离轴三反航天测绘相机焦距的计算

为了精确计算离轴三反相机的焦距以保证其测绘精度,对经典测绘模型和相关公式进行了必要的修正。首先,重新定义了离轴三反测绘相机的交会角,并对经典焦距计算公式做了修正;其次,分析了地球曲率对离轴三反测绘相机焦距计算的影响,进一步修正了焦距计算公式。实例计算表明:当要求地面像元分辨率为2m,在CCD像元尺寸为8μm,轨道高度为700km,离轴角为7°条件下,应用经典计算公式得出的斜视相机焦距与应用修正后的计算公式所得出的斜视相机焦距相对偏差达到2.6%,说明对测绘精度影响很大。因此,在采用离轴三反相机进行摄影测量时,斜视相机焦距的计算应考虑离轴角后对经典公式进行必要的修正,而正视相机的焦距计算可以沿用经典计算公式。

Calculation of focal length for off-axis TMA aerospace mapping camera

To calculate the focal length of an off-axis Three Mirror Anastigmat(TMA) camera precisely and to guarantee its mapping precision,this paper researches and amends the classic mapping model and related formulas. First, the intersection angle of the off-axis TMA camera is re-defined,and the classic calculating formula for the focal length is modified. Then, the effect of earth curvature on the calculating focal length is analyzed, and the formula is further corrected. Examples indicate that when GSD is set to be 2 m,and the size of CCD, orbital altitude and the off-axis angle are 8 μm,700 km and 7°, respectively, the relative error of the focal length of a tilt-looking camera calculated by the classic formula and that calculated by the modified formula can reach to 2.6%, which will effect significantly on the mapping precision. Therefore,it suggests that the calculating formula for focal length of tilt-looking camera should take the off-axis angle into account when a off-axis TMA camera is used in photography.Furthermore, the classic calculating formula is still applicable for the ortho-looking camera.