ELSEVIER Optik 115, No. 4 (2004) 169-172 http://www.elsevier.de/ijleo International Journal for light and Electron Optics Passively athermalised hybrid Petzval objective for high resolution MWIR detector arrays Yi-Nan Zhang, Zhao-Qi Wang Institute of Modern Optics, Nankai University, The Key Laboratory of Opto-electronic Information Science and Technology, Ministry of Education, Tianjin, 300071, China 1. Introduction Modern optical systems, particularly military and aero- space systems are usually expected to operate over a very wide temperature range. Variation in ambient temperature induces changes of refractive index, lens shape, and lens space. The thermal focus shift caused by such changes degrades the image quality of an ima- ging system. Particularly for infrared optical systems, because of infrared materials' high value of the change in refractive index with temperature (dnldT), environ- mental effects can greatly influence the performance of the optical systems [l-31. So when designing an infra- red optical system, we must consider the impact of temperatures. On the other hand, with the rapid devel- opment of infrared detector arrays technology, the pix- el size of the detector arrays is becoming smaller and smaller and the resolution is becoming higher and higher. In recent years, the pixel size is changed from Received 26 January 2004; accepted 18 March 2004. Correspondence to: Z. Q. Wang Fax: ++86-2223 508 332 E-mail:
[email protected] about 50 pm to 20 - 30 pm [4, 51. So the demands for the associated high resolution infrared optical systems are also rapidly increasing. Athermalisation methods for infrared optical system have been discussed many times [6, 71. It is well estab- lished that passive athermalisation by judicious choice of lens materials and powers will provide elegant solu- tions for many applications [8, 91. But in some cases, it is very difficult to design athermalised optical systems, because the available infrared materials are limited. Over the past few years, there have been many discus- sions on the design advantages provided by diffractive optics in infrared athermalised systems [lo, 111. Refer- ence [lo] showed a 3-element hybrid Petzval lens (f = 75 mm, F/1, f5.5" x f2.7" field), which was pas- sively athermalised over the temperature range -20 "C to +50 "C. But the lens was only suitable for a far infra- red imager with the pixel size of 56 pm. Reference [ l l ] showed a two-hybrid high resolution Petzval objective (f = 176 mm, F / l . l , f0.5" field) with geometrical ray errors controlled to within a spot diameter of 20 pm, which was used for a high resolution 3-5 pm staring array imager. But the thermal stability is very poor. In this paper, we present a passively athermalised hybrid high resolution Petzval objective, which can be used with a latest generation Middle Wave Infrared (MWIR) staring array imager with the pixel size of 25 pm. To meet both the high resolution and the ther- mal stability requirements, two materials and four ele- ments with a diffractive surface are used. 2. Thermal property of the diffractive element In a multilens system composed of thick lenses spaced apart, the following equations of power, longitudinal chromatic aberration and thermal aberration, which is expressed as the change of the back focus with the temperature, are obtained [12]: 0030-4026/04/115/04-169 S 30.0010 170 Yi-Nan Zhang et al., Passively athermalised hybrid Petzval objective for high resolution MWIR detector arrays Waveband Focal length (3) 3-5 pm 176 mm In eqs. (l), (2) and (3), h; represents the paraxial ray height at the i'th lens; @, f b denotes the overall power and the back focus of the system, respectively; A f b , - dT denotes the longitudinal chromatic aberration and thermal aberration, respectively; ipi and v; represent the power and the Abbe number of the i'th lens, re- spectively; 8; is the thermal dispersive power of the i'th lens material, which is defined by a f b ?he associated imager (4) staring array imager with the pixel size of 25 pm Achromatized and athermalised optical systems re- quire that the longitudinal chromatic aberration in- duced by the longitudinal variation of focus with wave- length in eq. (2) is zero and with the variation in ambient temperature, the thermal focus shift in eq. (3) caused by optical elements compensates that caused by the mounting materials. For the refractive element, the thermal dispersive power of the optical material