Abstract
A non-singular and explicit method of constructing a filter exactly for the rotational gradient vector is shown. Such a filter is expected to be useful in phase reconstruction and related problems in adaptive optics with Hartmann sensors. In the deduction of this method, great care is taken in the arrangement of coordinates in order to make the mathematical implementation exact and consistent. The most notable consequence of the deduction is that, after the rotation is eliminated on coordinates shifted a half-period from the original, integral paths should once more be shifted a half-period from the centre of rotations to obtain a consistent wavefront reconstruction. Differences from conventional least methods are shown with experimental results. This formula would be effective for accurate decomposition of the rotation component, which is useful for phase reconstruction and related problems.
| Original language | English |
|---|---|
| Pages (from-to) | 1705-1723 |
| Number of pages | 19 |
| Journal | Journal of Modern Optics |
| Volume | 50 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2003 Jul 20 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
An exact formulation of a filter for rotations in phase gradients and its applications to wavefront reconstruction problems. / Hattori, Masayuki; Komatsu, Shinichi.
In: Journal of Modern Optics, Vol. 50, No. 11, 20.07.2003, p. 1705-1723.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An exact formulation of a filter for rotations in phase gradients and its applications to wavefront reconstruction problems
AU - Hattori, Masayuki
AU - Komatsu, Shinichi
PY - 2003/7/20
Y1 - 2003/7/20
N2 - A non-singular and explicit method of constructing a filter exactly for the rotational gradient vector is shown. Such a filter is expected to be useful in phase reconstruction and related problems in adaptive optics with Hartmann sensors. In the deduction of this method, great care is taken in the arrangement of coordinates in order to make the mathematical implementation exact and consistent. The most notable consequence of the deduction is that, after the rotation is eliminated on coordinates shifted a half-period from the original, integral paths should once more be shifted a half-period from the centre of rotations to obtain a consistent wavefront reconstruction. Differences from conventional least methods are shown with experimental results. This formula would be effective for accurate decomposition of the rotation component, which is useful for phase reconstruction and related problems.
AB - A non-singular and explicit method of constructing a filter exactly for the rotational gradient vector is shown. Such a filter is expected to be useful in phase reconstruction and related problems in adaptive optics with Hartmann sensors. In the deduction of this method, great care is taken in the arrangement of coordinates in order to make the mathematical implementation exact and consistent. The most notable consequence of the deduction is that, after the rotation is eliminated on coordinates shifted a half-period from the original, integral paths should once more be shifted a half-period from the centre of rotations to obtain a consistent wavefront reconstruction. Differences from conventional least methods are shown with experimental results. This formula would be effective for accurate decomposition of the rotation component, which is useful for phase reconstruction and related problems.
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UR - http://www.scopus.com/inward/citedby.url?scp=1542337009&partnerID=8YFLogxK
U2 - 10.1080/0950034031000069460
DO - 10.1080/0950034031000069460
M3 - Article
AN - SCOPUS:1542337009
VL - 50
SP - 1705
EP - 1723
JO - Journal of Modern Optics
JF - Journal of Modern Optics
SN - 0950-0340
IS - 11
ER -