Abstract

We report novel approaches to the design of halftone masks for analog lithography. The approaches are derived from interferometric phase contrast. In a first step we show that the interferometric phase-contrast method with detour holograms can be reduced into a single binary mask. In a second step we introduce the interferometric phase-contrast method by interference of the object wavefront with the conjugate object wavefront. This method also allows for a design of a halftone mask. To use kinoform holograms as halftone phase masks, we show in a third step the combination of the zeroth-order phase-contrast technique with the interferometric phase-contrast method.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. D. R. Purdy, “Fabrication of complex micro-optic components using photo-sculpting through halftone transmission masks,” Pure Appl. Opt. 3, 167-175 (1994).
    [CrossRef]
  8. K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008 (1)

2007 (2)

2006 (1)

S. Osten, S. Krüger, and A. Steinhoff, “Spatial light modulators based on reflective microdisplays,” Tech. Mess. 73, 149-156 (2006).
[CrossRef]

2005 (1)

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, “Refractive mirco-optics fabrication with a 1-D binary phase grating mask applicable to MOEMS processing,” J. Microlith. Microfab. Microsyst. 4, 041603 (2005).
[CrossRef]

2004 (1)

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

2001 (1)

2000 (1)

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

1999 (1)

1997 (2)

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 36, 8427-8434 (1997).
[CrossRef]

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
[CrossRef]

1995 (3)

1994 (3)

U. Krackhardt, N. Streibl, and J. Schwider, “Fabrication errors of computer-generated multilevel phase holograms,” Optik (Stuttgart) 95, 137-146 (1994).

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

D. R. Purdy, “Fabrication of complex micro-optic components using photo-sculpting through halftone transmission masks,” Pure Appl. Opt. 3, 167-175 (1994).
[CrossRef]

1991 (2)

J. A. Cox, B. Fritz, and T. Werner, “Process error limitations on binary optics performance,” Proc. SPIE 1555, 80-88(1991).
[CrossRef]

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabrication binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. 9, 3117-3121 (1991).
[CrossRef]

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Brown, J.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, “Refractive mirco-optics fabrication with a 1-D binary phase grating mask applicable to MOEMS processing,” J. Microlith. Microfab. Microsyst. 4, 041603 (2005).
[CrossRef]

Campos, J.

Cirino, G. A.

J. C. Pizolato, Jr., G. A. Cirino, C. Goncalves, and L. G. Neto, “Zeroth-order phase-contrast technique,” Appl. Opt. 46, 7604-7613 (2007).
[CrossRef] [PubMed]

C. Goncalves, J. C. Pizolato, Jr., G. A. Cirino, and L. G. Neto, “White light computer-generated element based on halftoning technique,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (Optical Society of America, 2007).
[PubMed]

Cottrell, D. M.

Cox, J. A.

J. A. Cox, B. Fritz, and T. Werner, “Process error limitations on binary optics performance,” Proc. SPIE 1555, 80-88(1991).
[CrossRef]

Cui, Z.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Däschner, W.

Davis, J. A.

Du, J.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Fritz, B.

J. A. Cox, B. Fritz, and T. Werner, “Process error limitations on binary optics performance,” Proc. SPIE 1555, 80-88(1991).
[CrossRef]

Fritzsche, M.

Gao, F.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Ghodssi, R.

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

Glückstad, J.

Goncalves, C.

J. C. Pizolato, Jr., G. A. Cirino, C. Goncalves, and L. G. Neto, “Zeroth-order phase-contrast technique,” Appl. Opt. 46, 7604-7613 (2007).
[CrossRef] [PubMed]

C. Goncalves, J. C. Pizolato, Jr., G. A. Cirino, and L. G. Neto, “White light computer-generated element based on halftoning technique,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (Optical Society of America, 2007).
[PubMed]

Goodman, J. W.

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

Gross, H.

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems (Wiley, 2005).

Guo, Y.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Henke, W.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, “Simulation and experimental study of gray-tone lithography for the fabrication of arbitrarily shaped surfaces,” in Micro Electro Mechanical Syytems, MEMS '94, (IEEE, 1994), pp. 205-210.

Heyer, R.

Hockel, H.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, “Refractive mirco-optics fabrication with a 1-D binary phase grating mask applicable to MOEMS processing,” J. Microlith. Microfab. Microsyst. 4, 041603 (2005).
[CrossRef]

Holz, M.

