Abstract

Multi-Zonal computer generated holograms (MZ-CGHs) in combination with interferometric wavefront measurements are perfectly suited as optical adjustment tools - especially if the demands on the alignment accuracy are very high. After reviewing the basic idea for alignment with MZ-CGHs, we derive the analytic relation between the interferometrically observed tilt and power values and the associated lens placement errors, including estimates of the applied approximations. This analysis yields the parameters determining the principle sensitivity of the method. Subsequently, the achievable accuracy of large 6″ MZ-CGHs in practical application is tested with a series of different optical measurements which confirm the technical feasibility. The productive use of the technique will be presented in part II of the paper for different examples in the framework of the Euclid space telescope.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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  3. S. H. Lee, “Computer generated holography: an introduction,” Appl. Opt. 26(20), 4350 (1987).
    [Crossref] [PubMed]
  4. J. W. Goodman, Introduction to Fourier Optics, 2nd Edition (McGraw-Hill, New York, 1988), Chap. 7.3 and 9.
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    [Crossref]
  6. J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
    [Crossref]
  7. A. G. Poleshchuk, V. P. Korolkov, R. K. Nasyrov, and J.-M. Asfour, “Computer generated holograms: fabrication and application for precision optical testing,” Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 710206 (2008).
    [Crossref]
  8. H. Gross, ed., Handbook of Optical Systems (2012), Volume 5, Chap. 53.4.2.
  9. R. Laureijs and 216 co-authors, “Euclid definition study report (Red Book)”, ESA/SRE(2011)12 1 (2011).
  10. http://sci.esa.int/euclid/ ; http://www.euclid-ec.org/ .
  11. A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999).
    [Crossref] [PubMed]
  12. J.- M. Asfour, C. Bodendorf, A. Bode, F. Grupp, R. Bender, F. Weidner, A. G. Poleshchuk, R. K. Nasyrov, “Diffractive optics for precision alignment in the framework of the EUCLID space telescope mission”, Proc. SPIE 10401, Astronomical Optics: Design, Manufacture, and Test of Space and Ground Systems, 104010V (2017).
  13. F. Grupp, E. Prieto, N. Geis, A. Bode, C. Bodendorf, A. Costille, R. Katterloher, D. Penka, R. Bender, “Final tolerancing approach and the value of short-cutting tolerances by measurement”, Proc. SPIE 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, 99042M (2016).
  14. C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).
  15. T. Maciaszek, A. Ealet, K. Jahnke, E. Prieto, R. Barbier, Y. Mellier et al., “Euclid Near Infrared Spectrometer and Photometer instrument concept and first test results obtained for different breadboards models at the end of phase C,” Proc. SPIE 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, 99040T (29 July 2016).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  19. V. N. Mahajan, Aberration Theory Made Simple, Second Edition (SPIE Press Book TT93, 2011).
  20. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  21. F. Grupp, J. Kaminski, C. Bodendorf, N. Geis, R. Katterloher, and R. Bender, “Euclid’s near infrared optical assembly warm testing and a new approach combining CGH Interferometry and tactile precision measurement”, Proc. SPIE, Optics + Photonics (2019), submitted.
  22. C. Bodendorf, N. Geis, F. U. Grupp, J. Kaminski, R. Katterlohera, and R. Bender, “Testing the near-infrared optical assembly of the space telescope ‘Euclid ’”. Proc. SPIE, Optics + Photonics (2019), submitted.
  23. C. Bodendorf, A. Bode, N. Geis, D. Penka, and F. Grupp, R. Bender „Performance measurement of high precision optical assemblies for cosmological observations: comparison of different approaches”. Proc. SPIE 10009, Third European Seminar on Precision Optics Manufacturing, 100090F (2016).

2016 (1)

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

2010 (1)

2008 (1)

A. G. Poleshchuk, V. P. Korolkov, R. K. Nasyrov, and J.-M. Asfour, “Computer generated holograms: fabrication and application for precision optical testing,” Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 710206 (2008).
[Crossref]

2006 (1)

1999 (1)

1987 (1)

1981 (1)

K. M. Leung, S. M. Arnold, and J. C. Lindquist, “Using e-beam written computer-generated holograms to test deep aspheric wavefronts,” in Contemporary Methods of Optical Fabrication, SPIE Vol. 306, 161–167 (1981).

1980 (1)

J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
[Crossref]

1976 (1)

1967 (1)

Aftab, M.

Arnold, S. M.

K. M. Leung, S. M. Arnold, and J. C. Lindquist, “Using e-beam written computer-generated holograms to test deep aspheric wavefronts,” in Contemporary Methods of Optical Fabrication, SPIE Vol. 306, 161–167 (1981).

Asfour, J. M.

Asfour, J.-M.

A. G. Poleshchuk, V. P. Korolkov, R. K. Nasyrov, and J.-M. Asfour, “Computer generated holograms: fabrication and application for precision optical testing,” Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 710206 (2008).
[Crossref]

Bender, R.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Bode, A.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Burow, R.

J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
[Crossref]

Cherkashin, V. V.

Churin, E. G.

