Roland Wagner, Jenny Niebsch, and Ronny Ramlau, "Off-axis point spread function reconstruction for single conjugate adaptive optics," J. Opt. Soc. Am. A 40, 1382-1391 (2023)
Modern giant segmented mirror telescopes (GSMTs) such as the Extremely Large Telescope, which is currently under construction, depend heavily on adaptive optics (AO) systems to correct for atmospheric distortions. However, a residual blur always remains in the astronomical images corrected by single conjugate AO (SCAO) systems due to fitting and bandwidth errors, which can mathematically be described by a convolution of the true image with a point spread function (PSF). Due to the nature of the turbulent atmosphere and its correction, the PSF is spatially varying, which is known as an anisoplanatic effect. The PSF serves, e.g., as a quality measure for science images and therefore needs to be known as accurately as possible. In this paper, we present an algorithm for PSF reconstruction from pupil-plane data in directions apart from the guide star direction in an SCAO system. Our algorithm is adapted to the needs of GSMTs focused on estimating the contribution of the anisoplanatic and generalized fitting error to the PSF. Results obtained in an end-to-end simulation tool show a qualitatively good reconstruction of the PSF compared to the PSF calculated directly from the simulated incoming wavefront as well as stable performance with respect to imprecise knowledge of atmospheric parameters.
Yoshito H. Ono, Masayuki Akiyama, Shin Oya, Olivier Lardiére, David R. Andersen, Carlos Correia, Kate Jackson, and Colin Bradley J. Opt. Soc. Am. A 33(4) 726-740 (2016)
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns) and Layer Heights (Rows)a
Error on
GL
GL
GL
TL
TL
TL
Error on layer heights
0%
0%
−0.1%
1.5%
2.1%
2.8%
−2.6%
−3.9%
−5.1%
ML and TL
−0.9%
0.8%
1.5%
2.2%
−3.5%
−4.8%
−6.1%
ML and TL
−2.8%
−1.7%
−0.2%
−0.6%
−5.7%
−7.1%
−8.5%
ML and TL
2.5%
3.9%
4.5%
5.0%
0.3%
−0.7%
−1.8%
ML and TL
5.1%
6.2%
6.7%
7.1%
3.2%
2.3%
1.4%
ML and TL
−1.1%
0.6%
1.3%
2.0%
−3.8%
−5.1%
−6.3%
ML and TL
−3.4%
−1.5%
−0.7%
0.0%
−6.3%
−7.6%
−9.0%
The wind speeds are assumed to be known exactly. GL, ground layer; ML, mid layer; TL, top layer.
Table 6.
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns), Layer Heights (Rows), and Wind Speeds (+10% for Each Layer)a
Error on
GL
GL
GL
TL
TL
TL
Error on layer heights
0%
0%
0.2%
1.7%
2.4%
3.0%
−2.3%
−3.5%
−4.7%
ML and TL
−0.6%
1.0%
1.7%
2.4%
−3.2%
−4.5%
−5.8%
ML and TL
−2.7%
−0.8%
0.0%
0.7%
−3.6%
−5.3%
−8.1%
ML and TL
2.8%
4.1%
4.7%
5.2%
0.7%
−0.4%
−1.4%
ML and TL
5.4%
6.5%
6.9%
7.3%
3.6%
3.6%
1.8%
GL, ground layer; ML, mid layer; TL, top layer.
Table 7.
Weighted Two-Layer Atmosphere
Layer
1
2
Height (m)
149
3234
-profile
0.7088
0.2912
Wind speed (m/s)
14
20
Table 8.
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns) and Layer Heights (Rows)a
Error on
GL
GL
TL
TL
Error on layer heights
0%
0%
0.2%
−0.1%
−0.4%
0.4%
0.6%
TL
−1.2%
−1.5%
−1.7%
−1.1%
−0.9%
TL
−2.8%
−2.9%
−3.1%
−2.7%
−2.5%
TL
1.4%
1.1%
0.7%
1.7%
1.9%
TL
2.5%
2.1%
1.8%
2.8%
3.1%
The wind speeds are assumed to be known exactly. GL, ground layer; TL, top layer.