is given by It is dependent not only on the thermal expansion coefficient of the material ag, but also on the change in dn. index with temperature 2. dT For the diffractive element, its power is expressed as where r,,, is the radius of the m'th zone. The change in power with temperature is given by (7) where ag is the thermal expansion coefficient of the substrate material. Compared with eq. (4), the thermal dispersive power of the diffractive element is 8 d = -2ag. (8) Eq. (8) reveals that the thermal dispersive power of the diffractive lens is solely a function of a,; it is inde- pendent of the change in index with temperature. For most infrared materials, dn/dr >> a,. Eqs. (5) and (8) reveal that the thermal dispersive power of the diffrac- tive elements is negligible. Hybrid optics can provide the additional degree of freedom necessary for the cor- rection of chromatic aberration. If we can rationally distribute the powers of the refractive elements for athermalisation, then achromatism and athermalisation can be simultaneously achieved in an infrared optical system. 3. Design of the athermalised hybrid Petzval objective The optical and thermal stability requirements of the high resolution Petzval objective, which forms our de- sign targets, are showed in table 1. We start from a conventional 4-element Petzval ob- jective, which meets the requirements showed above, except the thermal stability requirement that is the ob- jective must have constant performance over the speci- fied temperature range. The optical layout of the con- ventional Petzval objective is showed in fig. 1. The material of the first and the fourth element is Si; the material of the second element is Ge and the material of the third element is ZnSe. Now considering the thermal stability requirement that the MTF performance must be substantially main- tained above 0.80 at 20 cycles/mm and the geometrical spot diameter is controlled to within 20pm over the operating range of -20 "C to +50 "C, it is then imme- diately apparent that the present solution will not suf- fice, as illustrated by fig. 2 and table 2. From fig. 2 and table 2, we can see if the operating temperature range is beyond the temperature range +17"C to +30"C, the thermal defocus has greatly degraded the imaging quality of this optical system. For mass and cost reasons, Si is the preferred optical material for positive power in the 3-5 pm waveband. However, the lower refractive index of Si in compari- son with that of Ge results in more powerful lens cur- vatures. Also, the dispersion of Si is such that other optical materials must be introduced for chromatic cor- rection, especially in the case where the system has a relatively long focal length and high aperture. Ge, which is with negative optical power, can be combined with Si to achromatize but in this case it is proved to be inadequate. Because the changes of the relative par- tial dispersions of the refractive and diffractive compo- nents in the same waveband are opposite, diffractive components are in favor of the correction of the sec- ondary spectrum, which is necessary in the designed system. I F-number I 1.1 I I Semifield I 0.5-deg I Yi-Nan Zhang et al., Passively athermalised hybrid Petzval objective for high resolution MWIR detector arrays 171 Temperature ("C) - 20 -10 0 Geometrical spot diameter (pm) 49.054 41.188 33.378 Fig. 1. Optical layout of the k l e m e n t Petzval objective. 10 20 30 40 50 25.613 17.885 15.154 23.261 31.351 1 0.8 h - 0.6 . P 0 N - I fi; 0.4 v 0 2 !i 0 -20 -10 0 10 20 30 40 50 Temperature [Degree] Fig. 2. Variation of axial polychromatic MTF of the conven- tional optical system with temperature. We select the 4-element conventional high resolu- tion Petzval objective showed in fig. 1 as our original structure. The actually replacing and optimizing proce- dures are as follows: 1) Replacing the material of the third element with Ge; replacing the fourth refractive surface with dif- fractive surface. 2) Making optimization of the system by introducing the effective focal length, the spherical aberration and the coma aberration introduced into the merit functions. In the optimization process, checking the MTF performance and the Spot diagram of the sys- tem under different temperatures and making the system having steady imaging quality. 3) Making optimization of the system with total track length introduced into the merit functions. In the optimization process, checking the MTF perfor- mance and the Spot diagram of the system under different temperatures and making the system hav- ing steady imaging quality. 