WO2015132752A2

WO2015132752A2 - Diffractive optical element of the holographic type for decoding information with a high security level

Info

Publication number: WO2015132752A2
Application number: PCT/IB2015/051616
Authority: WO
Inventors: Filippo Romanato; Gianluca Ruffato; Michele MASSARI
Original assignee: Veneto Nanotech S.C.P.A.
Priority date: 2014-03-05
Filing date: 2015-03-05
Publication date: 2015-09-11
Also published as: WO2015132752A3; EP3114533A2

Abstract

Diffractive optical element (6) of the holographic type, which forms, when illuminated by a first electromagnetic field (DOB) having non-zero orbital angular momentum, a second electromagnetic field (IOB) adapted to form a first image substantially lacking noise, indicative of information encoded by the diffractive optical element. In addition, the diffractive optical element forms, when illuminated by a third electromagnetic field, a fourth electromagnetic field adapted to form a second noisy image. The first and the third electromagnetic field have different topological charges and/or different spatial distributions of phase singularities.

Description

DIFFRACTIVE OPTICAL ELEMENT OF THE HOLOGRAPHIC TYPE FOR DECODING INFORMATION WITH A HIGH SECURITY LEVEL"

* * *

The present invention refers to a diffractive optical element of the holographic type for decoding information with a high security level.

As is known, holography is an optical technology widely applied for certifying authenticity and for protecting the originality of a document or product. Unlike a normal photograph, which records the intensity of the light that exposes the photographic medium, a hologram exploits the principle of optical interference in order to generate an electromagnetic field that contains information on the phase as well as information on the intensity of the light that comes from an object; therefore, the hologram allows displaying the three-dimensional image of an object.

The operation of any one hologram is based on the physical principle of diffraction of the incident light on the hologram itself. For such reason, holograms are also generically known as diffractive optical elements (DOE). In particular, a generic hologram is formed by a suitably microstructured surface, which defines the so-called plane of the hologram and is adapted to model the phase of the light incident thereon, for example in a manner such that it reconstructs the desired image in the so-called reconstruction plane (also known as observation plane) . For example, the reconstruction plane can be formed by the eye of an observer.

In detail, optical holography provides for making two coherent optical beams interfere, and in particular a reference beam and the corresponding wave reflected by an object; these light beams are also known as optical writing beams. The two coherent optical beams are made to interfere on a holographic medium, in a manner so as to generate an interference pattern, which is written on the holographic medium, thus forming the hologram. The thus generated hologram has one property: when it is illuminated with one of the abovementioned two optical writing beams, specifically by the reference beam, it causes the diffraction of such optical writing beam along the direction of the other optical writing beam. In such a manner, an observer perceives the hologram as if the source of the second writing beam was still present in the reconstruction plane.

In more detail, holograms can be divided into surface relief holograms and volume holograms. A surface relief hologram acts on an incident wave front by imparting a local phase change (phase displacement), proportional to the local height of the holographic material; therefore, it is verified that the local length of the optical path is proportional to the length of the corresponding physical path. On the other hand, a volume hologram acts on an incident wave front by imparting a local phase displacement which is proportional to the local refraction index of the holographic material; therefore, it is verified that the local length of the optical path is proportional to the local refraction index, while the length of the corresponding physical path length does not vary in the holographic material.

Due to their complex structure, diffraction holograms are often used as visual identification elements and thus as security elements capable of ensuring the originality of objects on which they are formed.

Irrespectively of the subdivision between surface relief holograms and volume holograms, holograms can be further subdivided on the basis of the security levels ensured by the same. For such purpose, the following hologram types are known: level one holograms, whose information can be interpreted (decoded) with the naked eye; level two holograms, whose information can be decoded by means of an auxiliary optical decoding instrument; and level three holograms, whose information can only be decoded with the aid of specialized laboratories, capable of validating the data deriving from the decoding. The degree of security provided by a hologram increases with the increase of the level of the hologram itself.

Since hologram counterfeiting is difficult, holograms are widely used in applications such as beam shapers, beam splitters and data storage media. In addition, due to the Bragg effects, multiple holograms can be encoded within a same volume of holographic material, by slightly varying the angle of the reference beam of each hologram. In addition, in order to increase security, the producers of holograms have developed the capacity to insert images hidden inside visible holograms, such hidden images only being detectable by means of optical readers; some producers implement bar codes inside the holograms.

With regard to the manufacturing of the holograms, these were originally formed, as mentioned above, by suitably transforming wave fronts, by means of microstructured surfaces. In particular, holograms were formed with interferential methods, by means of superimposition of a reference illumination with coherent light diffused by the object to be represented.

Today, the availability of computer-generated hologram (CGH) manufacturing techniques allows forming the hologram substantially of any virtual object, i.e. without having to physically arrange the object; in addition, the image reconstructed by the diffraction of the hologram can be numerically rather than experimentally optimized.

Typically, the manufacturing of holograms occurs by means of micro-manufacturing processes, well-known in the field of microelectronics and industrial molding. After the hologram has been projected and designed, it is converted into a numeric sequence adapted to guide an electron or ion or laser beam on a sensitive material. Subsequently, less costly techniques are used for making a replica of the original matrix mass.

