Recently, diffractive optical elements (DOEs) havebecome even more important in many fields of appli-cation, especially due to advances in design and fab-rication techniques. One of these prospective fieldsis optical security elements based on diffractive prin-ciples.1 Most of such structures consist of systemsof regular gratings that are assembled to create adesired image or visual effects. Usually these ele-ments are fabricated with synthetic technologiessuch as laser or e-beam lithography. For higher se-curity, the special structures are integrated intothese systems besides the regular gratings. Suchstructures, usually called diffractive cryptograms,are computer-generated holograms2 that contain en-crypted information in the reconstruction plane.Many approaches to application of cryptograms inoptical security exist.3–7 Such cryptograms are oftendesigned as Fourier elements with the reconstructionplane located in the far field. The security function ofthese structures is based on both fabrication complex-ity and sophisticated design. Nowadays, because ofwidespread availability of diffractive elements fabri-cation technologies, it is desirable to enhance thesecurity level of such elements even more. On the
other hand, these improvements should not lead to afurther principal increase of the requirements on thefabrication devices. In this contribution, several ideasare presented that can enhance the security level ofsuch elements fabricated with so-called dot-matrixlaser writers widely used in the field of securityapplications.8–15 Furthermore, the improved tech-nique of integral dot-matrix writing is presented thatopens new possibilities not only in security enhance-ment but also in other diffractive optics applications.
In Section 2, new ideas in design of diffractive cryp-tograms are presented. The problem of color of thecryptogram area is solved in order to disable easyidentification of the presence of encrypted informa-tion. Furthermore, cryptograms with covering noisehave been designed. In Section 3, approaches to fab-rication of diffractive cryptograms are discussed.Special attention is given to utilization of standarddot-matrix techniques widely used in optical security.Finally, the paper is concluded in Section 4.
2. Design Approaches
The most commonly used diffractive elements in secu-rity applications are based on Fourier-domain, low-carrier-frequency synthetic structures. In the simplestcase, the design can be performed by Fourier trans-forming the desired encrypted object signal. The stan-dard limitations on the elements surface-reliefproperties are especially strong in these security ap-plications, mostly because of the inability of the record-ing devices to record relief profiles precisely. In fact,binary phase elements are widely used. The problem oftransforming a continuous complex transmittancefunction (obtained by Fourier transforming the object)to the quantized phase-only form has been solved inthe theory of computer-generated holograms design.
The authors are with the Department of Physical Electronics,Faculty of Nuclear Sciences and Physical Engineering, CzechTechnical University in Prague, Brehová 7, Prague 1, 115 19,Czech Republic. M. Škeren’s e-mail address is [email protected].
Received 30 March 2005; revised 22 June 2005; accepted 23 June2005.
Various efficient algorithms can be used, depending onthe desired properties of the final element. In our case,a well-known iterative Fourier transform algorithm(IFTA) has been used for most of the designs.16–18
One important feature of the Fourier-domain low-carrier-frequency elements in security applications istheir viewing color. Because such elements are notstrictly periodical, they contain a relatively broadband of spatial frequencies that results, together withlow carrier frequency, in gray color of the cryptogramarea. The drawback of this “color property” is a rela-tively easy identification of the presence of the cryp-togram within the security hologram area. The areaof the cryptogram is dead in comparison with coloredgrating areas. One possible and efficient way of avoid-ing this problem is to encode the cryptogram withinthe grating area. This area will keep the original colorgiven by the “background” grating, and easy identi-fication of the cryptogram is not possible anymore.Now, the question is how to encode the modulationthat defines a cryptogram in the regular gratingarea? Our solution is based on the simple gratingtheory. To maintain the color of the whole area, itmust be filled out with a grating of the desired periodand orientation. The only parameter of the gratingthat can be used for additional modulation is thus itslocal phase shift. Hence, the whole area should bedivided into subareas (called traditionally dots)where each dot contains the same regular grating(with the same period and orientation), but thesegratings between particular dots are phase shifted(Fig. 1). If the elementary grating is represented byits complex transmittance function t�x�, its diffractionorders are characterized by Fourier coefficients19 cm
according to Eqs. (1) and (2):
t(x) � �m���
�
cme�2�im
�x, (1)
cm �1��
���2
��2
t(x)e2�im
�xdx, (2)
where � is the grating period and m is the number ofdiffraction order. If the grating is spatially shifted inthe x direction of the distance �, the cm coefficientsbecome
cm, � �1��
���2
��2
t(x � �)e2�im
�(x��)dx � e
2�im�
�cm. (3)
Equation (3) shows that, in principle, the desiredphase modulation of the security element under de-sign can be represented by proper horizontal shifts ofthe gratings in dots while otherwise keeping gratingsthe same (in Fig. 1, the four-level depth relief is trans-formed into the binary relief grating that consists ofphase-shifted parts). Note that the type of crypto-gram modulation, obtained in such a way, is com-pletely independent of types of elementary grating
modulation. One of the advantages of such an ap-proach is that it is much easier to ensure high preci-sion in the horizontal shift than in the vertical depthof relief. This enables us to fabricate quite preciselymultilevel security elements without complicatedtuning of the relief depth within the photoresist de-veloping process. The experimental verification of thedescribed encoding approach will be given in Section3.