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabrication binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. 9, 3117-3121 (1991).
[CrossRef]

Hoppe, W.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, “Simulation and experimental study of gray-tone lithography for the fabrication of arbitrarily shaped surfaces,” in Micro Electro Mechanical Syytems, MEMS '94, (IEEE, 1994), pp. 205-210.

Jahns, J.

S. Sinzinger and J. Jahns, Microoptics (Wiley, 2003).
[CrossRef]

Johnson, E. G.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, “Refractive mirco-optics fabrication with a 1-D binary phase grating mask applicable to MOEMS processing,” J. Microlith. Microfab. Microsyst. 4, 041603 (2005).
[CrossRef]

Jürss, M.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
[CrossRef]

Knowlden, R. E.

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabrication binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. 9, 3117-3121 (1991).
[CrossRef]

Krackhardt, U.

U. Krackhardt, N. Streibl, and J. Schwider, “Fabrication errors of computer-generated multilevel phase holograms,” Optik (Stuttgart) 95, 137-146 (1994).

Krizmanic, J.

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

Krüger, S.

S. Osten, S. Krüger, and A. Steinhoff, “Spatial light modulators based on reflective microdisplays,” Tech. Mess. 73, 149-156 (2006).
[CrossRef]

S. Krüger, S. Osten, and G. Wernicke, “Reflective spatial light modulators improve digital holography,” http://www.holoeye.com/publications1.html.

Larsson, M.

Lee, S. H.

Levi, U.

Loewen, E. G.

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

Lohmann, A. W.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 1992).

Marom, E.

Mayor, J. M.

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

Medeiros, S. S.

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabrication binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. 9, 3117-3121 (1991).
[CrossRef]

Mendlovic, D.

Mogensen, P. C.

Moreno, I.

Morgan, B.

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

Neto, L. G.

J. C. Pizolato, Jr., G. A. Cirino, C. Goncalves, and L. G. Neto, “Zeroth-order phase-contrast technique,” Appl. Opt. 46, 7604-7613 (2007).
[CrossRef] [PubMed]

C. Goncalves, J. C. Pizolato, Jr., G. A. Cirino, and L. G. Neto, “White light computer-generated element based on halftoning technique,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (Optical Society of America, 2007).
[PubMed]

Oppliger, Y.

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

O'Shea, D. C.

Osten, S.

S. Osten, S. Krüger, and A. Steinhoff, “Spatial light modulators based on reflective microdisplays,” Tech. Mess. 73, 149-156 (2006).
[CrossRef]

S. Krüger, S. Osten, and G. Wernicke, “Reflective spatial light modulators improve digital holography,” http://www.holoeye.com/publications1.html.

Pizolato, J. C.

J. C. Pizolato, Jr., G. A. Cirino, C. Goncalves, and L. G. Neto, “Zeroth-order phase-contrast technique,” Appl. Opt. 46, 7604-7613 (2007).
[CrossRef] [PubMed]

C. Goncalves, J. C. Pizolato, Jr., G. A. Cirino, and L. G. Neto, “White light computer-generated element based on halftoning technique,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (Optical Society of America, 2007).
[PubMed]

Popov, E.

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

Purdy, D. R.

D. R. Purdy, “Fabrication of complex micro-optic components using photo-sculpting through halftone transmission masks,” Pure Appl. Opt. 3, 167-175 (1994).
[CrossRef]

Quenzer, H. J.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
[CrossRef]

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, “Simulation and experimental study of gray-tone lithography for the fabrication of arbitrarily shaped surfaces,” in Micro Electro Mechanical Syytems, MEMS '94, (IEEE, 1994), pp. 205-210.

Rastogi, P. K.

P. K. Rastogi, Holographic Interferometry (Springer, 1994).

Regnault, P.

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

Reimer, K.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
[CrossRef]

Rockward, W. S.

Schwider, J.

U. Krackhardt, N. Streibl, and J. Schwider, “Fabrication errors of computer-generated multilevel phase holograms,” Optik (Stuttgart) 95, 137-146 (1994).

Shabtay, G.

Singer, W.

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems (Wiley, 2005).

Sinzinger, S.

Sixt, P.

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

Staudt-Fischbach, P.

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, “Simulation and experimental study of gray-tone lithography for the fabrication of arbitrarily shaped surfaces,” in Micro Electro Mechanical Syytems, MEMS '94, (IEEE, 1994), pp. 205-210.

Stauffer, J. M.

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

Steinhoff, A.

S. Osten, S. Krüger, and A. Steinhoff, “Spatial light modulators based on reflective microdisplays,” Tech. Mess. 73, 149-156 (2006).
[CrossRef]

Stern, M. B.

