Wavelength and angular selectivity of high diffractionefficiency reflection holograms in silver halidephotographic emulsion
J. M. Heaton and Laszlo Solymar
The diffraction properties of bleached reflection holograms, recorded by two plane waves in Agfa 8E56 pho-
tographic emulsion, are studied at different replay wavelengths. Measurements of the transmitted beamintensity against the replay angle of incidence are compared with a theoretical model to determine the wave-length dependence of the average refractive index, the average absorption, and the refractive-index modula-tion of the hologram.
1. Introduction
Volume phase reflection holograms formed in gela-tin-based recording materials are beginning to showmany potential applications as optical elements anddisplay holograms. One of the advantages of using thereflection geometry is that a reflection grating has astrong wavelength selectivity and can therefore be usedwith broadband or white light illumination. For thisreason it is of interest to understand the wavelengthdependence of the optical and material properties ofthis type of reflection hologram.
A detailed analysis of the properties of transmissionholographic optical elements in silver halide photo-graphic emulsion was presented recently by Syms andSolymar1: their approach involved the measurementof the transmitted beam intensity against angle of in-cidence, and a simple coupled wave model2 was used toestimate the grating properties (for example, the re-fractive-index modulation) which could not be mea-sured by independent methods. In their analysis theyconsidered the effects of replaying a plane transmissiongrating at different wavelengths and briefly mentionedthe dispersion properties of the recorded hologram. Amore detailed analysis of dispersion in transmissionholograms has been presented by Slinger et al. 3 usinga similar method although, because transmission grat-
The authors are with University of Oxford, Department of Engi-neering Science, Holography Group, Parks Road, Oxford OX1 3PJ,U.K.
ings are not very selective to different wavelengths, theeffects of dispersion in transmission holograms are notas important as in reflection holograms. Results pre-sented in this paper show that a significant error in theposition of the Bragg angle is introduced if dispersionis not allowed for in the analysis of reflection gratings.A simple method of analyzing reflection gratings waspresented recently by Owen et al. 4 using a combinationof coupled wave theory and Fresnel boundary coeffi-cients. However their analysis and experimental resultsdid not include replay at wavelengths other than thatused at recording and therefore the problem of disper-sion did not arise.
In this paper we concentrate on plane reflectiongratings recorded in silver halide photographic emulsionand present experimental results showing the angularand wavelength dependence of the transmitted beamintensity. Following Owen et al., we use a simple the-oretical model to describe the results and this model isused to estimate the wavelength dependence of theaverage refractive index, the refractive-index modula-tion, and the absorption of the recorded holograms. Toestimate the accuracy of this analysis an independentmethod of measuring the average refractive index of thegrating at different wavelengths was used and the re-sults were found to be in good agreement with thoseobtained from the transmission measurements.
II. Experimental
In this paper we consider one particular recordinggeometry which is shown in Fig. 1: the diagram showstwo collimated beams incident on an index matchingtank which contains the recording plate. The holo-grams were recorded in Agfa-Gevaert 8E56HD silverhalide photographic plates (Millimask HD, batch592503). These plates consist of a thin layer of fine
Fig. 1. Diagram of the hologram recording geometry using the indexmatching tank.
grain silver halide emulsion on a glass substrate. Theemulsion layer also contains an antiscatter dye and asensitizing dye which makes the plates particularlysensitive to green light. The emulsion layer typicallyhas a thickness of 6 jum and a refractive index, at therecording wavelength (514.5 nm), of 1.64 although thesefigures vary somewhat between different batches ofplates. The glass substrate has a thickness of 1.5 mmand a refractive index of -1.51. To reduce boundaryreflections, which could record spurious gratings,4 theplate was surrounded by an index matching liquid, di-n-butyl phthalate, and the liquid was held in a glass-sided tank as shown in Fig. 1.
