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Phase-only modulation with a spatial light modulator controlled by writing light intensity
1 July 1997 OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 139 (1997) 232-236
Phase-only modulation with a spatial light modulator controlled by writing light intensity Yun Zhisheng
*, Li Yulin ‘, Liu Jifang, He Zhengquan
Xi’an Institute of Optics and Precision Mechanics, Academia Sinicu, P.O. Box 80(24), Xi’an 710068, China
Received 23 October 1996; revised 18 December 1996; accepted 14 January 1997
Abstract A qualitative description of phase-only modulation with an optically addressed SLM controlled by writing light intensity is presented. Experimental verification is carried out, and the results are consistent with the theoretical conclusions.
1. Introduction Liquid crystals as spatial light intensity modulators have been widely used in coherent and incoherent signal processing. However, their features of phase-only modulation show more promising applications in adaptive optics (AO), pattern recognition and phase-only filters, etc. In recent years, these characteristics have been studied extensively [l--12]. Here, a twisted nematic liquid-crystal spatial light modulator (TNLC SLM) addressed by writing light working as a phase-only modulator is investigated. If the dependence of phase-only modulation of commercial SLMs on writing light intensity is clearly known, SLMs can more conveniently be used as compensators for A0 and phase division components. Vorontsov et al. [4,5] have studied the phase-only modulation of a SLM controlled by writing light. In this paper, we give a qualitative description of this issue in the following discussion. The SLM used in our experiment consists of a number of thin film layers sandwiched between two glass substrates [17]. A low voltage (1 to 10 V,,,) audio frequency power supply is connected to the two outer, thin film indium-tin-oxide (ITO) transparent electrodes. The lightsensitive layers are made of cadmium telluride (CdTe) and
* Corresponding author. E-mail: [email protected]. ’ Member SPlE.
cadmium sulfide (CdS). The dielectric mirror and the blocking layer separate the photoconductor from the readout light beam. These are the major design features of the SLM, which is much similar to the light valve described in Ref. 1131.
2. Theoretical
analyses
The equivalent circuit for a TNLC SLM [14,15] is shown in Fig. 1. The region in the dashed square represents the equivalent circuit of the light-sensitive element, C,, C, and C, represent the capacitances of the mirror, the liquid crystal and the light-sensitive element, respectively. The diode represents the CdTe/CdS heterojunction diode. According to Frass’s mode [14], the current flow in the illuminated element is larger than that in the nonilluminated element, i.e., the voltage applied to the LC element varies with the illuminating light intensities. If the current Z, in Fig. 1 is obtained, the voltage applied to the LC element will be known, and the relation between them can be described by the following equation, u=z,
XI,,
(la>
where, v is the voltage applied to the LC, z1 is the impedance of the LC. To study the phase variations of SLMs with writing light intensities, firstly we must know the relation between current I, and writing light intensity @. Supposing the
0030-4018/97/$17.00 Copyright 0 1997 Published by Elsevier Science B.V. All rights reserved. PII s0030-4018(97)00053-9
Y. Zhisheng et al. / Optics Communications
molecules varying expressed by [5],
with the applied
H=G-Zfan-t{exp[-(?)I),
Fig.
1.
Equivalent circuit of a resolution element in the SLM.
25
Writing Light Intensity @w/cm’) Fig. 2. Experimental data for the current I, versus the writing light intensity Cp.
relation is written as I, = FL@], which can be obtained experimentally, as shown in Fig. 2, we rewrite Eq. (la) as u=zj
(lb)
XF[@],
where F is a function of writing light intensity. We know that the impedance of the LC element depends on the frequency of the applied voltage. If the frequency is fixed, the impedance is constant. Then, the voltage (v) applied to the LC element varying with the writing light intensities (a) can qualitatively be described by Eq. (lb). It is known [2] that TNLC SLMs behave as phase-only modulators when they are operated below the conventional optical threshold. The tilt angle 0 of liquid-crystal
He-Ne Laser
233
139 (1997) 232-236
voltage
u>u,,
(2)
where uth is the threshold voltage below which no tilting occurs and ua is the excess voltage at which the tilt angle is 49.6”. The liquid crystal used in our experiment is TNLC E7, whose threshold voltage is 0.937 V. The ordinary refractive index n, and the extraordinary refractive index n, of the E7 are 1.5175 and 1.7434, respectively. The extraordinary refractive index exhibited by anisotropic molecules, which are tilted by an angle 0, is given by [16]
So the phase modulation controlled by writing light intensity is obtained by combining Eqs. (l), (2) and (3). If the distribution of writing light intensity is expressed by @(x, y), the phase modulation U( x, y) is obtained by the relationship U(x, y) = G[@(x, y)], where x, y are spatial variables on the SLM, G is a function of phase modulation of the SLM.
