Dry photopolymer filmsfor computer-generated infraredradiation focusing elements
Yuri B. Boiko, Vladimir S. Solovjev, Sergio Calixto, and Daniel-Joseph Lougnot
A new technological approach makes fabrication of relief computer-generated focusing elements for IRradiation by use of a dry photopolymer recording material possible. The formation of a relief structureby self-development takes place in the dark, subsequent to the holographic illumination, without wetprocessing. Consequently these diffractive elements exhibit low surface scattering. The formation of asurface wave of the monomer along the light-darkness boundary is observed for the first time to ourknowledge and confirms the previously proposed thermodynamic model of the mechanism of thehologram formation in photopolymerizable layers. Dye-sensitized polymerization of acrylamide is foundto produce nonlinearity of the relief recording. At least partial compensation of this nonlinearity isattained by the introduction of appropriate corrections into the computer-generated amplitude function.A diffraction efficiency of 55% is obtained for CO2 laser radiation (X = 10.6 atm).
Photopolymerizable liquid layers displaying relief-formation properties have been described recently.1This process permits the fabrication of relief com-puter-generated focusing elements for far-IR radia-tion.2 In addition, dry photopolymerizable layersare suitable for holographic recordings and can lead toimproved characteristics for refractive-index imag-ing4 and to a microrelief embossing technology. 5
However, to our knowledge, relief-formation proper-ties of this type of material have never been
When this research was performed, Yu Boiko and S. Calixto werewith the Holographic Laboratory, Centro de Investigaciones enOptica, Apartado Postal 948, Leon 37000, Guantajuato, Mexico; V.Solovjev was with the Department of Cybernetics, Samara AviationInstitute, 151 Molodogvardejskaya Street, Samara 443001, Russia;and D.-J. Lougnot was with the Laboratoire de PhotochimieGenerale, Unite de Recherche au Centre National de la RechercheScientifique no. 431, 3 rue A. Werner, 68093 Mulhouse Cedex,France. Y. Boiko, to whom correspondence should be addressed,is now with the Division of Chemicals and Polymers, Common-wealth Scientific and Industrial Research Organisation, PrivateBag 10, Clayton, Virginia 3168, Australia. The name of theinstitution with which V. Solovjev is affiliated has been changed toImage Processing Systems Institute, Russian Academy of Sciences.
investigated. The suitability of dry photopolymeriz-able films for fabricating relief diffraction elements isdiscussed in this paper. Special attention is paid tothe effect of the various parameters on relief-formation properties. A mechanism for the forma-tion of relief structure is also discussed.
2. Experimental Method
A technology suggested for the fabrication of diffrac-tive optical elements includes mainly four stages:(1) dry polymer preparation; (2) exposure through anamplitude mask (see Fig. 1), (3) relief self-develop-ment in the dark, and (4) fixing by overall exposure.The method used for preparation of the dry photopoly-mer mixture is given elsewhere.3 This mixture con-sisted of acrylamide (AA) as the monomer base,Methylene Blue (MB) as a sensitizer, triethanolamineas a coinitiator, and polyvinyl alcohol as a binder.The photopolymerizable water solution was spreadon a glass substrate and subjected to a drying periodunder normal room conditions (temperature 20°-30 0C, relative humidity 40%-50%) for 24-48 h.
The exposure of the sensitive layer through thecomputer-generated amplitude mask was performedby means of an initiating radiation. A 300-W halo-gen lamp was used for illumination. The amplitudeholograms used as amplitude masks were generated
with a microcomputer (IBM PC), displayed on amonitor, and then photographed with a reduction.Masks fabricated by the Central Design Institute forUnique Instrumentation (Russian Sciences Academy,Moscow and Samara Branches) were also used. Themodulation depth of the optical density for the ampli-tude masks was between zero and 1.0 in one case andbetween zero and 1.5 in another.
After exposure, the relief structure was permittedto develop in a dark environment. No special process-ing of the exposed layers was needed. This self-development stage took 20 h. The formation ofthe relief was observed through an interference micro-scope of the Michelson type. Throughout this paper,the phase shift analyzed by this technique is assumedto be essentially caused by the local change of thick-ness; it does not take into account the contribution ofthe refractive index. A cadmium lamp emittingblue-green light (coherence length of 1 mm) was used forthe in situ interferometric observation so that alter-ation of the relief pattern by the readout radiationwas prevented.
