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
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