3. Experiments
and discussions
To verify the previous theoretical conclusions, we carried out an experiment sketched schematically in Fig. 3, which is a Twyman-Green interferometer. The phase shifts introduced by writing light intensities were measured by placing a SLM at one arm of the interferometer. The projector lens images a transparency slide on the SLM writing surface. The transparency slide is divided into two parts. The transmissivity of one part in the transparency slide is unchangeable and the transmissivity of the other part of the transparency slide is changeable. By changing the transmissivity of the changeable part of the trans-
Projection Lens
I Slide Screen
u can be
ac Voltage Source
Fig. 3. Experimental scheme for phase modulation measurement based on the Twyman-Green interferometer.
234
Y. Zhisheng et al. / Optics Communications
Fig. 4. (al One of the transparency
slides; (b) interference
139 (1997) 232-236
pattern with the slide in (a); (c) theoretical
a
:II Fig. 5. Three transparency slides with different transmissivities (a), (b) and (c); the interferograms (d), (e) and (f> corresponding to (a), (b) and (c), respectively.
parency slide, we can get different writing light intensities. The beams reflected from the mirror and from the SLM interfere in the Twyman-Green interferometer. By measuring the shifts of the interference fringes at the two parts of the slide we can obtain the relative phase shifts varying with the writing light intensities.
phase modulation
distribution.
Fig. 4a is a transparency slide, in which the writing light can pass through the white squares and be blocked by the black squares. Fig. 4b shows the interferogram that clearly gives us the relative phase shifts. Fig. 4c shows the theoretical phase modulation distribution. From Fig. 4b, we can see that the interferogram does not agree exactly with the theoretical results as shown in Fig. 4c. This is caused by the wavefront errors of the SLM. The rms wavefront error of the SLM in our experiment is not better than h/3 [17] (A denotes the wavelength). Three main factors result in wavefront errors. First, the thickness of the liquid-crystal between the two glass plates is not constant across the whole interior surface of the plates. Second, the writing light intensity upon the writing surface of the SLM is not uniform. Third, the thickness of the glass substrates of the SLM is not the same across the whole surface. If the three drawbacks above are overcome, the phase modulation distribution will agree better with the theoretical results. Fig. 5a, 5b and 5c are three transparency slides with different transmissivities. When writing light goes through them, we can measure the shifts of interference fringes, respectively, as shown in Fig. 5d, 5e and 5f. By measuring the shifts of interference fringes versus different writing
. . theoretical results
MO
4ca
EGO
er.a
Iwo
Wriiing light intensity @w/cm*)
3
Writing light intensity (,uw/cm2)
Fig. 6. (a) Curves of the relative phase shifts versus writing light intensities; (b) the relative phase shifts versus the writing light intensities below 200 p,W/cm’. The solid curve represents the experimental data and the dotted curve represents the theoretical results.
Y. Zhisheng et al. / Optics Communications
light intensities, we plotted the curve of the relative phase shifts versus writing light intensities in Fig. 6a, which is shown by a solid line. The dotted curve in Fig. 6a is the theoretical results of the previous theoretical discussions. In order to see the relative phase shifts varying with the writing light intensities below 100 kW/cm’, we enlarge the curves of Fig. 6a as demonstrated in Fig. 6b. From Fig. 6b we see that the sensitivity threshold, i.e. the minimum level of writing light for the writing process, is very low. The value of the minimum level obtained experimentally is approximately 6.3 kW/cm’. When the writing light is below the sensitivity threshold, the relative phase shift is a constant given by 1.55~. When the writing light intensity is above the sensitivity threshold, the relative phase shift reduces to 1.33~ from 1.55~~ and continues decreasing gradually. When the writing light intensity exceeds 800 the curves in Fig. 6 become gradually flat, pW/cm’, indicating that the liquid crystal in SLM approaches the saturation state. We also see that the theoretical conclusions and the experimental data are consistent and the rms error calculated between the curves is 0.04~. If the slide transrnissivity changes gradually along the vertical direction, and allowing the writing light to pass through it, a liquid-crystal prism as described in the literature [6] can be achieved. Fig. 7b shows the phase profile modulated by the SLM when the writing light intensity changes gradually. After the transparency slide was projected to a region of approximately 1 X 1 cm* in the SLM, in which the wavefront error is smaller, we also observed lateral image displacement with a microscope and a long focal length lens. If the projector is replaced by a CRT, we can easily obtain any phase distribution. Indeed, the SLMs controlled by the writing light intensity are very convenient phase modulators, if their wavefront errors can be further improved. Several problems need to be considered in the experiment. First, the tilt angle 8 changes with the voltage u applied to the SLM, so we had to choose an applied voltage resulting in a sharp variation of the tilt angle 0. From Eq. (2), we get: 2 de (4) a,= Uo(eP + e-O> ’
235
139 (1997) 232-236
08
fu)
7
-6
-4
-2
0
2
4
6
The voltage applied to the SLM (VOLT) Fig. 8. First derivative of the tilting angle #/du applied voltage (~1.
