在Ⅳ型凹面全息光栅制作和使用过程中，各参数误差会影响其光谱性能。光栅均方根法优化函数表达式复杂且不能给出光谱的带宽。由费马原理推导出一种数值处理较为简单且能直接描述光谱带宽的光栅优化函数平方和法优化函数，验证了该函数的正确性。采用该函数对Ⅳ型凹面全息光栅使用参数和记录参数在参考平面内外的误差对光谱性能的影响及补偿做了定量分析，结果表明，Ⅳ型凹面全息光栅一个使用参数或记录参数在参考平面内的误差可通过分别调节其他使用参数或记录参数进行补偿，且当记录参数的误差不改变光栅常数时，可以通过调节使用参数对其进行补偿；而光栅记录参数在参考平面外的误差只能通过调节记录参数与参考平面的距离进行补偿。

There are errors between the theoretical values and the actual values for the parameters of type-Ⅳ concave holographic grating during its recording and using process, which will affect the spectral performance of the concave holographic grating. A simple grating optimization function which can be used to describe the spectral width is derived from the Fermat′s principle and a comparison to the root-mean-square (RMS) optimization function which is complex and disable to describe the spectral width is made to justify its validity. The errors are divided into two categories by their location relative to the reference plane and a quantitative analysis of their effects on the spectral performance of type-Ⅳ concave holographic grating is made. The results indicate that the error of one recording parameter or using parameter in the reference plane can be compensated by adjusting other recording parameters or other using parameters, and the recording parameter errors can be compensated by adjusting the using parameters when the grating constant is not changed; the compensation for the parameter error outside the reference plane can only be made by adjusting other parameter′s distance from the reference plane.