The second technique to be discussed is the use ofcovering noise to hide the encrypted information evenmore. As it has been mentioned, one of the disadvan-tages of the Fourier diffractive cryptograms is theireasy identification when an expanded reconstructionwave is used. If the power density of the testing waveis sufficiently high and the observing screen is placedat almost any distance, the cryptogram is easily seenwithout any additional knowledge about its locationor other parameters. One possible solution for pro-tecting a cryptogram against the wide-beam recon-struction is to create additional noise that overlapsthe encrypted image. The idea is relatively simple:the Fourier cryptogram is surrounded with similarFourier structures that carry the covering image (Fig.2). This structure can be either homogeneous noise oranother meaningful image that can overlap en-crypted information. Two important propertiesshould be reached to create succesful noise coveringof the image. First, the intensity of the covering sig-nal must be much higher than the intensity of theencrypted image to achieve sufficient covering. Sec-
Fig. 1. Basic idea of transforming the staircaselike depth relief tothe binary grating with phase-shifted dot areas. Each elementarystep of the original grating corresponds to the dot filled with aregular binary grating. The gratings within particular dots arephase shifted, relative to each other.
ond, the spatial position of the noise must correlatewith the position of the image at any plane to disableimage-noise separation. Of course, the new geometryof the cryptogram leads to complications by autho-rized reading because the reconstruction beam mustbe precisely positioned now. This problem can be par-tially solved by choosing periodic distibution of thesignal carrying segments. Then the reading maskneed not to be placed absolutely at the right positionbut can be shifted about multiples of this period.Practically, such a period is of the order of hundredsof micrometers, and thus positioning of the mask isrelatively easy. One of the simplest configurations ofthe cryptogram is indicated in Fig. 2 in which thecryptogram carrying encrypted information is sur-rounded with noise-carrying elements. The ratio ofthe cryptogram area to the noise producing area ischosen 1:3. When such an element is reconstructedwith an expanded beam, the noise overlaps the signaland encrypted information remains hidden. When anarrow beam is used or a wide beam is filtered with
a mask (Fig. 3), the reconstruction becomes readable.In Fig. 2(a), the element consists of 25 tiles, 16 withnoise signal and 9 with encrypted information. As itis seen, the structure seems compact, the bordersbetween noise and signal tiles are invisible. When anelement is observed with a microscope, the location ofthe cryptogram remains hidden as well. The only wayto read the encrypted information is to use a properreading mask.
An idea of noise covering can be further enhancedto increase the security level. One such modificationis based on a special arrangement of the signal-carrying cryptograms in the noise cryptograms area.The signal cryptograms are not aligned to the rect-angular grid as in Fig. 2; they are instead distributedaccording to the additional code. The image can beread only when the proper mask with the correct codeis used; otherwise the signal dissapears in noise.Clearly, the code must keep the requirements on theratio of the signal and noise area. Additionally, thesignal areas cannot be grouped together to disable a
Fig. 2. Example of possible segmentation of the element that (a) consists of two types of structure: one that carries the encryptedinformation (image DOEs indicated by dark gray rectangles) and a second that carries the covering noise (noise DOEs indicated by thelight gray area). After filling with corresponding microstructures, (b) the whole element seems compact and segmentation is practically notvisible.
