Abstract

Designing large Schmidt cameras using the polynomial expansion may yield a not-perfect spherical aberration correction. We indicate an alternative method to design the corrector, whose integration in a software package is in progress. The shape of the corrector can be determined with a simple recursive method. The incidence point can also be calculated for any ray, as well as the corresponding unitary vector normal to the surface.

© 2010 Optical Society of America

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References

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  1. M. Born and E. Wolfe, “Image-forming instruments,” in Principles of Optics, M.Born and E.Wolfe, eds. (Cambridge U. Press, 1980), pp. 233–255.
  2. V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).
  3. A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).
  4. M. Berek, “Die Seidel’sche Theorie der Aberrationen dritten Ordnung,” in Grundlagen der praktischen Optik (Verlag von Walter de Gruyter, 1930), pp. 41–71.
  5. W. T. Welford, “Finite raytracing,” in Aberrations of Optical Systems, E.R.Pike, B.E. A.Saleh, and W.T.Welford, eds. (Adam Hilger, 1989), pp. 50–66.
  6. M. Herzberger and H. O. Hoadley, “The calculation of aspherical correcting surfaces,” J. Opt. Soc. Am. A 36, 334–340 (1946).
    [Crossref]
  7. A. Romoli, A. Zuccaro Marchi, F. Simonetti, and L. Gambicorti, “The optical design and engineering package OPTOLAB,” in Proceedings of the Joint Meeting Deutsche Gesellschaft für Angwandte Optik/Società Italiana di Oottica e Fotonica(European Space Agency–European Space Research and Technology Centre, 2009).
    [PubMed]

1946 (1)

M. Herzberger and H. O. Hoadley, “The calculation of aspherical correcting surfaces,” J. Opt. Soc. Am. A 36, 334–340 (1946).
[Crossref]

Berek, M.

M. Berek, “Die Seidel’sche Theorie der Aberrationen dritten Ordnung,” in Grundlagen der praktischen Optik (Verlag von Walter de Gruyter, 1930), pp. 41–71.

Born, M.

M. Born and E. Wolfe, “Image-forming instruments,” in Principles of Optics, M.Born and E.Wolfe, eds. (Cambridge U. Press, 1980), pp. 233–255.

Bratina, V.

V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).

Bursi, A.

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

Gallieni, D.

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

Gambicorti, L.

A. Romoli, A. Zuccaro Marchi, F. Simonetti, and L. Gambicorti, “The optical design and engineering package OPTOLAB,” in Proceedings of the Joint Meeting Deutsche Gesellschaft für Angwandte Optik/Società Italiana di Oottica e Fotonica(European Space Agency–European Space Research and Technology Centre, 2009).
[PubMed]

V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

Herzberger, M.

M. Herzberger and H. O. Hoadley, “The calculation of aspherical correcting surfaces,” J. Opt. Soc. Am. A 36, 334–340 (1946).
[Crossref]

Hoadley, H. O.

M. Herzberger and H. O. Hoadley, “The calculation of aspherical correcting surfaces,” J. Opt. Soc. Am. A 36, 334–340 (1946).
[Crossref]

Lisi, F.

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

Mazzinghi, P.

V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).

Olivier, M.

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

Romoli, A.

A. Romoli, A. Zuccaro Marchi, F. Simonetti, and L. Gambicorti, “The optical design and engineering package OPTOLAB,” in Proceedings of the Joint Meeting Deutsche Gesellschaft für Angwandte Optik/Società Italiana di Oottica e Fotonica(European Space Agency–European Space Research and Technology Centre, 2009).
[PubMed]

Salinari, P.

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

Simonetti, F.

V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

A. Romoli, A. Zuccaro Marchi, F. Simonetti, and L. Gambicorti, “The optical design and engineering package OPTOLAB,” in Proceedings of the Joint Meeting Deutsche Gesellschaft für Angwandte Optik/Società Italiana di Oottica e Fotonica(European Space Agency–European Space Research and Technology Centre, 2009).
[PubMed]

Welford, W. T.

W. T. Welford, “Finite raytracing,” in Aberrations of Optical Systems, E.R.Pike, B.E. A.Saleh, and W.T.Welford, eds. (Adam Hilger, 1989), pp. 50–66.

Wolfe, E.

