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27 April 2019 Optical system design of four-channel dual-band infrared panoramic imaging
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Abstract
In order to reduce the volume of a panoramic optical system, a four-channel infrared dual-band panoramic imager was designed using spatial multicamera image mosaicking. Each optical system of the imaging channel was designed in a double imaging configuration with an F-number of 2, working bands of MWIR 3 to 5  μm and LWIR 8 to 12  μm, and a full field of view (FOV) of 122 deg. By adopting refractive-diffractive hybrid optical elements and introducing aspheric designs, the system was made to achieve temperature compensation from −40  °  C to 60°C by means of optical passive athermalization. Results indicate that the system attained almost 100% cold stop efficiency. At the Nyquist frequency of 18 lp/mm, the modulation-transfer-function (MTF) of the MWIR system was higher than 0.70 at the edges of the FOV, whereas the MTF of LWIR system was greater than 0.35 for the same condition, both approaching the diffraction limit.

1.

Introduction

With advancements in infrared (IR) detection technology, there is an increasing demand for high-performance optical systems, especially in modern military reconnaissance and space applications. Rapid target detection, real-time tracking, and accurate target measurement have become a major focus in the development of optical systems.1 Currently, most of the existing automotive systems achieve a 360-deg panorama in the horizontal direction by mechanical rotation of a platform. In order to ensure the desired scan rate, dwell time on each pixel is only tens of microseconds, resulting in reduced signal-to-noise ratio (SNR) which causes delays between detection and target judgment.2 Particularly, when capturing fast moving targets, the scanning system can be incapable of accurate searching and tracking, resulting in the loss of useful real-time target information.

HGH infrared system designed a type of IR 360-deg panoramic alert infrared camera which can capture photos at 360 deg azimuth and 20 deg vertical viewing angle. Raytheon developed an airborne distribution infrared sensor3 and used six identical sensors with 90 deg field angle each, and installed them around the joint strike fighter to provide full range coverage. Thales Optronique limited company researched a type of ARTEMIS IRST (Infrared Search and Track) named “Moon Goddess” where the system was designed using a distributed sensor structure.4 The three sensors contained FPA composed to realize the panoramic imaging (PI) of azimuth 360 deg and 25 deg elevation angle, with no blind spots in the imaging area. PI with 360 deg azimuth and 90 deg elevation angles was made possible with a five-channel panoramic optical system employing five spatially distributed objective lenses, each exceeding an FOV of 90 deg.5,6

In this work, we present a four-channel dual-band IR PI optical system based on spatially distributed multiple lenses to capture scenes at different angles which are then combined to form a panorama. A double imaging configuration was incorporated into the system that resulted in a large aperture, increased field of view (FOV), and high resolution. Optical aberration was suppressed in 3 to 5  μm MWIR and 8 to 12  μm LWIR bands and the proposed system exhibited fast target search and tracking capabilities.

2.

General Design of Panoramic System

2.1.

Working Concept

PI is achieved using specialized imaging devices to obtain a hemispheric FOV of more than 180 deg in the vertical and horizontal direction of 360 deg FOV.7 In order to acquire a full range of IR image data, the proposed design incorporates three IR objective lenses to divide the horizontal FOV for ensuring the integrity of data for two adjacent field parts, considering that fields of view of two adjacent lens need certain overlap. For that reason, the infrared lens field of each imaging channel is set to 122 deg, and then a complete PI system is obtained by splicing the images for all directions.

Three IR objective lenses in the horizontal direction receive the detected target information with different FOV. After transferring this information to the imaging system, detected light waves of various channels reach the focal plane array. Finally, after subsequent image splicing and matching, the panoramic image is displayed on a suitable display device. This process is shown in Fig. 1.

Fig. 1

The imaging principle of IR panoramic system.

OE_58_4_045104_f001.png

2.2.

