Abstract

The convex reflective diffraction grating is an essential optical component that lends itself to various applications. In this work, we first outline the design principles of convex diffraction gratings from wavefront quality and efficiency perspectives. We then describe a unique fabrication method that allows for the machining of convex diffraction gratings with variable groove structure, which is extendable to rotationally non-symmetric convex diffraction grating substrates. Finally, we demonstrate two quantitative wavefront measurement methods and respective experimental validation.

© 2017 Optical Society of America

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References

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  1. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (CRC, 1997).
  2. E. G. Loewen, “Diffraction gratings for spectroscopy,” J. Phys. Educ. 3(12), 953 (1970).
  3. A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14(2), 142130 (1975).
    [Crossref]
  4. M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. patent US5880834 A (March 9, 1999).
  5. D. R. Lobb, “Theory of concentric designs for grating spectrometers,” Appl. Opt. 33(13), 2648–2658 (1994).
    [Crossref] [PubMed]
  6. P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. 39(13), 2210–2220 (2000).
    [Crossref] [PubMed]
  7. R. B. Lockwood, T. W. Cooley, R. M. Nadile, J. A. Gardner, P. S. Armstrong, A. M. Payton, T. M. Davis, and S. D. Straight, “Advanced responsive tactically effective military imaging spectrometer (ARTEMIS): system overview and objectives,” in Proc. SPIE 6661, S. S. Shen and P. E. Lewis, eds. (2007), p. 666102.
  8. X. Prieto-Blanco, C. Montero-Orille, H. González-Nuñez, M. D. Mouriz, E. L. Lago, and R. de la Fuente, “The Offner imaging spectrometer in quadrature,” Opt. Express 18(12), 12756–12769 (2010).
    [Crossref] [PubMed]
  9. J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).
  10. Q. Zhou and L.-F. Li, “[Design method of convex master gratings for replicating flat-field concave gratings],” Guangpuxue Yu Guangpu Fenxi 29(8), 2281–2285 (2009).
    [PubMed]
  11. E. G. Loewen, E. K. Popov, J. Hoose, and L. V. Tsonev, “Experimental study of local and integral efficiency behavior of a concave holographic diffraction grating,” J. Opt. Soc. Am. A 7(9), 1764–1769 (1990).
    [Crossref]
  12. P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37(31), 7200–7208 (1998).
    [Crossref] [PubMed]
  13. M. Neviere and W. R. Hunter, “Analysis of the changes in efficiency across the ruled area of a concave diffraction grating,” Appl. Opt. 19(12), 2059–2065 (1980).
    [Crossref] [PubMed]
  14. M. C. Hettrick, “Varied line-space gratings: past, present and future,” in 29th Annual Technical Symposium (International Society for Optics and Photonics, 1986), pp. 96–108.
  15. Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
    [Crossref]
  16. M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
    [Crossref]
  17. P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopic data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
    [Crossref]
  18. W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241–280 (1965).
    [Crossref]
  19. Page 317–321, CODE V® Version 10.7 Reference Manual (Synopsys, Inc.) (2016).
  20. R. Kingslake, “Who discovered Coddington’s equations?” Opt. Photonics News 5(8), 20–23 (1994).
    [Crossref]

2017 (1)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).

2012 (1)

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

2010 (1)

2009 (2)

Q. Zhou and L.-F. Li, “[Design method of convex master gratings for replicating flat-field concave gratings],” Guangpuxue Yu Guangpu Fenxi 29(8), 2281–2285 (2009).
[PubMed]

Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
[Crossref]

2000 (2)

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopic data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[Crossref]

P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. 39(13), 2210–2220 (2000).
[Crossref] [PubMed]

1998 (1)

1994 (2)

D. R. Lobb, “Theory of concentric designs for grating spectrometers,” Appl. Opt. 33(13), 2648–2658 (1994).
[Crossref] [PubMed]

R. Kingslake, “Who discovered Coddington’s equations?” Opt. Photonics News 5(8), 20–23 (1994).
[Crossref]

1990 (1)

1980 (1)

1975 (1)

A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14(2), 142130 (1975).
[Crossref]

1970 (1)

E. G. Loewen, “Diffraction gratings for spectroscopy,” J. Phys. Educ. 3(12), 953 (1970).

1965 (1)

W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241–280 (1965).
[Crossref]

Bauer, A.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).

Chrien, T. G.

Davies, M. A.

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

de la Fuente, R.

Dutterer, B. S.

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

González-Nuñez, H.

Green, R. O.

Hettrick, M. C.

M. C. Hettrick, “Varied line-space gratings: past, present and future,” in 29th Annual Technical Symposium (International Society for Optics and Photonics, 1986), pp. 96–108.

