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Aberration athermal design for infrared search and trace optical system
G Model IJLEO-54358; No. of Pages 3
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Aberration athermal design for infrared search and trace optical system ManDe Shen a,∗ , QinXiu Jiang a , Cheng Li a , HuanHuan Ren a , LiangYi Chen b a b
Wuhan Textile University, Wuhan, Hubei 430073, China Xi’an Institute of Optics and Precision Mechanics Chinese Academy of Science, Xi’an 710119, China
a r t i c l e
i n f o
Article history: Received 15 July 2013 Accepted 6 January 2014 Available online xxx Keywords: Optical design Infrared optical system Diffractive optics
a b s t r a c t To satisfy environment requirement of infrared search and trace optical system, an infrared diffractive/refractive hybrid optical system in 3.7–4.8 m with 11.42◦ of field of view for passive athermalization is presented. The system is consisted of three lenses, including two aspheric surfaces and a diffraction surface, which has only two materials Ge and Si. The optical system has compact structure, small volume and light weight. The image quality of the system approaches the diffraction limit in the temperature range −80 ◦ C to 160 ◦ C. It is compatible with staring focal plane array which has a format of 320 × 240 and the pixel pitch of 30 m. The system need not move the compensated lens repeatedly to obtain the best images from −80 ◦ C to 160 ◦ C and enhances the performance of target tracking and recognition. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction
2. Athermal characteristic of diffractive optical element
Due to the possession of advantages of passivity working mode, good disguise, clarity character of image and easy observation, infrared search and trace optical system are used in a wide variety of applications, such as territorial surveillance, search and rescue etc. Focus shift with temperature is a significant problem in the infrared optical system. The infrared search and trace optical system needs to have the steady image in the working temperature from −80 ◦ C to 160 ◦ C. So athermalization for infrared search and trace optical system is an important issue. Recent advances in fabrication technologies such as diamondmachining and photolithography have made the production of hybrid refractive/diffractive optical elements realistic. Concurrently, advances in optical design software allow the designer to incorporate these components into practical designs. Based on the thermal properties of diffractive element, the paper shows a passive athermalization infrared search and trace optical system and the optical system demonstrated consistent quality throughout the analyze.
The phase function for a diffractive phase profile is most frequently stated by ϕ(r) =
2 (A1 r 2 + A2 r 4 + A3 r 6 + · · ·)
where ϕ(r) is phase term in radians, is center wavelength, pradial coordinate. A1 , A2 , A3 , etc. are the higher order phase coefficients. An important relationship to remember is C2 = −
1 2f
(2)
where f is focal length of the diffractive lens. The negative sign of C2 indicates the direction of the phase profile. To be more specific, a negative sign means that the focal length is positive and the phase profile moves in the direction of the lens substrate. For a positive C2 , the focal length is negative, and the phase profile moves away from the lens substrate. The athermal characteristic of diffractive optical element is different from the refractive element. It can be represented by ∂ϕ = ϕ(−2˛) ∂T
∗ Corresponding author. E-mail address: [email protected] (M. Shen).
(1)
(3)
where T is temperature and ϕ is the power of diffractive optical element; ˛ is the thermal coefficient of expansion of the substrate. For positive power, the focal length of diffractive optical element will become longer with increasing temperature while for
http://dx.doi.org/10.1016/j.ijleo.2014.01.076 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: M. Shen, et al., Aberration athermal design for infrared search and trace optical system, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.076
G Model
ARTICLE IN PRESS
IJLEO-54358; No. of Pages 3
M. Shen et al. / Optik xxx (2014) xxx–xxx
2 Table 1 The design requirements of the optical system. Parameter
Value
Spectral range Primary wavelength Focal length Field of view F number Optical transmission Back working length
3.7–4.8 m 4.2 m 60 mm 9.14◦ × 6.85◦ 2.0 >80% >15 mm
Fig. 1. Layout of optical system.
Fig. 2. Relationship of the phase in periods and period versus radius of diffractive surface.
refractive element, the focal length will become shorter. Hence passively athermal hybrid infrared optical system is much easier to be designed than the traditional refractive optical system. j
hi i =
(4)
i=1
where is the power of whole optical system, hi is the first paraxial ray height of incidence surface of the lens i, i is the power of the lens i. fbT =
k 1 2
h1
Fig. 3. MTF of the system at different temperature.
(h2i xi i ) = 0
(5)
i=1
3. The design of result analysis 3.1. Parameters of optical system
where xi is the dispersive coefficient of the lens i. dfbT dt
=
k 1 2
h1
h2i xi i = ˛h L
(6)
The system was designed to work primarily in the mid-wave region and possessed a resolution of 320 × 240 pixels. The parameters of optical system of the optical system are shown in Table 1.
i=1
where dfbT /dT is the off-focus of the system for the change of temperature, ˛h is the linear expansion coefficient of drawtube material, L is the total length of the drawtube.