Structural Design of the Panoramic System

The structure and deployment of IR in a panoramic system is critical for producing high quality panoramic images.5 Panoramic systems consist of an IR objective system, a transferring image optical system, an IR receiver lens and detectors. A cobeam prism cemented together with the four right-angle prisms lies in the center position of the sphere. The four flat mirrors are denoted by M1, M2, M3, and M4. Optical path 1 enters the system from the objective lens A and arrives at the beam splitter prism after one reflection on the cobeam prism; optical path 2 enters the system from the objective lens B, arrives at the cobeam prism after two reflections from mirrors M1 and M2, and then reaches the beam splitter prism after another reflection; optical path 3 enters the system from the objective lens C, arrives at the partially reflecting mirror after reflections from mirrors M3 and M4, and then passes through the beam splitter prism after the cobeam prism; optical path 4 enters the system from objective lens D, through the partially reflecting mirror and the cobeam prism, and then arrives at the beam splitter prism. MWIR and LWIR are separated using the beam splitter, making images on two high-resolution IR detection focal planes IFPD1 (infrared focal plane array) and IFPD2, respectively. Thereby, a complete panoramic image is created by splicing subsequent images. The four IR lenses are designed according to the common path structure so that the system can respond to MWIR and LWIR bands simultaneously. On the one hand, this system design avoids the need to switch lenses since the optical paths of the lenses are common, and also makes the system more compact. On the other hand, the system can fully exploit the benefits of MWIR and LWIR to meet the practical application needs (Fig. 2).

Fig. 2

Structural representation of the panoramic system.

OE_58_4_045104_f002.png

3.

Design Approach of Optical System

3.1.

Specifications of Optical System

The pixel size and resolution of MWIR and LWIR detectors is 28  μm and 640×512  pixels, respectively. The specifications of the optical system, determined by detector models and practical considerations, are shown in Table 1.

Table 1

Optical design specifications.

WorkbandF#FOVFocal lengthRequirements for image quality
MWIR3 to 5  μm2122 deg6.36 mmMTF>0.5
LWIR8 to 12  μmMTF>0.3

3.2.

Structure Design of the Optical System

The system adopts a hybrid refractive-diffractive structure, which can attain a larger FOV and meet our requirements. On the one hand, the introduction of the diffractive surfaces can weaken the vertical axis aberration and the chromatic aberration by taking advantages of unique dispersion characteristics of diffractive element; on the other hand, it can reduce the diameter of the system, making the system lightweight and portable.

It is necessary to consider the cold stop characteristics of the system itself with regard to a cooled IR system.8 Cold stop determines the location and size of the exit pupil of the optical system. Attaining a 100% cold stop efficiency indicates that the exit pupil of the optical system is able to match the cold stop of the detector. Otherwise, there is a risk of beam cutting which can reduce the system sensitivity or cause additional incident hybrid heat radiation entering the detector, which in turn can reduce the SNR of system.

Wide-field imaging systems typically have short effective focal lengths. In order to ensure a sufficient working distance, our system uses a double imaging configuration design known as the quadratic imaging configuration. A single imaging system requires a large aperture of the cooled IR system in order to achieve 100% efficiency of cold stop. Therefore, adding a secondary imaging configuration behind the first imaging position can reduce the radial dimension of the system. Moreover, for the double imaging configuration system, the first configuration group burdens the major diopter of the system, and latter configuration mainly plays a part in secondary imaging with the completion of residual aberration balance. The principal ray diagram of double imaging system is shown in Fig. 3.

Fig. 3

Principal ray diagram of a double-band optical system.

OE_58_4_045104_f003.png

In Fig. 3, L4, h4, h5, a1, a2 have been identified. According to equation for a paraxial optical system

Eq. (1)

L2=fM+f,

Eq. (2)

L3=ML2.

In the above equation, M denotes the total lateral magnification of double imaging system. We can obtain the following relationships from the geometrical arrangement shown in Fig. 3:

Eq. (3)

tana1=h2L1,

Eq. (4)

tana2=h5L4,

Eq. (5)

T=tana2tana1,

Eq. (6)

h3=(L3L4)tana2,

Eq. (7)

h3=(L+L2)tana1,

Eq. (8)

h3=L2tana1+h5M.

Combining with the equations from Eqs. (1)–(9), L3 can be derived as follows:

Eq. (9)

L3=ML4Th5tana11MT.

From these results, we can deduce that: (1) the distance from exit pupil to the final image surface shortens with the included angle between the principal ray and the optical axis gradually decreasing, which affects the aberration unfavorably. In order to achieve 100% cold stop efficiency, it needs to coincide with aperture stop of the system. This is required for eliminating stray light and ensuring that the detector detects only the image in its FOV. (2) With the increase of axial magnification of the double imaging system, spacing from the exit pupil to the final image surface gradually decreases. Although this can make the system more compact, the F number of the system can increase, should be avoided.

