- Email: [email protected]
Planar holographic elements with uniform diffraction efficiency
applied surface science ELSEVIER
Applied Surface Science 106 (1996) 369-373
Planar holographic elements with uniform diffraction efficiency R. Shechter *, S. Reinhorn, Y. Amitai, A.A. Friesem Department of Physics of Complex Systems, Weizmann Institute of Science, Rehol:ot 76100, Israel Received 17 September 1995; accepted 31 December 1995
Abstract
A planar holographic lens is investigated for imaging applications. The design and recording of the holographic lens are based on a transference of wavefronts method, where a desired grating function, with low aberrations, is transferred from a thin hologram to one recorded in thick recording materials. The resulting thick planar holographic lens fulfills the Bragg condition over a relatively large field of view. Experimental results, presented for planar holographic lenses recorded in photopolymers and dichromated gelatin materials, show that a high diffraction efficiency greater than 50% and uniform over a field of view of 16° can be obtained.
1. Introduction There have been significant advances in the area of holographic optical elements (HOEs) over the last twenty five years. These include advances in design, in efficient recording materials, and in the incorporation of the elements into a variety of applications. Yet, the usual free-space configurations with holographic elements have some drawbacks for imaging and processing applications. For example, when several holographic elements are needed, the overall optical configuration is bulky and space consuming. Also, free-space configurations do not lend themselves to easy modularization, and tolerances needed for aligning one element to another can be severe. Some of these problems can be overcome by incorporating the holographic elements into planar optics configurations [1-7]. This results in reducing the effective volume, relaxing the alignment sensitiv-
* Corresponding author. Tel.: +972-8342051; fax: +9728344109; e-maih [email protected].
ity, and lowering the chromatic aberrations and dispersion. The basic imaging planar holographic configuration is comprised of two HOEs recorded on a single substrate, as illustrated in Fig. 1. The first holographic lens diffracts the incident light from the display source so it will be trapped inside the substrate by total internal reflection, and the second hologram, which is just a linear grating, diffracts the light out from the substrate towards the observer. When the two holographic elements have the same spatial frequencies, the chromatic dispersion of the first hologram is compensated by the second one. In this configuration the alignment of the components is achieved during the formation stage, with relatively easy control, rather than later during the operation stage. Furthermore, the volume of the entire optical system is reduced, due to the fact that the light propagates through the substrate instead of free space. HOEs can be realized by either lithographic techniques or by holographic recording means. In planar configurations, it is advantageous to record the HOEs as volume phase gratings in order to increase the
0169-4332/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0 1 6 9 - 4 3 3 2 ( 9 6 ) 0 0 4 3 4 - 5
370
Display Source
Eye
R. ShechteretaL/AppliedSu,r'faceScience106(1996)369-373
/
t
Holographic Lens
Linear Grating
Fig. 1. A planar imaging configuration.
diffraction efficiencies and decrease the cross talk and aberrations. Moreover, volume phase gratings have higher angular and spectral selectivities than phase binary gratings formed with lithographic techniques. In this paper, we concentrate on developing the needed planar holographic recording method, so that resulting HOEs will have uniform and relatively high diffraction efficiency over a wide field of view. This method involves the transference of wavefronts from a holographic lens with low aberrations to one that will provide both low aberrations as well as uniform and high diffraction efficiency.
ume hologram that satisfies the Bragg relation. To ensure such compatibility, we developed a transference method, that transfers one desired wavefront into another. The transference method is described in Fig. 2. Here we assume that a holographic lens H with low optimized aberrations was already recorded with a grating function qbH on thin material. The wavefront from this H is first transferred to an intermediate h o l o g r a m H int as shown in Fig. 2(a). The holographic lens H is illuminated with a wavefront having a phase q~c, so the first diffracted order wavefront emerging from it inside the prism has a phase, of the form '/'i = 4,c - 4 , , .