versus the
where, ,!3= (u - vth)/vO. The curve of the first derivative of the tilting angle versus the applied voltage is shown in Fig. 8. From Fig. 8, we know that when the applied voltage is around 1.6 V, A@ varies sharply. So the applied voltage should be near 1.6 V in the experiment. Secondly, the beam splitter in Fig. 3 can be either a polarizing beam splitter or a common beam splitter. As we want to measure the phase shifts, not the intensity modulation, no polarizing splitters are necessary in such an operating configuration. Third, since the contrasts of interference fringes are dependent on the intensities of the two beams reflected from the mirror and from the SLM as shown in Fig. 3, we must adjust the measuring configuration to let the intensities of the two beams become as close as possible.
4. Conclusions In conclusion, a qualitative description of the SLM working as a phase modulator controlled by the writing light intensity is given. Experimental verification was car ried out, and in particular, the experimental data are consistent with the theoretical results with rms error of 0.04n between the curves.
Acknowledgements The authors would like to thank Prof. Miao Runcai and Dr. Chen Shaowu for valuable discussions. The work presented here is partly supported by the National Nature Science Foundation of China.
References Fig. 7. (a) The transparency slide with its transrnissivity changing gradually; (b) the theoretical phase profile modulated by the SLM.
[l] G.D. Love, J.S. Fender and S.R. Restaino, tonics News (October 1995) 16.
Optics and Pho-
236
Y. Zhisheng et al./ Optics Communications
[2] Konforti, N. and Marom, E. Optics Lett.., (Vol. 13) (1988) 251. [3] Vorontsov, M.A., Ricklin, J.C. and Carhart, G.W. Opt. Eng.., (Vol. 34) (1995) 3229. [41 Vorontsov, M.A., Katulin, V.A. and Naumov, A.F. Optics Comm.., (Vol. 71) (1989) 35. [51 Lu, K. and Saleh, B.E.A. Opt. Eng.., (Vol. 29) (1990) 240. [6] Love, G.D., Major, J.V. and Purvis, A. Optics Lett.., (Vol. 19) (1994) 1170. [7] Love, G.D. Appl. Optics., (Vol. 32) (1993) 2222. [81 Amako, J., Miura, H. and Sonehara, T. Appl. Optics., (Vol. 32) (1993) 4323. [9] Dou, R. and Giles, M.K. Optics Lett.., (Vol. 20) (1995) 1583. [lo] Carcole, E., Davis, J.A. and Cottrell, D.M. Appl. Optics., (Vol. 34) (1995) 5118. [ll] Love, G.D., Andrews, N., Birch, P., Buscher, D., Doel, P.,
[12] [13]
1141 [15] [16] 1171
139 (1997) 232-236
Dunlop, C., Major, J., Myers, R., Purvis, A., Sharples, R., Vick, A., Zadrozny, A., Restaino, S.R. and Glindemann, A. Appl. Optics., (Vol. 34) (1995) 6058. Yocky, D.A., Barnes, T.H., Matsumoto, K., Ooyama, N. and Matsuda, K. Optik., (Vol. 84) (1990) 140. Grinberg, J., Jacobson, A.D., Bleha, W.P., Mileer, L., Fraas, L.M., Bosweld, D. and Myer, G. Opt. Eng.., (Vol. 14) (1975) 217. Fraas, L.M., Grinberg, J., Bleha, W.P. and Jacobson, A.D. J. Appl. Phys.., (Vol. 47) (1976) 576. Fraas, L.M., Bleha, W.P., Grinberg, J. and Jacobson, A.D. J. Appl. Phys.., (Vol. 47) (1976) 584. B. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980) p. 680. Li, Y., Fu, X., Yun, 2. and He, 2. SPJE., (Vol. 2778) (1996) 977.
