正，为提高其测量精度提供了可行的解决方案。
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关键词:
- 多普勒非对称空间外差光谱 /
- 相位畸变 /
- 相位反演 /
- 大气风测量
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1. Introduction
Many trivalent rare-earth ions (RE3+) exhibit visible radiative transitions, potentially enabling visibly emitting all solid-state lasers[1-2]. So far, various visible lasers based on RE3+-doped crystalline media have been demonstrated. Among them, trivalent praseodymium ion (Pr3+) is recognized as one of the most useful active ions for achieving efficient visible lasers because the visible transitions of Pr3+ perform as a four energy level system, and they have larger emission cross sections than other RE3+. Praseodymium trivalent ion (Pr3+) doped materials have been used to realize laser operation in the visible region, such as Pr:YLF at green, orange, and red wavelengths.
An important and successful application of Pr:YLF crystals is the generation of a continuous wave ultraviolet laser with second harmonic generation. This process has high conversion efficiency and high output power, especially in the deep ultraviolet range below 280 nm. Deep ultraviolet (UV) lasers with wavelengths shorter than 280 nm have found many promising applications in sterilization, communication, optical storage, spectral analysis, and biochemical detection. Most papers on ultraviolet radiation concentrate on the third and fourth harmonic generation. There is little research on continuous-wave ultraviolet radiation generated by second harmonic generation.
Continuous-wave laser operation in the green range at 522 nm and 546 nm has been reported under the application of Pr:YLF. In 2014, P. W. Metz et al. demonstrated the performance of 2ω-OPSL (optically pumped semiconductor laser) Pr:YLF laser with output powers of 2.9 W and 2 W at 522 nm and 546 nm, respectively[3]. High efficiency is achieved by using 2ω-OPSL as a pump source because of the matched absorption wavelength and its perfect beam quality. However, OPSLs operating at blue wavelengths are much more expensive than InGaN-based diode lasers. In 2016, S.Y.Luo et al. reported a blue-InGaN pumped Pr:YLF laser at a wavelength of 522 nm with a maximum output power of 1.6 W[4]. The Pr:YLF-based ultraviolet wavelengths were reported at 261 nm[5], 303 nm[6], and 320 nm[7]. To the best of our knowledge, the corresponding frequency doubled Pr:YLF ultraviolet laser at 275 nm has not been reported.
In this paper, we demonstrate the generation of a compact deep UV laser at 275 nm through efficient frequency doubling of a CW laser diode-pumped Pr:YLF laser at 550 nm. With an incident pump power of 4.82 W, a TEM00 mode deep UV laser radiation of 275 nm with an output power of 351 mW was achieved. The novel generated deep UV laser emission of 275 nm has potential applications in optical storage, spectral analysis, and industrial applications. We anticipate that the 275 nm emission in a Pr:YLF crystal will prove to be a promising new UV laser.
2. Experimental Setup
The experimental setup of a frequency doubling of laser-diode pumped Pr:YLF yellow-green laser is shown in Figure 1.
Figure 1. Schematic of the 275 nm laserThe laser gain medium is an a-cut Pr:YLF crystal with a dopant concentration of 0.5 %, and its dimensions are 4 mm×4 mm×15 mm. Both end faces of the crystal are polished and coated antireflection (AR) film (400 nm to 700 nm). The crystal is wrapped with indium foil and held in a water-cooled copper block to remove the heat. Fig. 2 (color online) is the energy level schematics and room temperature polarization-dependent emission Pr:YLF cross-sections in the green spectral region.
Figure 2. The energy level and room temperature polarization-dependent emission Pr:YLF cross-sectionsThe fluorescence spectrum from 500 nm to 570 nm is shown in Fig. 3. A spatially-combined InGaN laser diode module with a maximum output power of 4.82 W was used as the pump source. The pump source emits a blue laser at a peak wavelength of approximately 444.2 nm with a spectral width of about 1.8 nm. The M2 factors of the pump source are
${\mathrm{M}}^2_{\mathrm{x}} $ =46.91 and${\mathrm{M}}^2_{\mathrm{y}} $ =15.53 in the horizontal and vertical directions corresponding to the slow and fast axes. This bad beam quality influences the beam quality of the output laser. Usually, a spherical lens is stuck near the LD to compress the divergence angle of the fast axis. With this method, the divergence angles of the two directions differ greatly. The focus spot injected into the crystal has a large ellipticity, which could not satisfy the mode matching condition of DPSSL. In our research, an aspherical lens was fixed between the blue LD and focusing lens. The aspherical lens was adopted to suppress the divergence angle of the fast axis LD singly, and there is no influence on the slow axis. A proper location for the fast axis collimation lens could be found, which gave the pump beam perfect ellipticity. Under this condition, a perfect pump beam spot was obtained, as shown in Fig. 4, which is beneficial for generating a laser with good beam quality.
Figure 3. Pr:YLF fluorescence spectrum from 500 nm to 570 nm
Figure 4. Focusing shape and size of pump beam spot with a fast-axis collimating blue diodeThe pump beam was focused into the laser crystal with a plane-convex lens with a 90 % transmission rate of the pump laser and a 15 mm focal length. The absorption efficiency of the Pr:YLF crystal for the pump beam was about 75 %. The folded V-type cavity consisted of one plane input mirror (M1) and two curved mirrors (M2 and M3) with radii of curvature of 200 mm. The input coupler M1 was AR coated at 444.2 nm and high-reflection (HR) coated from 500 nm to 750 nm. The input mirror could be used to research all Pr:YLF wavelengths.