The design of a hologram can therefore be subdivided into three steps: understanding the physical problem (analysis), translating the problem into a numeric coding algorithm (synthesis) ; and actual manufacturing of the hologram (implementation), which occurs by means of use, as stated above, of technologies such as ion or electron beam writing, as well as replica technologies.

Generally, in step of hologram design, the use of a scalar theory of the light is sufficient. In addition, in accordance with the technique used by the hologram for modeling the incident light, holograms are classified into: holograms which only modify the phase of the incident wave ("phase-only DOE", PDOE) , holograms which only modify the amplitude of the incident wave ("amplitude-only DOE" - ADOE) and holograms which modify both the amplitude and the phase of the incident wave ("complex-amplitude DOE" or "phase and amplitude DOE", PADOE) . As stated above, the abovementioned step of analysis consists of identifying the hologram that obtains the desired image as diffraction pattern, for example in the eye of the observer. The physical principle on which the mechanism under examination is based is known as Huygens- Fresnel principle; according to such principle, each point of the hologram, when illuminated by the incident light, can be considered a source of secondary spherical waves which, being propagated in space and interfering with each other, arrive at the observer's eye where they reconstruct the diffraction pattern. The analysis thus consists of determining the hologram which models the incident light in the desired manner, given a predetermined image that one wishes to form in the eye of the observer, under a specific illumination. A more rigorous formulation of the Huygens principle is expressed by the Helmolt z-Kirchhoff integral, derived from the Maxwell equations by using the properties of the electromagnetic field. The setting of the paraxial approximation, generally valid in the considered physical problem, leads to the simplification of the preceding integral into the Kirchhoff-Fresnel diffraction formula, which represents the basic mathematical instrument for the analysis of holograms.

A further approximation, allowed by the generally limited dimensions of the holograms (on the millimeter order) with respect to the distance of the observer (approximately one meter) , leads to the formulation of the so-called Fraunhofer regime. In these conditions, the analysis is simplified from a mathematical and hence numeric standpoint, since the action on the incident light achieved by the hologram becomes mathematically expressible as the Fourier transform of the hologram. On the other hand, the inverse problem, relative to the encoding of the hologram adapted to construct the predetermined image, is analytically expressible as the inverse Fourier transform (anti-Fourier transform) of the desired design, i.e. of the predetermined image that one wishes to form in the reconstruction plane. These transformations are commonly implemented in already-optimized software packets that can be integrated in proprietor codes, so as to facilitate the numeric design of the hologram.

With regard to the synthesis, the abovementioned analysis must consider the design limits set by the employed manufacturing process. For example, in the case of phase modulation holograms, it is necessary to account for the fact that such phase cannot be modulated in a continuous manner, but only in a discrete manner, over a limited number of values, which depend on the resolution of the lithographic technique, as well on the need to have non-excessive writing times. The manufacturing limits result in hologram design constraints, i.e. into approximations of the hologram design. The approximations not only involve a worsening of the image, which will result distorted with respect to the original, but also high background noise, which will limit the clearness of the image formed in the reconstruction plane. For the purpose of reducing these aberrations and optimizing the design of the hologram, various numeric techniques have been proposed in recent decades, including the so-called Iterative Fourier Transform Algorithm (IFTA), in one of its variants, for example the algorithms described in F. Wyrowski and 0. Bryngdahl, Journal of Optical Society of America A 5, 7, 1058-1065, 1988, or the so-called Gerchberg-Saxton, algorithm described in R.W. Gerchberg and W.O. Saxton, Optik 35, 237-246, 1972.

Generally, any one IFTA algorithm provides for iterating a precise sequence of operations between the reconstruction plane and the hologram plane, during which the hologram is progressively redefined, in a manner so as to progressively reduce the noise, until an optimized design is attained. In particular, at each step, the hologram is quantized, in phase and/or amplitude, in order to adapt it to the manufacturing constraints. The efficiency of the algorithm is given by a suitable selection of the quantization operator Q; to this regards, the literature reports various alternatives, including the so-called direct amplitude elimination - direct partial phase quantization, deemed the most effective for designing phase modulation holograms. According to such version, with each iteration, in the plane of the hologram, a direct elimination of the amplitude and a quantization of the phase are executed, according to amplitude intervals increasing with the number of the iteration. With each iteration, the quality of the reconstructed image is monitored by means of control parameters that provide a quantitative description of the noise level and of the deviation of the image with respect to the original. The fundamental parameters are the diffraction efficiency , the mean square error (MSE) and the signal-to-noise ratio (SNR) .

Now, therefore, there is presently the need to provide holograms capable of ensuring a greater security level than the levels of security provided by current holograms. The object of the present invention is thus to provide a hologram improved with respect to currently-available holograms . According to the invention, a diffractive optical element of the holographic type is provided, as defined in the enclosed claims.