4.

Design Results and Image Quality Evaluation of Optical System

4.1.

System Design

Figure 4 shows the optical arrangement for the proposed MWIR/LWIR dual-band panoramic system, with an FOV of 122 deg and the F number equivalent to 2. A hybrid refractive-diffractive structure was employed in the design. Optical surfaces marked with numbers 1, 6, and 11 are aspheric, surfaces 2, 4, and 13 are diffractive, while the remaining surfaces are spherical. IR materials such as ZnSe, ZnSe, and ZnS were chosen to match, with the total length of system set to 220 mm.

Fig. 4

Initial structure of signal IR objective optical system.

OE_58_4_045104_f004.png

Surfaces 1, 6, and 11 are even, while 2, 4, and 13 are binary aspheric. One of the imaging channels of the IR dual-band panoramic system is shown in Fig. 5. Each imaging channel contains two configurations of MWIR and LWIR, a coaperture, a cobeam a prism, a beam splitter prism, a receiving objective lens of IR detector, and a focal plane of MWIR and LWIR. Dual-band coaperture form is applied in the former configuration of IR objective lens to achieve the synchronized imaging of MWIR and LWIR without the need for a switching mechanism.

Fig. 5

Structure of the dual-band co-aperture optical system. (a) Light path 1, (b) light path 2, (c) light path 3, and (d) light path 4.

OE_58_4_045104_f005.png

Five lenses were used in the coaperture design of the system. The cobeam prism in the middle was composed of four identical isosceles right angle prisms that were mutually glued together at the oblique side coated with a semi-reflective film. Antireflection film was coated on the surfaces of rectangular prism, to minimize any loss of the incident radiation. According to the transmittance of half transparent half reflecting mirror and cobeam prism is 50%, and the beam splitter will not attenuate energy, which splitting wavelength rather than splitting energy, it can be estimated that the transmittance of light path 1 and 2 is about 50%, and the light path 3 and 4 is about 25%. Four lenses were used in the IR detector objective lens, for allocating the optical diopter of system and balancing the overall system aberrations. Ge, ZnSe, and ZnS satisfy the required physical and chemical properties. They were selected according to their refractive indexes and Abbe numbers for achromatism and athermalization.

4.2.

Image Quality Evaluation

4.2.1.

Modulation-transfer-function

In this optical system, image quality of light path 1 is similar to that of light path 4, with light paths 2 and 3 also having similar image quality.

In light paths 1 and 4, from the modulation-transfer-function (MTF) analysis of MWIR and LWIR shown in Figs. 6(a) and 6(b), it can be observed that the MTF values are all close to the diffraction limit at the Nyquist frequency of 18 lp/mm. The MTF of MWIR>0.72 and the MTF of LWIR>0.45, satisfying the requirements of imaging quality.9

Fig. 6

The MTF of light paths 1 and 4. (a) MWIR and (b) LWIR.

OE_58_4_045104_f006.png

The MTF analysis of MWIR and LWIR for light paths 2 and 3 is shown in Figs. 7(a) and 7(b). It can be seen that the MTF is higher than 0.70 in MWIR and 0.35 in LWIR, at the Nyquist frequency of 18 lp/mm.

Fig. 7

The MTF of 2 and 3 light path. (a) MWIR and (b) LWIR.

OE_58_4_045104_f007.png

4.2.2.

Energy distribution and calculation

The energy distribution of the light spot along with radial variations of light paths 1 and 4 can be obtained from Zemax software, as shown in Fig. 8. It can be seen that the energy concentration rate within a single pixel reached 85% and 75% under the full FOV for MWIR and LWIR, respectively.

Fig. 8

Energy distribution of optical paths 1 and 4. (a) MWIR and (b) LWIR.

OE_58_4_045104_f008.png

The energy concentration rate of light focused on Fig. 9 shows the light spot energy distribution of MWIR and LWIR along with radial variations for light paths 2 and 3. It can be seen that the energy concentration rate within one pixel size reached 80% and 63% under the full FOV for MWIR and LWIR systems, respectively.

Fig. 9

Energy distribution of the optical system. (a) MWIR and (b) LWIR.

