뗚 38 뻭뗚 1 웚 2019 쓪 2 퓂 뫬췢폫뫁쏗늨톧놨 J. Infrared Millim. Waves Vol. 38ꎬ No. 1 Februaryꎬ 2019 ÎÄÕ±àºÅ : 1001 - 9014⠩⁔樍 2019⤩⁔樍 01 - 0039 - 05 DOI㨩⁔樍 10. 11972 / j. issn. 1001 - 9014. 2019. 01. 007 Received date㨩⁔樍 2018-04-24ꎬ revised date㨩⁔樍 2018-10-20 쫕룥죕웚㨩⁔樍 2018-04-24ꎬ 탞믘죕웚㨩⁔樍 2018-10-20 Foundation items㨩⁔樍 Supported by Nationa Natural Science Foundation of China ⠩⁔樍 61875227⤩⁔樍 Biography㨩⁔樍 WANG Hao⠩⁔樍 1992- ⤩ⴳ㌹⢣갩崠告 maleꎬ Nantongꎬ Chinaꎬ Ph. D. Research area involves optical design and laser propagation in undewater turbulence. E-mail㨩⁔樍 wanghao14@ mails. ucas. ac. cn * Corresponding author㨩⁔樍 E-mail㨩⁔樍 kangfuzeng@ opt. ac. cn An optical design for dual-band infrared diffractive telescope WANG Hao 1ꎬ 2 ꎬ KANG Fu-Zeng 1* ꎬ ZHAO Wei 1 ꎬ LI Yi-Chao 1ꎬ 2 ⠩⁔樍 1. State Key Laboratory of Transient Optics and Photonicsꎬ Xi’ an Institute of Optics and Precision Mechanicsꎬ Chinese Academy of Sciencesꎬ Xi’ an 710119ꎬ China㬩⁔樍 2. University of Chinese Academy of Sciencesꎬ Beijing 100049ꎬ China⤩⁔樍 Abstract㨩⁔樍 In this paperꎬ the double-layer harmonic diffractive element ⠩⁔樍 HDE⤩⁔樍 structure is investigated and the op- timization procedure is based on the equation of diffraction efficiency of the double-layer diffractive optical ele- ment. The diffraction efficiency of the system in the designed middle and far infrared wavebands is larger than 99% ꎬ which improves the image contrast and the imagequality significantly. A new dual-band infrared double-layer HDE telescope is designedꎬ which can work in the middle and far infrared wavebands. It is shown that the system approximately attains diffraction limit and is easy to processed. Key words㨩⁔樍 diffraction efficiency ꎬ HDEꎬ optical design PACS㨩⁔樍 42. 15. Eqꎬ 07. 57. Kp 튻훖뫬췢쮫늨뛎퇜짤췻풶뺵뗄맢톧짨볆 Íõê» 1£¬ 2 £¬¿µ¸£Ôö 1* £¬ÕÔÎÀ 1 £¬ÀîÒ㳬 1£¬ 2 ⠩⁔樍 1. 훐맺뿆톧풺컷낲맢톧뺫쏜믺킵퇐뺿쯹 쮲첬맢톧폫맢ퟓ벼쫵맺볒훘뗣쪵퇩쫒ꎬ짂컷 컷낲 710119㬩⁔樍 2. 훐맺뿆톧풺듳톧ꎬ놱뺩 100049⤩⁔樍 햪튪㨩⁔樍 É鏸ëÑо¿ÁËË«²耙³ÑÜÉ荵簷§Ôª¼þ £¬ »ùÓÚÑÜÉ菻§ÂÊ·½³Ì¶ÔË«²耜ÜÉ蕚ª¼þµÄÑÜÉ菻§ÂʽøÐÐ . ¹âѧϵͳÔÚ Öв¨ºìÍ篌ͳ¤²¨ºìÍ箚¨¶ÎµÄÑÜÉ菻§Âʾù³¬¹ýÁË 99% £¬ ¼«´óµØÌ盧ßÁËͼÏñµÄ¶Ô±È¶ÈºÍÏñÖÊ . É霈ÆÁËÒ»¿隯ÂÐ굀 ºìÍ簍«²¨¶ÎÑÜÉ莽鋕¶¾µ £¬ È¡µÃÁ˽ӽüÑÜÉ莨«Ï޵ijÉÏñÖÊÁ¿ £¬ Ò×ÓÚ¼Ó¹¤ . 맘 볼 듊㨩⁔樍 ÑÜÉäЧÂÊ ; HDE;¹âѧÉè¼Æ 훐춼럖샠뫅㨩⁔樍 O439 컄쿗뇪쪶싫㨩⁔樍 A Introduction A significant improvement in reconnaissance capa- bility is the primary goal of equipment development. It is one method to improve the equipment reconnaissance a- bility by using various infrared spectrum to detect the in- frared radiation of the scene at the same time. Due to the influence of atmospheric transmissionꎬradiation charac- teristics of different scene in the short-wavelength infra- red ⠩⁔樍 SWIR⤩ⴳ㌰⢣갩崠告 medium-wavelength infrared ⠩⁔樍 MWIR⤩⁔樍 and