(1)
This output wavefront propagates towards an intermediate hologram H int , and serves as its object wavefront where it interferes with a reference wavefront having a phase (Print. T h e grating function of H int thus has the form (/)~/nt = ( / ) ; - (/)rint
(2)
(a)
2. The transference of wavefronts method It is, in general, difficult to record a planar holographic element whose performance must include both low aberrations and uniform, high diffraction efficiency over a large field of view. This is so because it is difficult to ensure that the two-dimensional grating distribution on which the phase function and aberrations depend will be also compatible with the three-dimensional grating distribution on which the diffraction efficiency depends. Whereas the two-dimensional distribution can be recorded directly by means of either computer generated masks and lithographic technology [1,2] or a recursive design method [3-5], the three-dimensional distribution must be recorded interferometrically to form a vol-
~
Hint
HF Fig. 2. The geometry of the transference method. (a) Geometry for recording an intermediate hologram H int. (b) Geometry for recording the final hologram Hv.
371
R. Shechter et al./Applied Surfilce Science 106 (1996) 369-373
where ~ is the modified q>i phase after propagation, at the plane of Hint, and ¢:~rint can be a plane wave. In Fig. 2(b) the intermediate hologram H int is reconstructed with the conjugate of the reference wave used to record Hint, i.e. qb~int= -~b~ i°t. This will result in an output wave from the intermediate hologram, whose phase has the form (j~]nt
(jOcint
-
,+,,,
i n t _-
_
¢
int
-
(,I,; _
(/)rint) :
_
¢i, (3)
After propagating towards the location of the final holographic lens H v and through the prism, the phase of the wavefront impinging on H F is @i, and serves as a new object wavefront. This new object wavefront interferes with a reference wave whose phase qbrF is the conjugate wave of the one originally used for reconstructing the holographic lens H whose aberrations were optimized, i.e. q b r F = - - q b . The interference pattern is recorded in thick materials, to yield the final holographic lens H F, whose grating function has the form
(4)
= +,q.
The final holographic lens H F recorded in thick materials, simultaneously has the desired grating function that optimizes the aberrations and fulfills the Bragg relation for ensuring high diffraction efficiency. The prism that is used in the recording stages is needed in planar configurations to ensure that, in operation, the light diffracted by the final holographic lens will be trapped inside a substrate by total internal reflection.
function [3] for such a lens, that would result in low aberrations, can be approximated by 27r/., ( x 2 q-y 2
(/)H~ --RA
2 R2
and results •~
As an experimental illustration we designed, recorded and evaluated a relatively simple planar holographic imaging lens. We assumed that the lens would be used for imaging an array of points to infinity, where the image will be viewed directly by the eye of an observer, as illustrated in Fig. 1. The distance from the display source to the lens was chosen as R = 160 ram, and the eye diameter as 4 mm, so the f-number for the lens is 40. The grating
x ,
(5)
l
0.8 --
i_.M. 0.6tl=
procedure
)
R
where v is the refractive index of the glass substrate, a is the operating wavelength, x and y are the lateral coordinates at the plane of the lens, and /3 is the off-axis angle inside the glass substrate. First, we recorded H, which in our case is a simple linear grating, on Shipley photoresist S-140017 with A = 457.9 rim. The grating period was d = 0.44 /~m, and the grating thickness was only 0.4 ~m. We then reconstructed the linear grating with an on-axis spherical wave of wavelength of a = 514.5nm, that emerged from a point source at a distance R = 160 ram. Thus, the phase of the diffracted wave was equal to the desired grating function Eq. (5). This diffracted wave was then used as an object wave and a plane wave was used as the reference wave, for recording the intermediate hologram H int. The recording material was Agfa SilverHalide 8E56 holographic film. The object wave, diffracted at an angle of about 50 °, passed through a prism, as illustrated in the configuration of Fig. 2. We then recorded the final hologram H v. The object wave, derived by reconstructing H int with a conjugate plane wave, i.e. @cint= - ~ i ° t , was coupled into H F by means of the same prism. The
o=>, 3. Experimental
sin/3
0.4
--
0.2-
I
I
I
I
I
I
-6
-4
+2
2
4
6
Angle of Incidence (Deg)
Fig. 3. Calculated diffraction efficiency as a function of the angle of incidence. Dashed line - holographic lens recorded with the transference method. Solid line - directly recorded holographic lens.