For a better understanding of the invention, embodiments thereof are now described, as a merely non- limiting example and with reference to the enclosed drawings, in which:

- figure 1 qualitatively shows, for each from among four different optical beams, the spatial progression of phase fronts, a spatial distribution of intensity and a spatial distribution of phase;

- figures 2, 5, 6, 7 and 10 show block diagrams of optical circuits including the present diffractive optical element ;

- figure 3 shows, for each from among three different phase plates, a corresponding top view and a corresponding perspective view, with a grey scale which is a function of the height;

figures 4a, 4b schematically show the operation principle of the present diffractive optical element;

- shows, in a qualitative manner, a front view of a portion of one embodiment of the present diffractive optical element; and

- figure 9 shows, a qualitative manner, a front view of a hologram of "fork" type ("fork hologram") .

In summary, the present diffractive optical element is set to further increase the security level offered by a holographic certification, by combining it with the use of light structured with orbital angular momentum (OAM) . In particular, the present diffractive optical element allows decoding information starting from a light structured with orbital angular momentum. Generally, the orbital angular momentum of an optical beam confers a particular spatial distribution of intensity to the beam. In addition, the (non-zero) orbital angular momentum is a property of the optical beams that exhibit known phase defects such as optical vortices; in particular, in such optical beams, the wave front has a helical form, and therefore the Poynting vector proceeds around the propagation direction. Optical beams with phase singularities can be described as a superimposition of Laguerre-Gauss modes characterized by two integer indices 2 and p, wherein the azimuthal index 1 indicates the number of twists of the helical wave front, i.e. the number of coaxial helices intertwined with central singularity, while the radial index p indicates the number, equal to p+1, of radial nodes of the mode, i.e. the number of concentric discs on which the light intensity is distributed. Examples of Laguerre-Gauss optical beams are shown in figure 1; such beams have zero radial index and increasing topological charge 1.

Optical beams provided with non-zero orbital angular momentum are known in nature; nevertheless, generally, such optical beams have optical vortices in random positions and with random topological charge. However, in the laboratory it is possible to generate optical beams provided with orbital angular momentum, in a controlled manner, i.e. in a manner such that the optical vortices in predetermined positions and with pre-established topological charges occur .

The artificial generation of an optical beam provided with orbital angular momentum can occur in different ways. In particular, it is possible to obtain an optical beam provided with orbital angular momentum starting from a Gaussian beam.

In more detail, in order to generate an optical beam provided with orbital angular momentum, it is for example possible to illuminate, with an optical beam, a diffraction grating provided with a phase displacement arranged along one axis, termed "fork hologram", as described for example in Z.S. Sacks, D. Rozas, G.A. Swartzlander, Journal of Optical Society of America B 15, 8, 2226-2234, 1998. Alternatively, rather than employing a diffractive optical component, it is possible to use an equivalent refractive optical component, as described for example in G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, M.J. Padgett, Optics Communications 127, 183-188, 1996. In particular, it is possible to employ a so-called spiral phase plate (SPP) , which has a thickness t=Alcp/ (2πΔη) , where φ is the azimuthal coordinate, λ is the wavelength of the light that illuminates the phase plate, 1 is the abovementioned azimuthal index, and Δη is the difference between the refraction index of the phase plate and the refraction index of the surrounding environment.

In the description and in the following claims, the term "first electromagnetic field (DOB)" and "optical decoding beam DOB" will be indiscriminately used, as well as "second electromagnetic field (IOB)" and "optical information beam IOB".

Analogously, with the term "third electromagnetic field", in the description and in the following claims it is intended a radiation or an optical beam having different topological charges and/or different spatial distributions of phase singularities with respect to the optical decoding beam DOB or first electromagnetic field.

Now, therefore, figure 2 shows an optical system 1, which comprises an optical source 2, a first phase plate 4, of spiral type, and a diffractive. optical element 6 of the holographic type and operating in reflection. In particular, without any loss of generality, it is assumed hereinbelow that the diffractive optical element 6 is of PDOE type and of surface relief type, with binary or multi^¬ level micro-structuring.

In detail, the optical source 2 is of coherent type and is adapted to generate an optical beam OB, such as a Gaussian mode of TEMoo type, while the first phase plate 4, of per se known type, is adapted to receive the optical beam OB generated by the optical source 2 and to generate an optical beam, which is of Laguerre-Gauss type with azimuthal index 2 and radial index p, and to which reference is made hereinbelow as the optical decoding beam (or electromagnetic field) DOB. In detail, the optical decoding beam DOB can be described as:

e'^{fe +}'* _{2 e}/(2,₊|/|₊l)i(r)

(1) where (r,cp) are the polar coordinates on the plane or ination direction lying on the axis he bandwidth (wo is the so-called

"b being the Rayleigh length, Lp¹ is

the Laguerre polynomial associated with indices [p,l) ,

2 2

Z + Z,

R = is the radius of curvature of the beam and is the so-called Gouy phase.

In more detail, the first phase plate can have a complex transmittance of the type:

with

-1 x<0

sign ^x) =

+1 >0 and

where R is the external radius of the phase plate 4. Possible embodiments of the first phase plate 4 are shown in figure 3, in which a) and b) refer to the case in which a Laguerre-Gauss mode is generated with p=0, 1=1, while c) and d) refer to the case in which a Laguerre-Gauss mode is generated with p=l, 1=2, and finally e) and f) refer to the case in which a Laguerre-Gauss mode is generated with p=2, 1=3.

In practice, the first phase plate 4 can be formed by concentric masks separated by phase edges, whose positions coincide with the zeroes of the corresponding associated Laguerre polynomial.