Hoose, J.

Hunter, W. R.

Ishida, T.

Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
[Crossref]

Kawai, T.

Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
[Crossref]

Kim, E. D.

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

Kingslake, R.

R. Kingslake, “Who discovered Coddington’s equations?” Opt. Photonics News 5(8), 20–23 (1994).
[Crossref]

Lago, E. L.

Li, L.-F.

Q. Zhou and L.-F. Li, “[Design method of convex master gratings for replicating flat-field concave gratings],” Guangpuxue Yu Guangpu Fenxi 29(8), 2281–2285 (2009).
[PubMed]

Lobb, D. R.

Loewen, E. G.

Maker, P. D.

McKerns, M. M.

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopic data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[Crossref]

Montero-Orille, C.

Mouriz, M. D.

Mouroulis, P.

Muller, R. E.

Neviere, M.

Offner, A.

A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14(2), 142130 (1975).
[Crossref]

Popov, E. K.

Prieto-Blanco, X.

Reimers, J.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).

Rolland, J. P.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).

Silny, J. F.

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

Suleski, T. J.

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

Takeuchi, Y.

Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
[Crossref]

Thompson, K. P.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).

Tsonev, L. V.

Welford, W. T.

W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241–280 (1965).
[Crossref]

Wilson, D. W.

Yoneyama, Y.

Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
[Crossref]

Zhou, Q.

Q. Zhou and L.-F. Li, “[Design method of convex master gratings for replicating flat-field concave gratings],” Guangpuxue Yu Guangpu Fenxi 29(8), 2281–2285 (2009).
[PubMed]

Appl. Opt. (4)

CIRP Ann. - Manuf. Technol. (1)

Y. Takeuchi, Y. Yoneyama, T. Ishida, and T. Kawai, “6-Axis control ultraprecision microgrooving on sculptured surfaces with non-rotational cutting tool,” CIRP Ann. - Manuf. Technol. 58(1), 53–56 (2009).
[Crossref]

Guangpuxue Yu Guangpu Fenxi (1)

Q. Zhou and L.-F. Li, “[Design method of convex master gratings for replicating flat-field concave gratings],” Guangpuxue Yu Guangpu Fenxi 29(8), 2281–2285 (2009).
[PubMed]

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

J. Phys. Educ. (1)

E. G. Loewen, “Diffraction gratings for spectroscopy,” J. Phys. Educ. 3(12), 953 (1970).

Light Sci. Appl. (1)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6, e17026 (2017).

Opt. Eng. (2)

A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14(2), 142130 (1975).
[Crossref]

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopic data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[Crossref]

Opt. Express (1)

Opt. Photonics News (1)

R. Kingslake, “Who discovered Coddington’s equations?” Opt. Photonics News 5(8), 20–23 (1994).
[Crossref]

Precis. Eng. (1)

M. A. Davies, B. S. Dutterer, T. J. Suleski, J. F. Silny, and E. D. Kim, “Diamond machining of diffraction gratings for imaging spectrometers,” Precis. Eng. 36(2), 334–338 (2012).
[Crossref]

Prog. Opt. (1)

W. T. Welford, “Aberration Theory of Gratings and Grating Mountings,” Prog. Opt. 4, 241–280 (1965).
[Crossref]

Other (5)

Page 317–321, CODE V® Version 10.7 Reference Manual (Synopsys, Inc.) (2016).

R. B. Lockwood, T. W. Cooley, R. M. Nadile, J. A. Gardner, P. S. Armstrong, A. M. Payton, T. M. Davis, and S. D. Straight, “Advanced responsive tactically effective military imaging spectrometer (ARTEMIS): system overview and objectives,” in Proc. SPIE 6661, S. S. Shen and P. E. Lewis, eds. (2007), p. 666102.

M. C. Hettrick, “Varied line-space gratings: past, present and future,” in 29th Annual Technical Symposium (International Society for Optics and Photonics, 1986), pp. 96–108.

M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. patent US5880834 A (March 9, 1999).

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (CRC, 1997).

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Figures (15)

Fig. 1
Fig. 1

Schematic diagrams of grating spacing designs in which the groove spacing is (a) equal-along-arc and (b) equal-along-projection. The cutout shows a linear approximation of each groove step when the groove spacing is much smaller than the grating clear aperture.

Fig. 2
Fig. 2

Spectral full field displays for (a) & (d) RMSWE, (b) & (e) Fringe Zernike Z5/6, and (c) & (f) Fringe Zernike Z7/8 of the spectrometer with an equal-along-projection grating (top row) comparing against that with an equal-along-arc grating (bottom row). Note that each point on the plot is scaled to the local wavelength reported along the X-axis and is reported in waves.

