Abstract

We propose and demonstrate a self-referencing alignment technique to conveniently enlarge fabricated grating area. The latent image gratings are used as the reference objects to align (adjust and lock) the attitude and position of the substrate relative to the exposure beams between and during consecutive exposures. The adjustment system and the fringe-locking system are combined into the exposure system, eliminating the drift errors between them and making the whole system low-cost and compact. For the fabricated 1 × 4 mosaics of 50 × (30 + 30 + 30 + 30) mm2 area and 1 × 2 mosaics of 90 × (80 + 80) mm2 area, the typical peak-valley −1st-order wavefront errors measured by a 100-mm-diameter interferometer are not more than 0.06 λ and 0.09 λ, respectively.

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2010 (2)

D. Clery, “Power. Laser fusion energy poised to ignite,” Science 328(5980), 808–809 (2010).
[CrossRef] [PubMed]

L. Shi and L. Zeng, “Fabrication of optical mosaic gratings by consecutive holographic exposures employing a latent-fringe based alignment technique,” Proc. SPIE 7848, 78480S, 78480S-9 (2010).
[CrossRef]

2009 (1)

2008 (2)

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

2007 (2)

C. T. Black, “Block copolymers: nanowire arrays build themselves,” Nat. Nanotechnol. 2(8), 464–465 (2007).
[CrossRef]

K. Kawamura, T. Otsuka, M. Hirano, T. Kamiya, and H. Hosono, “Development of latent images due to transient free carrier electrons by femtosecond laser pulses and its application to grating shape trimming,” Appl. Phys. Lett. 90(1), 011107 (2007).
[CrossRef]

2006 (1)

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

2005 (1)

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

1998 (1)

H. Sugimura and N. Nakagiri, “Force microscopy imaging of photopatterned organosilane monolayers: application to probe alignment in AFM patterning following photolithography,” Appl. Phys., A Mater. Sci. Process. 66(7), S427–S430 (1998).
[CrossRef]

1997 (1)

B. R. Napier and N. J. Phillips, “Use of real time latent images to write long holographic diffraction gratings in photoresist,” Proc. SPIE 3011, 182–193 (1997).
[CrossRef]

1996 (1)

X. Chen, S. H. Zaidi, S. R. J. Brueck, and D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14(5), 3339–3349 (1996).
[CrossRef]

Albrow, M. D.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Barnes, S. I.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Black, C. T.

C. T. Black, “Block copolymers: nanowire arrays build themselves,” Nat. Nanotechnol. 2(8), 464–465 (2007).
[CrossRef]

Blanford, C. F.

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

Bolten, J.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Bramall, D.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Brink, J.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Brueck, S. R. J.

X. Chen, S. H. Zaidi, S. R. J. Brueck, and D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14(5), 3339–3349 (1996).
[CrossRef]

Buckley, D. A. H.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Chen, X.

X. Chen, S. H. Zaidi, S. R. J. Brueck, and D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14(5), 3339–3349 (1996).
[CrossRef]

Chen, Y.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Clark, P.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Clausnitzer, T.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Clery, D.

D. Clery, “Power. Laser fusion energy poised to ignite,” Science 328(5980), 808–809 (2010).
[CrossRef] [PubMed]

Cottrell, P. L.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Denning, R. G.

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

Deshpande, A. J.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Devine, D. J.

X. Chen, S. H. Zaidi, S. R. J. Brueck, and D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14(5), 3339–3349 (1996).
[CrossRef]

Frost, N.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Graham, G.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Hirano, M.

K. Kawamura, T. Otsuka, M. Hirano, T. Kamiya, and H. Hosono, “Development of latent images due to transient free carrier electrons by femtosecond laser pulses and its application to grating shape trimming,” Appl. Phys. Lett. 90(1), 011107 (2007).
[CrossRef]

Hosono, H.

K. Kawamura, T. Otsuka, M. Hirano, T. Kamiya, and H. Hosono, “Development of latent images due to transient free carrier electrons by femtosecond laser pulses and its application to grating shape trimming,” Appl. Phys. Lett. 90(1), 011107 (2007).
[CrossRef]

Jeong, J.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Jones, D.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Kamiya, T.

K. Kawamura, T. Otsuka, M. Hirano, T. Kamiya, and H. Hosono, “Development of latent images due to transient free carrier electrons by femtosecond laser pulses and its application to grating shape trimming,” Appl. Phys. Lett. 90(1), 011107 (2007).
[CrossRef]

Kawamura, K.

K. Kawamura, T. Otsuka, M. Hirano, T. Kamiya, and H. Hosono, “Development of latent images due to transient free carrier electrons by femtosecond laser pulses and its application to grating shape trimming,” Appl. Phys. Lett. 90(1), 011107 (2007).
[CrossRef]

Kershaw, G.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Kley, E.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Koo, N.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Kurz, H.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Lee, E.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Li, L.

Luke, P.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Mueller, G.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Nakagiri, N.

H. Sugimura and N. Nakagiri, “Force microscopy imaging of photopatterned organosilane monolayers: application to probe alignment in AFM patterning following photolithography,” Appl. Phys., A Mater. Sci. Process. 66(7), S427–S430 (1998).
[CrossRef]

Napier, B. R.