OE_58_4_045104_f009.png

Although the energy concentration rate of light focused on the detector focal plane can reach above 75% ideally, the optical system exhibits energy losses mainly due to three effects: (a) reflection loss of MWIR and (b) absorption loss of LWIR.

4.2.3.

Detection blind area range calculation

Figure 10 shows the detection blind area range schematic of the PI system. The system uses the A, B, and C IR lenses to divide the horizontal FOV, achieving 360 deg PI in the horizontal direction. Each IR lense has an FOV of 122 deg, so that the detection FOV of two adjacent lens has overlaps in the horizontal direction in order to ensure a complete panoramic image. A blind area denoted by AOCH exists where all IR lenses are incapable of detecting. O denotes the center point of the system, and A, B, and C denote the entrance pupil centers of the IR lenses. From the design parameters, it follows that AO=136.241  mm.

Fig. 10

Detection blind area range of the panoramic system.

OE_58_4_045104_f010.png

The geometric relations are given as

Eq. (10)

sinAOHAH=sinAHOAO.

From this relationship AH is found to be 6.760 m. Evidently, if the horizontal direction 360 deg FOV is divided between the three IR lenses, the target can evade detection when it enters the range within about 6.76 m. This structure with three IR lenses in the horizontal direction and one IR lens in the vertical axis direction constitutes the four-channel PI system. This approach remarkably reduces the volume and weight of the system, while meeting the design requirements.

4.2.4.

Cold stop analysis

In order to achieve 100% cold diaphragm, the pupil position and size of the optical system are required to be the same as that of the cold diaphragm of the refrigeration detector. It is known that the cold diaphragm of the detector is 25 mm in front of the photosensitive surface, and its diameter is 12.5 mm. The optical system has a pupil distance of 25 mm and a diameter of 12.5 mm. It matches the detector cold aperture perfectly and meets 100% cold aperture effect.

5.

System Athermalization and Narcissus Analysis

5.1.

Optical Passive Athermalization

Athermalization has to be considered in the system in order to account for ambient temperature changes that affect the refractive index, thickness, interval, and the radius of curvature for IR materials. The system is analyzed in the 40°C to 60°C temperature range in order to find the dependence of defocus on temperature of the two bands, with the goal of eliminating defocus by compensating through athermalization. For achieving passive optical athermalization, the thermal expansion coefficient and the dispersion factor need to meet the following criteria:10

Eq. (11)

{(1h1ψ)2i=1n(hi2ηiψi)=0(1h1ψ)2i=1n(hi2χiψi)+αjL=0,
where hi is the height of the paraxial rays at the lens number i; Ψ is the dioptry of system; Ψi is the dioptry of the number i lens; ni is the dispersion factor of lens; χi is the thermal expansion coefficient; aj is the thermal expansion coefficient of the barrel mechanical structure; and L is the barrel length. From Eq. (11), it follows that passive athermalization of the system can be achieved when the dispersion defocus is equal to zero and the thermal defocus of the lens offsets that of the mechanical structure. Diffractive elements are incorporated in the design for the purpose of simplification. Diffraction and the thermal expansion coefficient of the refractive lens are be given by the following expression:11

Eq. (12)

{Cd=2αg+1n0dn0dtCr=αg1nn0(dndtndn0dt),
where ag is the thermal expansion coefficient of lens; n and n0 denote the refractive index of the lens and the media, respectively; dn/dt and dn0/dt represent the refractive index temperature coefficient of the material and the medium, respectively. It can be seen that the temperature characteristic of diffractive elements depends solely on the thermal expansion coefficient of the materials. Therefore, introducing the optimal diffractive surfaces can accomplish athermalization. Due to spatial considerations, only the analysis of the athermal difference of light path 1 is given here.

Figures 11 and 12 denote the MTF of MWIR and LWIR systems at the temperature of 40°C, 20°C, and 60°C, respectively. It can be seen that for all temperatures, the MTF values for the MWIR and LWIR systems at the Nyquist frequency of 18 lp/mm are greater than 0.6 and 0.4, respectively. This indicates that the image quality meets the design requirements after athermalization.

Fig. 11

Exit pupil of optical system.

OE_58_4_045104_f011.png

Fig. 12

The MTF of MWIR after athermalization. (a) 40°C, (b) 20°C, and (c) 60°C.

