Design of compact high resolution imaging system for cold atom experiments

Shen Xiao-Yang; Cheng Yi-Hao; Xia Lin

doi:10.7498/aps.73.20231689

Abstract

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.

Keywords:

Authors and contacts

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Songshan Lake Materials Laboratory, Dongguan 523808, China

Corresponding author: Xia Lin, linxia@iphy.ac.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFA1400900, 2021YFA0718302) and the National Natural Science Foundation of China (Grant No. 11874418).

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References

[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
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[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
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[14]	Trisnadi J, Zhang M, Weiss L, Chin C 2022 Rev. Sci. Instrum. 93 083203 Google Scholar
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[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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图 1 成像系统的光路结构

Figure 1. Layout of the imaging system.

DownLoad: Full-Size Img PowerPoint

图 2 显微物镜的光路结构

Figure 2. Layout of the microscope objective.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 4 远摄物镜示意图

Figure 4. Telephoto lens group.

DownLoad: Full-Size Img PowerPoint

图 5 远摄物镜的光路结构

Figure 5. Layout of the telephoto objective.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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.

Magnification	L/mm	Ref.
40.6	$ \sim $1678	[21]
32	1000	[23]
18.9	1000	[24]
21.4	1000	[25]
14.9	1000	[28]
50	874	This work

DownLoad: CSV

表 2 真空窗厚度范围(R)的比对

Table 2. Comparison of the vacuum window thickness ranges (R).

NA	R /mm	Ref.
0.52	6—10	[21]
0.55	3—7	[23]
0.78	3—7	[23]
0.44	0—13	[24]
0.4	5—7	[27]
0.47	0—15	This work

DownLoad: CSV

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

DownLoad: CSV

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

DownLoad: CSV

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
Assembling tolerance	Clear aperture tilt	±0.02°

DownLoad: CSV

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

DownLoad: CSV

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/mm	d₁/mm	d₂/mm	d₃/mm	Diffraction-limited FOV/μm	Magnification	Track length/mm
470	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

DownLoad: CSV

[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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