long-wavelength infrared ⠩⁔樍 LWIR ⤩⁔樍 have different per- formance. In the case of stray radiation or near the heat sourceꎬLWIR has a strong reconnaissance capabilityꎬ while in hot and humid environmentꎬMWIR has great advantage over other. It is obviously to see the difference between the image of the same scene in MWIR and LWIR ꏛ 1 ꏝ ⠩⁔樍 Fig. 1 ⤩⁔樍 . By using the spectrum of different wavelength range in infrared bandꎬthe target camouflage information can be effectively eliminatedꎬthe detection and recognition ability of the target can be improved and the false alarm rate of the system can be reduced. The refractive index of materials in the two bands varies greatlyꎬ bringing difficulty in achromatism in infra- red dual band optical system. We often take a reflective structure to design dual band system to avoid the achro- matic difficulty. Reflective system structure is complex that coaxial system with a central blockꎬ affects the sys- tem modulation transfer functionꎬwhile off-axis system without center block is difficult to align. Refractive struc- tures which have no center block and are easy to align
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An optical design for dual-band infrared diffractive telescope
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Received date: 2018-04-24,revised date: 2018-10-20 收稿日期: 2018-04-24,修回日期: 2018-10-20Foundation items: Supported by Nationa Natural Science Foundation of China ( 61875227)Biography: WANG Hao( 1992-) ,male,Nantong,China,Ph. D. Research area involves optical design and laser propagation in undewater turbulence. E-mail:wanghao14@ mails. ucas. ac. cn* Corresponding author: E-mail: kangfuzeng@ opt. ac. cn
An optical design for dual-band infrared diffractive telescope
WANG Hao1,2, KANG Fu-Zeng1* , ZHAO Wei1, LI Yi-Chao1,2
( 1. State Key Laboratory of Transient Optics and Photonics,Xi’an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi’an 710119,China;
2. University of Chinese Academy of Sciences,Beijing 100049,China)
Abstract: In this paper,the double-layer harmonic diffractive element ( HDE) structure is investigated and the op-timization procedure is based on the equation of diffraction efficiency of the double-layer diffractive optical ele-ment. The diffraction efficiency of the system in the designed middle and far infrared wavebands is larger than99%,which improves the image contrast and the imagequality significantly. A new dual-band infrared double-layerHDE telescope is designed,which can work in the middle and far infrared wavebands. It is shown that the systemapproximately attains diffraction limit and is easy to processed.