Fig. 3
Fig. 3

Same spectral full field display as shown in Fig. 2(f) but with the scale adjusted to show the coma dependence. This scale is 40x larger than before, indicating the drastic worsening in optical performance.

Fig. 4
Fig. 4

(a) Diffraction efficiencies in the + 1 and + 2 orders for equal-along-arc gratings with groove depths of 325 nm, 374 nm, and 425 nm respectively. (b) Diffraction efficiencies for an equal-along-arc grating with 325 nm groove depth for diffraction orders from −2 to + 10. The equal-along-projection grating with the same groove depth yields equivalent efficiencies.

Fig. 5
Fig. 5

Representative ruling behavior of (a) super-clean aluminum 6061, (b) naval brass C46400, and (c) electroless nickel with approximately 12% phosphorous content.

Fig. 6
Fig. 6

(a) Typical diamond turning configuration for spheres and aspheres. (b) Diamond turning adapted to enable linear tool marks. (c) Configuration developed for turning straight lined grooves on a curved substrate.

Fig. 7
Fig. 7

Grating machining arrangement in (a) three-dimensional view, (b) top view, and (c) front view.

Fig. 8
Fig. 8

Blazed grating tested on a cylinder with pitch of 300 lines/mm and groove depth of 400 nm. (a) Photograph of the grating. (b) A scanning white light interferometer measurement surface map. (c) A profile corresponding to the slice location indicated with a dash line in (b).

Fig. 9
Fig. 9

Representative SEM images of the final spherical grating showing (a) the top view and (b) an edge view.

Fig. 10
Fig. 10

(a) Schematic diagram of the direct wavefront test method modelled in optical design software and the expected interferograms for (b) the equal-along-projection grating and (c) the equal-along-arc grating.

Fig. 11
Fig. 11

The experimentally obtained interferograms for (a) the equal-along-projection grating and (c) the equal-along-arc grating. (b) and (d) are the two gratings’ diffracted term in the wavefront, with (b) showing ~λ/50 RMS flatness and (d) showing the residual cubic behavior. Note the change in amplitude scale between (b) and (d).

Fig. 12
Fig. 12

(a) Schematic diagram of the Offner type null metrology method with a right-handed coordinate system shown and (b) the expected null interferogram with a RMSWE of 0.04 waves.

Fig. 13
Fig. 13

Experimental setup for the interferometric null test coupled to a phase-shifting Fizeau interferometer. The solid red line shows the laser beam path.

Fig. 14
Fig. 14

Dependence of dominant aberrations introduced by (a)-(f) decenter misalignments of the convex grating in the x, y, and z dimensions, (g) object conjugate error, and (h) field bias error. Note the difference in amplitude scale between (a), (d), and the remaining plots.

Fig. 15
Fig. 15

(a) The expected null wavefront from design with scale adjusted to show variations across the wavefront. (b) One instance of the null wavefronts obtained in experiment, shown with measurement mean and standard deviation across 100 consecutive measurements grouped quasi-randomly into 5 sets. The measurements are consistent with design expectations.

Tables (4)

Tables Icon

Table 1 Convex grating specifications

Tables Icon

Table 2 Convex grating phase polynomial coefficients

Tables Icon

Table 3 Relevant mechanical properties of grating substrate material candidates

Tables Icon

Table 4 Null test setup specifications

Equations (17)

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

z(y)= R 2 y 2 .
d dy z(y)= y R 2 y 2 =tan(θ(y)).
d proj (y)= d groove cosθ(y)= d groove R 2 y 2 R .
dφ dy = mλ d proj (y) .
φ(y)= dφ dy dy = mRλ d groove arctan( y R 2 y 2 ).
φ(y)=m λ d groove y+m λ 6 d groove R 2 y 3 +m 3λ 40 d groove R 4 y 5 +O( y 7 ).
T= N g N p (Δ t g +Δ t r ),
θ L = sin 1 ( mλ 2d ).
W m = M m +mD.
{ M k = M +k M ±j M ±k .
M ±k = 1 2 ( W +k + W k ).
D= 1 2k ( W +k W k ).
n' S' n S = n'cosi'ncosi R S ,
n' cos 2 i' T' n cos 2 i T = n'cosi'ncosi R T ,
S'= R 2cos θ L 1 ,
T'= Rcos θ L 2cos θ L .
P V astig =| (Φ/2) 2 2T' (Φ/2) 2 2S' |=| (Φ/2) 2 R sin 2 θ L cos θ L |,

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