R. Shechter et al. /Applied Surface Science 106 (1996) 369-373
372
1
I
q
-'4='-I-
+
+
+
+
+
+
+
+
+
+
0.9
0.8
--
0.7
--
-+
Theoetical Experimenttl
(a) o.6 -8
I
I
I
I
I
I
I
-6
-4
-2
0
2
4
6
8
Angle of Incidence (Deg)
+
+++++++++++
++
0.9--
0.8
--
0.7
--
Theoretical Experimmtal
(b) o.6 -8
I
I
I
I
I
I
I
-6
-4
-2
0
2
4
6
Angle of Incidence (Deg) Fig. 4. Experimental diffraction efficiency as a function of the angle of incidence for the final holographic lens H v. (a) H F recorded in DCG material. (b) H v recorded in photopolymer material.
reference wave was a plane wave oriented normally to H v. The grating function of the final hologram is thus the same as the desired one with low aberrations, given by Eqs. (4) and (5). In our experiments, the final hologram was recorded on two relatively thick emulsions in order to obtain high diffraction efficiency. One was Du Pont's photopolymer HRF700-20, with emulsion thickness of 20 #m, and index modulation of 0.0063. The other was dichromated gelatin [8] (DCG), prepared from Kodak plates 649/F, with emulsion thickness of 15 /xm, and index modulation of 0.0067. The recording wavelength was 514.5 nm derived from an Argon (Ar) laser. The geometry we used for recording the final hologram ensures that the diffraction efficiency is uniform, while retaining the optimal two-dimensional grating function that has low aberrations. We calculated the diffraction efficiency as a function of incidence angle for H v, as well as for a
holographic lens with the same grating function but which was recorded directly without the transference of wavefront method. For these calculations we used the coupled wave theory [9] for volume holograms. The calculated results are shown in Fig. 3. As shown, the diffraction efficiency for H v is uniform over a field of view of _+8°, whereas that of the directly recorded lens covers a much narrower field of view, i.e. about _+ 1°. Fig. 4 presents the experimental normalized diffraction efficiencies as a function of the incidence angle for two holographic lenses that were recorded with the transference method. For comparison, the corresponding theoretical efficiencies are also shown. Fig. 4(a) shows the results for a holographic lens that was recorded on the Du Pont photopolymer material. The actual measured average experimental diffraction efficiency was about 65%. Fig. 4(b) shows the results for a lens that was recorded on dichromate gelatin (DCG), prepared from Kodak 6 4 9 / F plates. Here, the measured experimental average diffraction efficiency was about 50%. As evident, the diffraction efficiency is essentially uniform over the designed range of incidence angles of 8° for both lenses.
4. Concluding remarks In this paper we investigated planar holographic lenses that can be used for imaging. We showed that it is possible to transfer any desired grating function with low aberrations onto a planar holographic lens that is recorded in thick phase materials. This results in a lens that does not only have low aberrations but high and uniform diffraction efficiencies as well. Such lenses can be incorporated into a number of compact imaging systems, most prominent of which is a visor display.
Acknowledgements This research was supported in part by the Minerva Foundation.
References [l] K.H. Brenner and F. Sauer, Appl. Opt. 27 (1988) 4251. [2] J. Jahns and S.J. Walker, Opt. Commun. 76 (1990) 313.
R. Shechter et al. /Applied Surface Science 106 (1996) 369-373
[3] Y. Amitai and A.A. Friesem, J. Opt. Soc. Am. A 5 (1988) 702. [4] Y. Amitai and J.W. Goodman, Appl. Opt. 30 (1991) 2376. [5] Y. Amitai, S. Reinhorn and A.A. Friesem, Appl. Opt. 34 (1995) 1352. [6] I. Shariv, Y. Amitai and A.A. Friesem, Opt. Lett. 18 (1993) 1268.
373
[7] Y. Amitai, I. Shariv, M. Kroch, A.A. Friesem and S. Reinhorn, Opt. Lett. 18 (1993) 1265. [8] B.J. Chang and C.D. Leonard, Appl. Opt. 18 (1979) 2407. [9] H. Kogelnik, Bell Syst. Tech. J. 48 (1969) 2909.