A significant improvement in reconnaissance capa-bility is the primary goal of equipment development. It isone method to improve the equipment reconnaissance a-bility by using various infrared spectrum to detect the in-frared radiation of the scene at the same time. Due to theinfluence of atmospheric transmission,radiation charac-teristics of different scene in the short-wavelength infra-red ( SWIR) ,medium-wavelength infrared ( MWIR) andlong-wavelength infrared ( LWIR ) have different per-formance. In the case of stray radiation or near the heatsource,LWIR has a strong reconnaissance capability,while in hot and humid environment,MWIR has greatadvantage over other. It is obviously to see the difference
between the image of the same scene in MWIR andLWIR[1]( Fig. 1) .
By using the spectrum of different wavelength rangein infrared band,the target camouflage information canbe effectively eliminated,the detection and recognitionability of the target can be improved and the false alarmrate of the system can be reduced.
The refractive index of materials in the two bandsvaries greatly,bringing difficulty in achromatism in infra-red dual band optical system. We often take a reflectivestructure to design dual band system to avoid the achro-matic difficulty. Reflective system structure is complexthat coaxial system with a central block,affects the sys-tem modulation transfer function,while off-axis systemwithout center block is difficult to align. Refractive struc-tures which have no center block and are easy to align
红 外 与 毫 米 波 学 报 38 卷
take four kind materials apochromatic way to correctchromatic aberration in dual band.
Fig. 1 The same scene in MWIR( a) and LWIR( b)图 1 在中波红外( a) 和长波红外( b) 的同一幅图像
The emergence of diffractive optical elements( DOEs) bring new direction to dual band optical sys-tem. Harmonic DOE can correct chromatic aberrationand simplify the optical structure. Due to low diffractionefficiency of harmonic DOE,we often use double-layerHDE to design optical system.
In this paper,a dual-band infrared optical systembased on Cooke structure working in both MWIR( 3. 4 ~4. 2 μm) and LWIR ( 8 ~ 11 μm ) has been designedwith the double-layer HDE. In this design,the systemcomponent number and the weight of the system are re-duced and the diffraction efficiency is ensured at thesame time. The chromatic aberration of the system is wellcorrected and the image quality is near diffraction limit.
Fig. 2 Schematic diagram of different DOEs. ( a) general single-layer DOE; ( b) single-layer HDE; ( c) double-layer HDE图 2 不同衍射元件的结构图( a) 单层衍射元件( b) 单层谐衍射元件( c) 双层衍射元件
1 Diffraction Efficiency
Diffraction efficiency is one of the most importantproperties of refractive-diffractive optical systems[2]. Ac-cording to the scalar diffraction theory,the diffraction ef-ficiency of the DOE is a function of the wavelength λ andthe diffraction order m:
η( λ,m) = sinc2 ( Φ( λ)2π
- m) . ( 1)
In formula,sincx = sinx /x,Ф( λ) is phase functionof DOE.
For general DOE[2],m = 1,the phase function is:
Φ( λ) =2πλ0
λ· n( λ) - 1
n( λ0 ) - 1 . ( 2)
It is obviously to know that the diffraction efficiency
of such elements can reach 100% at the design wave-length and drops rapidly away from the design wave-length,which is not suitable for the optical system withwide spectral range.
For HDE[3-4],m = p,p ± 1,…,p ± i,the phasefunction is:
Φ( λ) =ρ·2πλ0
λ· n( λ) - 1
n( λ0 ) - 1 . ( 3)
Compared with general single-layer DOE,the dif-fraction efficiency of the single-layer HDE decreasesmore rapidly away from the design wavelength when thedesigned wavelength is the same.