4. Design result Under the given constraints as described in table 1, the optical layout of the new athermalised hybrid high re- solution Petzval objective is showed in fig. 3. The mate- rial of the first and the fourth element with positive power is Si; the material of the second and the third element with negative power is Ge. The diffractive fea- ture is on the fourth surface. Fig.4 shows the calcu- lated MTF at 20 cycles/mm versus the ambient tem- perature from -20 "C to +50 "C. The difference of off- axis tangential MTF and the diffraction limit (0.88) is about 0.05. The difference of off-axis sagittal MTF and the diffraction limit is about 0.04. The differences are so small that the MTF is almost constant over the range of temperature and almost equal to the diffrac- tion limit. The temperature adaptability of the optical system is greatly improved. Table 3 shows the variation of geometrical spot diameter of the athermalised hy- brid optical system with temperature. From table 3, we can see that the geometrical spot diameter is con- trolled to within 20 pm over the range of temperature. Diffractive surface V Fig. 3. Optical layout of the hybrid athermalised high resolu- tion Petzval objective. 172 Yi-Nan Zhang et al., Passively athermalised hybrid Petzval objective for high resolution MWIR detector arrays Temperature ("C) -20 -10 0 10 20 30 Geometrical Spot Diameter (pm) 12.395 13.224 13.996 14.722 15.409 16.064 40 50 16.693 17.302 1 0.8 E 4 0.6 0.4 c Q - m LL v 5 0.2 0 - On-axis - 6- - Off-axis tan - - + - - Off-axis sag -20 -10 0 10 20 30 40 50 Temperature [Degree] Fig. 4. MTF of the athermalised hybrid optical system. 5. Fabrication issues of the diffractive elements In the above athermalised hybrid optical system de- sign, we adopt ZEMAX software, and the phase poly- nomial is described by eq. (9). When only first two terms exist, which is the case in our design, the ring number of the diffractive element n is given by: -2nn = A13 + A2r4. (9) The normalized radius of the nth ring can be then calculated by: The maximum number of the ring is given by: where ro is the normalized radial aperture of the dif- fractive element, and Int denotes the integration op- eration. For the diffractive surface, the normalization radius is 60.5 mm. The coefficients A1 and A2 are 20.6 and 2.3, respectively. The actual radius of the diffrac- tive surface is 63.7. According to eqs. (9) to ( l l ) , the normalized radial aperture is 1.05; the total ring num- ber is 4. When the etching level is eight, the minimum feature size is 875 pm, which is quite large for manu- facturing. 6. Conclusions We have presented one hybrid refractive-diffractive athermalised and high resolution Petzval objective, which consists of four elements and a diffractive sur- face. The lens is compatible with a latest generation MWIR staring array high resolution imager with the pixel size of 25 pm. Compared with the conventional system, the new hybrid system has greatly improved thermal stability with the same element number and cheaper material cost. The polychromatic MTF is above 0.80 at 20 cycles/mm and near diffraction-lim- ited; the geometrical spot diameter is within 20 pm over the range of temperature -20 "C to +50 "C. With pre- sent mature diamond machining technology, this appli- cation of diffractive elements in infrared athermalised optical system possesses importantly practical value. This research is partially supported by National Nature Science Foundation of China (number 60277021). References [l] Behrmann GP, Bowen J P Influence of temperature on diffractive lens performance. Appl. Opt. 32 (1993) 2483- 2489 [2] Tamagawa Y, Wakabayashi S: Multilens system design with an athermal chart. Appl. Opt. 33 (1994) 8009-8013 [3] Tamagawa Y, Tajime T: Expansion of an athermal chart into a multilens system with thick lenses spaced apart. Opt. 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Eng. 35 (1996) 3001-3006 (1999) 6-9 SPIE 1354 (1990) 742-751 (1992) 232-238 SPIE 1354 (1990) 752-759 SPIE 2744 (1996) 500-509 Passively athermalised hybrid Petzval objective for high resolution MWIR detector arrays 1. Introduction 2. Thermal property of the diffractive element 3. Design of the athermalised hybrid Petzval objective 4. Design result 5. Fabrication issues of the diffractive elements 6. Conclusions References