The two recording beams were produced by anargon-ion laser in single-mode operation with wave-length X = 514.5 nm. The recording beams were spa-tially filtered, expanded, collimated, and partiallymasked so that an area of the hologram, -40 mmsquare, was uniformly illuminated by each beam. Thetwo beams were polarized in the vertical direction,perpendicular to the plane of incidence. The interbeamangle in air was 900 and each beam was incident on thetank at 450 as shown in Fig. 1. To separate the dif-fracted beams and the specularly reflected beams atreplay, the plate was not positioned parallel to the tankwalls but was rotated by 1.7° from this position so thatthe effective external recording angles were 420 and 480.The recording beam intensities, incident on the tank,were both -200 jiW/cm 2 and exposure times rangingfrom 0.2 to 10 sec were used.
After exposure the photographic plates were devel-oped and bleached. The developer consisted of cate-chol (10 g/liter), sodium sulfite (5 g/liter), and sodiumcarbonate (30 g/liter) in distilled water. The bleachconsisted of parabenzoquinone (2 g/liter), citric acid (15g/liter), and potassium bromide (50 g/liter) also in dis-tilled water. This process is particularly suitable forreflection holograms because it leaves the thickness ofthe emulsion layer very similar to that of the unpro-cessed plate.5 Finally the plates were brominated toprevent print-out during replay.
Fig. 2. Diagram of the hologram replay geometry using a white lightsource and spectrometer.
The apparatus used to measure the transmitted beamintensity against angle for different wavelengths isshown in Fig. 2. This consisted of a collimated beamfrom a white light source incident on the hologramwhich was held on a rotation stage in an index matchingtank.' The incident beam was polarized in the samedirection as the axis of rotation and the transmittedbeam was examined using a spectrometer to separatea particular wavelength. A photomultiplier was usedto measure the intensity of the beam which emergedfrom the spectrometer and the signal from the photo-multiplier was normalized using the signal from aphotodiode which measured the intensity of the wholelight source. The hologram was rotated about a verticalaxis on a stepper motor controlled rotation stage whichwas driven by a computer. The normalized signal fromthe spectrometer was also connected to the computervia an A-D converter so that the transmitted beammeasurements could be stored digitally.
For each particular wavelength, measurements of thetransmitted beam intensity were made at intervals of0.50 as the hologram was rotated through 1500: from-75° to +750 where 0° corresponded to normal inci-dence. After each angle scan the recorded measure-ments were normalized with respect to the photomul-tiplier signal when the plate was temporarily removedfrom the tank. The measurements normalized in thisway give the change in the transmitted beam intensitydue to the hologram alone.
IMI. Theory
The theoretical model used to analyze the transmit-ted beam intensity measurements was similar to thatdescribed by Owen et al. 4 A wave vector diagram of therecording configuration, showing the recorded wavevectors (o and er), the recorded grating (Ko), and partof the Ewald sphere within the emulsion, is given in Fig.3(a). In this diagram the x direction is normal to thehologram surface and the polarization of each beam wasperpendicular to the x-z plane. The recorded hologramwas assumed to have a dielectric constant (r) givenby
within an emulsion layer of thickness d. The replayconfiguration which satisfies the Bragg conditions isshown as a vector diagram in Fig. 3(b) for three differentreplay wavelengths. At replay the grating vector K wasassumed to be similar to the recorded grating vector(Ko): the x component of this vector may have changedslightly during the development and bleaching pro-cesses.
