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Design of midwave infrared athermalization optical system with a large focal plane array
G Model IJLEO-54227; No. of Pages 3
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Design of midwave infrared athermalization optical system with a large focal plane array ManDe Shen a,∗ , Cheng Li a , HuanHuan Ren a , QinXiu Jiang a , LiangYi Chen b a b
Wuhan Textile University, Wuhan 430073, Hubei, 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 23 June 2013 Accepted 15 December 2013 Available online xxx Keywords: Optical design Infrared optical system Infrared lens
a b s t r a c t Based on the most advanced staring focal plane array which had a format of 640 × 480 and the pixel pitch of 15 m, a set of all-sphere midwave infrared ahermalization optical system was designed. The working wavelength was in 3–5 m, the full field of view was 8.58◦ , the relative aperture was 1/2, the efficient focal length (EFL) was 80 m. The opticalsystem consisted of four lenses with three kinds of material – Ge, ZnSe and Si. All surfaces were sphere, which was easier to process test, making the cost inexpensive, and it could avoid using diffractive surface and aspheric surface. The image quality of the system approaches the diffraction limit in the temperature range −60 ◦ C-180 ◦ C. The design results proved that, the high resolution midwave infrared optical system had compact structure, small volume, high resolution and excellent image quality, meeting the design requirements, so that it could be used for photoelectric detection and tracking system. © 2014 Published by Elsevier GmbH.
1. Introduction The resolution requirements required by a focal plan array (FPA) are a function of the pixel size. Current FPAs typically exhibit individual pixels measuring from 40 to 50 m2 . As arrays increase in size, pixels will be reduced in size to facilitate packaging due to limitations on substrate manufacturing technology. Currently, a minimum pixel size of 15 mm2 is estimated. The reduction in pixel size demands a decrease in lens F–number if the equivalent irradiance is expected on each pixel. This demands more complex lens design forms to facilitate aberration correction. Focal plane arrays are also increasing in size. The current state of the art in commercial FPAs is 256 × 256 for InSb and HeCdTe arrays and 512 × 512 for PtSi arrays. These larger format 512 × 512 InSb arrays are anticipated in the near future. There is considerable interest in 640 × 480 PtSi arrays, as well as evidence that similar sized arrays are being considered for InSb and HeCdTe devices. Due to the possession of advantages of passivity working mode, good disguise, clarity character of image and easy observation, infrared 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 paper introduced a spherical high resolution middle infrared athermalization optical system based on 15 m × 15 m
∗ Corresponding author. E-mail address: [email protected] (M. Shen).
pixel size. The spherical high resolution middle infrared athermalization optical system needs to have the steady image in the working temperature from −60 ◦ C to 180 ◦ C. So athermalization for infrared optical system is an important issue. 2. Athermal characteristic of diffractive optical element 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 + · · ·)
(1)
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
(3)
0030-4026/$ – see front matter © 2014 Published by Elsevier GmbH. http://dx.doi.org/10.1016/j.ijleo.2013.12.024
Please cite this article in press as: M. Shen, et al., Design of midwave infrared athermalization optical system with a large focal plane array, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.024
G Model
ARTICLE IN PRESS
IJLEO-54227; No. of Pages 3
M. Shen et al. / Optik xxx (2014) xxx–xxx
2
pitch of 15 m. The layout of the final design optical system is shown in Fig. 1.The total length is less than 120 mm. The optical system is consisted of four lenses. Three kinds of material – Ge, ZnSe and Si are selected as the refractive lens for the ultralow
Table 1 The design requirements of the optical system. Parameter
Value
Spectral range Primary wavelength Focal lenth Field of view F–number Optical transmission Back working lenth
3–5 m 4 m 80 mm 8.58◦ 2.0 > 80% > 20 mm
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 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. T
fb =
k 1 2
h1
h2i xi i = 0
(5)
i=1
where xi is the dispersive coefficient of the lens i. dfbT dt
=
k 1 2
h1
h2i xi i = ˛h L
(6)
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. The design of result analysis 3.1. Parameters of optical system The system was designed to work primarily in the midwave region and possessed a resolution of 640 × 480 pixels with 15 m × 15 m pixel size. The parameter of the optical system was showed in the following table (Table 1). 3.2. The results analysis According to design requirements of the optical system, a set of ahermalization and high resolution all-sphere midwave infrared optical system was designed based on the most advanced staring focal plane array which had a format of 640 × 480 and the pixel
Fig. 1. Layout of optical system.
Fig. 2. MTF of the system at different temperature.