Applied Surface Science 106 (1996) 369-373
Planar holographic elements with uniform diffraction efficiency R. Shechter *, S. Reinhorn, Y. Amitai, A.A. Friesem Department of Physics of Complex Systems, Weizmann Institute of Science, Rehol:ot 76100, Israel Received 17 September 1995; accepted 31 December 1995
Abstract
A planar holographic lens is investigated for imaging applications. The design and recording of the holographic lens are based on a transference of wavefronts method, where a desired grating function, with low aberrations, is transferred from a thin hologram to one recorded in thick recording materials. The resulting thick planar holographic lens fulfills the Bragg condition over a relatively large field of view. Experimental results, presented for planar holographic lenses recorded in photopolymers and dichromated gelatin materials, show that a high diffraction efficiency greater than 50% and uniform over a field of view of 16° can be obtained.
1. Introduction There have been significant advances in the area of holographic optical elements (HOEs) over the last twenty five years. These include advances in design, in efficient recording materials, and in the incorporation of the elements into a variety of applications. Yet, the usual free-space configurations with holographic elements have some drawbacks for imaging and processing applications. For example, when several holographic elements are needed, the overall optical configuration is bulky and space consuming. Also, free-space configurations do not lend themselves to easy modularization, and tolerances needed for aligning one element to another can be severe. Some of these problems can be overcome by incorporating the holographic elements into planar optics configurations [1-7]. This results in reducing the effective volume, relaxing the alignment sensitiv-
* Corresponding author. Tel.: +972-8342051; fax: +9728344109; e-maih [email protected].
ity, and lowering the chromatic aberrations and dispersion. The basic imaging planar holographic configuration is comprised of two HOEs recorded on a single substrate, as illustrated in Fig. 1. The first holographic lens diffracts the incident light from the display source so it will be trapped inside the substrate by total internal reflection, and the second hologram, which is just a linear grating, diffracts the light out from the substrate towards the observer. When the two holographic elements have the same spatial frequencies, the chromatic dispersion of the first hologram is compensated by the second one. In this configuration the alignment of the components is achieved during the formation stage, with relatively easy control, rather than later during the operation stage. Furthermore, the volume of the entire optical system is reduced, due to the fact that the light propagates through the substrate instead of free space. HOEs can be realized by either lithographic techniques or by holographic recording means. In planar configurations, it is advantageous to record the HOEs as volume phase gratings in order to increase the
0169-4332/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0 1 6 9 - 4 3 3 2 ( 9 6 ) 0 0 4 3 4 - 5
370
Display Source
Eye
R. ShechteretaL/AppliedSu,r'faceScience106(1996)369-373
/
t
Holographic Lens
Linear Grating
Fig. 1. A planar imaging configuration.
diffraction efficiencies and decrease the cross talk and aberrations. Moreover, volume phase gratings have higher angular and spectral selectivities than phase binary gratings formed with lithographic techniques. In this paper, we concentrate on developing the needed planar holographic recording method, so that resulting HOEs will have uniform and relatively high diffraction efficiency over a wide field of view. This method involves the transference of wavefronts from a holographic lens with low aberrations to one that will provide both low aberrations as well as uniform and high diffraction efficiency.
ume hologram that satisfies the Bragg relation. To ensure such compatibility, we developed a transference method, that transfers one desired wavefront into another. The transference method is described in Fig. 2. Here we assume that a holographic lens H with low optimized aberrations was already recorded with a grating function qbH on thin material. The wavefront from this H is first transferred to an intermediate h o l o g r a m H int as shown in Fig. 2(a). The holographic lens H is illuminated with a wavefront having a phase q~c, so the first diffracted order wavefront emerging from it inside the prism has a phase, of the form '/'i = 4,c - 4 , , .
