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.

Although thermal imaging systems are intended for military or security applications, it can be used for temperature measurement; however, they are not optimized for this purpose. The main aim is to detect, recognize or identify targets at long ranges by their shape; thus, resolution and sensitivity are favored over radiometric accuracy [1]. In some optical systems that have multiple fields of view, zoom lens with variable magnification and different resolving power had greatly improved the detection efficiency.

Recently, infrared zoom system aims to increase focal length for getting long-range detection. This requires large relative aperture, small size (compact) design and superior performance. Three different designs were given. First, a zoom lens system with variable focal length 100–300 mm, F/# 1–3.75, consisting of 9 lenses and with overall length 700 mm was designed [2]. Another zoom lens system with variable focal length 30–240 mm, F/# 2, consisting of 6 lenses and overall length 340 mm was designed [3]. The third zoom lens system with variable focal length 20–200 mm, F/# 2, consisting of 7 lenses and with overall length 300 mm was designed [4].

According to the previous work, this paper introduces an infrared zoom system with variable focal length 100–200 mm considering long-range detection in LWIR band, F/#1.4, only number of lenses are 4 and with overall length 200 mm and optimized at 5 focal length positions with good performance.

Technical design parameters

The design specifications for long-range zoom lens system in LWIR band are given in Table 1.

Table 1 Parameters of the design
Full size table

Imaging system performance can be described in the spatial domain or equivalently in the frequency domain. 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: \(2.44\lambda F/\# = \sqrt 2 d\).

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

$$ {\text{MRTD}} \left( {\xi_{t} } \right) = A.\frac{F/\# }{{D^{*} .{\text{MTF}}\left( {\xi_{t} } \right)}} , $$

where \({D}^{*}\) is the normalized detectivity.the average value is known as \(1.44\times {10}^{8} cmH{z}^\frac{1}{2}{W}^{-1}\) [7] [8].

A is a proportional constant depending on the detector.

\(MTF({\xi }_{t})\) is the modulation transfer function at target frequency of \({\xi }_{t}\).

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.

Table 2 F/# vs. MRTD
Full size table

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.

Table 3 Calculated ranges of the thermal imager (DRI performance)
Full size table

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]:

$$ Aq_{2}^{2} + Bq_{2} + C = 0 $$

where

$$ A = \left( {f_{2}^{^{\prime}} - \beta_{1} q_{1} } \right)\beta_{2} $$
$$ B = \beta_{1} \beta_{2} q_{1}^{2} + \left[ {f_{3}^{^{\prime}} \left( {1 - \beta_{2}^{2} } \right)\beta_{1} - f_{2}^{^{\prime}} \left( {1 - \beta_{1}^{2} } \right)\beta_{2} } \right]q_{1} - f_{2}^{^{\prime}} f_{3}^{^{\prime}} \left( {1 - \beta_{2}^{2} } \right) $$
$$ C = \beta_{2}^{2} f_{3}^{^{\prime}} [\beta_{1} q_{1} - f_{2}^{^{\prime}} \left( {1 - \beta_{1}^{2} } \right]q_{1} $$

The movement component

$$ q_{2} = \frac{{ - B \pm \sqrt {B^{2} - 4AC} }}{2A} $$

and

\(\beta_{1} \) represents the vertical axis magnification of variable group in initial position,

\(\beta_{2} \) 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,

\(f_{2}^{^{\prime}}\) is the focal length of variable group,

\(f_{3}^{^{\prime}}\) 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.

Fig. 1
figure 1

Optimized zoom lens configuration

Full size image

Design results

The optical zoom system having a good performance was obtained, and its design data are shown in Table 4.

Table 4 Optimized optical zoom system design data
Full size table

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

Fig. 2
figure 2

Five optimized steps for zoom lens configurations

Full size image

The spacing value(s) of every component at different focal length positions in which the sum of the space values have a constant value of 156.183 mm to keep image plane at same position as shown in Table 5.

Table 5 Spacing in different zoom positions
Full size table

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.

Table 6 Diffractive surface data
Full size table

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 wavelength-to-zone period ratio is very small across the entire lens, so an approximate expression for the polychromatic integrated efficiency ranging from \(\lambda_{min}\) to \(\lambda_{max}\) is given by [8]

$$ \eta_{{{\text{int}}{\text{. poly}}}} \cong 1 + \frac{{\pi^{2} }}{{3\lambda_{0} }}\left( {\lambda_{{{\text{min}}}} + \lambda_{{{\text{max}}}} - \lambda_{0} } \right) - \frac{{\pi^{2} }}{{9\lambda_{0}^{2} }}\left( {\lambda_{{{\text{min}}}}^{2} + \lambda_{{{\text{min}}}} \lambda_{{{\text{max}}}} - \lambda_{{{\text{max}}}}^{2} } \right) $$

where \(\lambda_{0} \) is the design wavelength for the diffractive lens.

For \(\lambda_{min} = 8\mu m, \lambda_{max} = 12\mu m and \lambda_{0} = 10\mu m,\) 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 \(\eta_{int. poly}\) 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.

Fig. 3
figure 3

Motion curves of variable component and compensation component component group

Full size image

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 diffraction-limited at each focal length position such that the system is perfect image quality.

Fig. 4
figure 4

a-e MTF for the five zoom positions (steps: 100, 125, 150, 175 and 200 mm)

Full size image

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.

Fig. 5
figure 5

a-e Spot diagrams for the five zoom positions (100,125,150,175and200 mm)

Full size image

Anti-reflection coating

According to Fresnel equations the reflection at normal incidence from a single interface separating two media of refractive indices \(n_{1}\) and \(n_{2}\) is \(R = \left| {\frac{{n_{1} - n_{2} }}{{n_{1} + n_{2} }}} \right|^{2}\), so the reflection in air at each surface of germanium (Ge) material will be about 36%. the optimized optical system consists of four Ge lenses (8 surfaces); hence, the total transmission of whole system is about 2% of incident energy; therefore, anti-reflection coating must be applied.

The condition of a double-layer film coating of thickness \(\frac{1}{4}\lambda_{0}\) is \(n_{s} = \left( {\frac{{n_{2} }}{{n_{1} }}} \right)^{2}\), where \(n_{1}\), \(n_{2}\) and \(n_{s}\) are refractive indices of first, second material film and lens, respectively, and \(\lambda_{0}\) is the monitoring wavelength [12].

Applying the above condition, the coating configuration for the Ge material is Air/GASIR5/PbTe/Ge, where \(t_{1}\) and \(t_{2}\) are the film thicknesses.

configuration

\(n_{1}\)

\(n_{2}\)

\(n_{s}\)

\(t_{1}\)

\(t_{2}\)

\(\lambda_{0}\)

Air/GASIR5/PbTe/Ge

2.777

5.646

4.004

0.8999 µm

0.4428 µm

10 µm

The reflectance of Ge before and after applying double-layer anti-reflection coating is shown in Fig. 6

Fig. 6
figure 6

Reflectance of Ge before and after coating

Full size image

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.