Fig. 3. Reconstruction geometry of the noise-covered security element. When reconstructing without a proper reading mask, theencrypted information remains hidden in the covering noise. If the proper mask is used, the encrypted image appears in the reconstructionplane.
wide-beam reconstruction. When a more complicatedmask is used, the problem of proper alignment shouldbe solved in detail. In the example presented above,the regular rectangular periodic structure has beenchosen. In fact, the group of periodic masks applica-ble is much wider; however, in most cases only theregular periodicity of the mask is acceptable. At thispoint, it is advisable to discuss the significance of thereading mask from point of view of the security func-tion. According to the usually used approaches basedon simple Fourier-domain diffractive elements, a nec-cesity of the presence of any reading mask (even foronly a regular rectangular raster) leads to the funda-mental improvement of security. Furthermore, thegeometric dimensions of the reading mask can beused for encoding the additional information (i.e., thedimensions, periodicity, and shape of the mask aper-tures can vary while the overall composition of themask is maintained). The second possible way ofmask individualization is to change the structure ofthe mask. A wide group of periodic rasters can beused such as chessboards, systems of linear slits, ormore complicated structures based on the polygonalsymmetry. Both of these methods have been succes-fully verified and tested. However, sometimes thedemands on the mask code can lead to the generalnonperiodical structure. Then the alignment becomesdifficult because the mask must be absolutely posi-tioned. One of the possible alignment techniques thathas been successfully tested is the use of specialalignment marks exposed within the area of the se-curity element. Such a mark (typically a system ofluminative lines, points, or crosses) is then integratedwithin the security elements design. The readingmask contains the corresponding sighting cross-referenced points. When the mask is aligned, thesepoints must correlate with the exposed marks. Suchan approach has been experimentally proved withsatisfactory results. Without any further consider-ations, the precision of positioning the mask approx-imately 0.1 mm has been achieved. When particulartiles of the cryptogram structure have a dimension of0.2 mm, such a precision is fully adequate for practi-cal usage.
However, in any configuration when the encryptedimage is completely stored within one compact area(although it is small), the cryptogram can be recon-structed with a focused narrow beam. Then, an un-authorized user can discover the cryptogram withinthe reconstruction mask. Although this situation isimprobable in practice, its risk can be decreased byuse of the following technique. The signal to be en-crypted is not encoded within one single diffractivestructure, but it is at first segmented into severalsubparts. Each such part itself cannot give a mean-ingful reconstruction. Only when the proper recon-struction mask is used, the readable image appearsas the combined reconstruction from all subparts. Anexample of such a segmented cryptogram is displayedin Fig. 4. This technique ensures a high security levelof the element. An unauthorized user cannot decodethe encrypted information without explicit informa-
tion on principles of the encoding technique and in-dividiual mask geometry.
All the described techniques with noise coveringhave a higher level of security and also one new andinteresting property: they enable the individualiza-tion of the reading device with respect to the readingmask. The reading device, that is, in a case of stan-dard Fourier cryptograms, more or less universal,can now be relatively easily and inexpensively indi-vidualized by adding the specific mask. Moreover, onediffractive structure can contain more than one en-crypted information while each of it requires a differ-ent reading mask. This issue can also be used forincreasing the security level of the diffractive crypto-grams. In Section 3, sample structures are presentedthat have been fabricated according to the above-described ideas. They verify experimentally the pre-dicted properties of the noise-covered cryptograms.
3. Realization of Elements
The elements designed for security applications aretypically recorded in the resist material using direct-write lithography. Both laser and e-beam writers areused. The main advantages of the e-beam-based tech-nologies are high accuracy and small elementarypixel size, whereas the drawbacks include long writ-ing times and expensive costs. Also, it is clearly notvery effective to write large regular grating areasusing e-beam, not only because of large time require-ments but also because of other problems connectedwith grating groove orientation. Integral laser writ-ers offer here an interesting alternative to the e-beamtechnique. “Integral” means that the grating area isnot recorded point by point but at once, within onesingle exposure. These so-called dot-matrix systemsencounter, however, other problems if applied to dif-fractive cryptograms: the elementary point is not suf-ficiently small, and the alignment error of suchhomogeneous grating areas (dots) is too big. The largeelementary point leads to small diffraction anglesand thus a visible pixelation of the element surface.
Fig. 4. Example of segmentation of the encrypted information. Anencoded image is divided into several parts that are individuallymore or less senseless, and each of them is recorded separately.The integral reconstruction of the whole object is possible onlywhen the proper reading mask is used.
