Abstract

The design and the analysis of an off-axis (50°) diffractive imaging optical system is presented in this paper. A 10°x15° field of view is considered. The optical system is composed of two diffractive optical elements. A static diffractive optical element having a frozen phase transfer function is used to perform a virtual point in the considered field of view. A dynamic diffractive optical element having an adapted calculated phase transfer function is used to compensate for aberrations of the static element. Using a sequential creation of virtual image points and considering human eye characteristics, it is shown that a nine points virtual image can be obtained with current technology. Moreover, it is presented that aberrations can be compensated whatever the position of the virtual point in the 10°x15° field of view. Finally, using rigorous coupled wave analysis, it is shown that an average diffraction efficiency of 79% can be reached across the considered field of view with a standard deviation of nearly 5%.

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2010 (3)

2009 (5)

2008 (1)

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A, Pure Appl. Opt. 10(8), 085007 (2008).
[CrossRef]

2007 (2)

2006 (2)

O. Cakmakci and J. Rolland, “Head-worn displays: a review,” J. Display Technol. 2(3), 199–216 (2006).
[CrossRef]

H. Nagahara, Y. Yagi, and M. Yachida, “A wide-field-of-view catadioptrical head-mounted display,” Electon. Commun. Jpn. 89, 33–43 (2006).

2001 (1)

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[CrossRef]

1999 (1)

T. Ando, T. Matsumoto, H. Takahashi, and E. Shimizu, “Head mounted display for mixed reality using holographic optical elements,” Mem. Fac. Eng. Osaka City Univ. 40, 1–6 (1999).

1997 (1)

R. T. Azuma, “A survey of augmented reality,” Presence (Camb. Mass.) 6, 355–385 (1997).

1996 (1)

1995 (2)

1994 (1)

C. Soutar and K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33(8), 2704–2712 (1994).
[CrossRef]

1989 (1)

1988 (2)

1983 (1)

1969 (1)

H. Kögelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Ambs, P.

Amitai, Y.

Ando, T.

T. Ando, T. Matsumoto, H. Takahashi, and E. Shimizu, “Head mounted display for mixed reality using holographic optical elements,” Mem. Fac. Eng. Osaka City Univ. 40, 1–6 (1999).

Azuma, R. T.

R. T. Azuma, “A survey of augmented reality,” Presence (Camb. Mass.) 6, 355–385 (1997).

Banyasz, I.

Barbastathis, G.

Barton, J. K.

Broomfield, S. E.

Buckley, E.

E. Buckley, D. Stindt, and R. Isele, “14.4: Novel human-machine interface (HMI) design enabled by holographic laser projection,” SID Symp. Dig. 40(1), 172–177 (2009).
[CrossRef]

Cakmakci, O.

Castro, J.

Cheng, D.

Dickensheets, D. L.

Endo, T.

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[CrossRef]

Engström, D.

Friesem, A. A.

Fuchs, H.

J. P. Rolland, R. L. Holloway, and H. Fuchs, “A comparison of optical and video see-through head-mounted displays,” Proc. SPIE 2351, 293–307 (1995).
[CrossRef]

Gaylord, T. K.

Goto, K.

Ha, Y.

Handschy, M. A.

Holloway, R. L.

J. P. Rolland, R. L. Holloway, and H. Fuchs, “A comparison of optical and video see-through head-mounted displays,” Proc. SPIE 2351, 293–307 (1995).
[CrossRef]

Hua, H.

Isele, R.

E. Buckley, D. Stindt, and R. Isele, “14.4: Novel human-machine interface (HMI) design enabled by holographic laser projection,” SID Symp. Dig. 40(1), 172–177 (2009).
[CrossRef]

Kasai, I.

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[CrossRef]

Kiss, G.

Kitaoka, M.

Kögelnik, H.

H. Kögelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kostuk, R. K.

Li, H.

Liu, X.

Lu, K.

C. Soutar and K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33(8), 2704–2712 (1994).
[CrossRef]

Luo, Y.

Mahmud, M. S.

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A, Pure Appl. Opt. 10(8), 085007 (2008).
[CrossRef]

Martins, R.

Matsumoto, T.

T. Ando, T. Matsumoto, H. Takahashi, and E. Shimizu, “Head mounted display for mixed reality using holographic optical elements,” Mem. Fac. Eng. Osaka City Univ. 40, 1–6 (1999).

Millán, M. S.

Moharam, M. G.

Nagahara, H.

H. Nagahara, Y. Yagi, and M. Yachida, “A wide-field-of-view catadioptrical head-mounted display,” Electon. Commun. Jpn. 89, 33–43 (2006).

Naydenova, I.

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A, Pure Appl. Opt. 10(8), 085007 (2008).
[CrossRef]

Neil, M. A. A.

O’Callaghan, M. J.

Otón, J.

Paige, E. G. S.

Pérez-Cabré, E.

Poelman, R.

D. W. F. Van Krevelen and R. Poelman, “A survey of augmented reality technologies, applications and limitations,”Int. J. Virtual Reality 9, 1–20 (2010).

