## 1.

## Introduction

Infrared systems operating in midwave infrared (MWIR, from 3 to 5 *μ*m) are used in civilian and military applications, such as law enforcement, life rescue, territorial surveillance, vehicle tracking, aerial surveillance, and stealth searching.^{1}2.^{–}^{3} In recent years, the demand for MWIR zoom systems has increased. In these systems, the wide field of view (WFOV) is used for observing a large scene area for possible targets of interest, and the narrow field of view (NFOV) is used for close-up identification of the target of interest.^{3}4.5.6.7.8.9.10.11.^{–}^{12} In some circumstances, such as aerial surveillance and life rescue, there is a need for wider observation of the scene.^{3} There is a significant need to design a MWIR zoom system with a large zoom ratio.

There are two types of zoom systems: optically compensated and mechanically compensated. Almost all infrared zoom systems are mechanically compensated.^{13} In a traditional mechanically compensated zoom system, the second component moves for changes in focal length, while the third component moves to eliminate image shift; the image stays in focus throughout the zoom range (refer to Fig. 1).^{13} Using a traditional four-component mechanically compensated type, MWIR zoom systems cannot achieve a large zoom ratio (such as 45) with a general F/number (such as 4).^{1}^{,}^{2}^{,}^{14}15.16.17.18.19.20.^{–}^{21} In this paper, we examine the six-component mechanically compensated type, which can achieve a large zoom ratio. The design concept is shown in Fig. 2; the second and fourth components are linked and move together for changes in focal length, while the third and fifth components are linked and move together to eliminate image shift. This type still involves just two moving groups. It is likely that the zoom range could also be achieved with a third moving group, but there is additional expense and complexity to do so. Section 2 presents the thin-lens theory. In Sec. 3, a MWIR continuous zoom system with a zoom ratio of 45 is designed. Finally, in Sec. 4, we present our conclusions.

## 2.

## Thin-Lens Theory

Figure 3 represents a general six-component zoom system, with the zoom components in their long-zoom positions. Capital letters indicate the long-zoom values. Thin-lens theory is used to investigate the zooming properties. For the second component,

where ${F}_{2}$ is the focal length of the component.This becomes

andLikewise, for the third component,

butFor the fifth component,

This becomes

andLikewise for the sixth component,

Likewise, for the fourth component,

but andTherefore, using Eqs. (2)–(5) and (7)–(11) in Eq. (12),

## (13)

$$\frac{{F}_{3}\cdot [\frac{{F}_{2}\cdot ({F}_{1}-{D}_{1})}{{F}_{2}+{F}_{1}-{D}_{1}}-{D}_{2}]}{{F}_{3}+\frac{{F}_{2}\cdot ({F}_{1}-{D}_{1})}{{F}_{2}+{F}_{1}-{D}_{1}}-{D}_{2}}-\frac{{F}_{4}\cdot [{D}_{4}+\frac{{F}_{5}\cdot ({D}_{5}+\frac{{F}_{6}\cdot {D}_{6}}{{F}_{6}-{D}_{6}})}{{F}_{5}-{D}_{5}-\frac{{F}_{6}\cdot {D}_{6}}{{F}_{6}-{D}_{6}}}]}{{F}_{4}-{D}_{4}-\frac{{F}_{5}\cdot ({D}_{5}+\frac{{F}_{6}\cdot {D}_{6}}{{F}_{6}-{D}_{6}})}{{F}_{5}-{D}_{5}-\frac{{F}_{6}\cdot {D}_{6}}{{F}_{6}-{D}_{6}}}}={D}_{3}.$$As the second, third, fourth, and fifth components move from their long-zoom positions, the image should stay in focus, and the following conditions must hold:

## (14)

$$\frac{{F}_{3}\cdot [\frac{{F}_{2}\cdot ({F}_{1}-{d}_{1})}{{F}_{2}+{F}_{1}-{d}_{1}}-{d}_{2}]}{{F}_{3}+\frac{{F}_{2}\cdot ({F}_{1}-{d}_{1})}{{F}_{2}+{F}_{1}-{d}_{1}}-{d}_{2}}-\frac{{F}_{4}\cdot [{d}_{4}+\frac{{F}_{5}\cdot ({d}_{5}+\frac{{F}_{6}\cdot {d}_{6}}{{F}_{6}-{d}_{6}})}{{F}_{5}-{d}_{5}-\frac{{F}_{6}\cdot {d}_{6}}{{F}_{6}-{d}_{6}}}]}{{F}_{4}-{d}_{4}-\frac{{F}_{5}\cdot ({d}_{5}+\frac{{F}_{6}\cdot {d}_{6}}{{F}_{6}-{d}_{6}})}{{F}_{5}-{d}_{5}-\frac{{F}_{6}\cdot {d}_{6}}{{F}_{6}-{d}_{6}}}}={d}_{3}.$$Small letters indicate the values at the new zoom position. As previously defined, ${Z}_{1}$ is the axial distance moved by the second and fourth components from the long-zoom position, and ${Z}_{2}$ is the axial distance moved by the third and fifth components at zoom setting ${Z}_{1}$ from the long-zoom position. Thus,

And by combining Eqs. (14)–(20),

## (21)

$${Z}_{2}+\frac{{a}_{1}\cdot {Z}_{2}^{2}+{b}_{1}\cdot {Z}_{2}+{c}_{1}}{{Z}_{2}^{2}-{b}_{2}\cdot {Z}_{2}-{c}_{2}}+\frac{{b}_{3}\cdot {Z}_{2}-2}{{Z}_{2}-{c}_{4}}-{c}_{5}=0,$$At the zoom setting ${Z}_{1}$, as the long-zoom values are known, the above values of ${a}_{1}$, ${b}_{1}$, ${b}_{2}$, ${b}_{3}$, ${c}_{1}$, ${c}_{2}$, ${c}_{3}$, ${c}_{4}$ and ${c}_{5}$ can then be evaluated. After rearrangement, Eq. (21) becomes

## (22)

$${Z}_{2}^{4}+{k}_{3}\cdot {Z}_{2}^{3}+{k}_{2}\cdot {Z}_{2}^{2}+{k}_{1}\cdot {Z}_{2}+{k}_{0}=0,$$Using Eq. (22), the motion of the third and fifth components ${Z}_{2}$ at the the zoom setting ${Z}_{1}$ may be evaluated. Using Eqs. (14)–(19), the distance values may be found. Then, the corresponding effective focal length (EFL) of the system is obtained.