The diffractive optical element 6 is such that it can only be decoded by the abovementioned optical decoding beam DOB, i.e. it is capable of producing a corresponding image substantially lacking noise, or in any case with a signal- to-noise ratio (SNR) greater than one, and preferably greater than ten, only when illuminated by the optical decoding beam DOB. For such purpose, the signal-to-noise ratio is defined as the ratio between the light intensity of the image, normalized with respect to the deviation from the ideal reference reconstruction.

For example, if the diffractive optical element 6 is obtained in the form of a multilevel pixel matrix, then the signal-to-noise ratio is calculated in the reconstruction plane as:

,n

where t_mn is the amplitude of the signal in the position (m,n) of the reconstruction plane, while g_mn is the amplitude of the reference signal corresponding to the same position .

If the diffractive optical element 6 is illuminated with an optical beam different from the optical decoding beam DOB, and in particular with an optical beam having a topological charge different from the topological charge of the optical decoding beam DOB and/or a different spatial distribution of the phase singularities (for example, a Laguerre-Gauss mode with radial index different from p and/or azimuthal index different from 1) , it generates an image affected by high noise, i.e. with signal-to-noise ratio substantially equal to one, hence not decodable.

In more detail, since an optical beam having non-zero topological charge has a distribution of phase singularities that can be identified as dark points (i.e. points where the light intensity is zero) , arranged in a plane orthogonal to the propagation direction, it is preferable to arrange an alignment device 8 (shown for the sake of simplicity only in figure 2), which controls the mutual arrangements of the optical source 2, of the first phase plate 4 and of the diffractive optical element 6. This allows controlling the alignment of the diffractive optical element 6 with respect to the distribution of phase singularities of the optical decoding beam DOB, whose light intensity, in the case of a pure Laguerre-Gauss mode with indices (p,l), is as previously mentioned distributed into p+1 concentric rings around a central singularity. In such a manner, it is possible to arrange the diffractive optical element 6 in a manner such that the geometric center of the latter is situated for example along the longitudinal axis of the optical decoding beam DOB, and more generally in a manner such that the diffractive optical element 6 has a position pre-established with respect to the optical decoding beam DOB, the design of the diffractive optical element 6 (described below) referring to such pre- established position, which in turn defines a kind of expected illumination condition.

Once again, with reference to the diffractive optical element 6, this is manufactured, for example, via computer, on the basis of the scalar diffraction of the light and the characteristics of the material that forms the same diffractive optical element 6, as well as on the basis of a desired electromagnetic field distribution and in that the desired distribution is an only-phase, only-amplitude or complex distribution.

In order to ensure the possibility to employ a scalar approach in the calculation algorithm for the generation of the diffractive optical element 6, it is suitable that the linear size L of the smallest element forming the diffractive optical element 6 (for example, the side of the pixels which form the matrix of the diffractive optical element) is at least one order of magnitude greater than the wavelength λ of the optical decoding beam DOB. For example, for a wavelength A=632.8nm, it is preferable that the linear size L is greater than 6 microns.

In the plane perpendicular to the propagation direction, the light (coherent and monochromatic) , is described by a complex function in two variables. In addition, the propagation of the light in the free space can be described by using the approximation of the Kirchhoff diffraction; in addition, the mathematical modeling of the propagation of the light through an optical element is based on the multiplication of the complex function of the incident light on the optical element by the complex transmittance of the optical element.

Now, therefore, hereinbelow a Cartesian reference system is considered whose origin lies in the diffractive optical element 6 and with axes x' and y' in the plane of the diffractive optical element 6; in addition, the positive direction z is selected for pointing the semi- space that contains an observation point P(x,y,z) lying in the observation plane (x,y) .

In such conditions, considering a generic wave Uⁱⁿ that illuminates a surface of a hologram S, the so-called far field (FF) is given by the Fresnel-Kirchhoff diffraction formula:

in which k is the modulus of the wave vector and r is the distance of the point (x,y,z) on the reconstruction plane from the point with coordinates ( χ ' , γ ' ) in the plane of the hologram: r - ^^ + (x~x')² ')² ·

In paraxial approximation, the following relation is thus valid:

dx^{'dy'

(4)

The transformation pursuant to equation (4) is a Fresnel transform, which, even if approximate, has the advantage that it can be implemented numerically in a computationally efficient manner. In addition, the evaluation of such transformation can be simplified by assuming to ignore the contributions with the quadratic terms in ' and y' ; the latter assumption is equivalent to making reference to the so-called Fraunhofer diffraction. The conditions of the Fraunhofer diffraction can be reached, for example, by arranging a thin convergent lens with focus f between the object plane (also known as reconstruction plane) and the plane of the hologram, the object plane being arranged against such lens, the plane of the hologram being spaced by a distance equal to the focus f from the object plane, in a manner such to coincide with the rear focal plane of the lens. If z=f, it is verified that the lens introduces a quadratic phase factor, which cancels the Fresnel factor, i.e. the abovementioned contributions with the quadratic terms in x' and y' . The Fresnel diffraction integral can be expressed in terms of Fourier transform of the function U=S*Uⁱⁿ multiplied by the quadratic Fresnel term, calculated at the spatial frequencies k_x'=kx'/z and k_y'=ky'/z:

(5)

By extending the integral to the entire plane (x',y') and defining S=0 outside the surface of the hologram, the following is obtained:

where with FT the Fourier transform has been indicated. Hereinbelow, it is assumed to refer to, without any loss of generality, diffractive optical elements that are so-called phase-only, i.e. PDOE. Nevertheless, the present method can also be employed for ADOE or PADOE holograms.