Establishing the 550 nm laser oscillation without the influence of other wavelengths was difficult. For Pr:YLF crystals, 519 nm, 538 nm, and 550 nm could establish the laser oscillation in the sigma-direction and 522 nm in the pi-direction as well as 546 nm. A Brewster plate (BP) was inserted into the cavity in the sigma-direction at a 56° incident angle to suppress the 522 nm and 546 nm in the pi-direction. Due to the thermal depolarization effect, BP could not thoroughly suppress the laser line at 522 nm and 546 nm. On the other hand, the lasers at 639 nm, 607 nm, and 720 nm were found to have larger emission cross sections than 5XX nm in Pr:YLF. A novel coating method was adopted to obtain the single fundamental laser line. The two curved mirrors, M2 and M3, were coated as short-wave-pass and long-wave-pass. The coating curves of M2 and M3 are shown in Fig. 5 and Fig. 6, respectively.
Figure 5. M2 coating curve (short-wave-pass)
Figure 6. M3 coating curve (long-wave-pass)M2 was coated simultaneously at high-transmissive below 550 nm and high-reflection above 550 nm. M2 could suppress the oscillation at 546 nm, 538 nm, 522 nm, and 519 nm. However, M2 is insufficient to suppress the other main laser lines at 607 nm, 639 nm, and 720 nm. M3 was coated at high-transmissive above 550 nm and anti-transmission below 550 nm simultaneously, which could suppress the 607 nm, 639 nm, and 720 nm in the cavity.
The CW 275 nm output laser did not transmit through the M2 mirror. The UV laser strongly damaged the coating material. A 1.5 mm thick Brewster plate was used to couple out the UV radiation. The plate was made of fused silica. One side is uncoated, and the other is HR coated for 275 nm and AR coated for 550 nm. This type of Brewster plate was proven to be a reliable UV output coupler with a long lifetime and small insertion losses for 550 nm. For intracavity frequency doubling of 550 nm, a 7 mm long Brewster/Brewster-cut BBO crystal was used with uncoated facets. The nonlinear crystal was mounted on TEC for temperature control. The BBO crystal was designed for critical type I phase matching (θ = 45.5°, Φ = 0°).
3. Results and discussion
Although the emission at about 522 nm has a 4.3 times higher emission cross-section than that of 550 nm, no lasing at other green lasers was observed in this experiment thanks to the novel coating conditions. The output characteristic of the CW intracavity frequency-doubled Pr:YLF laser in the deep UV spectral region at 275 nm is shown in Fig. 7.
Figure 7. The output power of 275 nm versus the incident pump powerThe laser oscillation threshold was found to be about 750 mW of the incident pump power. The maximum output power is 351 mW with an incident pump power of 4.82 W. The optical-to-optical slope efficiency is about 7.3%. The deep UV laser output power increases with the incident pump power, and no sign of saturation is observed, which suggests a potential to obtain higher deep UV power by increasing the power of the incident laser. Stable laser oscillation is always important for various applications. The spectrum of the 275 nm laser is registered in Fig.8 with a wavelength meter (High Finesse model LSA).
Figure 8. 275 nm laser spectrumThe central wavelength of a deep UV laser is 274.840 nm. To characterize the beam quality of the 275 nm deep UV laser beam, the beam profile and M square factor were measured in the x and y directions under maximum output power, which is shown in Fig. 9 (color online). The beam profile testing result shows that the 275 nm laser operates in TEM00 mode with a Gaussian far-field intensity distribution. Stable laser output is always desirable for various applications. The stability of the 275 nm laser is about 0.2 % (RMS, root-mean-square), as shown in Fig. 10. The stability demonstrates that there is no wavelength competition in the resonator, and this novel coating method could be adopted in the generation of other weak laser lines.
Figure 9. The beam spot and M-square of the 275 nm laser
Figure 10. 275 nm laser power stability4. Conclusion
This paper demonstrated the generation of a compact deep UV laser at 275 nm by efficient frequency doubling of a CW laser diode-pumped Pr:YLF laser at 550 nm. With an incident pump power of 4.82 W, a TEM00 mode deep UV laser radiation at 275 nm with an output power of 351mW was obtained. The novel generated deep UV laser emission at 275 nm has the highest conversion efficiency and novel CW deep UV laser wavelength.
Acknowledgements: Science and Technology Development Plan Project of Jilin Province, China (20230201062GX), Development and Industrialization on Pr doped solid state laser. -
Figure 2. Schematic diagram of limb sounding for spaceborne DASH interferometer. The angle between the tangent of the intersection of the
$m{\text{th}}$ LOS and the$n{\text{th}}$ layer is${\alpha _{mn}}$ 
Figure 4. Interferograms generated (a) without and (c) with Doppler frequency shift. (b) and (d) are correction results of (a) and (c). The simulated images have been vertically stretched, with the actual image proportions being
$82 \times 1024$ 
Figure 5. Comparison between input wind profile and retrieved wind profile. The red line represents the input wind profile, while the blue line represents the retrieved wind profile. (a) The data before phase distortion correction; (b) the data after phase distortion correction
Figure 6. After phase distortion correction, the phase changes caused by different angles
${\beta _1}$ in the residual phase distortion terms across different detector rowsTable 1. Parameters for simulation
Parameters Values Wavelengths/nm 557.7 Littrow wavelengths/nm 557.137 OPD offset/mm 20.363 Detector resolution 82× 1024 Grating groove density/(grooves·mm−1) 600 Diffraction order 1 Pixel pitch/µm 13 
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