Dubowy, M.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Gal, C.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Gawlik, K.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Grupp, F.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Grzanna, J.

J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
[Crossref]

Gubbini, E.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Kharissov, A. A.

Kiryanov, A. V.

Kiryanov, V. P.

Kokarev, S. A.

Korolkov, V. P.

A. G. Poleshchuk, V. P. Korolkov, R. K. Nasyrov, and J.-M. Asfour, “Computer generated holograms: fabrication and application for precision optical testing,” Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 710206 (2008).
[Crossref]

A. G. Poleshchuk, E. G. Churin, V. P. Koronkevich, V. P. Korolkov, A. A. Kharissov, V. V. Cherkashin, V. P. Kiryanov, A. V. Kiryanov, S. A. Kokarev, and A. G. Verhoglyad, “Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure,” Appl. Opt. 38(8), 1295–1301 (1999).
[Crossref] [PubMed]

Koronkevich, V. P.

Kuisl, A.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Lee, S. H.

Leung, K. M.

K. M. Leung, S. M. Arnold, and J. C. Lindquist, “Using e-beam written computer-generated holograms to test deep aspheric wavefronts,” in Contemporary Methods of Optical Fabrication, SPIE Vol. 306, 161–167 (1981).

Lindquist, J. C.

K. M. Leung, S. M. Arnold, and J. C. Lindquist, “Using e-beam written computer-generated holograms to test deep aspheric wavefronts,” in Contemporary Methods of Optical Fabrication, SPIE Vol. 306, 161–167 (1981).

Lohmann, A. W.

Mahajan, V. N.

Mecsaci, A.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Meister, A.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Mottaghibonab, A.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Nasyrov, R. K.

A. G. Poleshchuk, V. P. Korolkov, R. K. Nasyrov, and J.-M. Asfour, “Computer generated holograms: fabrication and application for precision optical testing,” Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 710206 (2008).
[Crossref]

Noll, R. J.

Paris, D. P.

Poleshchuk, A. G.

Schwider, J.

J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
[Crossref]

Spolaczyk, R.

J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
[Crossref]

Thiele, H.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Verhoglyad, A. G.

Wimmer, C.

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Appl. Opt. (4)

in Contemporary Methods of Optical Fabrication, SPIE Vol. (1)

K. M. Leung, S. M. Arnold, and J. C. Lindquist, “Using e-beam written computer-generated holograms to test deep aspheric wavefronts,” in Contemporary Methods of Optical Fabrication, SPIE Vol. 306, 161–167 (1981).

J. Opt. Soc. Am. (1)

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

Opt. Acta (Lond.) (1)

J. Schwider, J. Grzanna, R. Spolaczyk, and R. Burow, “Testing Aspherics in Reflected Light Using Blazed Synthetic Holograms,” Opt. Acta (Lond.) 27(5), 683 (1980).
[Crossref]

Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology (1)

A. G. Poleshchuk, V. P. Korolkov, R. K. Nasyrov, and J.-M. Asfour, “Computer generated holograms: fabrication and application for precision optical testing,” Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 710206 (2008).
[Crossref]

Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation (1)

C. Gal, H. Thiele, E. Gubbini, A. Mecsaci, A. Kuisl, A. Meister, A. Mottaghibonab, K. Gawlik, M. Dubowy, F. Grupp, A. Bode, C. Wimmer, and R. Bender, “Optical performance analysis and test results of the EUCLID near-infrared spectro-photometer,” Proc. SPIE 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II, 991216 (2016).

Other (13)

T. Maciaszek, A. Ealet, K. Jahnke, E. Prieto, R. Barbier, Y. Mellier et al., “Euclid Near Infrared Spectrometer and Photometer instrument concept and first test results obtained for different breadboards models at the end of phase C,” Proc. SPIE 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, 99040T (29 July 2016).

D. C. O'Shea, T. J. Suleski, A. D. Kathman, D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE Press Book TT62, 2003).

J. W. Goodman, Introduction to Fourier Optics, 2nd Edition (McGraw-Hill, New York, 1988), Chap. 7.3 and 9.

A. Vijayakumar; S. Bhattacharya, Design and Fabrication of Diffractive Optical Elements with MATLAB, Spie Press Book TT109 (2017).
[Crossref]

H. Gross, ed., Handbook of Optical Systems (2012), Volume 5, Chap. 53.4.2.

R. Laureijs and 216 co-authors, “Euclid definition study report (Red Book)”, ESA/SRE(2011)12 1 (2011).

http://sci.esa.int/euclid/ ; http://www.euclid-ec.org/ .

J.- M. Asfour, C. Bodendorf, A. Bode, F. Grupp, R. Bender, F. Weidner, A. G. Poleshchuk, R. K. Nasyrov, “Diffractive optics for precision alignment in the framework of the EUCLID space telescope mission”, Proc. SPIE 10401, Astronomical Optics: Design, Manufacture, and Test of Space and Ground Systems, 104010V (2017).

F. Grupp, E. Prieto, N. Geis, A. Bode, C. Bodendorf, A. Costille, R. Katterloher, D. Penka, R. Bender, “Final tolerancing approach and the value of short-cutting tolerances by measurement”, Proc. SPIE 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, 99042M (2016).