The double-layer HDE[5-6] is equivalent to a com-mon DOE ( m = 1) with two single-layer HDE,the phasefunction is:
Φ( λ) =2πh1
λ[n1 ( λ) - 1]-
2πh2
λ[n2 ( λ) - 1]
. ( 4)
Fig. 3 Diffraction efficiency curves of general single-layerDOE,single-layer HDE and double-layer HDE ( Red lineand green line are diffraction efficiency curves of single-lay-er DOE of diffraction order m = 1 and designed wavelengthλ0 = 4 μm and 10 μm,respectively. Blue line,yellowline,pink line and bright blue line are diffraction efficiencycurves of single-layer HDE of p = 3 and designed wave-length λ0 = 7 μm,which’s diffraction order m is 2,3,4and 5, respectively. Black line is diffraction efficiencycurve of double-layer HDE of diffraction order m = 1 anddesigned wavelength λ1 = 4 μm and λ2 = 10 μm )
From figure 3,we can see that diffraction efficiencyof double-layer HDE is much higher than that of single-layer DOE and single-layer HDE and associated with de-sign wavelengths. After selecting two different dispersivematerials and λ1 and λ2,the two design wavelengths inthe dual-design wavebands,we can obtain the following
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1 期 WANG Hao et al: An optical design for dual-band infrared diffractive telescope
Fig. 4 ( Color online) Structure of double-layer HDE. H1 andH2 are respectively the surface relief heights of the first and sec-ond HDE. D is the width of the air gap. The solid and dashedlines are the diffractive directions for MWIR and LWIR,respec-tively图 4 双层衍射元件的结构图. H1 和 H2 分别为第一层和第二层衍射元件的高度,D 是空气间隔. 实线和虚线分别为中波红外和长波红外的衍射方向
Then the value of the comprehensive average dif-fraction efficiency( CADE) [6] for dual wavebands can bewritten as:
η =w1
λ1max - λ1min∫
λ1max
λ1min
sinc2 ( Φ( λ)2π
- m) dλ
+w2
λ2max - λ2min∫
λ2max
λ2min
sinc2 ( Φ( λ)2π
- m) dλ , ( 7)
where λ1min and λ1max and λ2min and λ2max are respectivelythe minimum and maximum wavelength for the two wave-bands,and w1 and w2 are the weight factors of CADE foreach waveband. Because the imaging quality of the hy-brid diffractive-refractive optical system is analyzed alonefor each waveband,w1 and w2 are 0. 5.
In the paper,we choose ZnSe and SRF2 as the firstand second base material of double-layer HDE for differ-ent design wavelength pairs. According to Eq. ( 7 ) ,weuse Matlab to find the best chose wavelength pairs for thehighest diffraction efficiency. From the Fig. 5 and Fig. 6,we can see that when λ1 =3. 852 μm and λ2 =9. 485 μm,the CADE can reach 99. 84% . At the same time,H1 =22. 927 μm,H2 =59. 507 μm and m1 =7. 4,m2 = -6. 4.
2 Design of the infrared double-layer diffractivetelescope
The dual-band infrared double-layer HDE telescopeoptical system[7-10] with four different materials and four
Fig. 5 Diffraction efficiency of double-layer HDE underdifferent wave pair( front view )图 5 不同波长对下的双层衍射元件的平均衍射效率
Fig. 6 Diffraction efficiency of double-layer HDE underdifferent wave pair( top view )图 6 不同波长对下的双层衍射元件的平均衍射效率( 俯视)
Table 1 CADE of double-layer HDE with Different DesignWavelength Pairs
表 1 双层衍射元件在不同的设计波长对下面的平均衍射效率
Design wavelength/ μm
3. 852 and9. 485
3. 2 and 83. 8 and10. 5
4. 2 and 11
CADE /% 99. 84 96. 79 98. 92 98. 44
lenses must satisfy the three relations as follows:the total power:
Φ11 +Φ
21 +Φ
31 +Φ
41 +Φ
51d =Φ , ( 8)
zero axial color over the two wavebands:Φ1
1
v11+Φ2
1
v21+Φ3
1
v31+Φ4
1
v41+Φ5
1d
v51d, ( 9)
Φ12
v12+Φ2
2
v22+Φ3
2
v32+Φ4
2
v42+Φ5
2d
v52d, ( 10)
where Φ11,Φ2
1,Φ41and Φ
41 are the respective powers of the
three refractive lens in the mid-infrared waveband and
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红 外 与 毫 米 波 学 报 38 卷
Φ51d is that of the HDE. v11,v21,v31 and v41 are the respec-
tive dispersion coefficients for the materials of the lensand V5
1d is that of the HDE. Φi2,vi2,( i = 1,2,3,4 ) and
Φ52d,v52d are the corresponding quantities over the far-in-
frared waveband.
