Abstract

By distorting the plane grating into a concave cylinder, astigmatism found normally in the Czerny–Turner spectrometer can effectively be eliminated. The level of distortion would require metal grating blanks to avoid shearing stresses. The stigmatic principle has recently been demonstrated on a low resolution, uv illuminator patterned after the Czerny–Turner spectrograph. For the illuminator, it was desired that the image integrity of the circular entrance aperture be maintained at the focal plane. There is good reason to believe that medium resolution (~1 Å) instruments employing this stigmatic principle would maintain their resolution.

© 1966 Optical Society of America

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References

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  1. S. C. Miller, R. Mercure, W. A. Rense, Astrophys. J. 124, 580 (1956).
    [CrossRef]
  2. J. D. Purcell, R. Tousey, “Production of Toroidal Mirrors by Mechanical Bending”; J. D. Purcell, “Use of a Bent Grating in a Spectrograph for Lyman Alpha Solar Disc Photography,” papers presented at the 42nd Annual Optical Society Meeting, 1957.
  3. W. A. Rense, T. Violett, J. Opt. Soc. Am. 49, 139 (1959).
    [CrossRef]
  4. T. Namioka, J. Opt. Soc. Am. 51, 4 (1961).
    [CrossRef]
  5. A. H. Pfund, J. Opt. Soc. Am. 14, 337 (1927).
    [CrossRef]
  6. G. R. Rosendhal, J. Opt. Soc. Am. 52, 414 (1962).
  7. A. B. Shafer, L. R. Megill, L. Droppleman, J. Opt. Soc. Am. 54, 884 (1964).
    [CrossRef]
  8. H. N. Olsen, in Temperature, Its Measurement and Control in Science and Industry (Reinhold Publishing Corp., New York, 1962), Vol. 3, p. 593.
  9. G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Prentice Hall, Inc., Englewood Cliffs, N. J., 1959), p. 565.
  10. Refer to any optical text, for example: R. S. Longhurst, Geometrical and Physical Optics (Longmans, Green and Co., New York, 1957), p. 335.
  11. Recall that for flattening the focal plane, the grating is placed at approximately 0.84 R/2 from the line connecting the vertices of the two mirrors. See N. Sassa, Sci. Light (Tokyo) 10, 53 (1961).
  12. R. J. Roark, Formulas for Stress and Strain (McGraw–Hill Book Co., Inc., New York, 1954), p. 102.

1964 (1)

A. B. Shafer, L. R. Megill, L. Droppleman, J. Opt. Soc. Am. 54, 884 (1964).
[CrossRef]

1962 (1)

G. R. Rosendhal, J. Opt. Soc. Am. 52, 414 (1962).

1961 (2)

Recall that for flattening the focal plane, the grating is placed at approximately 0.84 R/2 from the line connecting the vertices of the two mirrors. See N. Sassa, Sci. Light (Tokyo) 10, 53 (1961).

T. Namioka, J. Opt. Soc. Am. 51, 4 (1961).
[CrossRef]

1959 (1)

1956 (1)

S. C. Miller, R. Mercure, W. A. Rense, Astrophys. J. 124, 580 (1956).
[CrossRef]

1927 (1)

Droppleman, L.

A. B. Shafer, L. R. Megill, L. Droppleman, J. Opt. Soc. Am. 54, 884 (1964).
[CrossRef]

Harrison, G. R.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Prentice Hall, Inc., Englewood Cliffs, N. J., 1959), p. 565.

Longhurst, R. S.

Refer to any optical text, for example: R. S. Longhurst, Geometrical and Physical Optics (Longmans, Green and Co., New York, 1957), p. 335.

Loofbourow, J. R.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Prentice Hall, Inc., Englewood Cliffs, N. J., 1959), p. 565.

Lord, R. C.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Prentice Hall, Inc., Englewood Cliffs, N. J., 1959), p. 565.

Megill, L. R.

A. B. Shafer, L. R. Megill, L. Droppleman, J. Opt. Soc. Am. 54, 884 (1964).
[CrossRef]

Mercure, R.

S. C. Miller, R. Mercure, W. A. Rense, Astrophys. J. 124, 580 (1956).
[CrossRef]

Miller, S. C.

S. C. Miller, R. Mercure, W. A. Rense, Astrophys. J. 124, 580 (1956).
[CrossRef]

Namioka, T.

Olsen, H. N.

H. N. Olsen, in Temperature, Its Measurement and Control in Science and Industry (Reinhold Publishing Corp., New York, 1962), Vol. 3, p. 593.