V. N. Mahajan, Aberration Theory Made Simple, Second Edition (SPIE Press Book TT93, 2011).

F. Grupp, J. Kaminski, C. Bodendorf, N. Geis, R. Katterloher, and R. Bender, “Euclid’s near infrared optical assembly warm testing and a new approach combining CGH Interferometry and tactile precision measurement”, Proc. SPIE, Optics + Photonics (2019), submitted.

C. Bodendorf, N. Geis, F. U. Grupp, J. Kaminski, R. Katterlohera, and R. Bender, “Testing the near-infrared optical assembly of the space telescope ‘Euclid ’”. Proc. SPIE, Optics + Photonics (2019), submitted.

C. Bodendorf, A. Bode, N. Geis, D. Penka, and F. Grupp, R. Bender „Performance measurement of high precision optical assemblies for cosmological observations: comparison of different approaches”. Proc. SPIE 10009, Third European Seminar on Precision Optics Manufacturing, 100090F (2016).

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Figures (12)

Fig. 1
Fig. 1 Sketch of a Multi-Zonal-CGH (front- and side view), designed to align three lenses of Euclid’s near infrared spectrometer and photometer instrument [13,15]. (a): Each zone generates a spherical wavefront with its unique focal length. This way, a series of spots along a straight line arises. (b): The spherical lens surfaces at their ideal positions, as defined by the MZ-CGH.
Fig. 2
Fig. 2 A MZ-CGH is mounted on the bayonet lock of a Fizeau interferometer in front of an air-bearing linear stage. In the right picture, the CGH is illuminated with a white light source for visualization of the different zones. It acts like a diffraction grating, decomposing the light into its constituent colours.
Fig. 3
Fig. 3 Transition from a blazed (a) to a binary (b) phase CGH.
Fig. 4
Fig. 4 (a) A spherical wavefront (red) is reflected at a spherical lens surface (blue). Both spheres differ in radius by ΔR. (b): Cutout enlargement of (a). The reflected rays pick up an additional optical path of 2δ, depending on ΔR.
Fig. 5
Fig. 5 (a) Relative deviations between exact and approximate defocus wavefront-error in percent according to Eq. (11) as function of NA for three different values of ΔR/R. (b): The same for the Tilt wavefront-error for five different values of ΔS/R.
Fig. 6
Fig. 6 A spherical wavefront (red) is reflected at a spherical lens surface (blue). The centres of the spheres are shifted with respect to one another by Δs in the x direction.
Fig. 7
Fig. 7 Sketch of the MZ-CGH verification setup. The measurement camera can alternatively be replaced by a reference sphere.
Fig. 8
Fig. 8 The 5 spots arising from the first diffraction orders of the CGH shown in Fig. 1. The spatial range of the plots is 80 µm. The intensity scale is logarithmic over 4 orders of magnitude. The upper row shows the camera measurements, while the lower row shows the ideal theoretical results. The shapes of the spots reflect the complexity of the associated zones on the CGH.
Fig. 9
Fig. 9 'Clouds’ of spot positions. Each dot denotes the spatial coordinates of the centroid for a measured light spot. The scatter plots arise due to tiny remaining vibrations or air turbulences for a series of 50 successive measurements.
Fig. 10
Fig. 10 Measurement of the straightness of the focal spot positions of a MZ-CGH. Note the tiny range in the lateral direction!
Fig. 11
Fig. 11 Zernike defocus coefficient as function of the z-coordinate in a small range around the best focus, defined as c4 = 0. The intercepts of the linear fits with the z-axis mark the deviation from the ideal positions.
Fig. 12
Fig. 12 Zernike tilt coefficient c3 as function of a lateral shift in a small range around c3 = 0.

Tables (1)

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Table 1 Spot locations and NA

Equations (13)

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

x 2 + ( R z 1 ) 2 = R 2 .
z 1 ( x ) = R { 1 1 ( x / R ) 2 }
z 2 ( x ) = ( R + Δ R ) { 1 1 ( x R + Δ R ) 2 } .
δ ( x ) = cos ( α ) [ z 1 ( x ) z 2 ( x ) ] = cos { arc sin ( x / R ) } [ z 1 ( x ) z 2 ( x ) ]
δ ( x ) = 1 ( x / R ) 2 [ z 1 ( x ) z 2 ( x ) ] .
δ ( x ) = x 2 2 ( 1 R 1 R + Δ R ) .
δ ( x ) = 1 2 ( x / R ) 2 Δ R
Δ W ( ρ ) = N A 2 Δ R ρ 2 .
Δ W ( ρ ) = 1 2 N A 2 Δ R ( 2 ρ 2 1 ) .
c 4 F r g = 1 2 N A 2 Δ R and c 4 S t d = 1 3 c 4 F r g = 1 2 3 N A 2 Δ R .
E r r = 100 ( δ 0 δ A p p r ) / δ 0 .
Δ W ( ρ ) = Δ s 2 R + 2 N A ρ sin ( θ ) Δ s
c 3 F r g = 2 N A Δ s and c 3 S t d = N A Δ s

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