OE_58_4_045104_f012.png

5.2.

Narcissus Analysis

Narcissus is the self-image of “cold light” emitted from the focal plane of the cooled IR detector. It is formed when the IR radiation passes the surface reflection of system lenses and then refocuses on the focal plane. Besides the detected target information, the detector also receives its own image, thereby seriously affecting the sensitivity of the system. Hence, during the design process of a cooled IR optical system, narcissus phenomenon has to be considered.11 Typically, YNI value is used to characterize the amount of narcissus, where Y is the incident height of paraxial rays on one optical surface, N is the refractive index of one optical material, and I is the incident angle of marginal rays at one optical surface. If the YNI value is greater than 1, it indicates that the impact of narcissus to the optical system can be ignored. For values of YNI below 1, further analysis is required.

Due to the limitation of space, the analysis of the narcissus of the 1 light path is given. The YNI values are shown in Table 2.

Table 2

YNI contribution value of 1 light path.

Surface numberYNISurface numberYNISurface numberYNI
12.119222.427431.01395
41.818150.978961.0917
70.374681.679393.4286
102.2687111.3889121.0241
133.8548142.6913152.9996
165.1189171.4699181.3313
190.5360201.6452211.5202

It can be seen from Table 2, the YNI value of surfaces 5, 7, 19 is less than 1, so it needs to undergo reverse ray tracing analysis, as shown from Figs. 13(a)13(c).

Fig. 13

The MTF of LWIR after athermalization. (a) 40°C, (b) 20°C, and (c) 60°C.

OE_58_4_045104_f013.png

It can be seen from Figs. 13(a)13(c) that the reflected light from the 5th, the 7th, and the 19th surface is diverging and cannot reach the IR focal plane, hence it can be ignored. Comprehensive analysis shows narcissus does not affect the image quality of the optical system (Fig. 14).

Fig. 14

Narcissus analysis of optical path 1. (a) Reverse ray tracing schematic of fifth surface. (b) Reverse ray tracing schematic of seventh surface. (c) Reverse ray tracing schematic of 19th surface.

OE_58_4_045104_f014.png

6.

Conclusion

A cooled, high-resolution, four-channel IR dual-band PI optical system was designed with spatially distributed multiple lenses. It was composed of MWIR/LWIR IR dual-band coaperture objective lenses and a double imaging structure. The design optimized relative apertures, FOV, and focal lengths and was capable of image fusion in IR dual-band while achieving 100% cold stop efficiency. IR materials such as Ge, ZnSe, and ZnS were combined with aspheric and diffractive surfaces to ensure excellent imaging quality of the system and stability in the 40°C to 60°C temperature range. The system has the advantages of a large relative aperture, large FOV, excellent image quality, high-resolution, thermal sensitivity, small size, and light weight. The compact and improved panoramic IR imaging system described in this work is promising for broad applications in IR search and tracking identification.

7.

Appendix of Lens Prescription

The B and D channels are common light path channels, which are the parameters of the first configuration of the lens (Table 3).

Table 3

The first configuration of BD channels.

Surf:typeRadiusThicknessGlass
StandardInfinityInfinity
Standard17.4798.278GERMANIUM
Standard18.5179.857
Standard42.8126.365AMTIR1
Binary 255.3862.13
Standard52.7316.067ZNSE
Even aspheric38.0488.741
Standard33.3655.677GERMANIUM
Even aspheric36.19629.015
Standard246.15111.415TI_1173
Standard58.97112.411ZNS_BROAD
Standard92.2181.14
StandardInfinity15GERMANIUM
Tilted15GERMANIUM
StandardInfinity44.455
StandardInfinity12GERMANIUM
Tilted12GERMANIUM
StandardInfinity32.08
Standard57.5715.091GE_OLD
Even aspheric73.3632.405
Standard53.57212.278ZNSE
Binary 2199.0341.171
Standard264.00312.651AMTIR1
Standard286.8343.191
Standard122.8028.621GE_OLD
Standard189.1813.511
StandardInfinity2GERMANIUM
StandardInfinity2
StandardInfinity25
StandardInfinity

The B and D channels are common light path channels, which are the parameters of the second configuration of the lens (Table 4).

Table 4

The second configuration of BD channels.