Optics Communications 139 (1997) 232-236
Phase-only modulation with a spatial light modulator controlled by writing light intensity Yun Zhisheng
*, Li Yulin ‘, Liu Jifang, He Zhengquan
Xi’an Institute of Optics and Precision Mechanics, Academia Sinicu, P.O. Box 80(24), Xi’an 710068, China
Received 23 October 1996; revised 18 December 1996; accepted 14 January 1997
Abstract A qualitative description of phase-only modulation with an optically addressed SLM controlled by writing light intensity is presented. Experimental verification is carried out, and the results are consistent with the theoretical conclusions.
1. Introduction Liquid crystals as spatial light intensity modulators have been widely used in coherent and incoherent signal processing. However, their features of phase-only modulation show more promising applications in adaptive optics (AO), pattern recognition and phase-only filters, etc. In recent years, these characteristics have been studied extensively [l--12]. Here, a twisted nematic liquid-crystal spatial light modulator (TNLC SLM) addressed by writing light working as a phase-only modulator is investigated. If the dependence of phase-only modulation of commercial SLMs on writing light intensity is clearly known, SLMs can more conveniently be used as compensators for A0 and phase division components. Vorontsov et al. [4,5] have studied the phase-only modulation of a SLM controlled by writing light. In this paper, we give a qualitative description of this issue in the following discussion. The SLM used in our experiment consists of a number of thin film layers sandwiched between two glass substrates [17]. A low voltage (1 to 10 V,,,) audio frequency power supply is connected to the two outer, thin film indium-tin-oxide (ITO) transparent electrodes. The lightsensitive layers are made of cadmium telluride (CdTe) and
* Corresponding author. E-mail: [email protected]. ’ Member SPlE.
cadmium sulfide (CdS). The dielectric mirror and the blocking layer separate the photoconductor from the readout light beam. These are the major design features of the SLM, which is much similar to the light valve described in Ref. 1131.
2. Theoretical
analyses
The equivalent circuit for a TNLC SLM [14,15] is shown in Fig. 1. The region in the dashed square represents the equivalent circuit of the light-sensitive element, C,, C, and C, represent the capacitances of the mirror, the liquid crystal and the light-sensitive element, respectively. The diode represents the CdTe/CdS heterojunction diode. According to Frass’s mode [14], the current flow in the illuminated element is larger than that in the nonilluminated element, i.e., the voltage applied to the LC element varies with the illuminating light intensities. If the current Z, in Fig. 1 is obtained, the voltage applied to the LC element will be known, and the relation between them can be described by the following equation, u=z,
XI,,
(la>
where, v is the voltage applied to the LC, z1 is the impedance of the LC. To study the phase variations of SLMs with writing light intensities, firstly we must know the relation between current I, and writing light intensity @. Supposing the
0030-4018/97/$17.00 Copyright 0 1997 Published by Elsevier Science B.V. All rights reserved. PII s0030-4018(97)00053-9
Y. Zhisheng et al. / Optics Communications
molecules varying expressed by [5],
with the applied
H=G-Zfan-t{exp[-(?)I),
Fig.
1.
Equivalent circuit of a resolution element in the SLM.
25
Writing Light Intensity @w/cm’) Fig. 2. Experimental data for the current I, versus the writing light intensity Cp.
relation is written as I, = FL@], which can be obtained experimentally, as shown in Fig. 2, we rewrite Eq. (la) as u=zj
(lb)
XF[@],
where F is a function of writing light intensity. We know that the impedance of the LC element depends on the frequency of the applied voltage. If the frequency is fixed, the impedance is constant. Then, the voltage (v) applied to the LC element varying with the writing light intensities (a) can qualitatively be described by Eq. (lb). It is known [2] that TNLC SLMs behave as phase-only modulators when they are operated below the conventional optical threshold. The tilt angle 0 of liquid-crystal
He-Ne Laser
233
139 (1997) 232-236
voltage
u>u,,
(2)
where uth is the threshold voltage below which no tilting occurs and ua is the excess voltage at which the tilt angle is 49.6”. The liquid crystal used in our experiment is TNLC E7, whose threshold voltage is 0.937 V. The ordinary refractive index n, and the extraordinary refractive index n, of the E7 are 1.5175 and 1.7434, respectively. The extraordinary refractive index exhibited by anisotropic molecules, which are tilted by an angle 0, is given by [16]
So the phase modulation controlled by writing light intensity is obtained by combining Eqs. (l), (2) and (3). If the distribution of writing light intensity is expressed by @(x, y), the phase modulation U( x, y) is obtained by the relationship U(x, y) = G[@(x, y)], where x, y are spatial variables on the SLM, G is a function of phase modulation of the SLM.