After we achieved the required relief depth (7.5 jimwhen the radiation wavelength is 10.6-jIm, the inci-dent angle of the original plane wave is 450, andfocusing is performed by reflection to the directionperpendicular to that of the incident wave), we car-ried out a fixation treatment to saturate the polymer-ization process and thus stabilize the layer andprevent further relief distortion. For this purposewe used a halogen lamp with an intensity of 0.5-2mW/cm2 to provide uniform exposure for 10 h withessentially no dye bleaching. UV radiation was to-tally avoided during the fixation procedure, as itcauses MB destruction, prevents fixation, and resultsin an unstable element.
After fixation, the relief surface was coated byvacuum sputtering with copper and/or aluminumfilm. The profile of the fixed-relief structure wasthen analyzed with a surface-analyzing instrument.
The final focusing efficiency was measured by useof a CO2 laser as a radiation source (with a poweroutput of 5 W in the continuous-mode regime). Theinitial output beam was collimated with the help of agermanium-lens telescope, which produced a beam of
5-cm diameter.
Fig. 2. Resolution capability of relief formation.
3. Experimental Results of Relief Formation
A. Resolution
The resolving-power measurements of these dry pho-topolymer films were made with the standard U.S.Air Force 1951 three-bar test chart used as a binaryamplitude mask. The result obtained is shown inFig. 2. It is apparent that the depth r of the formedrelief decreases for spatial frequencies > 15 mm-1 .The maximum value of r attained was 15 jim for apolymer-layer thickness of 100 jim. These valuesshow that the film modulation achieved on exposureto light is enough to fabricate diffraction elementsworking with IR radiation. Radiation from a CO2laser (wavelength = 10.6 jim) is particularly suit-able for this purpose.
B. Relief Development
The time development of the relief formation wasobserved through an interference microscope. Thestages of the relief formation are shown schematicallyin Fig. 3.
On exposure the image of the chart on the polymersurface became contoured by the surface wave [Fig.3(b)] alongthe light-darkness boundary. This mono-
(b)
3
(d)
Fig. 3. Monomer surface-wave formation: (a) initial state, (b)exposure, (c) dark development, (d) final relief response.
mer surface wave arises from the abrupt decrease inthe chemical potential of the monomer moleculesinside the illuminated areas as a result of photopoly-merization.6 The relief structure arises [Fig. 3(c)]through monomer mass transport from nonlight tolight-struck areas. This mass transport is producedby the wide spreading of the surface wave within thebright areas and results in the enhancement of therelief structure.
We then fixed the final relief structure by an overallexposure to prevent a reverse process caused by thedevelopment of polymerization in former dark areas.We found that the relief structure parallels the initialfield intensity structure; i.e., the relief maxima coin-cided with the brightest areas of the field. Interest-ingly this result is contrary to what one would haveexpected from matereial shrinkages 7 caused by poly-merization. The consequences of this, as far as ahologram formation mechanism is concerned, arediscussed in Section 5.
C. Photochemical Action
The shape of the relief structure obtained with thismaterial was found to depend on the light intensity ofthe exposure (see Fig. 4) because of the dye bleachingeffect in the highly lit areas. As polymerization isinitiated by the energy absorbed by the sensitizer,there are at least two processes that involve MBmolecules simultaneously 3 8- 11 :
(i) The first process is the photoreduction of ex-cited MB molecules by the coinitiator (amine electrondonor), a process that generates active free radicals
r/rmax
(a)
I I l l I
0
I.
0
0
l I II I I
I I I
* - .. - 4- .. I-..
I l I
s' I
I/max I II , (de)
K ~~~(e)
0 2 4 mm
Fig. 4. Influence of the intensity I on the relief profile (schematicrepresentation): (a) weak dye bleaching (I = 1 mW/cm
2), (b)
evident dye bleaching (I = 4 mW/cm 2 ), (c) strong dye bleaching (I =8 mW/cm 2 ), (d) distortion of zones borders (I = 12 mW/cm 2 ), (e)distribution of intensity of the exposure light.
and that does not consume the MB sensitizer becauseof a back reoxidation by dissolved oxygen:
*MB + amine -> MB - + amine +, (1)
amine + amine- + H+,amine- +
+ AA -* polymer,amineo
MB -+ 02 -~regeneration of MB.