To calculate the transmitted beam intensity weconsider the coupling between incident and diffractedwaves with wave vectors p and a, respectively. Thediameter of the Ewald sphere, and therefore the mag-nitude of both of these replay wave vectors, depends onthe replay wavelength and the average refractive indexof the emulsion at that wavelength. The coupled waveanalysis follows that given by Kogelnik2 but instead ofusing K vector closure the following procedure is used.The wave vector (a) of the diffracted beam is assumedto lie always on the Ewald sphere and the z componentof this vector (e,) is given by the difference between thez components of the vectors p and K:
oz = pz - Kz. (3)
For a general replay angle the corresponding expressionfor the x components contains an extra term (4') whichis an off-Bragg or dephasing parameter:
ax = p. - K. -0. (4)
The x dependence of the reference and signal beamamplitudes R (x) and S(x) is therefore described by thecoupled wave equations:
dRCR d + a0 R + jKS exp(+j4x) = 0, (5a)
dxdS
CS dS + a0S + jKR exp(-ji'x) = 0, (5b)
where the coupling constant K is defined by the ex-pression
K = - l- , : = (c0,Y0'E)1/2.4Ero 2
The parameters cR and cs are given by p/f3 and ux/3,respectively: for the reflection geometry cs is thereforenegative. A solution for the transmitted beam R (x =d) can be derived from the coupled wave equations andwritten in the form6
R(d) = exp -j - -I IcoshT- jI sinhT (6)CR 1
whereda (1 1 'd K2d2 \1/2=--- +-, and _ 22 CR CSJ 2 CRCS
Equation (6) was used in the theoretical model tocalculate the beam intensity on the boundary of thehologram emulsion layer.4
We must also include in the calculations reflectionsand refractions at boundaries, when the beam passes
b ).
z
x
x
Fig. 3. Vector diagrams showing (a) the construction of the recordedgrating vector within the emulsion, and (b) the replay construction
at three different wavelengths.
from one medium to another, using the Fresnel coeffi-cients and Snell's law, respectively.4 The two impor-tant refractive indices for calculations are those of theindex matching liquid (ni) and of the emulsion layer (no= \Jc). The refractive index of the hologram glasswas also included in calculations although it was foundto have little effect on the results and was thereforeassumed to be constant, with the value 1.51, for allwavelengths. Note that the refractive index of theindex matching liquid must be known as a function ofwavelength which, for di-n-butyl phthalate, has beenmeasured independently.
Before attempting to compare the experimentaltransmitted beam intensity measurements with thistheoretical model it was important to make estimatesof as many of the parameters in the model as possiblefrom independent measurements.1 One of the mostimportant parameters to know accurately was theemulsion layer thickness (d). At high angles of inci-dence, far from the Bragg angle, the emulsion layerbehaved as an etalon. This was seen on the spectrom-eter angle scan measurements [Figs. 4(a)-(d)] as weakoscillations which increased in strength at large anglesof incidence (0). Also a laser beam reflected from theemulsion layer at glancing incidence showed similaroscillations or interference fringes.5 It was possible tomodel this effect by assuming that the emulsion layerbehaved as a uniform parallel-sided dielectric slabsurrounded by a medium with the same dielectric con-stant as the index matching liquid. The dielectric slabwas assumed to have a uniform absorption (ao) and thetransmitted and reflected beam intensities were pre-dicted, for different incidence angles, by matching theboundary conditions and solving the relevant simulta-neous equations numerically.
Etalon interference fringes from laser (514.5-nm)transmission and reflection measurements were com-pared with this theoretical model to estimate the valuesof the average dielectric constant and the thickness of
Fig. 4. Graphs of the normalized transmitted beam intensity against angle for different replay wavelengths: (a) X = 464.5, 504.5, and 544.5nm; (b) X = 474.5, 514.5, and 554.5 nm; (c) X = 484.5, 524.5, and 564.5 nm; (d) X = 494.5, 534.5, and 570.0 nm (... experimental, -
theoretical).
the emulsion layer.5 The absorption (o) was estimatedfrom the transmitted beam measurements and used inthe calculations of the reflected beam intensity. Bymatching the frequency, strength, and phase of the re-flected beam oscillations it was possible to estimate theemulsion thickness to within 0.05 Am and the refractiveindex at this wavelength to three significant figures.
The spectrometer angle scan measurements alsoshowed etalon effects at high angles of incidence be-cause the di-n-butyl phthalate was index matched to thehologram glass rather than the emulsion layer. Thiswas observed for all replay wavelengths and was par-ticularly noticeable at longer wavelengths. Using theemulsion thickness given by the laser reflection mea-surements, it was possible to obtain an independentestimate of the wavelength dependence of the emulsionrefractive index by comparing the etalon fringes for allwavelengths with the etalon model.