Please cite this article in press as: M. Shen, et al., Design of midwave infrared athermalization optical system with a large focal plane array, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.024
G Model IJLEO-54227; No. of Pages 3
ARTICLE IN PRESS M. Shen et al. / Optik xxx (2014) xxx–xxx
3
Table 2 Variation of wave front error with temperature. Temperature (◦ C) −60 20 80 130 180
Fig. 3. Variation of spot and temperature.
chromatic dispersion, as shown in Fig. 1. Therefore, the total chromatic aberration of the system is so small that can be corrected. In order to ensure the infrared optical system fabricating easily, we avoided using diffractive surface and aspheric surface. The drawtube materials are composed of the material of aluminum. The linear expansion coefficient of aluminum is 23.6 × 10−6 ◦ C. The system was optimized with the help of ZEMAX commercial optical design software after the variables, merit function, and system constraints were assigned. In the optimize process, the weighing functions of the FOV were set equally on the axis, 0.3, 0.5, 0.707, and 1.0 FOV. The midwave infrared spectrum (3.0 m, 4.0 m, and 5.0 m), were distributed as the same weighing functions. The ZEMAX commercial optical design software utilized the damped least-square algorithm to minimize the merit function. Fig. 2 is MTF of the system at different temperature, (a), (b), (c) and (d) show respectively −60 ◦ C, 20 ◦ C, 90 ◦ C and 180 ◦ C. According to the four pictures, we know that the MTF of the midwave infrared athermalization optical system with a large focal plane array is close to the diffraction-limit in the temperature range −60–180 ◦ C.
Wavefront error () 0.0963 0.0692 0.0801 0.1048 0.1263
Fig. 3 is the relationship of variation of spot and temperature, maximum RMS spot diameter of the full field is less than 12.1 m, which is smaller than the IR FPA sensor pixel size 15 m. Table 2 is the variation of wave front error with temperature (−60–180 ◦ C). From the Table 2, we know that the maximal wave front error is 0.1263 when the temperature is 180 ◦ C, which is less than 0.25, so the image quality is great. For the F/2.0, 3.0–5.0 m infrared system, the focus depth is ±0.032 mm, the maximal offfocus from the temperature −60 ◦ C to 180 ◦ C is 0.0063 mm, the maximal off-focus is less than focus depth, so the optical system can be used. 4. Conclusion An F/2.0 midwave infrared athermalization optical system with a large focal plane array in the temperature range −60–180 ◦ C is described, and constructed with four lenses, where all surfaces are spherical. Three kinds of material (Ge, ZnSe and Si) are used. The lens can ensure compact structure, small volume and light weight. The maximal off-focus is less than focus depth, the system performance approaches the diffraction limit. The passive thermal compensation can ensure high image quality in a large temperature range −60−180 ◦ C.
Please cite this article in press as: M. Shen, et al., Design of midwave infrared athermalization optical system with a large focal plane array, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.024
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Design of midwave infrared athermalization optical system with a large focal plane array ManDe Shen a,∗ , Cheng Li a , HuanHuan Ren a , QinXiu Jiang a , LiangYi Chen b a b
Wuhan Textile University, Wuhan 430073, Hubei, 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 23 June 2013 Accepted 15 December 2013 Available online xxx Keywords: Optical design Infrared optical system Infrared lens
a b s t r a c t Based on the most advanced staring focal plane array which had a format of 640 × 480 and the pixel pitch of 15 m, a set of all-sphere midwave infrared ahermalization optical system was designed. The working wavelength was in 3–5 m, the full field of view was 8.58◦ , the relative aperture was 1/2, the efficient focal length (EFL) was 80 m. The opticalsystem consisted of four lenses with three kinds of material – Ge, ZnSe and Si. All surfaces were sphere, which was easier to process test, making the cost inexpensive, and it could avoid using diffractive surface and aspheric surface. The image quality of the system approaches the diffraction limit in the temperature range −60 ◦ C-180 ◦ C. The design results proved that, the high resolution midwave infrared optical system had compact structure, small volume, high resolution and excellent image quality, meeting the design requirements, so that it could be used for photoelectric detection and tracking system. © 2014 Published by Elsevier GmbH.
1. Introduction The resolution requirements required by a focal plan array (FPA) are a function of the pixel size. Current FPAs typically exhibit individual pixels measuring from 40 to 50 m2 . As arrays increase in size, pixels will be reduced in size to facilitate packaging due to limitations on substrate manufacturing technology. Currently, a minimum pixel size of 15 mm2 is estimated. The reduction in pixel size demands a decrease in lens F–number if the equivalent irradiance is expected on each pixel. This demands more complex lens design forms to facilitate aberration correction. Focal plane arrays are also increasing in size. The current state of the art in commercial FPAs is 256 × 256 for InSb and HeCdTe arrays and 512 × 512 for PtSi arrays. These larger format 512 × 512 InSb arrays are anticipated in the near future. There is considerable interest in 640 × 480 PtSi arrays, as well as evidence that similar sized arrays are being considered for InSb and HeCdTe devices. Due to the possession of advantages of passivity working mode, good disguise, clarity character of image and easy observation, infrared 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 paper introduced a spherical high resolution middle infrared athermalization optical system based on 15 m × 15 m
∗ Corresponding author. E-mail address: [email protected] (M. Shen).