(2)
(3)
(4)
(ii) The second process is the bleaching of MBthrough a complex process that involves the excitedstate of the sensitizer and the monomer base itself(acrylamide):
*MB + AA - oxydo-reduction
(MB.- + monomer-derived radicals). (5)
The quantum yield of processes (1)-(4) is known todecrease with an increase of an incident light inten-sity.9"10 Accordingly it leads to a corresponding de-crease in the initiation efficiency under these elevatedintensities of exposure. In turn this decrease ofinitiation efficiency results in variation of the quan-tum yield of the initiation process under spatiallyinhomogeneous illumination and thus gives rise tothe nonlinearity of the medium's recording response.Moreover, the recovery of leuco-Methylene Blue andsemireduced species arising in mechanism (5) is veryslow (- 5 h) and does not manifest itself in the timescale of this experiment. Since dye bleaching in-creases with increasing light intensity, process (5)leads to the same sense of nonlinearity as that causedby processes (1)-(4). This process [formula (5)] pro-duces an increase in the nonlinearity of the opticalresponse. Thus loci of the maximum values of therelief do not necessarily occur where the incidentpattern is brightest but may well correspond toshaded regions in which better conditions of polymer-ization, under the initiating conditions of the experi-ment, prevail [Fig. 4(c)]. The light intensity beingless than 8 mW/cm2, the nonlinearity can be counter-acted, at least in part, by a corresponding maskcorrection. But for intensities > 8 mW/cm2 therelief distortion becomes too strong [Fig. 4(d)].
The degradation of resolving power with the spatialfrequency is revealed by a distortion of the reliefprofile. Beyond an upper limit (- 10 lines/mm),however, the above-mentioned photochemical causesof the relief distortion resulted in a decreased reliefdepth rather than in a strong disturbance of the reliefshape.
The intensity of the light exposure has a stronginfluence on the shape of the response function of therecording material and in consequence on the accu-racy of the relief profile recorded. This effect wasdemonstrated experimentally with four radiation lev-els [see Fig. 4] in the range 1-12 mW/cm2. Forintensities less than 2 mW/cm2 the dye bleaching was
relatively small (< 20% decrease in initial opticalabsorption for red light), and there was no visiblerelief-shape distortion [Fig. 4(a)]. At intensities of2-4 mW/cm2 with dye bleaching of 20%-30% of theinitial absorption, the recording resulted in an obvi-ous distortion of the shape of the relief profile [Fig.4(b)]. A strong nonlinearity of the recording re-sponse of the medium [Fig. 4(c)] was observed forintensities of 4-8 mW/cm2, with dye bleaching corre-sponding to values of 50%-80% of the initial absorp-tion. For intensities exceeding 8 mW/cm2, strongdye bleaching (> 80% reduction of the initial absorp-tion) corresponded to an important distortion of therelief profile [Fig. 4(d)] in the brightest parts of thelow-order zones. Accordingly, in order to approxi-mate a linear optical response, we must reduce therecording intensity to 2 mW/cm2 or less. Undersuch an intensity of illumination, however, the corre-sponding exposure time may exceed 30 min. Inpractice this is not suitable. An increase in thesensitivity of the medium may solve the problem, andthis will be a subject of further investigation. Here,another possibility for coping with this nonlinearity isthe reshaping of the amplitude mask.
In essence such reshaping method counteracts thenonlinearity of the recording by the introduction ofcompensative shifts in the values of the amplitudefunction of the mask used in the recording. Experi-mentally this was performed by replication of thecomputer-generated amplitude mask on high-con-trast photographic film. This resulted in an ampli-tude mask [see Fig. 5] with function values correctedfor the nonlinearity of the dry photopolymer. Par-tial compensation of the dry-polymer nonlinearitywas achieved by exposure of the recording layerthrough this corrected amplitude mask. This com-pensation essentially led to narrowing of the zoneparts with a nonlinear response (Fig. 6). Accord-ingly in this case the improvement of the resultingphase function was the consequence of the localiza-tion of the nonlinearity. The areas of localizationstill remained unsuitable, but they became narrowerand they affected diffraction efficiency less. At thesame time, outside the pointed areas, the relief profileapproached the required shape. The diffraction effi-ciency thus obtained was less than that for linearrecording, but the exposure time (under an intensity
0.5
T/ Tmax
I / II I
I I /~~~I \1 I ,,
5ItO 15 0 m5 10 15 20 mm
Fig. 5. Nonlinear correction of the mask: representation of theamplitude function of the kinoform to be reproduced within thelinear recording media (dashed curve); the function with intro-duced corrections of recording nonlinearity (solid curve).
324
24w.