Finally, in this matching process, the known and es-timated parameters were used in the transmitted beamintensity calculations to compare the experimental re-sults from the spectrometer to the predictions of thetheoretical diffraction model. From this comparisonthe unknown refractive-index modulation (n1 E Erl/2no)and absorption modulation (a,) were estimated fordifferent wavelengths.
IV. Results
Results of the transmitted beam intensity measure-ments, for one of the recorded holograms, are shown in
Figs. 4(a)-(d) as graphs of hologram transmissionagainst the angle of incidence of the white light beam.The exposure time for this hologram was 2.0 sec and thereplay measurements were made at wavelengths be-tween 464.5 and 570.0 nm as shown. The results of thetheoretical calculations are also shown in Figs. 4(a)-(d),superimposed on the corresponding experimentalmeasurements. Note that, for each wavelength, thecalculated position, width, and depth of the transmis-sion minima due to the Bragg interaction are in goodagreement with the experimental results. As thewavelength is increased from 464.5 nm, the Bragg anglesmove toward normal incidence, as predicted by theEwald sphere construction shown in Fig. 3(b). Also, asexpected, the angular width of each transmission dipincreases with increasing wavelength until eventually,for a wavelength of 564.5 nm, the two Bragg dips com-bine to give one single transmission minimum. Thiscorresponds to backreflection of the incident beamwhen the wave vectors p and af are parallel to the gratingvector K. As the wavelength is increased further (570.0nm), the Bragg conditions can no longer be satisfied andthe diffraction efficiency decreases rapidly to zero asshown in Fig. 4(d).
For wavelengths close to the recording wavelength,the positions of the sidelobes of the Bragg interactionminima are predicted by the theoretical model althoughfor some wavelengths the sidelobe structure is not welldefined. The calculated average absorption level is inreasonable agreement with the experimental results
Fig. 5. Graphs of parameters used in numerical calwavelength: (a) refractive index of index matching 1refractive index of hologram emulsion layer, (c) av
of emulsion layer, (d) hologram refractive-inde
although, because we have neglected the second deriv-atives in the coupled wave equations, the superimposedetalon effects, particularly noticeable at high angles ofincidence, are not predicted by this model. These ef-fects were found to be unusually large for most of thehigher efficiency reflection holograms which weremeasured: compare, for example, with similar resultsfor transmission gratings given in the paper by Symsand Solymar.1 This suggests that the refractive indexof the emulsion layer is large and that the emulsion
a thickness is uniform over the hologram surface, possibly
600 64 0 due to the reflection development and bleaching pro-cess, or possibly because of the different orientation ofthe grating vector in a reflection hologram.
In matching the experimental curves at the variouswavelengths we had six parameters, namely, no, ni, ao,a,, d, and, the refractive index of the index matchingliquid, ni. Of these parameters, d, no, and ni weremeasured independently (to be discussed later) and wehad to choose the other three parameters to optimizethe agreement with the experimental curves.
The refractive index of the index matching liquid wasmeasured using an Abbe refractometer over a widerange of different wavelengths and the results, between440 and 640 nm, are given by the crosses in Fig. 5(a).
b The values of the average emulsion refractive index (no),560 580 estimated by matching the etalon effects at high angles
of incidence, are shown in Fig. 5(b) as a function ofwavelength. We can, at this stage, check whether theBragg angle derived from the values of no and ni agreeswith the positions of the experimentally measuredtransmission minima, and this was indeed found withhigh accuracy. The etalon effects also gave the valuefor the thickness of the emulsion layer as 6.13 ,im,somewhat above that reported previously for similarphotographic plates.14 5
A graph of average emulsion absorption (a0 ) againstreplay wavelength is given in Fig. 5(c). By indexmatching the hologram boundaries the effects of surfacereflections on the transmitted beam intensity were small
C so that the absorption could easily be measured accu-560 580 rately. The average absorption was found to depend
strongly on the wavelength, changing from 0.015/Mm to0.0044/Mm in the wavelength range considered. Thereare two effects which will contribute to the change of theabsorption with wavelength: one is the ohmic loss dueto the electrical conductivity of the emulsion and theother is the scattering from grains in the emulsion whichis strongly wavelength dependent. The parameter omeasures a combination of the two effects which wehave not been able to identify separately.
