Abstract

The position and dimensions of the circle of least confusion (CLC) on axis for a lensless Schmidt camera telescope operating at F 0.82 are calculated. The camera is to be used in the fluorescence detector of the Pierre Auger Observatory. Our analysis was developed for an aspherical mirror for any on-axis position of the point light source. Our technique uses the intersection of the marginal ray from one side of the aperture with the caustic produced by the intermediate rays from the opposite side of the aperture to locate the CLC.

© 1998 Optical Society of America

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References

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  1. H. Rutten, M. Van Venrooij, Telescope Optics, 2nd ed. (Willmann Bell, Richmond, Va., 1989), pp. 71–78.
  2. A. Cordero, E. Cantoral, J. Castro, A. Fernández, R. Pastrana, “Proposal for the optical system of the fluorescence detector of the Pierre Auger project,” Internal report, Auger Collaboration GAP-96-039 ( http://www-td-auger.fnal.gov:82/) .
  3. W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990).
  4. D. G. Burkhard, D. L. Shealy, “Formula for the density of tangent rays over a caustic surface,” Appl. Opt. 21, 3299–3306 (1982).
    [Crossref] [PubMed]
  5. T. B. Anderson, “Optical aberration functions: computation of caustic surfaces and illuminance in symmetrical systems,” Appl. Opt. 20, 3723–3728 (1981).
    [Crossref]
  6. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1929), pp. 120–125.
  7. D. Malacara, “Geometrical Ronchi test of aspherical mirrors,” Appl. Opt. 4, 1371–1374 (1965).
    [Crossref]
  8. V. A. Kudnyavtsev, V. P. Demidovich, A Brief Course of Higher Mathematics (Mir, Moscow, 1984), pp. 422–424.
  9. D. Malacara, “An optical surface and its characteristics,” in Optical Shop testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 743–753.
  10. O. N. Stavroudis, The Optics of Rays, Wavefront and Caustics (Academic, New York, 1972), pp. 79–179.
  11. Optical design program for IBM and PC Compatibles Ver. 4.7 Sigma P.C. (Kidger Optics, Ltd., Crowborough, East Sussex, UK, 1996).

1982 (1)

1981 (1)

1965 (1)

Anderson, T. B.

Burkhard, D. G.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1929), pp. 120–125.

Demidovich, V. P.

V. A. Kudnyavtsev, V. P. Demidovich, A Brief Course of Higher Mathematics (Mir, Moscow, 1984), pp. 422–424.

Kudnyavtsev, V. A.

V. A. Kudnyavtsev, V. P. Demidovich, A Brief Course of Higher Mathematics (Mir, Moscow, 1984), pp. 422–424.

Malacara, D.

D. Malacara, “Geometrical Ronchi test of aspherical mirrors,” Appl. Opt. 4, 1371–1374 (1965).
[Crossref]

D. Malacara, “An optical surface and its characteristics,” in Optical Shop testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 743–753.

Rutten, H.

H. Rutten, M. Van Venrooij, Telescope Optics, 2nd ed. (Willmann Bell, Richmond, Va., 1989), pp. 71–78.

Shealy, D. L.

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990).

Stavroudis, O. N.

O. N. Stavroudis, The Optics of Rays, Wavefront and Caustics (Academic, New York, 1972), pp. 79–179.

Van Venrooij, M.

H. Rutten, M. Van Venrooij, Telescope Optics, 2nd ed. (Willmann Bell, Richmond, Va., 1989), pp. 71–78.

Appl. Opt. (3)

Other (8)

V. A. Kudnyavtsev, V. P. Demidovich, A Brief Course of Higher Mathematics (Mir, Moscow, 1984), pp. 422–424.

D. Malacara, “An optical surface and its characteristics,” in Optical Shop testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 743–753.

O. N. Stavroudis, The Optics of Rays, Wavefront and Caustics (Academic, New York, 1972), pp. 79–179.

Optical design program for IBM and PC Compatibles Ver. 4.7 Sigma P.C. (Kidger Optics, Ltd., Crowborough, East Sussex, UK, 1996).

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1929), pp. 120–125.

H. Rutten, M. Van Venrooij, Telescope Optics, 2nd ed. (Willmann Bell, Richmond, Va., 1989), pp. 71–78.

A. Cordero, E. Cantoral, J. Castro, A. Fernández, R. Pastrana, “Proposal for the optical system of the fluorescence detector of the Pierre Auger project,” Internal report, Auger Collaboration GAP-96-039 ( http://www-td-auger.fnal.gov:82/) .

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990).

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Figures (5)

Fig. 1
Fig. 1

Schmidt camera without a correcting plate.

Fig. 2
Fig. 2

Transverse aberration parameters of an aspherical reflecting surface.

Fig. 3
Fig. 3

Caustic of the parabolic reflector surface. The position of the object is 4833 mm from the reflector of the vertex. The radius of curvature is 2415 mm, and the diameter is 1450 mm.

Fig. 4
Fig. 4

Transverse aberration (T cau, T mar) of the marginal ray versus L cau.

Fig. 5
Fig. 5

Spot size for the Schmidt camera evaluated in the text. Calculations were made for semifields of view of 0, 5, 10, and 15 deg.

Tables (1)

Tables Icon

Table 1 Parameters of the Lensless Schmidt Camera Design

Equations (22)

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T = S + L - z S 1 - d z d S 2 - 2 d z d S l - z l - z 1 - d z d S 2 + 2 d z d S   S ,
S = x 2 + y 2 ,
f = S 1 - d z d S 2 - 2   d z d S l - z l - z 1 - d z d S 2 + 2   d z d S   S
T = S + L - z f .
d T d S = 0 .
1 - z - L d f d S - d z d S   f = 0 ,
d f d S = 1 + d z d S 2 l - z + S   d z d S 1 + d z d S 2 - 2   d 2 z d S 2 l - z 2 + S 2 l - z 1 - d z d S 2 + 2 S   d z d S 2
d z d S = cS 1 - k + 1 c 2 S 2 1 / 2 .
L = z   d f d S + d z d S   f - 1 d f d S .
T = S + f d f d S d z d S   f - 1 .
z = cS 2 1 + 1 - K + 1 C 2 S 2 1 / 2 + A 2 S 2 + A 4 S 4 + A 6 S 6 ,
f = - 2 d z d S 1 - d z d S 2 ,
d f d S = - 2   d 2 z d S 2 1 - d z d S 2 1 - d z d S 2 2 .
L = 1 + 2 z   d 2 z d S 2 - d z d S 2 2   d 2 z d S 2 ,
T = S - d z d S d 2 z d S 2 .
d 2 z d S 2 = c 1 - k + 1 c 2 S 2 3 / 2 .
T = k + 1 c 2 S 3 ,
L = cS 2 1 + 1 - k + 1 c 2 S 2 1 / 2 + 1 - k + 2 c 2 S 2 2 c × 1 - k + 1 c 2 S 2 1 / 2 .
S = T k + 1 c 2 1 / 3 .
L = T 2 / 3 / k + 1 2 / 3 c 1 / 3 1 + 1 - k + 1 1 / 3 c 2 / 3 T 2 / 3 1 / 2 + 1 - k + 2 c 2 / 3 T 1 / 3 k + 1 2 / 3 2 c × 1 - k + 1 1 / 3 c 2 / 3 T 2 / 3 1 / 2 .
T mar = S mar - z mar f mar + f mar L cau .
r det = r mirror - Pos.bst.focus ,

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