(1)
This output wavefront propagates towards an intermediate hologram H int , and serves as its object wavefront where it interferes with a reference wavefront having a phase (Print. T h e grating function of H int thus has the form (/)~/nt = ( / ) ; - (/)rint
(2)
(a)
2. The transference of wavefronts method It is, in general, difficult to record a planar holographic element whose performance must include both low aberrations and uniform, high diffraction efficiency over a large field of view. This is so because it is difficult to ensure that the two-dimensional grating distribution on which the phase function and aberrations depend will be also compatible with the three-dimensional grating distribution on which the diffraction efficiency depends. Whereas the two-dimensional distribution can be recorded directly by means of either computer generated masks and lithographic technology [1,2] or a recursive design method [3-5], the three-dimensional distribution must be recorded interferometrically to form a vol-
~
Hint
HF Fig. 2. The geometry of the transference method. (a) Geometry for recording an intermediate hologram H int. (b) Geometry for recording the final hologram Hv.
371
R. Shechter et al./Applied Surfilce Science 106 (1996) 369-373
where ~ is the modified q>i phase after propagation, at the plane of Hint, and ¢:~rint can be a plane wave. In Fig. 2(b) the intermediate hologram H int is reconstructed with the conjugate of the reference wave used to record Hint, i.e. qb~int= -~b~ i°t. This will result in an output wave from the intermediate hologram, whose phase has the form (j~]nt
(jOcint
-
,+,,,
i n t _-
_
¢
int
-
(,I,; _
(/)rint) :
_
¢i, (3)
After propagating towards the location of the final holographic lens H v and through the prism, the phase of the wavefront impinging on H F is @i, and serves as a new object wavefront. This new object wavefront interferes with a reference wave whose phase qbrF is the conjugate wave of the one originally used for reconstructing the holographic lens H whose aberrations were optimized, i.e. q b r F = - - q b . The interference pattern is recorded in thick materials, to yield the final holographic lens H F, whose grating function has the form
(4)
= +,q.
The final holographic lens H F recorded in thick materials, simultaneously has the desired grating function that optimizes the aberrations and fulfills the Bragg relation for ensuring high diffraction efficiency. The prism that is used in the recording stages is needed in planar configurations to ensure that, in operation, the light diffracted by the final holographic lens will be trapped inside a substrate by total internal reflection.
function [3] for such a lens, that would result in low aberrations, can be approximated by 27r/., ( x 2 q-y 2
(/)H~ --RA
2 R2
and results •~
As an experimental illustration we designed, recorded and evaluated a relatively simple planar holographic imaging lens. We assumed that the lens would be used for imaging an array of points to infinity, where the image will be viewed directly by the eye of an observer, as illustrated in Fig. 1. The distance from the display source to the lens was chosen as R = 160 ram, and the eye diameter as 4 mm, so the f-number for the lens is 40. The grating
x ,
(5)
l
0.8 --
i_.M. 0.6tl=
procedure
)
R
where v is the refractive index of the glass substrate, a is the operating wavelength, x and y are the lateral coordinates at the plane of the lens, and /3 is the off-axis angle inside the glass substrate. First, we recorded H, which in our case is a simple linear grating, on Shipley photoresist S-140017 with A = 457.9 rim. The grating period was d = 0.44 /~m, and the grating thickness was only 0.4 ~m. We then reconstructed the linear grating with an on-axis spherical wave of wavelength of a = 514.5nm, that emerged from a point source at a distance R = 160 ram. Thus, the phase of the diffracted wave was equal to the desired grating function Eq. (5). This diffracted wave was then used as an object wave and a plane wave was used as the reference wave, for recording the intermediate hologram H int. The recording material was Agfa SilverHalide 8E56 holographic film. The object wave, diffracted at an angle of about 50 °, passed through a prism, as illustrated in the configuration of Fig. 2. We then recorded the final hologram H v. The object wave, derived by reconstructing H int with a conjugate plane wave, i.e. @cint= - ~ i ° t , was coupled into H F by means of the same prism. The
o=>, 3. Experimental
sin/3
0.4
--
0.2-
I
I
I
I
I
I
-6
-4
+2
2
4
6
Angle of Incidence (Deg)
Fig. 3. Calculated diffraction efficiency as a function of the angle of incidence. Dashed line - holographic lens recorded with the transference method. Solid line - directly recorded holographic lens.
