Freeform surface descriptions. Part II: Application benchmark

Abstract

Optical systems can benefit strongly from freeform surfaces; however, the choice of the right representation is not trivial, and many aspects must be considered. Many possibilities to formulate the surface equations in detail are available, but the experience with these newer representations is rather limited. Therefore, in this work, the focus is to investigate the performance of several classical descriptions as well as one extended freeform surface description in their performance in concrete design optimization tasks. There are different influencing factors characterizing the surface representations, the basic shape, the boundary function, the symmetry, a projection factor, as well as the deformation term describing higher order contributions. We discuss some possibilities and the consequences of describing and using these options with success. These surface representations were chosen to evaluate their impact on all these aspects in the design process. As criteria to distinguish the various options, the convergence over the polynomial orders, as well as the quality of the final solutions, is considered. As a result, recommendations for the right choice of freeform surface representations for practical issues in the optimization of optical systems can be given under restrictions of the benchmark assumptions.

Optical design of an underwater wide working distance robot vision lens

“…Each term of the Zernike polynomial and the 2-D Q-type polynomial can correspond to different aberrations, of which the Zernike polynomial is more commonly used, but its ability to express locally complex surfaces is weak, and it usually requires the use of higher orders to obtain good fitting accuracy. [11] In the meshing of finite element analysis, the coordinates of each node are described by Cartesian coordinate system, but there are many forms of meshing methods, such as Tet, Hex and Wed. For the structure to be analyzed, this means that the division of node coordinates is not uniform. After the underwater optical window is deformed, each node will also be displaced in the direction of the optical axis, and the definition of the surface vertex coordinates is inconsistent with that of the optical system.…”

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

“…However, in real systems with a large field of view and prominent pupil aberrations, the real chief rays intersect the optical axis often in a considerable distance from the common pupil plane. Thus, in order to provide lens designer with point-imaging properties of the system, the real chief ray is selected as a reference ray and the individual locations of the exit pupil reference spheres are assigned to each field point; see Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) requires subtraction of two terms, each with the order of magnitude similar to the length of the optical system (typically hundreds of mm), to obtain the wavefront error, which is measured with the multiple of the wavelength. Thus, in the past formulas reducing the demand on the numerical precision were developed [3].…”

“…properties [17][18][19] were developed. After the design stage, it is necessary to assess the performance of the "as-built" freeform system.…”

“…The geometry for deriving the OPD resulting from refraction on the surface of an ideal incoming wavefront.Thus, OPD accumulated along the real ray (RR) as a result of refraction is obtained as the deviation from the spherical wavefront:=´̅ ̅̅̅̅ −´̅ ̅̅̅̅ = ´̅ ̅̅̅̅ − ̅̅̅̅ (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). …”

Optical-digital joint optimization enables advanced specifications freeform imaging system design

“…More recently, there has been a growing focus on freeform surfaces, which offer the potential to provide much more degrees of design freedom. 1,2 By integrating freeform surfaces into the design process, advanced specifications can be achieved. [3][4][5] However, the ability of freeform surfaces are also limited when advanced system specifications of imaging systems are required.…”