空间外差光谱仪采用特定楔角的棱镜实现视场拓展是提高仪器通量和辐射灵敏度的重要手段之一。借鉴传统傅里叶变换光谱仪视场展宽基础理论，结合空间外差光谱仪的技术特点，研究了基于数值归纳方法进行视场展宽棱镜设计的理论依据和实现途径。分析了不同Littrow角和目标波数下视场展宽棱镜顶角的最优取值及最大视场展宽容限。结果表明数值归纳方法全面衡量各级次视场对相位差的影响给出视场展宽棱镜顶角的最优取值，与传统理论推导方法相比，沿色散主截面方向视场容限提高了10%~30%，且数值归纳方法设计空间外差视场展宽棱镜简单、直观，在设计过程中可同时分析仪器参数对视场展宽容限的影响。

It is one of the most important methods to use field-widened prism to increase the throughput or sensitivity for spatial heterodyne spectrometer. This paper borrows idea from the basic principle of traditional Fourier transform spectrometer with field-widened and combines the characteristics of spatial heterodyne spectroscopy, a method based on numerical reduction to design the field-widen prism of spatial heterodyne spectrometer is proposed. The optimum apex angle of field-widened prism and the maximum field are analyzed with certain Littrow angles and scene wave-numbers. The results indicate that numerical induction method can find the optimum solution of prism apex angle by judging the effect of all orders of field angle on the phase difference. Compared with the results obtained by theoretical deduce method, the maximum field angle along dispersive principal cross section increases by 10%~30%, and the numerical induction method is simple and obvious, the influencing factors on the maximum field angle can be analyzed in the process of optimizing field-widened prism angle.