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摘要: 大视场星模拟器可以提供更广的星图范围。但是现有星模拟器受显示芯片尺寸的限制，最大视场不超过30°。为了增大星模拟器光学系统视场，本文提出一种将同一规格的星模拟器视场进行拼接从而扩大视场的方法。为了降低成本及系统复杂程度、减少系统整体重量，以最少的拼接数目实现最大的拼接视场，文中针对视场重叠区域进行了详细计算与分析，提出以平面拼接为基础的形式简化拼接模型，得到正三角形、正四边形、正六边形3种典型的拼接方式，并推导了3种拼接方式下视场利用率的计算方法。提出了单一视场坐标计算方法，据此确定每个视场的中心位置，得到准确拼接数目。对比结果显示，正六边形拼接方式具有视场利用率更高、拼接数目更少的突出优势，为大视场星模拟器设计提供依据。Abstract: The large field-of-view (FOV) star simulator provides wider star maps but the existing star simulator is limited by the size of the display chip, and the maximum FOV is not more than 30°. In order to increase the FOV of the star simulator, a splicing method is proposed. In order to reduce the cost, the overall weight and complexity of the system, and to achieve the largest splice FOV with the least amount of splicing, we carry out detailed calculation and analysis of the overlapping area of the field of view and propose a simplified splicing model based on plane splicing. Three typical splicing methods are produced including a regular triangle, a regular quadrilateral and a regular hexagon, and the calculation of the FOV utilization is deduced. This paper also provides a coordinate calculation method, determining the center position of each FOV and obtaining an accurate number of the stitching. The final comparison result shows that the regular hexagon splicing method has the outstanding advantages of a higher utilization of the FOV and fewer splicing numbers, which provides a basis for the design of a large FOV star simulator.
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Key words:
- field of view splicing /
- star simulator /
- large field of view /
- splicing model
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图 7 正三角形拼接方式夹角计算示意图
Figure 7. Schematic diagram of the calculation of the included angle of the regular triangle splicing method
图 9 中心坐标与交点坐标位置排列
Figure 9. Arrangement of the center coordinates and intersection coordinates
图 10 坐标边界位置计算示意图
Figure 10. Schematic diagram of calculation of the coordinate boundary position
表 1 正三角形拼接方式的圈数与个数关系
Table 1. Relationship between the number of circles and the number of regular triangle splicing method
圈数$C$ 1 2 3 4 5 6 每圈个数${a_{3C}}$ 15 33 51 69 87 105 
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表 2 正四边形拼接方式的圈数与个数关系
Table 2. Relationship between the number of circles and the number of square splicing method
圈数$C$ 1 2 3 4 5 6 每圈个数${a_{4C}}$ 8 16 24 32 40 48
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表 3 正六边形拼接方式的圈数与个数关系
Table 3. Relationship between the number of circles and the number of regular hexagon splicing method
圈数$C$ 1 2 3 4 5 6 每圈个数${a_{6C}}$ 6 12 18 24 30 36
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表 4 3种方式的视场利用率对比
Table 4. Comparison of FOV utilization of three methods
拼接方式 n $\eta $ 正三角形 3 63.1% 正四边形 4 73.4% 正六边形 6 86.2%
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表 5 3种方式的拼接数目对比
Table 5. Comparison of the number of splices for three methods
拼接方式 拼接角度 90° 120° 150° 180° 正三角形 921 1321 2277 3255 正四边形 542 914 1481 2037 正六边形 421 673 1134 1554
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