16iy-
0
2 I
I
zVAA.AA.M4 ._-vA AA W,
0 5 10 15 mmFig. 6. Phase function of the kinoform [two-dimensional represen-tation, with theoretically calculated (curve 1) and experimentallyobtained (curve 2) values] for recording intensity I = 4 mW/cm 2
(i.e., with evident dye bleaching).
of 4 mW/cm2) was reduced to 15 min. (see Section 4and Fig. 6).
D. Effect of the Experimental Parameters
Parameters such as exposure dose, contrast of theamplitude mask, monomer concentration, and layerthickness were found to affect the efficiency of therecording process. This effect appears to be in agree-ment with the concept of monomer mass transportfrom dark to bright areas and also with the fundamen-tals of photopolymerization.
The dose of exposure required to achieve maximumrelief depth was found to go through an optimal valueHopt that depends on the incident intensity. Thusfor an intensity of 8 mW/cm2 the optimum expo-sure time was 15 min.; for an intensity of 4mW/cm2 it was 20 min., and for 2 mW/cm2 it was 30min. A departure from the optimal values of theexposure dose leads to a decrease in the r values.The intensity dependence of Hopt corresponds to themonomer mass transport models. As a matter offact, a general decrease in light intensity reduces thegradients responsible for monomer diffusion, and thisin turn leads to lower r values. On the other hand,with an increase in the exposure dose above itsoptimal value, the polymerization process is acceler-ated in darker areas to an extent that is not propor-tional to that observed in the brighter areas. Thisdisproportion may be from either the stronger dyebleaching in the light-struck areas and/or the satura-tion of the polymerization. In both cases there couldbe a decrease either in the efficiency of the monomermass transport and/or in the resulting r values.
Moreover, the diffusion rate of dissolved oxygenmay also introduce some limitation in the reciprocityfactor between the illumination power density andthe exposure time. Oxygen is known to exerciseboth a positive action on the initiation process and anegative one on the initiation efficiency itself. Thatis to say, it permits the semireduced form of MB to bereoxidized to the ground-state MB, thus recoveringthe absorptivity of the recording layer. On the other
hand, oxygen inhibits the activity of the amine-derived radicals, thus reducing the initiation efficiency.Its stationary concentration may thus become acrucial factor in the development of the photopolymer-ization process."
For intensities of 0.5-2 mW/cm2 the value of thedose optimal exposure Hopt was constant and equal to3.6 J/cm 2 . The Hopt value, however, increased athigher intensities, reaching 4.8 J/cm 2 for an intensity4 mW/cm 2 and 7.2 J/cm 2 for an intensity of 8mW/cm 2 . These increased Hopt values seem to re-sult from a corresponding decrease in the recording-layer sensitivity caused by decreased initiation quan-tum yield at higher intensities.
Obviously an increased contrast of the amplitudemask always results in an increased light-intensitygradient for each zone. In particularly interestingcases this actually brings about a correspondingincrease in relief depth. The experimental values ofthe maximal relief depth r for a layer thickness of 100jim and an exposure intensity of 4 mW/cm2 is 15 jlmfor an amplitude mask contrast of 1.5 and 7.5 jim fora mask contrast of 1.0.
Relief depth was found to be linearly dependent onboth monomer concentration and layer thickness.This is also in agreement with the above-mentionedmass transport model of the relief formation, sinceboth parameters linearly change the mass of mono-mer to be transported. In practice the decrease inlayer thickness is desirable, as it simplifies the adjust-ment of the initial flatness of the recording layer andthus increases the accuracy of the kinoform fabrica-tion. The lowest thickness suitable for the fabrica-tion of CO2 laser focusing elements was 60 jim. Thisis twice the value found with liquid photopolymeriz-able layers." 2 This parameter might be improved byan increase in the monomer concentration, but thepossibility is restricted by an undesirable monomercrystallization process. The maximum value of themonomer concentration in the initial solution was 3wt. %. Another way of increasing the amplitude ofthe observed effect could be based on an engineeringstudy aimed at finding the most appropriate chemicalstructures.
4. Focusing Performance
The efficiency of the kinoform produced depends onthe accuracy of the representation of the phasefunction by a kinoform structure (in the present case,by the relief structure). Let us now undertake amore detailed examination of the kinoform perfor-mance.
