Abstract

New optical phasing sensor technologies have been studied with a test bench experiment, called Active Phasing Experiment, on-sky at the European Southern Observatory Very Large Telescope. One of the sensors was of the Shack–Hartmann type using cylindrical lenslets across the segment borders for the measurement of the phasing errors. With bright stars, the precision of the measurement of piston steps at a single border was better than 9nm wavefront RMS, and the precision of the closed-loop correction of the piston errors of the segments across the whole mirror was better than 10nm wavefront RMS. With dimmer stars of magnitude up to 14.5, precisions of the order of 22nm wavefront RMS were obtained.

© 2011 Optical Society of America

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References

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  1. J. Nelson and G. H. Sanders , “Status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
    [CrossRef]
  2. R. Gilmozzi and J. Spyromilio , “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
    [CrossRef]
  3. G. A. Chanan , M. Troy , F. Dekens , M. Scott , J. Nelson , T. Mast , and D. Kirkmann , “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  4. G. A. Chanan , C. Ohara , and M. Troy , “Phasing the mirror segments of the Keck telescopes the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  5. F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
    [CrossRef]
  6. F. Gonté , C. Dupuy , B. Luong , C. Frank , R. Brast , and S. Babak , “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
    [CrossRef] [PubMed]
  7. R. Wilhelm , B. Luong , A. Courteville , S. Estival , F. Gonte , and N. Schuhler , “Dual-wavelength low-coherence instantaneous phase-shifting interferometer to measure the shape of a segmented mirror with subnanometer precision,” Appl. Opt. 47, 5473–5491 (2008).
    [CrossRef] [PubMed]
  8. R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
    [CrossRef]
  9. L. Noethe and H.-M. Adorf , “Optical measurements of phase steps in segmented mirrors-fundamental precision limits,” J. Mod. Opt. 54, 3–31 (2007).
    [CrossRef]
  10. M. S. Bessel , “UBVRI photometry. II. The Cousins VRI system, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
    [CrossRef]

2009

2008

R. Wilhelm , B. Luong , A. Courteville , S. Estival , F. Gonte , and N. Schuhler , “Dual-wavelength low-coherence instantaneous phase-shifting interferometer to measure the shape of a segmented mirror with subnanometer precision,” Appl. Opt. 47, 5473–5491 (2008).
[CrossRef] [PubMed]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

J. Nelson and G. H. Sanders , “Status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio , “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

2007

L. Noethe and H.-M. Adorf , “Optical measurements of phase steps in segmented mirrors-fundamental precision limits,” J. Mod. Opt. 54, 3–31 (2007).
[CrossRef]

1998

1979

M. S. Bessel , “UBVRI photometry. II. The Cousins VRI system, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
[CrossRef]

Adorf, H.-M.

L. Noethe and H.-M. Adorf , “Optical measurements of phase steps in segmented mirrors-fundamental precision limits,” J. Mod. Opt. 54, 3–31 (2007).
[CrossRef]

Araujo, C.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Babak, S.

Bessel, M. S.

M. S. Bessel , “UBVRI photometry. II. The Cousins VRI system, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
[CrossRef]

Bourtembourg, R.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Brast, R.

F. Gonté , C. Dupuy , B. Luong , C. Frank , R. Brast , and S. Babak , “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Chanan, G. A.

Checa, S.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Courteville, A.

Dekens, F.

Derie, F.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Duhoux, P.

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Dupuy, C.

F. Gonté , C. Dupuy , B. Luong , C. Frank , R. Brast , and S. Babak , “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Estival, S.

Frank, C.

F. Gonté , C. Dupuy , B. Luong , C. Frank , R. Brast , and S. Babak , “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio , “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Gonte, F.

R. Wilhelm , B. Luong , A. Courteville , S. Estival , F. Gonte , and N. Schuhler , “Dual-wavelength low-coherence instantaneous phase-shifting interferometer to measure the shape of a segmented mirror with subnanometer precision,” Appl. Opt. 47, 5473–5491 (2008).
[CrossRef] [PubMed]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Gonté, F.

F. Gonté , C. Dupuy , B. Luong , C. Frank , R. Brast , and S. Babak , “Active hexagonally segmented mirror to investigate new optical phasing technologies for segmented telescopes,” Appl. Opt. 48, 6392–6399 (2009).
[CrossRef] [PubMed]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Karban, R.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Kirkmann, D.

Luong, B.

Mast, T.

Mazzoleni, R.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Nelson, J.

Noethe, L.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

L. Noethe and H.-M. Adorf , “Optical measurements of phase steps in segmented mirrors-fundamental precision limits,” J. Mod. Opt. 54, 3–31 (2007).
[CrossRef]

Ohara, C.

Pinna, E.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Sanders, G. H.

J. Nelson and G. H. Sanders , “Status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

Schuhler, N.

Scott, M.