3. Experiments
and discussions
To verify the previous theoretical conclusions, we carried out an experiment sketched schematically in Fig. 3, which is a Twyman-Green interferometer. The phase shifts introduced by writing light intensities were measured by placing a SLM at one arm of the interferometer. The projector lens images a transparency slide on the SLM writing surface. The transparency slide is divided into two parts. The transmissivity of one part in the transparency slide is unchangeable and the transmissivity of the other part of the transparency slide is changeable. By changing the transmissivity of the changeable part of the trans-
Projection Lens
I Slide Screen
u can be
ac Voltage Source
Fig. 3. Experimental scheme for phase modulation measurement based on the Twyman-Green interferometer.
234
Y. Zhisheng et al. / Optics Communications
Fig. 4. (al One of the transparency
slides; (b) interference
139 (1997) 232-236
pattern with the slide in (a); (c) theoretical
a
:II Fig. 5. Three transparency slides with different transmissivities (a), (b) and (c); the interferograms (d), (e) and (f> corresponding to (a), (b) and (c), respectively.
parency slide, we can get different writing light intensities. The beams reflected from the mirror and from the SLM interfere in the Twyman-Green interferometer. By measuring the shifts of the interference fringes at the two parts of the slide we can obtain the relative phase shifts varying with the writing light intensities.
phase modulation
distribution.
Fig. 4a is a transparency slide, in which the writing light can pass through the white squares and be blocked by the black squares. Fig. 4b shows the interferogram that clearly gives us the relative phase shifts. Fig. 4c shows the theoretical phase modulation distribution. From Fig. 4b, we can see that the interferogram does not agree exactly with the theoretical results as shown in Fig. 4c. This is caused by the wavefront errors of the SLM. The rms wavefront error of the SLM in our experiment is not better than h/3 [17] (A denotes the wavelength). Three main factors result in wavefront errors. First, the thickness of the liquid-crystal between the two glass plates is not constant across the whole interior surface of the plates. Second, the writing light intensity upon the writing surface of the SLM is not uniform. Third, the thickness of the glass substrates of the SLM is not the same across the whole surface. If the three drawbacks above are overcome, the phase modulation distribution will agree better with the theoretical results. Fig. 5a, 5b and 5c are three transparency slides with different transmissivities. When writing light goes through them, we can measure the shifts of interference fringes, respectively, as shown in Fig. 5d, 5e and 5f. By measuring the shifts of interference fringes versus different writing
. . theoretical results
MO
4ca
EGO
er.a
Iwo
Wriiing light intensity @w/cm*)
3
Writing light intensity (,uw/cm2)
Fig. 6. (a) Curves of the relative phase shifts versus writing light intensities; (b) the relative phase shifts versus the writing light intensities below 200 p,W/cm’. The solid curve represents the experimental data and the dotted curve represents the theoretical results.
Y. Zhisheng et al. / Optics Communications
light intensities, we plotted the curve of the relative phase shifts versus writing light intensities in Fig. 6a, which is shown by a solid line. The dotted curve in Fig. 6a is the theoretical results of the previous theoretical discussions. In order to see the relative phase shifts varying with the writing light intensities below 100 kW/cm’, we enlarge the curves of Fig. 6a as demonstrated in Fig. 6b. From Fig. 6b we see that the sensitivity threshold, i.e. the minimum level of writing light for the writing process, is very low. The value of the minimum level obtained experimentally is approximately 6.3 kW/cm’. When the writing light is below the sensitivity threshold, the relative phase shift is a constant given by 1.55~. When the writing light intensity is above the sensitivity threshold, the relative phase shift reduces to 1.33~ from 1.55~~ and continues decreasing gradually. When the writing light intensity exceeds 800 the curves in Fig. 6 become gradually flat, pW/cm’, indicating that the liquid crystal in SLM approaches the saturation state. We also see that the theoretical conclusions and the experimental data are consistent and the rms error calculated between the curves is 0.04~. If the slide transrnissivity changes gradually along the vertical direction, and allowing the writing light to pass through it, a liquid-crystal prism as described in the literature [6] can be achieved. Fig. 7b shows the phase profile modulated by the SLM when the writing light intensity changes gradually. After the transparency slide was projected to a region of approximately 1 X 1 cm* in the SLM, in which the wavefront error is smaller, we also observed lateral image displacement with a microscope and a long focal length lens. If the projector is replaced by a CRT, we can easily obtain any phase distribution. Indeed, the SLMs controlled by the writing light intensity are very convenient phase modulators, if their wavefront errors can be further improved. Several problems need to be considered in the experiment. First, the tilt angle 8 changes with the voltage u applied to the SLM, so we had to choose an applied voltage resulting in a sharp variation of the tilt angle 0. From Eq. (2), we get: 2 de (4) a,= Uo(eP + e-O> ’
235
139 (1997) 232-236
08
fu)
7
-6
-4
-2
0
2
4
6
The voltage applied to the SLM (VOLT) Fig. 8. First derivative of the tilting angle #/du applied voltage (~1.