The kinoform relief structure was measured with asurface analyzer. The corresponding phase functionwas then determined in a way opposite that of thecoding procedure. The correspondence between re-lief depth and the value of the phase function wasdetermined by our taking into account the followingdata. For the wavelength X = 10.6 jm and the 450reflectance regime, a phase shift of 27r corresponds toa relief depth r = 7.5 jim. The reverse phase shift
3 2mr
24-r
16r
0-
III
/
7,42
5 IO 15 mm
Fig. 7. Phase function of the kinoform (curve 1, theoretical; curve2, experimental) obtained for the recording intensity I = 2 mW/cm2
(i.e., with weak dye bleaching).
2Trm was introduced to each zone, with m = 0, 1, 2, 3,.... The results of this procedure are shown inFigs. 6 and 7 for two samples with different recordingregimes. The value of the initiating intensity for thesample of Fig. 6 was 4 mW/cm2, and that for Fig. 7was 2 mW/cm 2 . A correction was applied to theamplitude function of the sample shown in Fig. 6 inthe way described in Section 3.C in order to compen-sate the polymer recording nonlinearity. The effectof partial compensation of the nonlinearity can beobserved in Fig. 6, as the recovered phase function isnearly coincident with the theoretically calculatedfunction. The only difference is in the brightestareas, in which the nonlinearity is located and inwhich the relief profile does not fit the required phasefunction, thus reducing the kinoform diffraction effi-ciency.
Better performance can be seen in Fig. 7. A valueof 2 mW/cm2 was taken for the exposure so that theresponse of the recording material was almost linear.The dye bleaching was < 20% of the initial absorption.The absorption of the layer did not significantlychange along the recording process, and the contribu-tion of bleaching process (5), which involves a reac-tion of the excited sensitizer with the monomermolecules, was reduced. Moreover, with such anintensity the possibility of creating cross-links be-tween the polymer chains and the binder through achain transfer mechanism was almost impossible,which eliminated the generation of an index patternthat might distort the response of the recordingmaterial. That is why the accuracy of the phasefunction reproduction is better than that shown inFig. 6. The corresponding diffraction efficiency wasmeasured with the radiation of a CO2 laser andexhibited a value of 55%.
It is worth noting that the absence of the wetprocessing stage in the element fabrication with thismaterial leads to a mirrorlike surface quality, withoutmuch scattering, even for visible light. Accordingly,in spite of the above-mentioned restrictions regardingthe resolving power, this medium can be considered
as suitable for the middle-IR region if a 4rr phase shiftis chosen between the zones.
5. Discussion
Two different mechanisms have been proposed previ-ouslyl 67 for relief formation in photopolymerizablelayers. Let us call the first one an orthogonal-shrinkage model.6 7 This concept was introduced todescribe relief formation for multicomponent sys-tems,7 in which the use of components exhibitingbasically different polymerization activities leads tomutual interdiffusion during the formation of thevolume holograms. It was suggested that the reliefformation results only from the orthogonality of thedirections of material shrinkage in the brightestareas (mainly along the layer) and in the dark areas(orthogonally to the layer plane). The correspond-ing orthogonality of the shrinkage was experimen-tally revealed (with a Michelson interferometer 7) bythe existence of two consecutive stages in the shrink-age of a polymerized layer.
Another approach that describes the relief forma-tion was proposed in Ref. 1. It relies on the thermo-dynamic model of hologram formation, which holdsthe polymer-monomer physical interaction respon-sible for monomer mass transport.' 2 Both of theproposed models accounted for experimentally ob-served properties of the relief formation, in particu-lar, the coincidence of the formation of the reliefmaxima with the brightest areas. No direct confir-mation of the validity of these models, however, wasobtained.
We should emphasize here that formation andspreading of the surface wave confirm directly thepreviously developed' thermodynamic model of themechanism of photopolymer hologram formation.Observation of formation of the surface wave revealsthat relief is produced not by shrinkage but bymonomer mass transport. By ensuring monomertransport, this surface wave spreads inside a brightarea, causing the relief to enlarge. From a thermody-namic point of view the monomer mass transport inthis case should be considered as arising from thegradient of chemical potential of the monomer. Thisoccurs as a result of monomer attraction to the newlyformed polymer microgel. However, this would nothave resulted from the gradient of monomer concen-tration, as the system includes at least two phases:monomer and polymer. The formation of the sur-face wave appears to be the first stage of a response ofthe system to the gradient of the chemical potential ofthe monomer. The subsequent spreading of thesurface wave within the bright regions is the finalstage of a response leading to the compensation ofthis gradient. Because of its chain character, thepolymerization process does not stop immediatelyafter the illumination ceases but proceeds as a post-polymerization in the dark, causing further hologramdevelopment 3" 4 and relief enlargement.