Table 9.
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns), Layer Heights (Rows), and Wind Speeds (10% for Each Layer)a
Error on
GL
GL
TL
TL
Error on layer heights
0%
0%
−0.2%
−0.6%
−1.1%
0.0%
0.2%
TL
−1.6%
−1.9%
−2.1%
−1.4%
−1.2%
TL
−3.1%
−3.3%
−3.5%
−3.0%
−2.8%
TL
1.0%
0.6%
0.3%
1.3%
1.6%
TL
2.1%
1.7%
1.2%
2.4%
2.7%
GL, ground layer; TL, top layer.
Tables (10)
Algorithm 1.
Off-Axis Point Spread Function Reconstruction for SCAO Systems
Input: WFS data , statistics of the noise , Fried parameter , directions of interest
Output: the long exposure PSF of the residual phase in direction ,
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns) and Layer Heights (Rows)a
Error on
GL
GL
GL
TL
TL
TL
Error on layer heights
0%
0%
−0.1%
1.5%
2.1%
2.8%
−2.6%
−3.9%
−5.1%
ML and TL
−0.9%
0.8%
1.5%
2.2%
−3.5%
−4.8%
−6.1%
ML and TL
−2.8%
−1.7%
−0.2%
−0.6%
−5.7%
−7.1%
−8.5%
ML and TL
2.5%
3.9%
4.5%
5.0%
0.3%
−0.7%
−1.8%
ML and TL
5.1%
6.2%
6.7%
7.1%
3.2%
2.3%
1.4%
ML and TL
−1.1%
0.6%
1.3%
2.0%
−3.8%
−5.1%
−6.3%
ML and TL
−3.4%
−1.5%
−0.7%
0.0%
−6.3%
−7.6%
−9.0%
The wind speeds are assumed to be known exactly. GL, ground layer; ML, mid layer; TL, top layer.
Table 6.
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns), Layer Heights (Rows), and Wind Speeds (+10% for Each Layer)a
Error on
GL
GL
GL
TL
TL
TL
Error on layer heights
0%
0%
0.2%
1.7%
2.4%
3.0%
−2.3%
−3.5%
−4.7%
ML and TL
−0.6%
1.0%
1.7%
2.4%
−3.2%
−4.5%
−5.8%
ML and TL
−2.7%
−0.8%
0.0%
0.7%
−3.6%
−5.3%
−8.1%
ML and TL
2.8%
4.1%
4.7%
5.2%
0.7%
−0.4%
−1.4%
ML and TL
5.4%
6.5%
6.9%
7.3%
3.6%
3.6%
1.8%
GL, ground layer; ML, mid layer; TL, top layer.
Table 7.
Weighted Two-Layer Atmosphere
Layer
1
2
Height (m)
149
3234
-profile
0.7088
0.2912
Wind speed (m/s)
14
20
Table 8.
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns) and Layer Heights (Rows)a
Error on
GL
GL
TL
TL
Error on layer heights
0%
0%
0.2%
−0.1%
−0.4%
0.4%
0.6%
TL
−1.2%
−1.5%
−1.7%
−1.1%
−0.9%
TL
−2.8%
−2.9%
−3.1%
−2.7%
−2.5%
TL
1.4%
1.1%
0.7%
1.7%
1.9%
TL
2.5%
2.1%
1.8%
2.8%
3.1%
The wind speeds are assumed to be known exactly. GL, ground layer; TL, top layer.
Table 9.
Error of the Strehl Ratio of the Reconstructed Off-Axis PSF for Input Errors on -Values (Columns), Layer Heights (Rows), and Wind Speeds (10% for Each Layer)a
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