Rolland, J.

Rolland, J. P.

J. P. Rolland, R. L. Holloway, and H. Fuchs, “A comparison of optical and video see-through head-mounted displays,” Proc. SPIE 2351, 293–307 (1995).
[CrossRef]

Shaoulov, V.

Shimizu, E.

T. Ando, T. Matsumoto, H. Takahashi, and E. Shimizu, “Head mounted display for mixed reality using holographic optical elements,” Mem. Fac. Eng. Osaka City Univ. 40, 1–6 (1999).

Soutar, C.

C. Soutar and K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33(8), 2704–2712 (1994).
[CrossRef]

Stindt, D.

E. Buckley, D. Stindt, and R. Isele, “14.4: Novel human-machine interface (HMI) design enabled by holographic laser projection,” SID Symp. Dig. 40(1), 172–177 (2009).
[CrossRef]

Takahashi, H.

T. Ando, T. Matsumoto, H. Takahashi, and E. Shimizu, “Head mounted display for mixed reality using holographic optical elements,” Mem. Fac. Eng. Osaka City Univ. 40, 1–6 (1999).

Talha, M. M.

Tanijiri, Y.

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[CrossRef]

Toal, V.

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A, Pure Appl. Opt. 10(8), 085007 (2008).
[CrossRef]

Ueda, H.

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[CrossRef]

Van Krevelen, D. W. F.

D. W. F. Van Krevelen and R. Poelman, “A survey of augmented reality technologies, applications and limitations,”Int. J. Virtual Reality 9, 1–20 (2010).

Varga, P.

Walker, C.

Wang, Y.

Weiss, V.

Xu, L.

Yachida, M.

H. Nagahara, Y. Yagi, and M. Yachida, “A wide-field-of-view catadioptrical head-mounted display,” Electon. Commun. Jpn. 89, 33–43 (2006).

Yagi, Y.

H. Nagahara, Y. Yagi, and M. Yachida, “A wide-field-of-view catadioptrical head-mounted display,” Electon. Commun. Jpn. 89, 33–43 (2006).

Zheng, Z.

Appl. Opt. (7)

Bell Syst. Tech. J. (1)

H. Kögelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Electon. Commun. Jpn. (1)

H. Nagahara, Y. Yagi, and M. Yachida, “A wide-field-of-view catadioptrical head-mounted display,” Electon. Commun. Jpn. 89, 33–43 (2006).

Int. J. Virtual Reality (1)

D. W. F. Van Krevelen and R. Poelman, “A survey of augmented reality technologies, applications and limitations,”Int. J. Virtual Reality 9, 1–20 (2010).

J. Display Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

M. S. Mahmud, I. Naydenova, and V. Toal, “Implementation of phase-only modulation utilizing a twisted nematic liquid crystal spatial light modulator,” J. Opt. A, Pure Appl. Opt. 10(8), 085007 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Mem. Fac. Eng. Osaka City Univ. (1)

T. Ando, T. Matsumoto, H. Takahashi, and E. Shimizu, “Head mounted display for mixed reality using holographic optical elements,” Mem. Fac. Eng. Osaka City Univ. 40, 1–6 (1999).

Opt. Eng. (1)

C. Soutar and K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33(8), 2704–2712 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Photonics News (1)

J. Rolland and O. Cakmakci, “Head-worn displays: The future through new eyes,” Opt. Photonics News 20(4), 20–27 (2009).
[CrossRef]

Opt. Rev. (1)

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[CrossRef]

Presence (Camb. Mass.) (1)

R. T. Azuma, “A survey of augmented reality,” Presence (Camb. Mass.) 6, 355–385 (1997).

Proc. SPIE (1)

J. P. Rolland, R. L. Holloway, and H. Fuchs, “A comparison of optical and video see-through head-mounted displays,” Proc. SPIE 2351, 293–307 (1995).
[CrossRef]

SID Symp. Dig. (1)

E. Buckley, D. Stindt, and R. Isele, “14.4: Novel human-machine interface (HMI) design enabled by holographic laser projection,” SID Symp. Dig. 40(1), 172–177 (2009).
[CrossRef]

Other (3)

P. Ambs, J. Otόn, M. S. Millán, A. Jaulin, and L. Bigué, “Spatial light modulators for information processing: applications and overview,” in AIP Conference Proceedings of Sixth International Workshop on Information Optics, B. Javidi, and J.A. Benediktsson eds.(Reykjavik, Islande, 2007), 226–233.

Boulder Nonlinear Systems, “Liquid crystal reference,” white paper (Boulder Nonlinear Systems, 2001), http://www.bnonlinear.com/papers/LCReference.pdf .

P. Ambs and L. Bigué, “Characterization of an analog ferroelectric spatial light modulator. Application to dynamic diffractive optical elements and optical information processing,” presented at the Fourth Euro American Workshop on Optoelectronic Information Processing, Valencia, Spain, 2001.

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Figures (12)

Fig. 1
Fig. 1

An illustration of the proposed setup.