In order to compensate for the errors of the aggregate field reconstructed in a so-called signal window, in the reconstruction plane, an iterative process is executed between the plane of the hologram and the reconstruction plane. In addition, it is assumed hereinbelow, without any loss of generality, that the diffractive optical element 6 is designed in a manner such that the so-called image reconstructed from the diffraction of the hologram in the reconstruction plane is an image with only determined amplitude . Now, therefore, in order to manufacture the diftractive optical element 6, a reference image is assumed within the abovementioned signal window, such reference image being an image of a given object. In addition, given that the goal is to obtain an image reconstructed with only amplitude, phase freedom is applied (assuming for example an initial pseudorandom distribution, possibly symmetric for the purpose of facilitating the convergence of the algorithm) within the signal window, as well as the amplitude freedom is applied outside the signal window.

Starting from the reference image, represented in the signal window of the reconstruction plane, this is transformed from the reconstruction plane to the plane of the hologram, by means of Fourier transform. Since the manufacturing processes today available generally allow producing structures with discrete transmittance functions, it is possible to project the complex continuous spectrum obtained in the plane of the hologram in a corresponding discrete plane, for example on a number of levels equal to 2ⁿ (preferably with n>l, in order to prevent the formation of twin images) . The discretization can be carried out by means of an iterative process, in which at each iteration the spectrum of the hologram is partially quantized by an IFTA algorithm, as described hereinbelow. Hence the spectrum of the hologram, partially quantized, is transformed in the reconstruction plane by using the inverse Fourier transform. The partial quantization introduces noise in the reconstruction plane, which can be removed by substituting, within the signal window, the amplitude of a noisy signal with the desired amplitude of the reference image. The process is then repeated, for example until a pre-established quality has been achieved, i.e. until the signal-to-noise ratio exceeds a pre- established threshold.

In mathematical terms, the IFTA procedure can be summarized as follows:

1) gi(j,k) is the input signal at the i-th iteration, in the reconstruction plane, j and k being the positions respectively of line and column of the pixels which form the signal matrix; such signal, at the first iteration, is therefore equal to the reference image, which is zero outside the signal window. The size of the signal window is predetermined and fixed.

2) By calculating the Fourier transform of the input signal, one passes into the plane of the hologram, obtaining the function:

Gi(m, n)=FT[gi(j, k) ]

wherein n and m are the positions respectively of line and column of the pixels in the plane of the hologram.

3) Renormalizing with respect to the optical decoding beam DOB, one obtains:

Gi^*(m,n)= Gi(m,n) /Uⁱⁿ(m,n)

4) By applying a quantization operator Q in the plane of the hologram, one obtains the function

Hi*(m,n)= Q[Gi*(m,n) ]

which represents an i-th definition of the diffractive optical element 6, since it defines a matrix of quantized phase values, on the basis whereof it is possible to form a corresponding approximate version of the diffractive optical element 6.

5) Renormalizing the function Hi^*(m,n) for the optical decoding beam DOB, one thus obtains:

Hi(m,n)= Hi^*(m,n)* Uⁱⁿ(m,n)

6) The simulated reconstruction of the image in the reconstruction plane is thus equal to an output signal h±(j,k), obtainable through an inverse Fourier transform (IFT) , and in particular as:

hi(j,k)= IFT[Hi(m,n) ]

7) Finally, a new signal gi+i(j,k) is obtained by means of a substitution operator R, which substitutes, within the signal window, the output signal h±(j,k) with the reference image; outside of the signal window, the amplitude remains that of the output signal hi(j,k). Such operation can be expressed as:

g_i+i(j,k)=R[hi(j,k) ]

8) Subsequently, a new iteration is executed, starting from step 1) . It is noted that, in the course of the iterations, the substitution operator R, the quantization operator Q and the signal window are fixed, i.e. their definitions do not vary.

In practice, a number N of iterations is executed, until the IFTA procedure converges. In addition, the efficiency of the . IFTA procedure depends on the selection of the quantization operator Q and of the abovementioned substitution operator R. The operator Q can be expressed as Q=P*A, in which the operator A acts on the amplitude, while the operator P acts on the phase.

The operator P, which at each iteration determines the amplitudes of corresponding quantization intervals that are separated from each other, and fixes the phase values at the quantization levels, assumes particular importance, as explained in M. Skeren, I. Richter, P. Fiala, Journal of Modern Optics 49, 11, 1851-1870, 2002. Once a phase angle is fixed, this cannot be used in a further optimization process, since it does not represent an additional control parameter that can affect the improvement of the convergence. Therefore, at each step, only the additional degrees of freedom that have remained are represented by the non-processed values, i.e. by the phase values not yet assigned to the quantized levels, since they are arranged outside the M quantization intervals relative to the considered iteration. Therefore, in order to allow further optimizations, it is suitable to maintain, as much as possible, a sufficient number of non-processed values during the IFTA procedure, and at the same time allow the already-processed values to pass from one target phase level to another target phase level among the M quantization values defined by the operator P, or to the set of values that are not yet quantized.