versus the
where, ,!3= (u - vth)/vO. The curve of the first derivative of the tilting angle versus the applied voltage is shown in Fig. 8. From Fig. 8, we know that when the applied voltage is around 1.6 V, A@ varies sharply. So the applied voltage should be near 1.6 V in the experiment. Secondly, the beam splitter in Fig. 3 can be either a polarizing beam splitter or a common beam splitter. As we want to measure the phase shifts, not the intensity modulation, no polarizing splitters are necessary in such an operating configuration. Third, since the contrasts of interference fringes are dependent on the intensities of the two beams reflected from the mirror and from the SLM as shown in Fig. 3, we must adjust the measuring configuration to let the intensities of the two beams become as close as possible.
4. Conclusions In conclusion, a qualitative description of the SLM working as a phase modulator controlled by the writing light intensity is given. Experimental verification was car ried out, and in particular, the experimental data are consistent with the theoretical results with rms error of 0.04n between the curves.
Acknowledgements The authors would like to thank Prof. Miao Runcai and Dr. Chen Shaowu for valuable discussions. The work presented here is partly supported by the National Nature Science Foundation of China.
References Fig. 7. (a) The transparency slide with its transrnissivity changing gradually; (b) the theoretical phase profile modulated by the SLM.
[l] G.D. Love, J.S. Fender and S.R. Restaino, tonics News (October 1995) 16.
Optics and Pho-
236
Y. Zhisheng et al./ Optics Communications
[2] Konforti, N. and Marom, E. Optics Lett.., (Vol. 13) (1988) 251. [3] Vorontsov, M.A., Ricklin, J.C. and Carhart, G.W. Opt. Eng.., (Vol. 34) (1995) 3229. [41 Vorontsov, M.A., Katulin, V.A. and Naumov, A.F. Optics Comm.., (Vol. 71) (1989) 35. [51 Lu, K. and Saleh, B.E.A. Opt. Eng.., (Vol. 29) (1990) 240. [6] Love, G.D., Major, J.V. and Purvis, A. Optics Lett.., (Vol. 19) (1994) 1170. [7] Love, G.D. Appl. Optics., (Vol. 32) (1993) 2222. [81 Amako, J., Miura, H. and Sonehara, T. Appl. Optics., (Vol. 32) (1993) 4323. [9] Dou, R. and Giles, M.K. Optics Lett.., (Vol. 20) (1995) 1583. [lo] Carcole, E., Davis, J.A. and Cottrell, D.M. Appl. Optics., (Vol. 34) (1995) 5118. [ll] Love, G.D., Andrews, N., Birch, P., Buscher, D., Doel, P.,
[12] [13]
1141 [15] [16] 1171
139 (1997) 232-236
Dunlop, C., Major, J., Myers, R., Purvis, A., Sharples, R., Vick, A., Zadrozny, A., Restaino, S.R. and Glindemann, A. Appl. Optics., (Vol. 34) (1995) 6058. Yocky, D.A., Barnes, T.H., Matsumoto, K., Ooyama, N. and Matsuda, K. Optik., (Vol. 84) (1990) 140. Grinberg, J., Jacobson, A.D., Bleha, W.P., Mileer, L., Fraas, L.M., Bosweld, D. and Myer, G. Opt. Eng.., (Vol. 14) (1975) 217. Fraas, L.M., Grinberg, J., Bleha, W.P. and Jacobson, A.D. J. Appl. Phys.., (Vol. 47) (1976) 576. Fraas, L.M., Bleha, W.P., Grinberg, J. and Jacobson, A.D. J. Appl. Phys.., (Vol. 47) (1976) 584. B. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980) p. 680. Li, Y., Fu, X., Yun, 2. and He, 2. SPJE., (Vol. 2778) (1996) 977.