Surf:typeRadiusThicknessGlass
StandardInfinityInfinity
Standard17.4798.278GERMANIUM
Standard18.5179.857
Standard42.8126.365AMTIR1
Binary 255.3862.13
Standard52.7316.067ZNSE
Even aspheric38.0488.741
Standard33.3655.677GERMANIUM
Even aspheric36.19629.015
Standard246.15111.415TI_1173
Standard58.97112.411ZNS_BROAD
Standard92.2181.14
StandardInfinity15GERMANIUM
Tilted15GERMANIUM
StandardInfinity44.455
StandardInfinity12GERMANIUM
Tilted12GERMANIUM
StandardInfinity32.08
StandardInfinity2.469GERMANIUM
Standard85.6723.186
Even aspheric103.0112
Standard52.6352.01AMTIR3
Binary 2122.1286
Standard3087.622IG2
Standard9495.8964.141
Standard95.59413.446IRG205
Standard237.6587.588
StandardInfinity2GERMANIUM
StandardInfinity2
StandardInfinity25
StandardInfinity

Both A and C channels are common light path channels, which are parameters of the first configuration of the lens (Table 5).

Table 5

The first configuration of AC channels.

Surf:typeRadiusThicknessGlass
StandardInfinityInfinity
Standard13.215.993GAAS
Standard12.8694.999
Standard25.9929.328AMTIR1
Binary 236.761.498
Standard62.5885.243ZNSE
Even aspheric34.0715.007
Standard43.4529.921IG2
Even aspheric43.29933.709
Standard1.22E+048.537CDSE
Standard81.20919.191ZNS_BROAD
Standard102.7975
StandardInfinity18GERMANIUM
Tilted18GERMANIUM
StandardInfinity45.4
StandardInfinity12GERMANIUM
Tilted12GERMANIUM
StandardInfinity32.675
Standard57.5685.092GE_OLD
Even aspheric73.3692.395
Standard53.57912.268ZNSE
Binary 2199.2531.169
Standard263.88612.631AMTIR1
Standard286.6273.178
Standard122.8258.613GE_OLD
Standard189.1763.506
StandardInfinity2GERMANIUM
StandardInfinity2
StandardInfinity25
StandardInfinity

Both A and C channels are common light path channels, which are parameters of the second configuration of the lens (Tables 6 and 7).

Table 6

The second configuration of AC channels.

Surf:typeRadiusThicknessGlass
StandardInfinityInfinity
Standard13.215.993GAAS
Standard12.8694.999
Standard25.9929.328AMTIR1
Binary 236.761.498
Standard62.5885.243ZNSE
Even aspheric34.0715.007
Standard43.4529.921IG2
Even aspheric43.29933.709
Standard1.22E+078.537CDSE
Standard81.20919.191ZNS_BROAD
Standard102.7975
StandardInfinity18GERMANIUM
Tilted18GERMANIUM
StandardInfinity45.4GERMANIUM
StandardInfinity12
Tilted12GERMANIUM
StandardInfinityInfinityGE_LONG
StandardInfinity2
Standard85.7363.208
Even aspheric102.9922.039
Standard52.6552.022AMTIR3
Binary 2122.0676
Standard3141.0851.999AGCL
Standard9600.3944.044
Standard95.66413.409IRG205
Standard236.6367.579
StandardInfinity2GERMANIUM
StandardInfinity2
StandardInfinity25
StandardInfinity

Table 7

The extra data.

Norm radius
Binary 21224.54114.5393.908
Binary 21448.2196.40226.873
Binary 229144.683474.9348200.672

Acknowledgments

This paper was supported by Army equipment pre-research project (Grant No. 301XXX102) and Key Laboratory of Shaanxi Provincial Department of Education (Grant No. 17JS052).

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Biography

Gao Ming is a doctor, professor, and doctoral supervisor. His current main research direction is photoelectric precision detection and photoelectric instruments, optical design theory and technology, and laser atmospheric transmission theory and technology.

Biographies of the other authors are not available.

© The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
Gao Ming, Chen Yang, and Zhang Xibin "Optical system design of four-channel dual-band infrared panoramic imaging," Optical Engineering 58(4), 045104 (27 April 2019). https://doi.org/10.1117/1.OE.58.4.045104
Received: 3 November 2018; Accepted: 8 March 2019; Published: 27 April 2019
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