In practice, the IFTA procedure allows defining, from the start, the ratio between the size W of the signal window and the total size of the hologram, as well as the number M of phase quantization levels, the abovementioned number N of iterations, as well as the properties of the optical decoding beam DOB (indices 1 and p and beam waist wo) .

Once again with reference to figure 2, following the incidence of the optical decoding beam DOB on the diffractive optical element 6, the latter generates via reflection a new optical beam, referred to as the optical information beam IOB.

The optical information beam IOB can be received, for example, by an optical receiver 10, in a manner so as to form inside the latter the abovementioned reconstructed image. Even if not shown, it is still possible that, in place of the optical receiver 10, an observer is present, as mentioned above.

In practice, the diffractive optical element 6 encodes an object, two-dimensional or three-dimensional, corresponding to the abovementioned reference image. In addition, since the IFTA procedure was based on the optical decoding beam DOB, i.e. on the same optical beam, provided with an orbital angular momentum, which during use illuminates the diffractive optical element 6, the image reconstructed in the optical receiver 10 is characterized by a high signal-to-noise ratio, as shown in figure 4a. Therefore, the optical receiver 10 can correctly decode the information contained in the reconstructed image, i.e. in the reference image, and thus the information encoded by the diffractive optical element 6. In an equivalent manner, when illuminated by the optical decoding beam DOB, the diffractive optical element 6 generates a desired distribution of electromagnetic field, such to allow the clear formation of the reconstructed image.

On the other hand, if the diffractive optical element 6 is illuminated with radiation that is different from the optical decoding beam DOB, the image reconstructed inside the optical receiver 10 is very noisy, as shown in figure 4b. Hence, it is not possible to decode the information encoded by the diffractive optical element 6.

It is also observed that, even if not shown in figure 4a, it is possible that the diffractive optical element 6 is such that the reconstructed image is a so-called two- dimensional bar code, also known as code QR.

In more detail, in order to be able to validly use the Fraunhofer approximation, it is possible to arrange the optical receiver 10 at a sufficiently large distance from the diffractive optical element 6 ( >\0*2πΐ /λ ) , otherwise only the Fresnel approximation is valid. Alternatively, as shown in figure 5, it is possible to interpose a lens 12 (e.g., of cylindrical or spherical type) between the diffractive optical element 6 and the optical receiver 10, in a manner so as to focus the optical information beam IOB on the optical receiver 10; in such case, the optical receiver 10 can lie at a distance from the lens 12 equal to the focal length of the lens 12. In such a manner, the distance between the diffractive optical element 6 and the optical receiver 10 can be reduced.

As shown in figure 6, between the diffractive optical element 6 and the optical receiver 10, a second phase plate 14 can be interposed in a manner such that it is possible to modify the characteristics of the optical information beam IOB, for example by modifying the topological charge thereof. In addition, as shown in figure 7, between the diffractive optical element 6 and the optical receiver 10 both the second phase plate 14 and the lens 12 can be interposed .

Generally, irrespectively of the employed analysis method, the diffractive optical element 6 can be formed with a technique that combines a binary approach with single manufacturing step with a multilevel phase patterning, in a manner so as to reduce the manufacturing times and complexity without reducing the efficiency of the diffractive optical element 6, which increases with the increase of the phase levels. For such purpose, it is possible to manufacture so-called structures with size smaller than the wavelength ( "subwavelength structures", SWS) , which behave as artificial dielectric means, as described for example in W. Freese, T. Kampfe, W. Rockstroh, E. Kley and A. Tunnermann, Optics Express 19, 9, 8684-8692, 2011. For example, figure 8 shows an embodiment in which the diffractive optical element 6 comprises a plurality of structures with size smaller than the wavelength; in particular, by way of example, structures of a first and second type are respectively indicated with 32 and 34.

In greater detail, by changing the surface characteristics, in terms of design and/or fill factor, it is possible to locally control the equivalent diffraction indices. Therefore, it is possible to synthesize multilevel phase elements with a binary structure, which can be formed with an electron-beam lithography, or with a single-step photolithography followed by an etching process. On the basis of such technique, the required phase modulation, corresponding to a pixel of the diffractive optical element 6, is obtained by means of division of the pixel into a periodic nanostructure pattern SWS.

The refraction indices and hence the phase displacements imparted by the nanostructures SWS can be modified; they depend on the structural characteristics and their values can be calculated on the basis of the theory of approximation of the effective medium, as described for example in P. Lalanne, D. Lemercier-Lalanne, "On the effective medium theory of subwavelength periodic structures", Journal of Modern Optics 43, 10, 2063-2085 (1996) . Therefore, if the nanostructures SWS are synthesized on the basis of the required phase modulations of the pixels, it is possible to implement the diffractive optical element 6 by means of manufacturing a binary structure on a dielectric substrate, i.e. by means of manufacturing a metasurface.