M. Born and E. Wolfe, “Image-forming instruments,” in Principles of Optics, M.Born and E.Wolfe, eds. (Cambridge U. Press, 1980), pp. 233–255.

Zuccaro Marchi, A.

V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

A. Romoli, A. Zuccaro Marchi, F. Simonetti, and L. Gambicorti, “The optical design and engineering package OPTOLAB,” in Proceedings of the Joint Meeting Deutsche Gesellschaft für Angwandte Optik/Società Italiana di Oottica e Fotonica(European Space Agency–European Space Research and Technology Centre, 2009).
[PubMed]

J. Opt. Soc. Am. A (1)

M. Herzberger and H. O. Hoadley, “The calculation of aspherical correcting surfaces,” J. Opt. Soc. Am. A 36, 334–340 (1946).
[Crossref]

Other (6)

A. Romoli, A. Zuccaro Marchi, F. Simonetti, and L. Gambicorti, “The optical design and engineering package OPTOLAB,” in Proceedings of the Joint Meeting Deutsche Gesellschaft für Angwandte Optik/Società Italiana di Oottica e Fotonica(European Space Agency–European Space Research and Technology Centre, 2009).
[PubMed]

M. Born and E. Wolfe, “Image-forming instruments,” in Principles of Optics, M.Born and E.Wolfe, eds. (Cambridge U. Press, 1980), pp. 233–255.

V. Bratina, L. Gambicorti, P. Mazzinghi, F. Simonetti, and A. Zuccaro Marchi, “Large aperture and wide field of view space telescope for the detection of ultra high energy cosmic rays and neutrinos,” in Proceedings of the 6th International Conference on Space Optics, A.Wilson, ed. (European Space Agency–European Space Research and Technology Centre, 2006).

A. Zuccaro Marchi, L. Gambicorti, F. Simonetti, P. Salinari, F. Lisi, A. Bursi, M. Olivier, and D. Gallieni, “A technology demonstrator for development of ultra-lightweight, large aperture, deployable telescope for space applications,” in Proceedings of the 7th International Conference on Space Optics (European Space Agency–European Space Research and Technology Centre, 2008).

M. Berek, “Die Seidel’sche Theorie der Aberrationen dritten Ordnung,” in Grundlagen der praktischen Optik (Verlag von Walter de Gruyter, 1930), pp. 41–71.

W. T. Welford, “Finite raytracing,” in Aberrations of Optical Systems, E.R.Pike, B.E. A.Saleh, and W.T.Welford, eds. (Adam Hilger, 1989), pp. 50–66.

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Figures (4)

Fig. 1
Fig. 1

Complete and unambiguous characterization of the aspheric surface of the Schmidt corrector can be achieved by means of the sagitta function x ( y , z ) = x ( h ) .

Fig. 2
Fig. 2

Schmidt cameras. From top to bottom: refractive with external corrector, with internal corrector, and reflective.

Fig. 3
Fig. 3

Iterative method of determining Schmidt corrector shape. Bottom: the particular recursive approximation of the incidence points I i on the surface S.

Fig. 4
Fig. 4

Ray tracing of a skew ray r: the crossing point on the corrector is found in a recursive process.

Equations (21)

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h = y 2 + z 2 ,
x ( h ) = k o j = 1 m a 2 j 1 | h | 2 j 1 + k e i = 1 n a 2 i h 2 i ,
x ( h ) = i = 1 n z C i Z i ( h ) ,
s = s · M ,
Δ x = t n 1 n ,
OP ( h ) = OP ( 0 ) .
OP ( 0 ) = CV + VF = R + R 2 = 3 2 R ,
OP ( 0 ) = R 2 + D ,
x P = h P 2 c 1 + ( 1 h P 2 · c 2 ) 1 / 2 ,
Δ OP 1 = OP ( 0 ) OP 1 .
Δ t = Δ OP 1 / n ,
Δ t = Δ OP k / n ,
Δ r = ρ · Δ t .
Δ h = h h 1 .
Δ h = h 2 h 1 ,
k = Δ h Δ h .
δ = cos 1 ( r · r ) ,
φ = tan 1 ( n · sin δ n n · cos δ ) ,
φ = φ + δ ,
T = r r ,
r · n = cos φ r · n = cos φ n · T = 0 ,

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