title: Analysis of nodal aberration properties in off-axis freeform system design.
abstract: Freeform surfaces have the advantage of balancing off-axis aberration. In this paper, based on the framework of nodal aberration theory (NAT) applied to the coaxial system, the third-order astigmatism and coma wave aberration expressions of an off-axis system with Zernike polynomial surfaces are derived. The relationship between the off-axis and surface shape acting on the nodal distributions is revealed. The nodal aberration properties of the off-axis freeform system are analyzed and validated by using full-field displays (FFDs). It has been demonstrated that adding Zernike terms, up to nine, to the off-axis system modifies the nodal locations, but the field dependence of the third-order aberration does not change. On this basis, an off-axis two-mirror freeform system with 500 mm effective focal length (EFL) and 300 mm entrance pupil diameter (EPD) working in long-wave infrared is designed. The field constant aberrations induced by surface tilting are corrected by selecting specific Zernike terms. The design results show that the nodes of third-order astigmatism and coma move back into the field of view (FOV). The modulation transfer function (MTF) curves are above 0.4 at 20 line pairs per millimeter (lp/mm) which meets the infrared reconnaissance requirement. This work provides essential insight and guidance for aberration correction in off-axis freeform system design.
authors.forename: Haodong
authors.initials: H
authors.lastname: Shi
authors.forename: Huilin
authors.initials: H
authors.lastname: Jiang
authors.forename: Xin
authors.initials: X
authors.lastname: Zhang
authors.forename: Chao
authors.initials: C
authors.lastname: Wang
authors.forename: Tao
authors.initials: T
authors.lastname: Liu