Preferably, most of the input energy is diffracted on the order of zero diffraction. Therefore, preferably the ratio between the period Λ of each nanostructure SWS (e.g. of binary type) and the wavelength λ is low (e.g. Λ<0.5*λ, and preferably Λ<0.1*λ) so as to prevent diffraction phenomena .

Embodiments are also possible in which the nanostructures SWS are of aperiodic type, and in such case each of these has a maximum size, intended as maximum distance between any two points of the nanostructure SWS, preferably smaller than half of the wavelength λ.

The advantages that the present diffractive optical element of the holographic type allows obtaining clearly emerge from the preceding description. In particular, the present diffractive optical element allows integrating the holographic technology with the use of an illumination structured with orbital angular momentum, in order to offer an innovative system for encoding the image and a greater security level with respect to the systems on the market. A hologram obtained with this technique indeed allows a correct reconstruction of the enclosed information only if illuminated with the structured light for which it was designed. Alternatively, the hologram can be made in a manner such it modifies the orbital angular momentum of the incident light which must be correctly encoded.

In addition, the present diffractive optical element can be implemented in all hologram types available today, such as diffractive grating holograms, 2D/3D holograms, computer-generated holograms (CGH) and so-called "nano/raicro text".

Finally, it is clear that modifications and variations can be made to the present diffractive optical element, without departing from the scope of the present invention, as defined by the enclosed claims.

For example, in order to generate the optical decoding beam DOB, instead of employing a phase plate, it is possible to make use of a hologram of "fork" ("fork hologram") type, operating in reflection and generated optically or via computer, as described for example in M. Granata, C. Buy, R. Ward, M . Barsuglia, Physical Review Letters 105, 231102, 2010. An example of a fork hologram is shown in figure 9, where it is indicated with 40.

In addition, the diffractive optical element can be configured for operating in transmission, rather than in reflection.

It is also possible that the diffractive optical element be configured for generating a reconstructed image that also contains phase information. In such case, the abovementioned phase 7 provides that the substitution operator R substitutes, within the signal window, the phase profile of the output signal hi(j,k) with the phase profile of the reference image, in addition to substituting the amplitude profile of the output signal hi(j,k) with the amplitude profile of the reference image.

Independent of whether the diffractive optical element operates in reflection or transmission, it is possible that this is of ADOE type, and in such case the function Gi(m,n) represents a matrix of quantized amplitude values. In addition, the diffractive optical element can be of PADOE type. Nevertheless, it is generally preferable that the diffractive optical element be of PDOE type and operate in reflection, since it is thus possible to obtain greater efficiency.

In addition, it is possible that the diffractive optical element be configured in a manner such to allow the decoding of the information only when illuminated by a combination of superimposed Laguerre-Gauss modes, in a manner such to further increase the information encoding security and capacity.

In addition, the diffractive optical element may not be computer-generated, but rather, for example, it may be conventionally generated via optical interference. In such case, the diffractive optical element records the interference pattern between the coherent light diffused by an object and a coherent reference light beam, which has non-zero orbital angular momentum.

Finally, as shown in figure 10, it is possible that the first phase plate 4 is absent, and only the second phase plate 14 is present; in such case, the diffractive optical element, indicated herein with 60, is illuminated with radiation lacking orbital angular momentum and, unlike that stated above, is such that it produces (for example, via reflection or transmission) , in a per se known manner, radiation lacking orbital angular momentum, which acquires a non-zero orbital angular momentum only after having crossed the second phase plate 14. Therefore, the diffractive optical element 60 is configured in a manner such that it does not encode the desired image, if not due to the coupling with the second phase plate 14, or due to the coupling (not shown) with a fork hologram.

Claims

1. Diffractive optical element (6) of the holographic type configured for:

- forming, when illuminated by a first electromagnetic field (DOB) having non-zero orbital angular momentum, a second electromagnetic field (IOB) adapted to form, at a reconstruction plane, a first image lacking noise, indicative of information encoded by said diffractive optical element; and

- forming, when illuminated by a third electromagnetic field, a fourth electromagnetic field adapted to form a second noisy image, said first and third electromagnetic field having different topological charges and/or different spatial distributions of phase singularities.

2. Diffractive optical element according to claim 1, wherein said first and second image are such that the information encoded by said diffractive optical element (6) is decodable starting from said first image, but is not decodable starting from said second image.

3. Diffractive optical element according to claim 1 or

2, wherein said first electromagnetic field (DOB) is substantially a Laguerre-Gauss mode, or a combination of multiple Laguerre-Gauss modes.

4. Diffractive optical element according to any one of the preceding claims, configured for modulating the phase, or the amplitude, or the phase and the amplitude of the first electromagnetic field (DOB) .

5. Diffractive optical element according to claim 4, forming a computer-generated hologram.

6. Diffractive optical element according to claim 4, which records a pattern of interference between a light diffused by an object and a reference light beam containing at least one phase singularity.

7. Diffractive optical element according to any one of the preceding claims, forming a multi-relief surface.

8. Diffractive optical element according to any one of the preceding claims, wherein said first image is a two- dimensional bar code.