3.2. The results analysis The resolution requirements required by an FPA are a function of the pixel size. Current FPAs typically exhibit individual
Please cite this article in press as: M. Shen, et al., Aberration athermal design for infrared search and trace optical system, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.076
G Model IJLEO-54358; No. of Pages 3
ARTICLE IN PRESS M. Shen et al. / Optik xxx (2014) xxx–xxx
Fig. 4. Relationship of wavefront error and temperature (−80 to 160 ◦ C).
pixels measuring from 40 to 50 m square. As arrays increase in size, pixels will be reduced in size to facilitate packaging due to limitations on substrate manufacturing technology. The FPA pixels of optical system are 30 m according to design requirements of the optical system, a passive athermalization infrared search and trace optical system is designed. The total length is less than 100 mm. The optical system is consisted of three lenses, which has only two materials Ge and Si. In order to reduce the spherical aberration and coma, we set an aspheric surface on the rear surface of the third lens which is near to the stop and an aspheric surface on the rear surface of the second lens, as shown in Fig. 1. The DOE surface is far from the stop, which can reduce off-axis aberration, the advanced aberration and chromatic aberration. The
3
drawtube materials are composed of the material of titanium. The linear expansion coefficient of aluminum is 8.0 × 10−6 ◦ C−1 . Fig. 2 is relationship of the phase in periods and period versus radius of DOE surface respectively. Fig. 3 is the curve of system MTF at different temperature, (a), (b), (c) and (d) show respectively −80 ◦ C, 20 ◦ C, 90 ◦ C and 160 ◦ C. According as the four pictures, we know that the MTF of the infrared diffractive/refractive hybrid optical system is close to the diffraction-limit in the temperature range −80 ◦ C to 160 ◦ C. Fig. 4 is the relationship of wavefront error and temperature (−80 to 160 ◦ C). From Fig. 4, we know that the maximal wavefront error is 0.122, which is less than 0.25, so the image quality is great. For the F/2.0, 3.7–4.8 m system, the focus depth is ±0.034 mm, the maximal off-focus from the temperature −80 to 160 ◦ C is 0.0086 mm, the maximal off-focus is less than focus depth, so the optical system can be used. 4. Conclusion An F/2.0 middle wavelength infrared search and trace optical system in the temperature range −80 ◦ C to 160 ◦ C is described, and constructed of three lenses, including two aspheric surfaces and a diffraction surface. The system performance approaches the diffraction limit. The passive thermal compensation can ensure high image quality in a large temperature range −80 ◦ C to 160 ◦ C. In this design, the refractive/diffractive middle wavelength infrared search and trace optical system is proved to be able to reduce athermalization and ensure compact structure, small volume and light weight.
Please cite this article in press as: M. Shen, et al., Aberration athermal design for infrared search and trace optical system, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.076
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Aberration athermal design for infrared search and trace optical system ManDe Shen a,∗ , QinXiu Jiang a , Cheng Li a , HuanHuan Ren a , LiangYi Chen b a b
Wuhan Textile University, Wuhan, Hubei 430073, China Xi’an Institute of Optics and Precision Mechanics Chinese Academy of Science, Xi’an 710119, China
a r t i c l e
i n f o
Article history: Received 15 July 2013 Accepted 6 January 2014 Available online xxx Keywords: Optical design Infrared optical system Diffractive optics
a b s t r a c t To satisfy environment requirement of infrared search and trace optical system, an infrared diffractive/refractive hybrid optical system in 3.7–4.8 m with 11.42◦ of field of view for passive athermalization is presented. The system is consisted of three lenses, including two aspheric surfaces and a diffraction surface, which has only two materials Ge and Si. The optical system has compact structure, small volume and light weight. The image quality of the system approaches the diffraction limit in the temperature range −80 ◦ C to 160 ◦ C. It is compatible with staring focal plane array which has a format of 320 × 240 and the pixel pitch of 30 m. The system need not move the compensated lens repeatedly to obtain the best images from −80 ◦ C to 160 ◦ C and enhances the performance of target tracking and recognition. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction
2. Athermal characteristic of diffractive optical element
Due to the possession of advantages of passivity working mode, good disguise, clarity character of image and easy observation, infrared search and trace optical system are used in a wide variety of applications, such as territorial surveillance, search and rescue etc. Focus shift with temperature is a significant problem in the infrared optical system. The infrared search and trace optical system needs to have the steady image in the working temperature from −80 ◦ C to 160 ◦ C. So athermalization for infrared search and trace optical system is an important issue. Recent advances in fabrication technologies such as diamondmachining and photolithography have made the production of hybrid refractive/diffractive optical elements realistic. Concurrently, advances in optical design software allow the designer to incorporate these components into practical designs. Based on the thermal properties of diffractive element, the paper shows a passive athermalization infrared search and trace optical system and the optical system demonstrated consistent quality throughout the analyze.