pixel size. The spherical high resolution middle infrared athermalization optical system needs to have the steady image in the working temperature from −60 ◦ C to 180 ◦ C. So athermalization for infrared optical system is an important issue. 2. Athermal characteristic of diffractive optical element 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 + · · ·)
(1)
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
(3)
0030-4026/$ – see front matter © 2014 Published by Elsevier GmbH. http://dx.doi.org/10.1016/j.ijleo.2013.12.024
Please cite this article in press as: M. Shen, et al., Design of midwave infrared athermalization optical system with a large focal plane array, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.024
G Model
ARTICLE IN PRESS
IJLEO-54227; No. of Pages 3
M. Shen et al. / Optik xxx (2014) xxx–xxx
2
pitch of 15 m. The layout of the final design optical system is shown in Fig. 1.The total length is less than 120 mm. The optical system is consisted of four lenses. Three kinds of material – Ge, ZnSe and Si are selected as the refractive lens for the ultralow
Table 1 The design requirements of the optical system. Parameter
Value
Spectral range Primary wavelength Focal lenth Field of view F–number Optical transmission Back working lenth
3–5 m 4 m 80 mm 8.58◦ 2.0 > 80% > 20 mm
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 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. T
fb =
k 1 2
h1
h2i xi i = 0
(5)
i=1
where xi is the dispersive coefficient of the lens i. dfbT dt
=
k 1 2
h1
h2i xi i = ˛h L
(6)
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. The design of result analysis 3.1. Parameters of optical system The system was designed to work primarily in the midwave region and possessed a resolution of 640 × 480 pixels with 15 m × 15 m pixel size. The parameter of the optical system was showed in the following table (Table 1). 3.2. The results analysis According to design requirements of the optical system, a set of ahermalization and high resolution all-sphere midwave infrared optical system was designed based on the most advanced staring focal plane array which had a format of 640 × 480 and the pixel
Fig. 1. Layout of optical system.
Fig. 2. MTF of the system at different temperature.
Please cite this article in press as: M. Shen, et al., Design of midwave infrared athermalization optical system with a large focal plane array, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.024
G Model IJLEO-54227; No. of Pages 3
ARTICLE IN PRESS M. Shen et al. / Optik xxx (2014) xxx–xxx
3
Table 2 Variation of wave front error with temperature. Temperature (◦ C) −60 20 80 130 180
Fig. 3. Variation of spot and temperature.
chromatic dispersion, as shown in Fig. 1. Therefore, the total chromatic aberration of the system is so small that can be corrected. In order to ensure the infrared optical system fabricating easily, we avoided using diffractive surface and aspheric surface. The drawtube materials are composed of the material of aluminum. The linear expansion coefficient of aluminum is 23.6 × 10−6 ◦ C. The system was optimized with the help of ZEMAX commercial optical design software after the variables, merit function, and system constraints were assigned. In the optimize process, the weighing functions of the FOV were set equally on the axis, 0.3, 0.5, 0.707, and 1.0 FOV. The midwave infrared spectrum (3.0 m, 4.0 m, and 5.0 m), were distributed as the same weighing functions. The ZEMAX commercial optical design software utilized the damped least-square algorithm to minimize the merit function. Fig. 2 is MTF of the system at different temperature, (a), (b), (c) and (d) show respectively −60 ◦ C, 20 ◦ C, 90 ◦ C and 180 ◦ C. According to the four pictures, we know that the MTF of the midwave infrared athermalization optical system with a large focal plane array is close to the diffraction-limit in the temperature range −60–180 ◦ C.
Wavefront error () 0.0963 0.0692 0.0801 0.1048 0.1263
Fig. 3 is the relationship of variation of spot and temperature, maximum RMS spot diameter of the full field is less than 12.1 m, which is smaller than the IR FPA sensor pixel size 15 m. Table 2 is the variation of wave front error with temperature (−60–180 ◦ C). From the Table 2, we know that the maximal wave front error is 0.1263 when the temperature is 180 ◦ C, which is less than 0.25, so the image quality is great. For the F/2.0, 3.0–5.0 m infrared system, the focus depth is ±0.032 mm, the maximal offfocus from the temperature −60 ◦ C to 180 ◦ C is 0.0063 mm, the maximal off-focus is less than focus depth, so the optical system can be used. 4. Conclusion An F/2.0 midwave infrared athermalization optical system with a large focal plane array in the temperature range −60–180 ◦ C is described, and constructed with four lenses, where all surfaces are spherical. Three kinds of material (Ge, ZnSe and Si) are used. The lens can ensure compact structure, small volume and light weight. The maximal off-focus is less than focus depth, the system performance approaches the diffraction limit. The passive thermal compensation can ensure high image quality in a large temperature range −60−180 ◦ C.
Please cite this article in press as: M. Shen, et al., Design of midwave infrared athermalization optical system with a large focal plane array, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.024