Pfund, A. H.

Purcell, J. D.

J. D. Purcell, R. Tousey, “Production of Toroidal Mirrors by Mechanical Bending”; J. D. Purcell, “Use of a Bent Grating in a Spectrograph for Lyman Alpha Solar Disc Photography,” papers presented at the 42nd Annual Optical Society Meeting, 1957.

Rense, W. A.

W. A. Rense, T. Violett, J. Opt. Soc. Am. 49, 139 (1959).
[CrossRef]

S. C. Miller, R. Mercure, W. A. Rense, Astrophys. J. 124, 580 (1956).
[CrossRef]

Roark, R. J.

R. J. Roark, Formulas for Stress and Strain (McGraw–Hill Book Co., Inc., New York, 1954), p. 102.

Rosendhal, G. R.

G. R. Rosendhal, J. Opt. Soc. Am. 52, 414 (1962).

Sassa, N.

Recall that for flattening the focal plane, the grating is placed at approximately 0.84 R/2 from the line connecting the vertices of the two mirrors. See N. Sassa, Sci. Light (Tokyo) 10, 53 (1961).

Shafer, A. B.

A. B. Shafer, L. R. Megill, L. Droppleman, J. Opt. Soc. Am. 54, 884 (1964).
[CrossRef]

Tousey, R.

J. D. Purcell, R. Tousey, “Production of Toroidal Mirrors by Mechanical Bending”; J. D. Purcell, “Use of a Bent Grating in a Spectrograph for Lyman Alpha Solar Disc Photography,” papers presented at the 42nd Annual Optical Society Meeting, 1957.

Violett, T.

Astrophys. J. (1)

S. C. Miller, R. Mercure, W. A. Rense, Astrophys. J. 124, 580 (1956).
[CrossRef]

J. Opt. Soc. Am. (5)

W. A. Rense, T. Violett, J. Opt. Soc. Am. 49, 139 (1959).
[CrossRef]

T. Namioka, J. Opt. Soc. Am. 51, 4 (1961).
[CrossRef]

A. H. Pfund, J. Opt. Soc. Am. 14, 337 (1927).
[CrossRef]

G. R. Rosendhal, J. Opt. Soc. Am. 52, 414 (1962).

A. B. Shafer, L. R. Megill, L. Droppleman, J. Opt. Soc. Am. 54, 884 (1964).
[CrossRef]

Sci. Light (Tokyo) (1)

Recall that for flattening the focal plane, the grating is placed at approximately 0.84 R/2 from the line connecting the vertices of the two mirrors. See N. Sassa, Sci. Light (Tokyo) 10, 53 (1961).

Other (5)

R. J. Roark, Formulas for Stress and Strain (McGraw–Hill Book Co., Inc., New York, 1954), p. 102.

J. D. Purcell, R. Tousey, “Production of Toroidal Mirrors by Mechanical Bending”; J. D. Purcell, “Use of a Bent Grating in a Spectrograph for Lyman Alpha Solar Disc Photography,” papers presented at the 42nd Annual Optical Society Meeting, 1957.

H. N. Olsen, in Temperature, Its Measurement and Control in Science and Industry (Reinhold Publishing Corp., New York, 1962), Vol. 3, p. 593.

G. R. Harrison, R. C. Lord, J. R. Loofbourow, Practical Spectroscopy (Prentice Hall, Inc., Englewood Cliffs, N. J., 1959), p. 565.

Refer to any optical text, for example: R. S. Longhurst, Geometrical and Physical Optics (Longmans, Green and Co., New York, 1957), p. 335.

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Figures (3)

Fig. 1
Fig. 1

Astigmatism for a spherical surface. cosξ/2 = SS/SS′ = ST/ST′ [see Eqs. (1) and (2)].

Fig. 2
Fig. 2

Over-all view of the apparatus.

Fig. 3
Fig. 3

(a) Astigmatism, no correction; (b) astigmatism, partial correction; (c) astigmatism, near complete correction.

Equations (6)

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1 / S T + 1 / S = ( 2 / R cos ξ / 2 )
1 / S s + 1 / S = ( 2 cos ξ / 2 / R ) .
S s - S T = R / 2 sin ξ / 2 tan ξ / 2.
Δ L T / ( S S - S T ) = D / S S .
Δ L T = D R / 2 sin ξ / 2 tan ξ / 2 R / 2 cos ξ / 2 = D tan 2 ξ / 2.
Δ L T R / 2 # [ tan 2 ξ 1 / 2 + tan 2 ξ 2 / 2 ] .

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