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In cold atom experiments, high resolution imaging systems have been used to extract in-situ density information when studying quantum gases, which is one of the hot topics in this field. Such a system is usually called “quantum-gas microscope”. In order to achieve a long working distance and large magnification, high resolution imaging of cold atoms through a vacuum window usually requires a long distance between the atoms and the camera. However, due to space limitation caused by a large number of nearby optical elements, it may be difficult to realize a long imaging system, which is a common case in cold atom experiments. Herein we present an imaging system that can achieve a short distance between the atoms and the image plane with diffraction-limited 1 μm resolution and 50 magnification. The telephoto lens design is adopted to reduce the back focal length and enhance the pointing stability of the imaging lens. The system is optimized at an operating wavelength of 767 nm and corrects aberrations induced by a 5-mm-thick silica vacuum window. At a working distance of 32 mm, a diffraction-limited field of view of 408 μm is obtained. The simulation result shows that by changing the air space between lenses, our design operates across a wide range of window thicknesses (0–15 mm), which makes it robust enough to be used in typical laboratories. This compact imaging system is made from commercial on-shelf Φ2 in (1 in = 2.54 cm) singlets and consists of two components: a microscope objective with a numerical aperture of 0.47 and a telephoto objective with a long effective focal length of 1826 mm. Both are infinitely corrected, allowing the distance between them to be adjusted to insert optical elements for irradiating atoms with laser beams of different wavelengths without affecting the imaging resolution. Taking the manufacturing and assembling tolerances into consideration, the Monte Carlo analyses show that more than 95% of the random samples are diffraction-limited within the field of view. This high success rate ensures that these two objectives can be achieved easily in the experiment. Combined with its performance with other wavelengths (470–1064 nm), this imaging system can be used for imaging different atom species, such as sodium, lithium, and cesium.
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Keywords:
- cold atom experiments /
- high resolution imaging /
- optical design
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图 3 显微物镜的仿真结果 (a) 不同视场角下出瞳不同位置光线的波像差(单位为767 nm); (b) 不同视场角下的点列图, 圆圈表示艾里斑大小; (c) 0.13°视场角时的MTF曲线, 插图为1000 cycles/mm处的MTF曲线
Fig. 3. Simulated results of the microscope objective. (a) Wavefront error at different positions of the exit pupil at different fields (The unit is 767 nm). (b) Spot diagrams at different fields. The black circles represent the Airy disks. (c) MTF curves at 1.0 field. The inset plots the MTF near 1000 cycles/mm.
图 6 远摄物镜的仿真结果 (a) 不同视场角下出瞳不同位置光线的波像差; (b)不同视场角下的点列图; (c) 0.13°视场角时的MTF曲线
Fig. 6. Simulated results of the telephoto objective: (a) Wavefront error inside the circular pupil at different fields; (b) spot diagrams at different fields; (c) MTF curves at 1.0 field.
图 7 中心视场处的分辨率仿真 (a) 物平面上的USAF 1951分辨率板; (b) 像平面上的仿真结果; (c) 像平面上PSF的径向分布, 插图为PSF在像平面上的投影, 峰值对应斯特列尔比率
Fig. 7. Simulation of the system’s resolution at 0 field: (a) The USAF 1951 resolution target in the object plane; (b) the simulation result in the image plane; (c) PSF along the radial direction in the image plane. The inset in panel (c) shows the projection of the PSF on the image plane, where the peak value corresponds to the Strehl ratio.
表 1 相机附近长焦成像镜组光路长度(L)的比对
Table 1. Comparison of the optical path lengths (L) of the long foci imaging lens group near the camera.
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表 2 真空窗厚度范围(R)的比对
Table 2. Comparison of the vacuum window thickness ranges (R).
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表 3 成像系统的设计要求
Table 3. Design requirements of the imaging system.
Items Specifications Resolution/μm 1 Wavelength/nm 767 Working distance/mm ＞20 Magnification 50 Track length/m ＜1 Image diameter/mm 8.2
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表 4 显微物镜的参数
Table 4. Specifications of the microscope objective.