The phase function for a diffractive phase profile is most frequently stated by ϕ(r) =
2 (A1 r 2 + A2 r 4 + A3 r 6 + · · ·)
where ϕ(r) is phase term in radians, is center wavelength, pradial coordinate. A1 , A2 , A3 , etc. are the higher order phase coefficients. An important relationship to remember is C2 = −
1 2f
(2)
where f is focal length of the diffractive lens. The negative sign of C2 indicates the direction of the phase profile. To be more specific, a negative sign means that the focal length is positive and the phase profile moves in the direction of the lens substrate. For a positive C2 , the focal length is negative, and the phase profile moves away from the lens substrate. The athermal characteristic of diffractive optical element is different from the refractive element. It can be represented by ∂ϕ = ϕ(−2˛) ∂T
∗ Corresponding author. E-mail address: [email protected] (M. Shen).
(1)
(3)
where T is temperature and ϕ is the power of diffractive optical element; ˛ is the thermal coefficient of expansion of the substrate. For positive power, the focal length of diffractive optical element will become longer with increasing temperature while for
http://dx.doi.org/10.1016/j.ijleo.2014.01.076 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: M. Shen, et al., Aberration athermal design for infrared search and trace optical system, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.076
G Model
ARTICLE IN PRESS
IJLEO-54358; No. of Pages 3
M. Shen et al. / Optik xxx (2014) xxx–xxx
2 Table 1 The design requirements of the optical system. Parameter
Value
Spectral range Primary wavelength Focal length Field of view F number Optical transmission Back working length
3.7–4.8 m 4.2 m 60 mm 9.14◦ × 6.85◦ 2.0 >80% >15 mm
Fig. 1. Layout of optical system.
Fig. 2. Relationship of the phase in periods and period versus radius of diffractive surface.
refractive element, the focal length will become shorter. Hence passively athermal hybrid infrared optical system is much easier to be designed than the traditional refractive optical system. j
hi i =
(4)
i=1
where is the power of whole optical system, hi is the first paraxial ray height of incidence surface of the lens i, i is the power of the lens i. fbT =
k 1 2
h1
Fig. 3. MTF of the system at different temperature.
(h2i xi i ) = 0
(5)
i=1
3. The design of result analysis 3.1. Parameters of optical system
where xi is the dispersive coefficient of the lens i. dfbT dt
=
k 1 2
h1
h2i xi i = ˛h L
(6)
The system was designed to work primarily in the mid-wave region and possessed a resolution of 320 × 240 pixels. The parameters of optical system of the optical system are shown in Table 1.
i=1
where dfbT /dT is the off-focus of the system for the change of temperature, ˛h is the linear expansion coefficient of drawtube material, L is the total length of the drawtube.
3.2. The results analysis The resolution requirements required by an FPA are a function of the pixel size. Current FPAs typically exhibit individual
Please cite this article in press as: M. Shen, et al., Aberration athermal design for infrared search and trace optical system, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.076
G Model IJLEO-54358; No. of Pages 3
ARTICLE IN PRESS M. Shen et al. / Optik xxx (2014) xxx–xxx
Fig. 4. Relationship of wavefront error and temperature (−80 to 160 ◦ C).
pixels measuring from 40 to 50 m square. As arrays increase in size, pixels will be reduced in size to facilitate packaging due to limitations on substrate manufacturing technology. The FPA pixels of optical system are 30 m according to design requirements of the optical system, a passive athermalization infrared search and trace optical system is designed. The total length is less than 100 mm. The optical system is consisted of three lenses, which has only two materials Ge and Si. In order to reduce the spherical aberration and coma, we set an aspheric surface on the rear surface of the third lens which is near to the stop and an aspheric surface on the rear surface of the second lens, as shown in Fig. 1. The DOE surface is far from the stop, which can reduce off-axis aberration, the advanced aberration and chromatic aberration. The
3
drawtube materials are composed of the material of titanium. The linear expansion coefficient of aluminum is 8.0 × 10−6 ◦ C−1 . Fig. 2 is relationship of the phase in periods and period versus radius of DOE surface respectively. Fig. 3 is the curve of system MTF at different temperature, (a), (b), (c) and (d) show respectively −80 ◦ C, 20 ◦ C, 90 ◦ C and 160 ◦ C. According as the four pictures, we know that the MTF of the infrared diffractive/refractive hybrid optical system is close to the diffraction-limit in the temperature range −80 ◦ C to 160 ◦ C. Fig. 4 is the relationship of wavefront error and temperature (−80 to 160 ◦ C). From Fig. 4, we know that the maximal wavefront error is 0.122, which is less than 0.25, so the image quality is great. For the F/2.0, 3.7–4.8 m system, the focus depth is ±0.034 mm, the maximal off-focus from the temperature −80 to 160 ◦ C is 0.0086 mm, the maximal off-focus is less than focus depth, so the optical system can be used. 4. Conclusion An F/2.0 middle wavelength infrared search and trace optical system in the temperature range −80 ◦ C to 160 ◦ C is described, and constructed of three lenses, including two aspheric surfaces and a diffraction surface. The system performance approaches the diffraction limit. The passive thermal compensation can ensure high image quality in a large temperature range −80 ◦ C to 160 ◦ C. In this design, the refractive/diffractive middle wavelength infrared search and trace optical system is proved to be able to reduce athermalization and ensure compact structure, small volume and light weight.
Please cite this article in press as: M. Shen, et al., Aberration athermal design for infrared search and trace optical system, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.076