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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 9 — Sep. 1, 1999
  • pp: 2253–2268

Geometric aberration theory of double-element optical systems

Shin Masui and Takeshi Namioka  »View Author Affiliations


JOSA A, Vol. 16, Issue 9, pp. 2253-2268 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002253


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Abstract

A third-order aberration theory has been developed for a plane-symmetric double-element optical system that consists of an extended source, two ellipsoidal gratings, and an image plane. The gratings can have any of the groove patterns producible by means of currently available technologies. Analytic formulas of spot diagrams are derived for the system by analytically following a ray-tracing formalism. With these formulas coma, spherical aberration, astigmatism, field curvature, and distortion of the system are discussed in detail together with the focusing conditions. The spot-diagram formulas are critically evaluated in comparison with ray tracing. The result shows their capability in reproducing ray-traced spots with a high degree of accuracy.

© 1999 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(080.0080) Geometric optics : Geometric optics
(080.1010) Geometric optics : Aberrations (global)

Citation
Shin Masui and Takeshi Namioka, "Geometric aberration theory of double-element optical systems," J. Opt. Soc. Am. A 16, 2253-2268 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-9-2253


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References

  1. H. Petersen, “The plane grating and elliptical mirror: a new optical configuration for monochromators,” Opt. Commun. 40, 402–406 (1982).
  2. M. Domke, A. Puschmann, C. Xue, D. A. Shirley, G. Kaindl, and H. Petersen, “Spectral resolution in the soft-x-ray region up to 11, 000,” Synchrotron Radiat. News 3 (No. 5), 21–22 (1990).
  3. M. Koike and T. Namioka, “Optimization and evaluation of varied line spacing plane grating monochromators for third-generation synchrotron radiation sources,” J. Electron Spectrosc. Relat. Phenom. 80, 303–308 (1996).
  4. K. Ito, T. Namioka, Y. Morioka, T. Sasaki, H. Noda, K. Goto, T. Katayama, and M. Koike, “High-resolution VUV spectroscopic facility at the Photon Factory,” Appl. Opt. 25, 837–847 (1986).
  5. T. Namioka, H. Noda, K. Goto, and T. Katayama, “Design studies of mirror-grating systems for use with an electron storage ring source at the Photon Factory,” Nucl. Instrum. Methods Phys. Res. 208, 215–222 (1983).
  6. T. Harada and T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
  7. M. Koike, Y. Harada, and H. Noda, “New blazed holographic grating fabricated by using an aspherical recording with an ion-etching method,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena III, J. M. Lerner, ed., Proc. SPIE 815, 96–101 (1987).
  8. T. Namioka and M. Koike, “Aspheric wave-front recording optics for holographic gratings,” Appl. Opt. 34, 2180–2186 (1995). Misprints in Eqs. (23)–(25) should be corrected as follows. VC in the last line of Eqs. (23e) should read VD. KC in the third line of Eq. (23f) should read KD. Both a1 and a2 in the first and second of Eqs. (24) should read a. The minus signs in the third and fourth lines of Eq. (25b) should be plus signs. The term in the third line of Eq. (25c) should be multiplied by cos ηC.
  9. D. Bajuk and R. Kestner, “Fabrication and testing of EUVL optics,” in JSPE Proceedings on Soft X-Ray Optics: Technical Challenges, T. Namioka, H. Kinoshita, and K. Ito, eds. (Japan Society for Precision Engineering, Tokyo, 1997), pp. 325–335.
  10. C. T. Chen, “Concept and design procedure for cylindrical element monochromators for synchrotron radiation,” Nucl. Instrum. Methods Phys. Res. A 256, 595–604 (1987).
  11. For example, see T. Namioka and M. Seya, “Optical properties of a system consisting of a mirror and a grating,” Appl. Opt. 9, 459–464 (1970), and references therein.
  12. G. R. Rosendahl, “Contributions to the optics of mirror systems and gratings with oblique incidence. I. Ray tracing formulas for meridional plane,” J. Opt. Soc. Am. 51, 1–3 (1961); “Contributions to the optics of mirror systems and gratings with oblique incidence. II. A discussion of aberrations,” J. Opt. Soc. Am. 52, 408–411 (1962); “Contributions to the optics of mirror systems and gratings with oblique incidence. III. Some applications,” J. Opt. Soc. Am. JOSAAH 52, 412–415 (1962).
  13. M. P. Crisp, “Aberration of holographic toroidal grating systems,” Appl. Opt. 22, 1508–1518 (1983).
  14. M. P. Crisp, “X-ray spectrograph design,” Appl. Opt. 22, 1519–1529 (1983).
  15. T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994). The following misprints should be corrected. The numerator in the first line of Eq. (4) should read M−M+ mλ(∂n/∂w). λ in the last line of Eq. (21) should read λ0. The last terms in Eqs. (23) and (24) should read O(w4/R4). The second line of Eq. (26e) should read +2 tan2 Φ)−[(3/2)F300F020+F120F200]sec β0 tan Φ. The last term in the fifth line of Eq. (26e) should read +2 tan2 Φ. The term 3/r0 in the last line of Eq. (26g) should read (1/r0)(3−2 tan β0 tan Φ). A bracket [ ] is missing at the end of Eq. (35). O(w3/R) in the last term of Eq. (36) should read O(w3/R2).
  16. C. H. F. Velzel, “A general theory of the aberrations of diffraction gratings and gratinglike optical instruments,” J. Opt. Soc. Am. A 66, 346–353 (1976).
  17. H. G. Beutler, “The theory of the concave grating,” J. Opt. Soc. Am. 35, 311–350 (1945).

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