The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems
The ray-aberrations in axis-symmetrical systems are conventionally derived from wavefront functions or characteristic functions using classical approximate partial derivatives. However, the resulting aberrations typically have fifth-order errors, as described by Restrepo et al. (2017) [1]. According...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-09-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844022018199 |
| _version_ | 1811255001702465536 |
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| author | Psang Dain Lin |
| author_facet | Psang Dain Lin |
| author_sort | Psang Dain Lin |
| collection | DOAJ |
| description | The ray-aberrations in axis-symmetrical systems are conventionally derived from wavefront functions or characteristic functions using classical approximate partial derivatives. However, the resulting aberrations typically have fifth-order errors, as described by Restrepo et al. (2017) [1]. Accordingly, in the present study, the secondary ray-aberration coefficients for object placed at finite distance are determined using the fifth-order Taylor series expansion of a skew ray. Notably, the derived expressions are exact since they are determined without any approximations. It is found that some of the aberration coefficients are not constants, but are functions of the polar angle of the entrance pupil. It is additionally found that, once the required derivative matrices have been generated, determination of the secondary aberration coefficients is straightforward without iteration, and incurs only a low computational cost. |
| first_indexed | 2024-04-12T17:17:09Z |
| format | Article |
| id | doaj.art-ad380894bff04914ab805f58227d696c |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-12T17:17:09Z |
| publishDate | 2022-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-ad380894bff04914ab805f58227d696c2022-12-22T03:23:37ZengElsevierHeliyon2405-84402022-09-0189e10531The determination of secondary ray-aberration coefficients for axis-symmetrical optical systemsPsang Dain Lin0Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, TaiwanThe ray-aberrations in axis-symmetrical systems are conventionally derived from wavefront functions or characteristic functions using classical approximate partial derivatives. However, the resulting aberrations typically have fifth-order errors, as described by Restrepo et al. (2017) [1]. Accordingly, in the present study, the secondary ray-aberration coefficients for object placed at finite distance are determined using the fifth-order Taylor series expansion of a skew ray. Notably, the derived expressions are exact since they are determined without any approximations. It is found that some of the aberration coefficients are not constants, but are functions of the polar angle of the entrance pupil. It is additionally found that, once the required derivative matrices have been generated, determination of the secondary aberration coefficients is straightforward without iteration, and incurs only a low computational cost.http://www.sciencedirect.com/science/article/pii/S2405844022018199Taylor series expansionDerivative matricesAxis-symmetrical systemRay-aberrations |
| spellingShingle | Psang Dain Lin The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems Heliyon Taylor series expansion Derivative matrices Axis-symmetrical system Ray-aberrations |
| title | The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems |
| title_full | The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems |
| title_fullStr | The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems |
| title_full_unstemmed | The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems |
| title_short | The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems |
| title_sort | determination of secondary ray aberration coefficients for axis symmetrical optical systems |
| topic | Taylor series expansion Derivative matrices Axis-symmetrical system Ray-aberrations |
| url | http://www.sciencedirect.com/science/article/pii/S2405844022018199 |
| work_keys_str_mv | AT psangdainlin thedeterminationofsecondaryrayaberrationcoefficientsforaxissymmetricalopticalsystems AT psangdainlin determinationofsecondaryrayaberrationcoefficientsforaxissymmetricalopticalsystems |