Therefore, conventional dot-matrix systems are un-easily applicable to gray cryptograms recording.Additionally, the idea of transforming the crypto-gram modulation to the phase shifts of gratings, asdescribed in Section 2, can be used only when itis possible to position the dot gratings with sub-period precision (i.e., of several hundreds of nanome-ters). Again, conventional dot-matrix systems cannotachieve such phase synchronization among gratings.In our case, an inhouse-developed, enhanced dot-matrix system was used that recorded the dotsintegrally and ensured their desired phase synchro-nization. The device was capable of synchronizing thephase within the area of 200 �m � 200 �m, ideallywithout any error. In practice, the stitching error ofsuch 200 �m tiles without any additional interfero-metric alignment technique was approximately1 �m. Figure 5 shows a photograph of such a typicalstructure recorded on the system. Because of thestitching error, the whole cryptogram must be con-tained within one 200 �m � 200 �m tile. Clearly, ifthe interferometric precision for alignment is en-abled, it is possible to synchronize gratings also be-tween tiles. For several types of security element, thedithering technique can be used for modulation of thediffraction efficiency of grating areas. In such a case,a different approach to cryptogram design can beeffectively used. Then the cryptogram is representedthrough a binary amplitude modulation of the ele-mentary grating. Two kinds of dots are exposed, i.e.,with and without the grating. The cryptogram worksnow as a low-carrier-frequency element when thedots with gratings recorded drain the energy from thezeroth order and behave as dark areas of an ampli-
tude element. In contrast, the dots without gratingsdo not affect the reconstruction beam and behave asbright areas. Another advantage of this approach isthat it is not sensitive to the stitching error of thetiles. It follows from Eq. (3) that the zeroth order cm
coefficient does not depend on the shift �. The impor-tant value is now the dot size (instead of the gratingperiod), which is much bigger than the stitching errorof the tiles and also in the case when interferometricalignment is not used. As a result, the whole crypto-gram area still possesses the right color. In Fig. 5, afabricated microstructure based on this ditheringtechnique is displayed as an example.
The color cryptograms designed according to thegrating approach described above have also been fab-ricated with the enhanced integral dot-matrix sys-tem. In Fig. 6, an example of such a structure ispresented. In Fig. 6(a), there is an image of the struc-ture photographed out of the first diffraction order. InFig. 6(b), there is the same structure photographed inthe direction of the first diffraction order of the car-rier gratings. Clearly, the whole cryptogram arealights up and has the color given by the appropriategrating. In other words, if integrated within a usualsecurity element, the cryptogram does not differ fromother areas. In Fig. 6(c), the reconstruction of thecryptogram from Figs. 6(a) and 6(b) is displayed. Ithas been obtained by illuminating the cryptogramarea with a narrow red laser beam.
Figure 7 presents another example of a fabricatedstructure. In Figs. 7(a) and 7(b) the optical recon-structions of the noise-covered cryptogram are dis-played with and without the proper reading mask,respectively. In Fig. 7(c), the reading mask used isshown. The mask was realized on a standard com-mercial laser writer in photosensitive film. As it isseen from these figures, the predicted functionality ofthe noise-covered cryptograms was fully verified. Un-authorized reading without a reading mask leads tonoisy reconstruction, and the encrypted image re-mains completely hidden. When the proper mask isused, a good quality reconstruction of the image ap-pears.
4. Conclusion
Possible enhancements to the security level of diffrac-tive elements have been studied. It has been shownthat it is possible to encode diffractive cryptograms tothe “color areas” of the structures. The shifted grating
Fig. 6. Example of the color cryptogram. The cryptogram areaphotographed (a) out of the first diffraction order and (b) in thedirection of first diffraction order. (c) Reconstruction of the cryp-togram in the laser light.
Fig. 7. Experimental demonstration of the noise-covered crypto-gram. Reconstruction (a) with and (b) without a proper readingmask. (c) Image of the reading mask used.
Fig. 5. (a) Microscopic image of the fabricated microstructure and(b) its detail realized with the enhanced integral dot-matrix sys-tem.
approach has been demonstrated in connection withthe specialized dot-matrix fabrication technique.Alignment problems connected with phase synchro-nization of the dot gratings have been analyzed andsolved. Several samples have been successfully fab-ricated and tested. Furthermore, the new idea of cov-ering noise in diffractive cryptography has beenpresented. Several stages of the security improve-ment have been indicated and tested. Experimentalsamples have been fabricated with the enhanced dot-matrix laser writer that verified the presented the-ory. Besides the enhanced security level, thedescribed ideas bring new possibilities to the field ofdiffractive cryptograms such as easy individualiza-tion of the reading devices and additional coding inthe reading masks. Collaterally, the special attentionwas kept so as not to increase the requirements onfabrication devices rapidly. The enhanced integraldot-matrix technique was used in most of the exper-iments.
The research has been partially supported with theMinistry of Industry and Trade research project1H-PK/02.
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