As a corollary to this consideration, an independentconfirmation of the thermodynamic model of the
mechanism of volume-hologram recording'2 can beprovided. The formation of the relief by monomermass transport is a direct consequence of thesethermodynamic considerations. To be more specific,the relief formation corresponds to a general thermo-dynamic model when applied to the case in which theingredients have approximately equal affinities to thepolymer phase formed. In this way, the above-mentioned experimental observation of a particularcase of the model implies the validity of the generalmodel.'2 In both cases (relief and volume holo-grams) the general thermodynamic model does notsupport the assertion that the diffusion process in thecorrespondent systems arises from the gradient of themonomer concentration.4,' 5,' 6 Instead, the thermo-dynamic model considers gradients of the chemicalpotentials of the ingredients to be responsible for thecorresponding diffusion to occur. In the frame ofthis model the reason is precisely the absence of thediffusion stream, which might have been a counter-part of the interdiffusion with a monomer for produc-ing the volume recording, that results in the above-mentioned formation of a relief structure.
If one assumes that the gradient of the monomerconcentration controls the monomer diffusion,4,' 5"16one may conclude that only volume holograms formin photopolymerizable layers. More precisely, onewould think only photochemically stable hologramswould form. But this line of thought can in no waybe consistent with the experimental observations ofthe relief-structure formation. For this reason thethermodynamic model'2 seems to be the only ap-proach that describes interactions under the holo-grams recording in photopolymerizable layers. Thismodel permits one to treat consistently all experimen-tally observed cases, namely, recording of volumeholograms (both photochemically stable and unstableones) as well as relief holograms.
Additional conclusions can be drawn regarding theresolution power of the relief formation. The samerestrictions of the resolution were observed' for therelief formation in liquid photopolymerizable layers,and the surface strength was supposed to be respon-sible for the decrease in resolution. In accordancewith this suggestion, a partially successful attemptwas made to increase the resolution by use of surfaceactive agents for reducing surface free energy. Fromthe above-mentioned viewpoint of surface-wave forma-tion it is precisely the wavelength value of this surfacewave that restricts the resolution of the relief forma-tion. This wavelength value obviously depends onthe surface free energy and the elasticity of the film,so the decrease of the last two parameters can beconsidered as a way to improve the resolution of therelief recording.
The drawback of the described material is itssensitivity to humidity. Quite long term (6-month)storage of the recorded kinoforms at the humidity ofapproximately 40%-50% and at temperatures of 20°-30 C revealed no degradation of the relief structure.But increased humidity values (near 80% and more)
and temperatures of 20°-30 C led to the destructionof the quality of the kinoform surface. The solutionto this problem may be found in the development ofthe materials, which do not include water-solublecomponents. This is supposed to be the next stage ofthe investigation.
6. Conclusions
Some general conclusions can be drawn from theresults reported in this paper. Dry photopolymerfilms appear to be a suitable system for the recordingof IR computer-generated focusing elements. Thismaterial provides a resolving power of 15 mm-' forthe formation of a sufficiently deep relief structure(up to 15 jim for a layer thickness of 100 Lm) with adiffraction efficiency of 55% for X = 10.6 jim.
A process that leads to a relief formation throughmonomer mass transport by means of a surface wavehas been observed. The formation and the spread-ing of this wave into the highly lit areas can beconsidered as a direct confirmation of the thermody-namic model of hologram (relief and/or volume)formation in photopolymerizable materials.
The nonlinearity of the dry polymer relief record-ing is the consequence of a gradient of the quantumyield of the initiation process and a spatially inhomo-geneous bleaching rate of the sensitizer. This nonlin-earity can be compensated, at least partially, by theintroduction of appropriate corrections into the ampli-tude function generated. If the intensity of the lightexposure is low enough (less than 2 mW/cm 2 ), theresponse of the material is linear (with an accuracy of+ 10%).
This research has been supported financially by theConsejo Nacional de Ciencia y Technologia of Mexico.Thanks are due to Jan Petter Isaksen for help inpreparation of the manuscript, to Orestes Stavrudisfor valuable and helpful discussions, to Daniel Mala-cara, Iosif I. Dilung, and Vitalii D. Pokhodenko fororganizational efforts in arranging this work, andalso to Fernando Mendoza-Santoyo and ArquimedesMorales for their encouragement and support.
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