R. Shechter et al. /Applied Surface Science 106 (1996) 369-373
372
1
I
q
-'4='-I-
+
+
+
+
+
+
+
+
+
+
0.9
0.8
--
0.7
--
-+
Theoetical Experimenttl
(a) o.6 -8
I
I
I
I
I
I
I
-6
-4
-2
0
2
4
6
8
Angle of Incidence (Deg)
+
+++++++++++
++
0.9--
0.8
--
0.7
--
Theoretical Experimmtal
(b) o.6 -8
I
I
I
I
I
I
I
-6
-4
-2
0
2
4
6
Angle of Incidence (Deg) Fig. 4. Experimental diffraction efficiency as a function of the angle of incidence for the final holographic lens H v. (a) H F recorded in DCG material. (b) H v recorded in photopolymer material.
reference wave was a plane wave oriented normally to H v. The grating function of the final hologram is thus the same as the desired one with low aberrations, given by Eqs. (4) and (5). In our experiments, the final hologram was recorded on two relatively thick emulsions in order to obtain high diffraction efficiency. One was Du Pont's photopolymer HRF700-20, with emulsion thickness of 20 #m, and index modulation of 0.0063. The other was dichromated gelatin [8] (DCG), prepared from Kodak plates 649/F, with emulsion thickness of 15 /xm, and index modulation of 0.0067. The recording wavelength was 514.5 nm derived from an Argon (Ar) laser. The geometry we used for recording the final hologram ensures that the diffraction efficiency is uniform, while retaining the optimal two-dimensional grating function that has low aberrations. We calculated the diffraction efficiency as a function of incidence angle for H v, as well as for a
holographic lens with the same grating function but which was recorded directly without the transference of wavefront method. For these calculations we used the coupled wave theory [9] for volume holograms. The calculated results are shown in Fig. 3. As shown, the diffraction efficiency for H v is uniform over a field of view of _+8°, whereas that of the directly recorded lens covers a much narrower field of view, i.e. about _+ 1°. Fig. 4 presents the experimental normalized diffraction efficiencies as a function of the incidence angle for two holographic lenses that were recorded with the transference method. For comparison, the corresponding theoretical efficiencies are also shown. Fig. 4(a) shows the results for a holographic lens that was recorded on the Du Pont photopolymer material. The actual measured average experimental diffraction efficiency was about 65%. Fig. 4(b) shows the results for a lens that was recorded on dichromate gelatin (DCG), prepared from Kodak 6 4 9 / F plates. Here, the measured experimental average diffraction efficiency was about 50%. As evident, the diffraction efficiency is essentially uniform over the designed range of incidence angles of 8° for both lenses.
4. Concluding remarks In this paper we investigated planar holographic lenses that can be used for imaging. We showed that it is possible to transfer any desired grating function with low aberrations onto a planar holographic lens that is recorded in thick phase materials. This results in a lens that does not only have low aberrations but high and uniform diffraction efficiencies as well. Such lenses can be incorporated into a number of compact imaging systems, most prominent of which is a visor display.
Acknowledgements This research was supported in part by the Minerva Foundation.
References [l] K.H. Brenner and F. Sauer, Appl. Opt. 27 (1988) 4251. [2] J. Jahns and S.J. Walker, Opt. Commun. 76 (1990) 313.
R. Shechter et al. /Applied Surface Science 106 (1996) 369-373
[3] Y. Amitai and A.A. Friesem, J. Opt. Soc. Am. A 5 (1988) 702. [4] Y. Amitai and J.W. Goodman, Appl. Opt. 30 (1991) 2376. [5] Y. Amitai, S. Reinhorn and A.A. Friesem, Appl. Opt. 34 (1995) 1352. [6] I. Shariv, Y. Amitai and A.A. Friesem, Opt. Lett. 18 (1993) 1268.
373
[7] Y. Amitai, I. Shariv, M. Kroch, A.A. Friesem and S. Reinhorn, Opt. Lett. 18 (1993) 1265. [8] B.J. Chang and C.D. Leonard, Appl. Opt. 18 (1979) 2407. [9] H. Kogelnik, Bell Syst. Tech. J. 48 (1969) 2909.