Fig. 2
Fig. 2

Top view of the optical system (not to scale). Q is a point of the plane of DOE 1, P is point of the plane of DOE 2 and I is a point of the plane of the virtual image. α1 is the angle between the normal to DOE 2 and the direction (O1O2). α2 is the angle between the normal to DOE 2 and the direction (OO2). The thickness of DOEs is not drawn.

Fig. 3
Fig. 3

The blue line represents the number of points of the virtual image versus frequency rate considering an afterimage effect of 50ms. The corresponding domain for each type of liquid crystal has been placed on the curve.

Fig. 4
Fig. 4

Pixelated structure of a spatial light modulator.

Fig. 5
Fig. 5

(a) Recording geometry of the static element. θR is the incidence angle of the plane reference wave. S is the point source of the spherical object wave. (b) Reconstruction setup. I is the reconstructed virtual point.

Fig. 6
Fig. 6

Representation of the unit propagation vectors uC1 , uD1 , uC2, uD2 for a ray going through points Qij (sampling grid of DOE 1), Pij (sampling grid of the DOE 2) and Ikl (virtual image). (a) Three-dimensional view. (b) Top view.

Fig. 7
Fig. 7

Three-dimensional representation of the oblique incidence (θ1, δ1) of the incident plane wave at the surface of the dynamic DOE. θ1is the angle between the wave normal uC1 and the z1 axis. δ1 is the angle between the plane of incidence and the x1 axis.

Fig. 8
Fig. 8

Nine-points virtual image used for the simulations. Point I22 is at the same position than point source S used for the recording of the static element. Others points are at the periphery of the 10°x15° field of view.

Fig. 9
Fig. 9

Configurations of the incident plane wave used for the calculation of the ideal PTF. (a) the incidence is normal whatever the virtual image point. (b) the incidence varies in function of the position of the virtual image point. The unit propagation vector uC1 is identical to the main unit propagation vector uD1 of the wave diffracted by the dynamic DOE which depends on the position of the virtual image point.

Fig. 10
Fig. 10

Modulation transfer functions for the nine points of the simulated image. Blue curves: no aberration compensation; red curves: calculated aberration compensation.

Fig. 11
Fig. 11

Zoom to the localized planar grating description of the static DOE. Λ is the local grating period, Φ is the local slanted angle, (K) is the local grating vector, uC2 is the local unit propagation vector of the reading wave, θ2 is the local incidence, δ2 is the angle between the plane of incidence and the x-axis, e is the thickness of the element, ψ is the arbitrary polarization angle.

Fig. 12
Fig. 12

Optimized (Δn = 6.5%, e = 6µm) diffraction efficiency over the 10°x15° field of view sampled into 81x81 uniformly distributed virtual image points.

Tables (3)

Tables Icon

Table 1 Characteristics of the current different technologies for one LCD

Tables Icon

Table 2 Coordinates in the (xOy) plane of the nine image points of the virtual image

Tables Icon

Table 3 Spatial frequencies in (O1x1) and (O1y1) direction of the optimized PTFs of the SLM for the nine points of the grid defined in Fig. 8

Equations (15)

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

u = λ 0 2 π n ϕ ,
ϕ P T F 2 ( x 2 , y 2 ) = ϕ O ( x 2 , y 2 ) ϕ R ( x 2 , y 2 ) ,
ϕ P T F 2 ( x 2 , y 2 ) = k 0 { d ( S , P ) d ( S , O ) x sin ( θ R ) } ,
ϕ D 2 ( x 2 , y 2 ) = ϕ C 2 ( x 2 , y 2 ) + ϕ P T F 2 ( x 2 , y 2 ) ,
u D 2 = I k l P i j Ι k l P i j .
u C 2 = u D 2 ( u O u R ) ,
u O = S P i j S P i j   and   u R = ( sin ( θ R ) 0 cos ( θ R ) ) ,
ϕ D 2 i d ( x i j P , y i j P , z i j P ) = k 0 d ( I k l , P i j ) + φ D 2 ,
ϕ C 2 i d ( x i j P , y i j P , z i j P ) = k 0 d ( I k l , P i j ) k 0 ( d ( S , P i j ) d ( S , O 2 ) x i j P sin ( θ R ) ) + φ D 2 .
ϕ C 2 i d ( x i j Q , y i j Q , z i j Q ) = ϕ C 2 i d ( x i j P , y i j P , z i j P ) + k 0 d ( P i j , Q i j ) .
ϕ P T F 1 ( x i j Q , y i j Q , z i j Q ) = ϕ D 1 ( x i j Q , y i j Q , z i j Q ) ϕ C 1 ( x i j Q , y i j Q , z i j Q ) ,
ϕ P T F 1 ( x 1 , y 1 ) = 2 π λ 0 k l a k l x 1 k y 1 l .
| ν X ( x 1 , y 1 ) | = 1 2 π | ϕ P T F 1 ( x 1 , y 1 ) x 1 | ,
| ν Y ( x 1 , y 1 ) | = 1 2 π | ϕ P T F 1 ( x 1 , y 1 ) y 1 | .
η = i j η i j N ,

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