Surface No. Radius/mm Thickness/mm Material 1 Infinity 4.00 N-BK7 2 51.46 31.50(d1) Air 3 127.37 8.12 N-BK7 4 –127.37 0.50 Air 5 256.59 5.52 N-BK7 6 –256.59 0.50 Air 7 47.87 7.29 N-BK7 8 119.32 1.40 Air 9 30.34 9.70 N-BK7 10 65.80 17.0264 Air 11 Infinity 5.00 Silica 12 Infinity 15.00 Vacuum
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表 5 公差分析中使用的公差值
Table 5. Tolerances used in the tolerance analysis.
Tolerance type Items Value Manufacturing tolerance Lens thickness ±0.1 mm Air space ±0.05 mm Radii ±3${\lambda _{633}}$ Refractive index ±0.001 Centering ±3 arcmin Assembling tolerance Decentration ±0.05 mm Clear aperture tilt ±0.02°
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表 6 远摄物镜的参数
Table 6. Specifications of the telephoto objective.
Surface No. Radius/mm Thicknesses/mm Material 1 64.38 8.22 N-BK7 2 Infinity 9.60(d2) Air 3 –517.255 2.50 N-BK7 4 517.255 71.00(d3) Air 5 –38.59 3.50 N-BK7 6 Infinity 772.016 Air 7 Infinity 1.50 Silica 8 Infinity 5.55 Vacuum
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表 7 不同真空窗厚度与波长下的表现
Table 7. Performance of the imaging system at different window thicknesses and wavelengths.
Wavelength/nm Window
thickness/mmd1/mm d2/mm d3/mm Diffraction-limited
FOV/μmMagnification Track
length/mm470 0 26.1 226 –48.8 963 5 31.4 0.624 83.9 230 –51.5 969 15 50.8 173 –50.0 827 767 0 26.2 398 –47.7 986 5 31.5 9.6 71.0 408 –50.6 993 15 50.8 404 –61.6 1013 1064 0 26.2 440 –48.9 1022 5 31.4 11.0 69.4 440 –51.7 1028 15 50.5 502 –63.0 1048
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[1] Sherson J F, Weitenberg C, Endres M, Cheneau M, Bloch I, Kuhr S 2010 Nature 467 68
Google Scholar
[2] Cheuk L W, Nichols M A, Okan M, Gersdorf T, Ramasesh V V, Bakr W S, Lompe T, Zwierlein M W 2015 Phys. Rev. Lett. 114 193001
Google Scholar
[3] Wei D, Rubio-Abadal A, Ye B, Machado F, Kemp J, Srakaew K, Hollerith S, Rui J, Gopalakrishnan S, Yao N Y, Bloch I, Zeiher J 2022 Science 376 716
Google Scholar
[4] Bakr W S, Gillen J I, Peng A, Fölling S, Greiner M 2009 Nature 462 74
Google Scholar
[5] Bakr W S, Peng A, Tai M E, Ma R, Simon J, Gillen J I, Folling S, Pollet L, Greiner M 2010 Science 329 547
Google Scholar
[6] Salim E A, Caliga S C, Pfeiffer J B, Anderson D Z 2013 Appl. Phys. Lett. 102 084104
Google Scholar
[7] Preiss P M, Ma R C, Tai M E, Lukin A, Rispoli M, Zupancic P, Lahini Y, Islam R, Greiner M 2015 Science 347 1229
Google Scholar
[8] Britton J W, Sawyer B C, Keith A C, Wang C C J, Freericks J K, Uys H, Biercuk M J, Bollinger J J 2012 Nature 484 489
Google Scholar
[9] Graham T M, Song Y, Scott J, Poole C, Phuttitarn L, Jooya K, Eichler P, Jiang X, Marra A, Grinkemeyer B, Kwon M, Ebert M, Cherek J, Lichtman M T, Gillette M, Gilbert J, Bowman D, Ballance T, Campbell C, Dahl E D, Crawford O, Blunt N S, Rogers B, Noel T, Saffman M 2022 Nature 604 457