## 3.

## Example of the Design

A MWIR zoom system designed with a $320\times 240$ staring focal plane array, and the dimension of detector pixel is $30\times 30\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mu \mathrm{m}}^{2}$. The characteristics of the design are shown in Table 1.

## Table 1

Characteristics of the system.

Zoom range | 45 |

Focal length range | −10 to −450 mm |

F/number | 4 |

Image plane diagonal | 12 mm |

Spectral band | 3.7 to 4.8 μm |

## 3.1.

### Thin-Lens Results

The initial data of the thin-lens system at the long-zoom position ($\mathrm{EFL}=-450\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mm}$) are listed in Table 2. Using Eqs. (22) and (14)–(19), setting three different values of ${Z}_{1}$, thin-lens data of the system at the three zoom positions are calculated and listed in Table 3.

## Table 2

The initial data of the thin-lens zoom system.

F1 | 135.646 | D1 | 79.188 |

F2 | −36.930 | D2 | 9.528 |

F3 | 71.126 | D3 | 105.237 |

F4 | −38.214 | D4 | 15.312 |

F5 | 50.702 | D5 | 172.529 |

F6 | 27.052 | D6 | 51.512 |

NOTE: Unit: mm.

## Table 3

Thin-lens data of the system at three zoom positions.

Long EFL | Mid EFL | Short EFL | |
---|---|---|---|

Z1 | 0 | −17.121 | −53.587 |

Z2 | 0 | 30.708 | 43.004 |

d1 | 79.188 | 62.067 | 25.601 |

d2 | 9.528 | 57.357 | 106.119 |

d3 | 105.237 | 57.408 | 8.646 |

d4 | 15.312 | 63.141 | 111.903 |

d5 | 172.529 | 141.821 | 129.525 |

d6 | 51.512 | 51.512 | 51.512 |

EFL | −450 | −63.2 | −10 |

NOTE: Unit: mm.

## 3.2.

### Actual Results

According to the thin-lens design results, the original structure of the actual system was obtained. Computer optimization was initiated at three zoom positions and was expanded to nine and eventually to 34 zoom positions. The actual zoom system consists of eight elements, made from silicon and germanium to achieve achromatization. There are four aspheric surfaces utilized for compactness in order to achieve the desired optical performance. Layouts of the system at three zoom positions are shown in Fig. 4. Characteristics of the system are shown in Table 1. The overall length of the zoom system is 400 mm. The second and fourth elements are linked and move together; the length of the move is 53.45 mm over the entire zoom range. The third and fifth elements are also linked and move together; the length of the move is 41.40 mm over the entire zoom range. The overall length and moving lengths are short compared with those of the typical zoom systems.^{1}^{,}^{15} Figure 5 shows the continuous motions of the zoom elements; the focal length of the system is smooth and continuous. To have 100% cold shielding efficiency, the cold shield of the detector and the exit pupil of the system have to be superposed.

## 3.3.

### Performance

The modulation transfer function (MTF) performances of the system at three zoom positions are shown in Fig. 6. The MTF value in Nyquist limit ($16l\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{p}/\mathrm{mm}$) is more than 0.3 over the entire zoom range. Figure 7 illustrates spot diagrams for three different zoom positions. Root mean square (RMS) radius of the spot is less than 30 *μ*m over the full zoom range. The MWIR zoom system has high image quality.

## 4.

## Conclusions

Using six-component mechanically compensated type, a MWIR zoom system is designed in this paper. The results present this zoom lens achieving good image quality, with specifications of 45 zoom ratio and $F/4$, by utilizing the layout of interlaced mechanical linkage to perform the role of variator and compensator. The six-component mechanically compensated type system can achieve a large zoom ratio with short overall length and moving lengths. The continuous motions of the zoom elements are smooth. Image qualities are good over the entire zoom range. The six-component mechanically compensated type has advantages in the design of MWIR zoom system with a large zoom ratio.

## References

## Biography

**Zhou Hao** received a BS degree in optical information science and technology from Hefei University of Technology in 2009. He is currently pursuing his PhD at the Graduate School of the Chinese Academy of Sciences. His research interests are infrared optical systems and system evaluation.

**Liu Ying** received a PhD degree in optical engineering from Graduate School of the Chinese Academy of Sciences in 2010. She is currently a research assistant at the Changchun Institute of Optics, Fine Mechanics, and Physics, Chinese Academy of Sciences. Her research interests are infrared optical systems and spectrometer.

**Sun Qiang** received a PhD degree in optical engineering from Nankai University in 2003. He is currently a professor at the Changchun Institute of Optics, Fine Mechanics, and Physics, Chinese Academy of Sciences. His research interests are infrared optical systems and spectrometer.

**Li Chun** received an MS degree in optical engineering from Graduate School of the Chinese Academy of Sciences in 2010. He is currently a research assistant at the Changchun Institute of Optics, Fine Mechanics, and Physics, Chinese Academy of Sciences. His research interests are image enhancement and image fusion.