González-Núñez Héctor, Prieto-Blanco Xesús, de la Fuente Raúl
Departamento de Física Aplicada, Escola Universitaria de Óptica e Optometría, Universidade de Santiago de Compostela, 15782 Galicia, Spain.
J Opt Soc Am A Opt Image Sci Vis. 2012 Apr 1;29(4):442-9. doi: 10.1364/JOSAA.29.000442.
The light path function (LPF) of an Offner spectrometer is presented. The evaluation of the LPF of this spectrometer enables its imaging properties to be studied for arbitrary object and image positions, while avoiding the more complicated analysis of intermediate images generated by the diffraction grating, which is often involved. A power series expansion of the LPF on the grating coordinates directly determines pupil aberrations of the generated spectrum and facilitates the search for configurations with small low-order aberrations. This analysis not only confirms the possibility of reducing low-order aberrations in Rowland-type mounts, namely astigmatism and coma, as predicted in previous studies, but also proves that all third-order terms in the series expansion of the aberration function can be canceled at the image of the design point and for the corresponding design wavelength, when the design point is located on a plane orthogonal to the optical axis. Furthermore, fourth-order terms are computed and shown to represent the most relevant contribution to image blurring. Third- and fourth-order aberrations are also evaluated for Rowland mounts with the design point located outside the aforementioned plane. The study described in this manuscript is not restricted to small angles of incidence, and, therefore, it goes beyond Seidel and Buchdahl aberrations.
本文介绍了一种Offner光谱仪的光路函数（LPF）。对该光谱仪的LPF进行评估，能够在避免对通常涉及的衍射光栅所产生的中间图像进行更复杂分析的情况下，研究其在任意物像位置的成像特性。LPF在光栅坐标上的幂级数展开直接确定了所产生光谱的光瞳像差，并有助于寻找低阶像差较小的配置。该分析不仅证实了如先前研究所预测的那样，在罗兰型装置中减少低阶像差（即像散和彗差）的可能性，而且还证明了当设计点位于与光轴正交的平面上时，像差函数级数展开中的所有三阶项在设计点的像处以及对于相应的设计波长都可以被消除。此外，计算了四阶项，并表明它们对图像模糊的贡献最为显著。还对设计点位于上述平面之外的罗兰装置评估了三阶和四阶像差。本手稿中描述的研究不限于小入射角，因此超出了赛德尔和布赫达尔像差的范围。