Google Scholar
[10] Weiss D S, Saffman M 2017 Phys. Today 70 44
Google Scholar
[11] Wu X L, Liang X H, Tian Y Q, Yang F, Chen C, Liu Y C, Tey M K, You L 2021 Chin. Phys. B 30 020305
Google Scholar
[12] Meng Z M, Wang L W, Han W, Liu F D, Wen K, Gao C, Wang P J, Chin C, Zhang J 2023 Nature 615 231
Google Scholar
[13] 王良伟, 刘方德, 李云达, 韩伟, 孟增明, 张靖 2023 物理学报 72 064201
Google Scholar
Wang L W, Liu F D, Li Y D, Han W, Meng Z M, Zhang J 2023 Acta Phys. Sin. 72 064201
Google Scholar
[14] Trisnadi J, Zhang M, Weiss L, Chin C 2022 Rev. Sci. Instrum. 93 083203
Google Scholar
[15] Raithel G, Duspayev A, Dash B, Carrasco S C, Goerz M H, Vuletić V, Malinovsky V S 2023 Quantum Sci. Technol. 8 014001
Google Scholar
[16] Rispoli M, Lukin A, Schittko R, Kim S, Tai M E, Léonard J, Greiner M 2019 Nature 573 385
Google Scholar
[17] Lukin A, Rispoli M, Schittko R, Tai M E, Kaufman A M, Choi S, Khemani V, Léonard J, Greiner M 2019 Science 364 256
Google Scholar
[18] Kaufman A M, Tai M E, Lukin A, Rispoli M, Schittko R, Preiss P M, Greiner M 2016 Science 353 794
Google Scholar
[19] Gemelke N, Zhang X B, Hung C L, Chin C 2009 Nature 460 995
Google Scholar
[20] Preiss P M, Ma R C, Tai M E, Simon J, Greiner M 2015 Phys. Rev. A 91 041602
Google Scholar
[21] Gempel M W, Hartmann T, Schulze T A, Voges K K, Zenesini A, Ospelkaus S 2019 Rev. Sci. Instrum. 90 053201
Google Scholar
[22] Knottnerus I H A, Pyatchenkov S, Onishchenko O, Urech A, Schreck F, Siviloglou G A 2020 Opt. Express 28 11106
Google Scholar
[23] Li S K, Li G, Yang P F, Wang Z H, Zhang P F, Zhang T C 2020 Opt. Express 28 36122
Google Scholar
[24] Li X, Zhou F, Ke M, Xu P, He X D, Wang J, Zhan M S 2018 Appl. Opt. 57 7584
Google Scholar
[25] Bennie L M, Starkey P T, Jasperse M, Billington C J, Anderson R P, Turner L D 2013 Opt. Express 21 9011
Google Scholar
[26] Shen C Y, Chen C, Wu X L, Dong S, Cui Y, You L, Tey M K 2020 Rev. Sci. Instrum. 91 063202
Google Scholar
[27] Li S K, Li G, Wu W, Fan Q, Tian Y L, Yang P, Zhang P F, Zhang T C 2020 Rev. Sci. Instrum. 91 043104
Google Scholar
[28] Pritchard J D, Isaacs J A, Saffman M 2016 Rev. Sci. Instrum. 87 073107
Google Scholar
[29] Müller T 2011 Ph. D. Dissertation (Zurich: ETH Zurich
[30] 徐睆垚, 徐亮, 沈先春, 徐寒杨, 孙永丰, 刘文清, 刘建国 2021 物理学报 70 184201
Google Scholar
Xu H Y, Xu L, Shen X C, Xu H Y, Sun Y F, Liu W Q, Liu J G 2021 Acta Phys. Sin. 70 184201
Google Scholar
[31] Fischer R, Tadic-Galeb B, Yoder P 2008 Optical System Design (2nd Ed.) (New York: McGraw-Hill Education) pp136–137
[32] Knottnerus I 2018 M. S. Thesis (Amsterdam: University of Amsterdam
[33] Alt W 2002 Optik 113 142
Google Scholar
[34] Gross H, Zügge H, Peschka M, Blechinger F 2006 Image Quality Criteria (Weinheim: Wiley-VCH) pp91–99
[35] Öttl T 2019 M. S. Thesis (Innsbruck: University of Innsbruck
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