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabrication binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. 9, 3117-3121 (1991).
[CrossRef]

Stoebenau, S.

Streibl, N.

U. Krackhardt, N. Streibl, and J. Schwider, “Fabrication errors of computer-generated multilevel phase holograms,” Optik (Stuttgart) 95, 137-146 (1994).

Su, J.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Sung, J.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, “Refractive mirco-optics fabrication with a 1-D binary phase grating mask applicable to MOEMS processing,” J. Microlith. Microfab. Microsyst. 4, 041603 (2005).
[CrossRef]

Teschke, M.

Totzeck, M.

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems (Wiley, 2005).

Voirin, G.

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

Wagner, B.

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
[CrossRef]

W. Henke, W. Hoppe, H. J. Quenzer, P. Staudt-Fischbach, and B. Wagner, “Simulation and experimental study of gray-tone lithography for the fabrication of arbitrarily shaped surfaces,” in Micro Electro Mechanical Syytems, MEMS '94, (IEEE, 1994), pp. 205-210.

Waits, C. M.

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

Werner, T.

J. A. Cox, B. Fritz, and T. Werner, “Process error limitations on binary optics performance,” Proc. SPIE 1555, 80-88(1991).
[CrossRef]

Wernicke, G.

S. Krüger, S. Osten, and G. Wernicke, “Reflective spatial light modulators improve digital holography,” http://www.holoeye.com/publications1.html.

Yao, J.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Yzuel, M. J.

Zalevsky, Z.

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Zhang, Y.

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Appl. Opt. (8)

J. Microelectromech. Syst. (1)

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113-120 (2004).
[CrossRef]

J. Microlith. Microfab. Microsyst. (1)

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, “Refractive mirco-optics fabrication with a 1-D binary phase grating mask applicable to MOEMS processing,” J. Microlith. Microfab. Microsyst. 4, 041603 (2005).
[CrossRef]

J. Vac. Sci. Technol. (1)

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabrication binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. 9, 3117-3121 (1991).
[CrossRef]

Microelectron. Eng. (2)

Y. Oppliger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449-454 (1994).
[CrossRef]

J. Yao, J. Su, J. Du, Y. Zhang, F. Gao, F. Gao, Y. Guo, and Z. Cui, “Coding gray-tone mask for refractive microlens fabrication,” Microelectron. Eng. 53, 531-534 (2000).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

U. Krackhardt, N. Streibl, and J. Schwider, “Fabrication errors of computer-generated multilevel phase holograms,” Optik (Stuttgart) 95, 137-146 (1994).

Proc. SPIE (2)

J. A. Cox, B. Fritz, and T. Werner, “Process error limitations on binary optics performance,” Proc. SPIE 1555, 80-88(1991).
[CrossRef]

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279-288 (1997).
[CrossRef]

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[CrossRef] [PubMed]

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[PubMed]

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Figures (18)

Fig. 1
Fig. 1

Interferometric phase contrast setup using a detour-phase hologram as the transmission.

Fig. 2
Fig. 2

Interferometric phase contrast setup using a diffraction grating and detour hologram.

Fig. 3
Fig. 3

Merging of the diffraction grating and the adapted detour-phase hologram: (a) splitting diffraction grating for δ 2 = π ; (b) section of the detour-phase hologram for the adapted phase distribution, (d); (c) physical merging of (a) and (b) to a halftone mask; (d) adapted phase distribution visualized by a gray-level image; and (e) desired intensity distribution (Fresnel lens) in the observation plane.

Fig. 4
Fig. 4

Lohmann type I detour-phase hologram: (a) graphic coding of phase and amplitude by position and width of the transmissive area (white stripe) and (b) intensity curve by variation of W in comparison with the desired intensity curve.

Fig. 5
Fig. 5

Setup for the reconstruction of the desired intensity pattern with the halftone mask type I in transmission: (a) film mask and (b) intensity pattern in the observation plane.

Fig. 6
Fig. 6

Setup for the reconstruction of the desired intensity pattern with halftone mask type I as the phase object: (a) intensity pattern of the + 1 st diffraction order and (b) intensity pattern of the zeroth diffraction order.

Fig. 7
Fig. 7

Interferometric phase contrast setup using the conjugate object wavefront.

Fig. 8
Fig. 8

Phase disturbance ϕ ( x , y ) to intensity mapping as a function of the axial phase difference ( δ 2 δ 1 ).

