Abstract

We present a new device, the diffractive optics calibrator (DOC), for measuring etching variations of computer-generated holograms (CGHs). The intensity distribution of the far-field diffraction pattern is captured and fitted to a parametric model to obtain local etching parameters such as the duty cycle, etching depth, and grating period. The sensitivity of each etching parameter is analyzed, and design choices are provided. For the wavefront created by the CGH, the DOC is capable of measuring variations in these parameters that cause 1 nm peak-to-valley phase errors. System performance is verified by measurements from a phase shift Fizeau interferometer. This device will be used primarily for quality control of the CGHs. The measurement results can be used to evaluate the fabrication performance and guide future design. DOC is also capable of generating an induced phase error map for calibration. Such calibration is essential for measuring free-form aspheric surfaces with 1 nm root-mean-square accuracy.

© 2014 Optical Society of America

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References

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    [CrossRef]
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2013 (2)

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

W. Cai, P. Zhou, C. Zhao, and J. H. Burge, “The diffractive optics calibrator: design and construction,” Opt. Eng. 52, 124101 (2013).
[CrossRef]

2007 (2)

2006 (1)

2003 (1)

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

1980 (1)

1978 (1)

Burge, J. H.

Cai, W.

W. Cai, P. Zhou, C. Zhao, and J. H. Burge, “The diffractive optics calibrator: design and construction,” Opt. Eng. 52, 124101 (2013).
[CrossRef]

Cao, Z.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Chang, Y. C.

Cherkashin, V. V.

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

Evans, M. S.

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

Farmiga, N. O.

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grimard, D.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

He, G.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Hirsh, J. I.

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

Kleinknecht, H. P.

Knop, K.

Konchenko, A. S.

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

Korolkov, V. P.

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed., Vol. 59 of Wiley Series in Pure and Applied Optics (Wiley, 2007).

Marciante, J. R.

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

Meier, H.

Mironnikov, N. G.

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

Najafi, K.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Owen, K. J.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Peterson, R. L.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Poleshchuk, A. G.

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

Ta, H. T.

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

Van Der Elzen, B.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Yan, J.

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

Zhao, C.

W. Cai, P. Zhou, C. Zhao, and J. H. Burge, “The diffractive optics calibrator: design and construction,” Opt. Eng. 52, 124101 (2013).
[CrossRef]

Zhou, P.

Appl. Opt (1)

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt 42, 3234–3240 (2003).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

V. P. Korolkov, A. S. Konchenko, V. V. Cherkashin, N. G. Mironnikov, and A. G. Poleshchuk, “Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry,” Opt. Eng. 52, 091722 (2013).
[CrossRef]

W. Cai, P. Zhou, C. Zhao, and J. H. Burge, “The diffractive optics calibrator: design and construction,” Opt. Eng. 52, 124101 (2013).
[CrossRef]

Opt. Express (1)

Other (3)

D. Malacara, Optical Shop Testing, 3rd ed., Vol. 59 of Wiley Series in Pure and Applied Optics (Wiley, 2007).

Z. Cao, B. Van Der Elzen, K. J. Owen, J. Yan, G. He, R. L. Peterson, D. Grimard, and K. Najafi, “DRIE of fused silica,” in Proceedings of the 26th IEEE International Conference on Micro Electro Mechanical Systems (2013), pp. 361–364.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (18)

Fig. 1.
Fig. 1.

System layout for the diffractive optics calibrator (DOC).

Fig. 2.
Fig. 2.

Binary, linear grating profile: t is the etching depth; S is the grating period; b/S is the duty cycle; c/S is the sidewall slope ratio; and A0 and A1 are the amplitudes of the output wavefront from the unetched and etched areas of the grating, respectively. ϕ is the phase step between the two areas.

Fig. 3.
Fig. 3.

Diffraction efficiency as a function of duty cycle for order 0 to 3 with 0.35λ phase depth.

Fig. 4.
Fig. 4.

Duty cycle variations that cause 1 nm P-V wavefront phase error between zero and nonzero diffraction orders.

Fig. 5.
Fig. 5.

Phase depth variations that cause 1 nm P-V wavefront phase error between zero and nonzero diffraction orders.

Fig. 6.
Fig. 6.

Diffraction efficiency variations due to 1% duty cycle deviation. (Nominal phase depth is 0.35λ. Diffraction orders m=0, 1, 2, 3 are included.)

Fig. 7.
Fig. 7.

Diffraction efficiency variations due to 0.01λ phase depth deviation. (Nominal phase depth is 0.35λ. Diffraction orders m=0, 1, 2, 3 are included.)

Fig. 8.
Fig. 8.

Monte Carlo simulation of the duty cycle fitting uncertainty (phase depth is 0.35λ and fitting includes ±7 orders).

Fig. 9.
Fig. 9.

Induced phase error versus nominal duty cycle value (0.5% duty cycle variation and 5 nm etching depth variation).

Fig. 10.
Fig. 10.

(a) Schematic layout of the DOC, (b) DOC hardware with LabVIEW user interface, and (c) block diagram of the DOC measurement postprocessing in MATLAB.

Fig. 11.
Fig. 11.

Duty cycle measured values comparison between Veeco and the DOC.

Fig. 12.
Fig. 12.

Etching depth measured values comparison between Veeco and the DOC.

Fig. 13.
Fig. 13.

Interferometric test of a pattern with three sets of gratings with duty cycle variations from 41% to 53%. The induced phase error was measured at zero order (solid line). ±1st orders were used to calibrate the grating substrate error (dotted lines).

Fig. 14.
Fig. 14.

Zero-order measurement comparison between interferometer and DOC. (a) Induced phase offset map comparison and (b) average phase offset profile comparison.

Fig. 15.
Fig. 15.

(a) CGH fringe pattern representation (fringe interval=300 waves). (b) DOC scanning route (3 mm resolution in both directions).

Fig. 16.
Fig. 16.

2D maps for etching parameters. (a) Duty cycle map (values in %), (b) etching depth map (values in nm), and (c) fringe spacing map (values in μm).

Fig. 17.
Fig. 17.

The etch bias is calculated as the product of the fringe spacing and the duty cycle offset in percentage. (a) Etch bias map (values in μm), (b) etch bias histogram.

Fig. 18.
Fig. 18.

Etching-variation-induced phase error maps. (a) Duty-cycle-variation-induced phase error map, (b) etching-depth-variation-induced phase error map, (c) fitting uncertainty of duty-cycle-variation-induced phase error estimated Monte Carlo simulation, and (d) fitting uncertainty of etching-depth-variation-induced phase error estimated Monte Carlo simulation.

Tables (3)

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Table 1. Summary of Equations for Parametric Model Analysis

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Table 2. Specifications of a Set of Gratings with Different Duty Cycles

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Table 3. DOC Measurement Results of the Etching Parameters

Equations (1)

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u(x)=A0+(A1eiϕA0)·rect(xb)*1crect(xc)*1Scomb(xS),

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