dorsal/arxiv
View SchemaAnalytical expressions for optimum alignment modes of highly segmented mirrors
| Authors | L. Noethe |
|---|---|
| Categories | |
| ArXiv ID | physics/0406071 |
| URL | https://arxiv.org/abs/physics/0406071 |
| DOI | 10.1080/09500340410001731057 |
Abstract
The major sources causing deterioration of optical quality in extremely large optical telescopes are misadjustments of the mirrors, deformations of monolithic mirrors, and misalignments of segments in segmented mirrors. For active optics corrections, all three errors, which can partially compensate each other, are measured simultaneously. It is therefore of interest to understand the similarities and differences between the three corresponding types of modes which describe these errors. The first two types are best represented by Zernike polynomials and elastic modes respectively, both of them being continuous and smooth functions. The segment misaligment modes, which are derived by singular value decomposition, are by their nature not smooth and in general discontinuous. However, for mirrors with a large number of segments, the lowest modes become effectively both smooth and continuous. This paper derives analytical expressions for these modes, using differential operators and their adjoints, for the limit case of infinitesimally small segments. For segmented mirrors with approximately 1000 segments, it is shown that these modes agree well with the corresponding lowest singular value decomposition modes. Furthermore, the analytical expressions reveal the nature of the segment misalignment modes and allow for a detailed comparison with the elastic modes of monolithic mirrors. Some mathematical features emerge as identical in the two cases.
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"abstract": "The major sources causing deterioration of optical quality in extremely large\noptical telescopes are misadjustments of the mirrors, deformations of\nmonolithic mirrors, and misalignments of segments in segmented mirrors. For\nactive optics corrections, all three errors, which can partially compensate\neach other, are measured simultaneously. It is therefore of interest to\nunderstand the similarities and differences between the three corresponding\ntypes of modes which describe these errors. The first two types are best\nrepresented by Zernike polynomials and elastic modes respectively, both of them\nbeing continuous and smooth functions. The segment misaligment modes, which are\nderived by singular value decomposition, are by their nature not smooth and in\ngeneral discontinuous. However, for mirrors with a large number of segments,\nthe lowest modes become effectively both smooth and continuous. This paper\nderives analytical expressions for these modes, using differential operators\nand their adjoints, for the limit case of infinitesimally small segments. For\nsegmented mirrors with approximately 1000 segments, it is shown that these\nmodes agree well with the corresponding lowest singular value decomposition\nmodes. Furthermore, the analytical expressions reveal the nature of the segment\nmisalignment modes and allow for a detailed comparison with the elastic modes\nof monolithic mirrors. Some mathematical features emerge as identical in the\ntwo cases.",
"arxiv_id": "physics/0406071",
"authors": [
"L. Noethe"
],
"categories": [
"physics.optics"
],
"doi": "10.1080/09500340410001731057",
"title": "Analytical expressions for optimum alignment modes of highly segmented mirrors",
"url": "https://arxiv.org/abs/physics/0406071"
},
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