Table 3 Structural parameters of infrared double-layer HDE optical system ( unit: mm)表 3 红外双波段衍射望远镜的结构参数( 单位: mm)
Based on the discussion,we can select the four ma-terials as follows: ZnS,Ge,ZnSe and SRF2. And theoptical system uses Selex Company’s MW/LW CCD in-frared detector( HxV is 640 × 512,Pixel Pitch is 30 μm×30 μm) . The optical specifications of the optical sys-tem are summarized in Table 2.
Table 2 Design specifications表 2 设计参数
Waveband 3. 4 ~ 4. 2 μm and 8 ~ 11 μmFocal length 50 mmF number 2
Field of view 16°MTF Above 0. 5 at 17 pl /mm
Fig. 7 Structure of the infrared double-layer HDE telescopeoptical system图 7 红外双波段衍射望远镜的结构图
In figure 7,the surface 1 is aspheric surface whichwell corrects spherical aberration and improves the imagequality of system. The achromatic surface 6 and surface 7are binary optical surfaces.
In figure 8,the maximum RMS radius in 3. 4 ~ 4. 2μm and 8 ~ 11 μm are10. 279 μm and 15. 327 μm,re-spectively,which means that the lens can match with theinfrared CCD detector that has a format of 640 × 512 anda pixel pitch of 30 μm.
The curve of the modulation transfer function( MTF) in mid-and far-infrared wavebands are shown inFig 9. At the spatial frequency of 17 lp /mm,the MTF atthe center FOV ( 0o ) in dual wavebands attained above
Fig. 8 Spot diagram of the infrared double-layer HED tele-scope. Left: spot diagram of the optical system in the mid-in-frared waveband; right: spot diagram of the optical system inthe far-infrared waveband图 8 红外双波段衍射望远镜在中波红外( 左边) 和长波红外( 右边) 波段的点列图
Fig. 9 MTF of the infrared double-layer HDE telescope opticalsystem. Left: MTF of the optical system in the mid-infraredwaveband; right: MTF of the optical system in the far-infraredwaveband图 9 红外双波段衍射望远镜在中波红外( 左边) 和长波红外( 右边) 波段的 MTF
0. 57 and that of edge FOV( 8o ) in 3. 4 ~ 4. 2 μm and 8~ 11 μm attained 0. 78 and 0. 56,respectively. The dif-fraction efficiency of the system at each wavelength in thetwo designed wavebands is larger than 99%,which im-proves the image contrast and the imaging quality signifi-cantly.
In figure 10,we can easy find that the feature sizeof surface 6 is 29. 6 μm and that of surface 7 is 30. 9μm. Under existing level of manufacture, DiamondTurning can meet the requirement of manufacture.
3 Conclusion
In conclusion, the optimization structure of thedouble-layer HDE is investigated in order to conquer thedifficulty of the diffraction efficiency of the single layer
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1 期 WANG Hao et al: An optical design for dual-band infrared diffractive telescope
Fig. 10 Phase plot of binary surface. Left: phase plot of theoptical system in the mid-infrared waveband; right: phase plotof the optical system in the far-infrared waveband图 10 二元面在中波红外( 左边) 和长波红外( 右边) 波段的相位分布图
HDE,and the optimization method is investigated. Thenan infrared telescope with a double-layer HDE is de-signed. Its diffraction efficiency is larger than 99% ateach wavelength in the mid and far-infrared wavebands,which improves the image contrast and the image per-formance significantly. MTF is above 0. 5 at 17 lp /mmand image performance is near-diffraction. And it is ap-plicable to the uncooled infrared dual waveband CCD de-tector that has a format of 640 × 512 which’s pixel pitchis 30 μm. By introducing double-layer HDE in opticaldesign,chromatic aberration is well corrected.
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