Optical Design of a Reflecting Omnidirectional Vision System for Long-wavelength Infrared Light

원적외선용 반사식 전방위 비전 시스템의 광학 설계

Abstract

A reflecting omnidirectional optical system with four spherical and aspherical mirrors, for use with long-wavelength infrared light (LWIR) for night surveillance, is proposed. It is designed to include a collecting pseudo-Cassegrain reflector and an imaging inverse pseudo-Cassegrain reflector, and the design process and performance analysis is reported in detail. The half-field of view (HFOV) and F-number of this optical system are $40-110^{\circ}$ and 1.56, respectively. To use the LWIR imaging, the size of the image must be similar to that of the microbolometer sensor for LWIR. As a result, the size of the image must be $5.9mm{\times}5.9mm$ if possible. The image size ratio for an HFOV range of $40^{\circ}$ to $110^{\circ}$ after optimizing the design is 48.86%. At a spatial frequency of 20 lp/mm when the HFOV is $110^{\circ}$, the modulation transfer function (MTF) for LWIR is 0.381. Additionally, the cumulative probability of tolerance for the LWIR at a spatial frequency of 20 lp/mm is 99.75%. As a result of athermalization analysis in the temperature range of $-32^{\circ}C$ to $+55^{\circ}C$, we find that the secondary mirror of the inverse pseudo-Cassegrain reflector can function as a compensator, to alleviate MTF degradation with rising temperature.

야간 감시를 위해 원적외선에서 사용하는 4개의 구면 및 비구면 거울을 갖는 반사식 전방위 비전 시스템 광학계를 제안한다. 이 반사식 전방위 비전 시스템은 유사 카세그레인식 수광부 반사경 시스템과 역 유사 카세그레인식 결상부 반사경 시스템으로 설계되었으며, 그에 따른 설계 과정과 성능 분석을 상세히 제시한다. 이 비전 시스템의 반화각과 F-수는 각각 $40{\sim}110^{\circ}$와 1.56으로 설정하였다. 그리고 원적외선 파장 영역에서 비전 시스템을 사용하기 위해서 상의 크기가 원적외선용 마이크로 볼로미터의 크기와 가능한 같아야 하므로 상의 크기를 $5.9mm{\times}5.9mm$에 맞추어 설계를 진행하였다. 최적화 설계 후 $40{\sim}110^{\circ}$의 반화각 범위에서의 상 크기의 비율은 48.86%이며, 나이퀴스트 주파수인 20 lp/mm의 공간주파수에서 원적외선의 변조전달함수 값이 0.381에 도달하였다. 또한 20 lp/mm의 공간주파수에서 원적외선 영역에 대한 공차의 누적 확률은 99.75%였다. 또한 역 유사 카세그레인식 구조의 결상부 부경을 온도 변화에 따른 변조전달함수 값을 개선시키는 보상자로 선택하여 반사식 전방위 비전 시스템의 운용 온도 범위인 $-32^{\circ}C$에서 $+55^{\circ}C$의 온도 범위에서 비열화 해석 및 보상화 과정을 진행하였다.

Fig. 1. Geometrical ray tracing of the principal ray incident to the collecting reflector system of a reflecting omnidirectional optical system with a wide field of view. (a) Principal ray entering at an upward angle and (b) principal ray entering at a downward angle.

Fig. 2. Geometrical ray tracing of the principal ray that is incident to the imaging reflector system of a reflecting omnidirectional optical system to focus an image to an optical sensor.

Fig. 3. Paraxial ray tracing of the optical path in the collecting reflector system and imaging reflector system. Although the geometrical arrangement of these mirrors is M2, M1, M3, and M4 in order, rays strike in the order of M1, M2, M4, and M3.

Fig. 4. Optical path of the initial design of the reflecting omnidirectional optical system with four spherical mirrors with various fields.

Fig. 5. Optical path of the reflecting omnidirectional optical system composed of a spherical mirror and three aspherical mirrors designed by the optimization design method starting from the initial design.

Fig. 6. Various MTFs as a function of spatial frequency from 0 to 28 lp/mm, which are dependent on fields in LWIR ranges of the reflecting omnidirectional optical system obtained by the optimized optical design. The red, green, blue, and brown curves are MTF curves of 0.36 field, 0.55 field, 0.73 field, and 1.00 field, respectively, and the black curve corresponds to the MTF in case at the diffraction limit. The solid and dotted curves depict the MTFs of the meridional and sagittal ray, respectively.

Fig. 7. Spot diagram showing the position and shape of the ray arriving at the effective area of an imaging sensor in the optimized design.

Fig. 9. MTFs according to various fields before (small graphs) and after (large graphs) performing the compensation process by the athermalization analysis for the LWIR ranges at (a) -32°C and (b) 55°C. We choose M3, the nearest component to the image sensor, as the compensator.

Fig. 10. Variation of the image distance (black triangles) and the moving distance of compensator (black squares) by means of the athermalization analysis.

Fig. 11. EFL variation before (black squares) and after (black triangles) the compensating process in the range of temperature from -32°C to 55°C.

Fig. 8. Cumulative probability as a function of MTF according to various fields in LWIR ranges. F1 (red curve), F2 (green curve), F3 (blue curve), and F4 (pink curve) correspond to cumulative probabilities, which depict the tolerance of MTF according to 0.36 field, 0.55 field, 0.73 field, and 1.0 field, respectively.

Table 1. Various specifications of the reflecting omnidirectional optical system for long wavelength infrared determined by initial optical system design

Table 2. RDN data according to initial design of the reflecting omnidirectional optical system

Table 3. RDN data according to optimized design of the reflecting omnidirectional optical system

Table 4. Aspheric coefficient data according to optimized design of the reflecting omnidirectional optical system