B. R. Napier and N. J. Phillips, “Use of real time latent images to write long holographic diffraction gratings in photoresist,” Proc. SPIE 3011, 182–193 (1997).
[CrossRef]

Otsuka, T.

K. Kawamura, T. Otsuka, M. Hirano, T. Kamiya, and H. Hosono, “Development of latent images due to transient free carrier electrons by femtosecond laser pulses and its application to grating shape trimming,” Appl. Phys. Lett. 90(1), 011107 (2007).
[CrossRef]

Otto, M.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Phillips, N. J.

B. R. Napier and N. J. Phillips, “Use of real time latent images to write long holographic diffraction gratings in photoresist,” Proc. SPIE 3011, 182–193 (1997).
[CrossRef]

Plachetka, U.

N. Koo, U. Plachetka, M. Otto, J. Bolten, J. Jeong, E. Lee, and H. Kurz, “The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography,” Nanotechnology 19(22), 225304 (2008).
[CrossRef] [PubMed]

Quetschke, V.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Reitze, D. H.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Ritchie, R.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Roche, O. M.

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

Schmoll, J.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Scrimgeour, J.

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

Sharp, D. N.

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

Sharples, R.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Shi, L.

L. Shi and L. Zeng, “Fabrication of optical mosaic gratings by consecutive holographic exposures employing a latent-fringe based alignment technique,” Proc. SPIE 7848, 78480S, 78480S-9 (2010).
[CrossRef]

L. Shi, L. Zeng, and L. Li, “Fabrication of optical mosaic gratings with phase and attitude adjustments employing latent fringes and a red-wavelength dual-beam interferometer,” Opt. Express 17(24), 21530–21543 (2009).
[CrossRef] [PubMed]

Sugimura, H.

H. Sugimura and N. Nakagiri, “Force microscopy imaging of photopatterned organosilane monolayers: application to probe alignment in AFM patterning following photolithography,” Appl. Phys., A Mater. Sci. Process. 66(7), S427–S430 (1998).
[CrossRef]

Tanner, D. B.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Tünnermann, A.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95(1), 013901 (2005).
[CrossRef] [PubMed]

Turberfield, A. J.

J. Scrimgeour, D. N. Sharp, C. F. Blanford, O. M. Roche, R. G. Denning, and A. J. Turberfield, “Three-dimensional optical lithography for photonic microstructures,” Adv. Mater. (Deerfield Beach Fla.) 18(12), 1557–1560 (2006).
[CrossRef]

Tyas, L.

S. I. Barnes, P. L. Cottrell, M. D. Albrow, N. Frost, G. Graham, G. Kershaw, R. Ritchie, D. Jones, R. Sharples, D. Bramall, J. Schmoll, P. Luke, P. Clark, L. Tyas, D. A. H. Buckley, and J. Brink, “The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” Proc. SPIE 7014, 70140K, 70140K-12 (2008).
[CrossRef]

Whiting, B. F.

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Figures (4)

Fig. 1
Fig. 1

Mosaic system: holographic exposure, and alignment of attitude and phase. (a) Oblique view. (b) Side view of the capture of L fringes.

Fig. 2
Fig. 2

Mosaic steps, including projections of relevant elements in the directions of beams B1 and B2 onto the grating substrate G and the L fringes. (a) Step I, the first exposure. (b) Step II, the recording of the reference L1 II fringes. (c) The recorded reference L1 II fringes. (d) Step III, the second exposure with the real-time L1 III fringes locked to the reference L1 II fringes. (e) Step IV, after moving G for monitoring the L1 IV and L2 IV fringes simultaneously, the recording of the reference L2 IV fringes with the real-time L1 IV fringes locked to the reference L1 II fringes. (f) The recorded reference L2 IV fringes. (g) Step V, after moving G, the third exposure with the real-time L2 V fringes locked to the reference L2 IV fringes. (h) Completed exposure areas and their groove position. In half image pairs of L fringes the arrows indicate the borders between the reference and real-time fringes. On the surface of G both the exposure fringes and the latent grating are partly plotted, to clearly show the phase difference between them.

Fig. 3
Fig. 3

The −1st-order interferograms and wavefronts of (a) a 1 × 2 mosaic grating and (b) a 1 × 4 mosaic grating. The peak-valley and root-mean-square errors in (a) are 0.087 λ and 0.018 λ, respectively; the ones in (b) are 0.060 λ and 0.012 λ, respectively.

Fig. 4
Fig. 4

The SEM images of one grating’s (a) ordinary area and (b) area for generating L fringes, and another grating’s (c) one ordinary area and (d) another ordinary area.

Tables (2)

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Table 1 The Phase Changes According to the Mosaic Steps

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Table 2 The Groove Data from the SEM Images of Ordinary Areas and Areas for Generating L Fringes

Equations (6)

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P Ei j 0 ,
P Li k = P Ei k + C ,
| mod ( Δ x ' d + 1 2 , 1 ) 1 2 | = 1 e 3 ( Δ p 1 ) 2 + 2 ( Δ p 3 ) 2 ,
| Δ θ z | = d h ' e 3 ( Δ p 1 ) 2 + 3 ( Δ p 2 ) 2 ,
δ P = 0 .5 e 3 ( Δ p 1 ) 2 + 2 ( Δ p 3 ) 2  λ,
δ V = 0 .5 e 3 ( Δ p 1 ) 2 + 3 ( Δ p 2 ) 2  λ,

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