Spyromilio, J.

R. Gilmozzi and J. Spyromilio , “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Surdej, I.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Troy, M.

Vigan, A.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Whilhlem, R.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Wilhelm, R.

Yaitskova, N.

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

L. Noethe and H.-M. Adorf , “Optical measurements of phase steps in segmented mirrors-fundamental precision limits,” J. Mod. Opt. 54, 3–31 (2007).
[CrossRef]

Proc. SPIE

J. Nelson and G. H. Sanders , “Status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

F. Gonté , C. Araujo , R. Bourtembourg , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , R. Mazzoleni , L. Noethe , I. Surdej , N. Yaitskova , R. Whilhlem , B. Luong , E. Pinna , S. Checa , and A. Vigan , “Active phasing experiment: preliminary results,” Proc. SPIE 7012, 70120Z(2008).
[CrossRef]

Proc. SPIE

R. Mazzoleni , F. Gonte , I. Surdej , C. Araujo , R. Brast , F. Derie , P. Duhoux , C. Dupuy , C. Frank , R. Karban , L. Noethe , and N. Yaitskova , “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio , “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Publ. Astron. Soc. Pac.

M. S. Bessel , “UBVRI photometry. II. The Cousins VRI system, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Design of the lenslet array of SHAPS. The dimensions in the drawing are given in millimeters.

Fig. 2
Fig. 2

Signals with wavefront piston steps of 0 (left) and λ / 2 (right) between adjacent segments, obtained in the laboratory without disturbance by the atmosphere.

Fig. 3
Fig. 3

Theoretical monochromatic SHAPS signals for different wavefront piston steps.

Fig. 4
Fig. 4

Typical distributions of segment piston values given in wavefront nanometers [Random 100 (left), Family 150 (right)] used for the measurement of the repeatability of the results for single borders and as starting points for the closed-loop corrections.

Fig. 5
Fig. 5

Reference measurement (left) and signal measurement for the Family 150 configuration (right) with a bandwidth of 100 nm centered at 650 nm .

Fig. 6
Fig. 6

Variation of the signal shape due to the seeing (solid curve, 0.6 ; dashed curve, 0.9 ) with wavefront piston steps of the order of 0, λ / 5 , λ / 3 , λ / 2 , 3 λ / 4 , 5 λ / 6 from top left to bottom right. The amplitude of the signal is normalized compared to a diffraction-limited signal, and the x axis is arbitrary.

Fig. 7
Fig. 7

Precision of the piston step measurement for a random position and for the flat configuration as functions of the star magnitude (central wavelength, 650 nm ; bandwidth, 100 nm ; exposure time, 20 s ; seeing between 0.7 and 1 ).

Fig. 8
Fig. 8

Variation of the coherence signal due to a modulation of the wavefront piston by step of 170 nm in wavefront from 3728 nm to + 3738 nm wavefront. The top diagram shows in green (the secondary y axis) the amplitude of the piston step and in blue the amplitude of the coherence signal (the primary y axis) for the corresponding piston step. The bottom diagram is a three-dimensional representation of the phasing signal. The X axis represents the step number (the piston step values are given for some steps); the Y axis represents the width of the piston signal (given with the coordinates ξ / ξ 0 as in Fig. 3). Finally, the color represents the normalized amplitude of the phasing signal (0 for black and 1 for white).

Fig. 9
Fig. 9

Correspondence between the expected visibility (smooth curve) and the square of the coherence factor during the phase-step modulation measurement (central wavelength, 700 nm ; bandwidth, 400 nm ).

Fig. 10
Fig. 10

Closed-loop piston correction of the ASM with SHAPS using stars of two different magnitudes (gain, 0.5; central wavelength, 650 nm ; bandwidth, 100 nm ; exposure time, 30 s ). The piston is given in wavefront nanometers RMS.

Fig. 11
Fig. 11

SHAPS correction accuracy versus magnitude. The measurements were taken under seeing conditions between 0.6 and 0.9.

Fig. 12
Fig. 12

Piston correction precision versus integration time. (central wavelength, 650 nm ; bandwidth, 100 nm ).

Fig. 13
Fig. 13

Piston correction accuracy versus seeing with integration times between 15 s and 30 s and bandwidth of 100 nm centered at 650 nm .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

p ( ξ , λ | θ ) = [ sin ( π ξ ξ 0 + 2 π θ λ ) sin ( 2 π θ λ ) ] 2 ( π ξ / ξ 0 ) 2 ,
p ( ξ , λ 1 , λ 2 | θ ) = λ 1 λ 2 p ( ξ , λ | θ ) d λ .
I ¯ s = ( I s D s B ) / max ( I s D s ) .
C ( θ ) = Δ ξ ξ 0 P m P m , incoh .
V ( θ ) = ( 2 · J 1 ( π θ / 2 Λ ) π θ / 2 Λ ) 2 .

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