We are now left with the two modulation parameters,ni and a,, to match the experimental results to thetheory. These cannot be estimated from independent
;d measurements. The most important parameter, as may560 5 0 be expected, is the modulation of the refractive index,
which will determine the depth of the transmissionlculations against minima. The choice of nj, given in the form of a graphiquid, (b) average in Fig. 5(d), together with the previously obtained pa-erage absorption rameters, now yield the theoretical curves shown pre-x modulation. viously in Figs. 4(a)-(d). Note that the calculated
values of nl do not lie on a monotonically decliningcurve but show a slight increase near the recordingwavelength. This means that the depth of the trans-mission dips at these wavelengths was larger than wouldbe expected from dispersion effects alone. We believethat the actual values of n, fall close to the continuouscurve in Fig. 5(d) and the difference can be accountedfor by the presence of "noise gratings" 7,8 which wereformed during the recording process between the re-cording beams and their own scattered light within theemulsion. When measuring the transmitted beam in-tensity, some of the incident light would have beendiffracted by noise gratings when the replay conditions,wavelength and angle, were similar to the recordingconditions. Therefore the transmitted beam intensitywould be depleted more strongly than if the noisegratings were not present.
In contrast to transmission holograms, the value ofa, affects only slightly the calculated curves of trans-mitted beam intensity. Selecting values of al/ao be-tween 0 and 10% made hardly any difference in theagreement between the experimental and theoreticalresults. Therefore all that we can say is that the ab-sorption modulation appears to be small and, verylikely, its dispersion follows that of ao0.
The results presented were for the hologram ofhighest diffraction efficiency at the recording wave-length. No detailed comparisons have been made be-tween the experimental results from other hologramsand the theoretical model but the measurements wehave performed on other holograms showed similartendencies to the results reported here.
V. Conclusions
The diffraction properties of reflection holograms,recorded in Agfa 8E56 silver halide emulsion by twoplane waves, have been studied at different replaywavelengths. Of the six parameters considered in themodel, three were determined using independentmeasurements and, by adjusting the other three, goodagreement between experiment and theory was foundfor all wavelengths. Using this method we have beenable to determine the wavelength dependence of theaverage emulsion refractive index, the average emulsionabsorption, and the modulation of the refractive indexwhich forms the hologram.
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Formed in Bleached Photographic Emulsions," Appl. Opt. 22,1479(1983).
2. H. Kogelnik, "Coupled Wave Theory for Thick Hologram Grat-ings," Bell Syst. Tech. J. 48, 2909 (1969).
3. C. W. Slinger, R. R. A. Syms, and L. Solymar, "Nonlinear Re-cording in Silver Halide Planar Volume Holograms," Appl. Phys.B 36, 217 (1985).
4. M. P. Owen, A. A. Ward, and L. Solymar, "Internal Reflections inBleached Reflection Holograms," Appl. Opt. 22, 159 (1983).
5. D. J. Cooke and A. A. Ward, "Reflection-Hologram Processing forHigh Efficiency in Silver-Halide Emulsions," Appl. Opt. 23, 934(1984).
6. L. Solymar and D. J. Cooke, Volume Holography and VolumeGratings (Academic, New York, 1981).
7. R. R. A. Syms and L. Solymar, "Noise Gratings in PhotographicEmulsion," Opt. Commun. 43, 107 (1982).
8. A. A. Ward, J. M. Heaton, and L. Solymar, "Efficient NoiseGratings in Silver Halide Emulsions," Opt. Quantum Electron. 16,365 (1984).
The authors would like to thank the Science andEngineering Research Council for support.