Fig. 9
Fig. 9

Experimental results from the setup shown in Fig. 7: (a) phase distribution, which was transformed into a detour-phase hologram; (b) intensity pattern in the observation plane for ( δ 2 δ 1 ) = 0 ; and (c) intensity pattern in the observation plane for ( δ 2 δ 1 ) = π .

Fig. 10
Fig. 10

Interferometric phase contrast setup using two detour-phase holograms.

Fig. 11
Fig. 11

Merging of the detour-phase hologram with the inverse detour-phase hologram: (a) detour-phase hologram for the adapted phase distribution shown in (d); (b) detour-phase hologram for the inverse adapted phase distribution shown in (e); (c) halftone mask type II; (e) intensity pattern achieved by the mask (c); desired intensity pattern in the observation plane.

Fig. 12
Fig. 12

Halftone mask type II: (a) desired intensity pattern, which was transformed into the halftone mask and addressed to the LCoS and (b) intensity pattern in the observation plane.

Fig. 13
Fig. 13

Lohmann type II detour-phase hologram: (a) graphic coding, (b) detour-phase hologram with the invert phase, and (c) intensity curve for the hologram shown in (b).

Fig. 14
Fig. 14

Encoding amplitude A and phase ϕ of the macropixel by the two-phase cell.

Fig. 15
Fig. 15

Phase disturbance ϕ ( x , y ) to intensity mapping as a function of δ.

Fig. 16
Fig. 16

Test object for the zeroth-order phase contrast: (a) Lenna and (b) intensity pattern in the observation.

Fig. 17
Fig. 17

Lohmann type III detour-phase hologram: (a) graphic coding of amplitude A by H, W and phase by P; (b) test object; (c) halftone mask based on the type III hologram for a section of (b); and (d) experimental result.

Fig. 18
Fig. 18

Hsueh and Sawchuk type VII detour-phase hologram: (a) graphic coding of amplitude A by W and phase by P 1 and P 2 ; (b) test object; (c) halftone mask based on the type III hologram for a section of (b); and (d) experimental result.

Tables (1)

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Table 1 Feature Comparison of Halftone Masks

Equations (23)

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I ( x , y ) = | exp [ i δ 2 ] + exp [ i δ 1 ] exp [ i ϕ ( x , y ) ] | 2 = 2 + 2 cos [ ϕ ( x , y ) ( δ 2 δ 1 ) ] .
I ( x , y ) = | exp [ i δ 1 ] exp [ i δ 2 ] + exp [ i δ 1 ] exp [ i ϕ ( x , y ) ] | 2 = 2 + 2 cos [ ϕ ( x , y ) δ 2 ] .
A sin ( π W ) .
I sin 2 ( π W ) = 1 cos ( 2 π W ) 2 .
I desired = W desired .
I desired = W desired = 1 cos ( 2 π W adapt ) 2 .
W adapt = arccos ( 1 2 I desired ) 2 π .
I ( x , y ) = | exp [ i δ 1 ] exp [ i ϕ ( x , y ) ] + exp [ i δ 2 ] exp [ i ϕ ( x , y ) ] | 2 = 2 + 2 cos [ 2 ϕ ( x , y ) ( δ 2 δ 1 ) ] .
2 π ϕ desired = 2 + 2 cos ( 2 ϕ adapt ) .
ϕ adapt = arccos ( 1 + ϕ desired π ) 2 .
I ( x , y ) = | exp [ i δ 1 ] exp [ i ϕ ( x , y ) ] + exp [ i δ 1 ] exp [ i ϕ ( x , y ) ] | 2 = 2 + 2 cos [ 2 ϕ ( x , y ) ] .
A 2 sin ( π W ) cos ( π Δ P ) ,
I sin 2 ( 2 π W ) = 1 cos ( 4 π W ) 2 .
ϕ = ( ϕ 1 + ϕ 2 2 ) ,
A = cos ( ϕ 1 ϕ 2 2 ) .
A = cos ( δ ϕ 2 2 ) = 1 + cos ( δ ϕ 2 ) 2 .
I = 1 + cos ( δ ϕ 2 ) 2 .
1 2 π ϕ desired = 1 cos ( ϕ adapt ) 2 .
ϕ adapt = arccos ( 1 ϕ desired π ) .
I H 2 sin 2 ( π W ) .
I H 2 .
I sin 2 ( π W ) cos 2 ( π Δ P ) ,
I cos 2 ( π P 2 ) = 1 + cos ( 2 π P 2 ) 2 .

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