Design of IR zoom lens system for long-range detection in uncooled LWIR camera

A new compact optical zoom lens system with variable focal length 100–200 mm for uncooled LWIR (8–12 μm) camera is designed. It is used for long-range detection. The optimized IR zoom lens consists of four group elements. The F/# of the zoom system is F/1.4 at all zoom positions. Its performance reaches the diffraction limit at each focal length position. Moreover, optical design and image quality are calculated by ZEMAX optical software. The imaging quality performance is steady during zoom process. In addition to the above benefits, the optimized IR zoom lens is light and compact (200 mm) with 4 lenses and only one of them has diffractive surface to lower production cost. Upon applying anti-reflection coating, the total transmittance of the optical system is enhanced from 2 to 99% at λ = 10 µm.


Introduction
In recent times, military demands for the thermal imaging camera have been increasing. Thermal imaging system does not require illumination to operate. In addition to their ability to form images through most forms like smoke and dust, civilian demands also have been increasing in the medical, industry, security and other fields.
Basically, spatial resolution of an infrared optical system is based on specifications of the infrared detector. The target acquisition performance is based on the number of line pairs resolvable across a target's critical dimension. Consequently, an infrared optical system should be designed to have a diffraction-limited performance [5].
The F/# of the optical system was estimated to be 1.4 from airy disk and MRTD analysis [6]. In diffraction-limited system, the airy disk diameter should be equal to pixel's diagonal size of the detector as follows: 2.44 F∕# = √ 2d. where λ is the operating wavelength and d is the a pixel size of the detector.
For detector with pixel size 25 μm from the above equation, the F/# is given by F/1.4 at central wavelength of 10 μm.
The minimum resolvable temperature difference) MRTD (is one of the important criteria representing the infrared imaging system performance. MRTD is given by where D * is the normalized detectivity.the average value is known as 1.44 × 10 8 cmHz A is a proportional constant depending on the detector. MTF( t ) is the modulation transfer function at target frequency of t .
The MRTD combines both spatial resolution and thermal sensitivity. Meanwhile, modulation transfer function (MTF) measures the attenuation in contrast (modulation) versus spatial resolution without taking into account the thermal property of the target (object). Moreover, F/# is directly proportional to MRTD. A large F/# results in a large MRTD value with a reduced spatial resolution, whereas a small F-number gives a small MRTD value with a better spatial resolution. However, a large aperture is limited by cost and detector. The relationships between the F/# and MRTD are summarized in Table 2.
The MRTD at F/1.4 is so small that it may give enough resolution, so optimum F/# of the system is confirmed to be 1.4 The focal length 100-200 mm is chosen according to the Johnson criteria [9]. The target is detected, recognized and identified depending on the number of line pairs resolvable across a target's critical dimension. The range for detection, recognition and identification of a target with its critical dimension is shown in Table 3.

Structure of zoom system
Concerning optical transmittance of IR materials, most optical glasses do not transmit above 2.5 μm. Certain special types of optical glasses can transmit up to 4 μm. The most common types of IR transmitting materials are germanium, zinc sulfide, zinc selenide and GASIR5 with transmission band between 8 and 12 μm. So, we have limited selection among these materials. Zooming definition is one in which the focal length (and thus angle of view) can be varied by changing component positions while image position being maintained at a fixed plane. The image plane can be fixed either by optical or mechanical compensation.
The optical compensation is only guaranteed for short focal length, whereas for longer focal length, mechanical compensation must be adopted. The mechanical compensation components may be either negative focal length or positive focal length [10].
In order to design IR zoom lens for long-range detection with long focal length and a large relative aperture, the spherical aberration, the chromatism and secondary spectrum are serious aberration and difficult to correct. Therefore, a binary surface (aspheric plus diffractive terms) is adopted to balance these aberrations. For optical zoom system which has two variable groups, the variable component and compensation component relationship will be given by calculation [11]: where The movement component and 1 represents the vertical axis magnification of variable group in initial position, 2 represents the vertical axis magnification of compensation group in initial position, q 1 represents the displacement of variable group along the optical axis, q 2 represents the displacement of compensation group along the optical axis, f ′ 2 is the focal length of variable group, f ′ 3 is the focal length of compensation group. According to the parameters from Table 1, consult to the lens library and the patents, finally a four-component type zoom structure with negative compensated element is determined as the initial structure of the system [13,14,16].

Optimized configuration
The optimized zoom lens is shown in Fig. 1. It consists of four elements: the prefixed element, the zoom element, the compensation element and the back fixed element. The whole system is composed of only 4 lenses with overall length 200 mm.

Design results
The optical zoom system having a good performance was obtained, and its design data are shown in Table 4.
The configurations of the five optimized steps for IR zoom lens system from short focal length 100 mm to long focal length 200 mm are shown in Fig. 2 The spacing value(s) of every component at different focal length positions in which the sum of the space values  Table 5.
This system consists of 4 lenses. Only one diffractive lens on L1 and one conical surface on L2 are used to balance the wave-front aberration. The design data for the diffractive surface are shown in Table 6.
For a diffractive lens, the diffraction efficiency with respect to wavelength needs to be considered when evaluating the imaging performance. As the diffractive lens are very weakly powered. In addition to that, the wavelengthto-zone period ratio is very small across the entire lens, so an approximate expression for the polychromatic integrated efficiency ranging from min to max is given by [8] int. poly ≅ 1 + where 0 is the design wavelength for the diffractive lens.
For min = 8 m, max = 12 mand 0 = 10 m, the polychromatic integrated efficiency is about 95.61% and diffraction efficiency reduced by 4.39% due to background noise. The polychromatic MTF is scaled by int.poly and drops down at zero frequency. this loss slightly reduces  image contrast. However, the optical design has enough image quality as shown in Fig. 4 The zoom curves that are shown in Fig. 3 clearly have no inflection points. While the focal length changes the whole curve is smooth, so the motion of the variable component and compensation component can by driven by cam in this infrared optical zoom system.
The MTF curves for the designed zoom system at different zoom positions are shown in Fig. 4 (a-e). MTF is an important parameter which reflects the imaging performance. As shown, its performance is nearly diffractionlimited at each focal length position such that the system is perfect image quality.
The spot diagrams for different zoom positions with different field angles after ray tracing are shown in Fig. 5 (a-e); the spot diagram makes use of the intensity of light spot, where the RMS radius at all positions is less than one detector pixel size 25 μm. The reflectance of Ge before and after applying doublelayer anti-reflection coating is shown in Fig. 6 By applying this coating configuration, the transmittance of the whole system reaches 99% at 10 µm.

Conclusion
A compact infrared zoom lens system (200 mm length) is designed and evaluated which matches an uncooled focal plane array (FPA) with array of 384*288 pixels and pixel pitch 25 μm. The compact design is only with 4 lenses for variable focal length 100-200 mm and uses only one diffractive surface to balance wave-front aberration. The optimum F/# of the optical system was determined to be F/1.4 from airy disk and MRTD analysis. The objects can be detected from 20 m to ∞ by movement of lenses controlled by software. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.