9. Diffractive optical element, obtained by means of a method comprising the steps of:

arranging a reference image, represented in a reconstruction plane;

transforming said reference image from the reconstruction plane to a plane of said diffractive optical element (6), by means of Fourier transform;

- quantizing said reference image in the plane of said diffractive optical element (6);

transforming, in the reconstruction plane, said reference image thus quantized, by using an inverse Fourier transform;

reducing the noise of said reference image transformed in the reconstruction plane, by means of a function of substitution of the amplitude and/or phase of said noisy image, with the desired amplitude and/or the phase of said reference image;

iterating the aforesaid steps, until a pre- established quality of said transformed reference image is obtained, that is until the signal-to-noise ratio exceeds a pre-established threshold.

10. Diffractive optical element according to claim 9, wherein said step of arranging a reference image, represented in a reconstruction plane, requires mathematically representing said reference image according to the formula gi ( j , k)

wherein gi(j,k) is a reference image transformed in the reconstruction plane at the i-th iteration, i being a value comprised between 1 and N, wherein j and k are the positions respectively of line and column of the pixels which form said image; said transformed image, at the first iteration gi(j,k), corresponding to said reference image.

11. Diffractive optical element according to claim 10, wherein said step of transforming said reference image from the reconstruction plane to a plane of said diffractive optical element (6), by means of Fourier transform, comprises mathematically representing said reference image in said plane of said diffractive optical element (6) according to the formula:

wherein n and m are the positions respectively of line and column of the pixels of said transformed image in said plane of said diffractive optical element (6).

12. Diffractive optical element according to claim 11, wherein said step of transforming said reference image from the reconstruction plane to a plane of said diffractive optical element (6), further comprises the step of renormalizing said transformed image in said plane of said diffractive optical element (6) with respect to said first electromagnetic field (DOB) , obtaining:

Gi^*(m,n)= Gi (m, n) /Uⁱⁿ (m, n)

wherein

Uⁱⁿ(m,n) is the value of said first electromagnetic field (DOB) at the positions n and m of line and column of the pixels of said transformed image in said plane of said diffractive optical element (6).

13. Diffractive optical element according to claim 12, wherein said step of quantizing said reference image in the plane of said diffractive optical element (6) comprises applying a quantization operator Q in the plane of said diffractive optical element (6), according to the function

Hi^*(m,n)= Q[Gi^*(m,n) ]

which represents an i-th definition of the diffractive optical element (6), since it defines a matrix of quantized phase values, based whereon it is possible to form a corresponding approximate version of the diffractive optical element (6).

14. Diffractive optical element according to claim 13, further comprising the step of renormalizing said function Hi^*(m, n) for said first electromagnetic field (DOB), according to the relation:

Hi(m,n)= Hi^*(m,n)* Uⁱⁿ(m,n)

15. Diffractive optical element according to claim 14, wherein said step of transforming in the reconstruction plane said reference image thus quantized, by using an inverse Fourier transform, comprises applying the following mathematical formula:

hi(j, k)= IFT[Hi(m,n) ]

16. Diffractive optical element according to claim 15, wherein said step of reducing the noise of said reference image transformed in the reconstruction plane, by means of a function of substitution of the amplitude and/or phase of said noisy image, with the desired amplitude and/or phase of said reference image, comprises using a substitution operator R which substitutes said reference transformed image in the reconstruction plane hi(j,k) with said reference image gi(j,k); the amplitude and/or the phase remaining that of the output signal hi(j,k) and said operation being expressible as: g_i+i(j,k)=R[hi(j,k) ] .

17. Diffractive optical element according to claims 13 and 16 wherein, in the course of said iterations, the substitution R and quantization Q operators are fixed.

18. Diffractive optical element according to any one of the claims from 13 to 17 when dependent on claim 13, said quantization operator Q is expressible as Q=P*A, wherein the operator A acts on the amplitude, while the operator P acts on the phase.

19. Diffractive optical element according to any one of the claims from 9 to 18, wherein said pre-established threshold of said signal-to-noise ratio is greater than 1, preferably greater than 10.

20. Optical system comprising a diffractive optical element (6) according to any one of the preceding claims and generator means (4) configured for generating said first electromagnetic field (DOB) , starting from an optical input beam (OB) having zero orbital angular momentum.

21. Optical system according to claim 20, wherein said generator means comprise a first phase plate (4), or a fork type hologram (40) .

22. Optical system comprising a diffractive optical element (6) according to any one of the claims 1-19 and a lens (12) configured for receiving and focusing said second electromagnetic field (IOB).

23. Optical system comprising a diffractive optical element (6) according to any one of the claims 1-19 and a second phase plate (14), optically arranged downstream of the diffractive optical element.

24. Optical system comprising a diffractive optical element (6) according to any one of the claims 1-19 and an optical receiver (10) configured in a manner such that said first and second image are formed, during use, inside said optical^' receiver.

25. Optical system comprising a diffractive optical element (6) according to any one of the claims 1-19 and an optical source (2,4) configured for generating said first electromagnetic field (DOB) , and wherein said first electromagnetic field (DOB) has a wavelength and said diffractive optical element (6) is formed by a plurality of periodic regions (32,34), each periodic region having a respective spatial period that is shorter than half of said wavelength .

26. Optical system comprising a diffractive optical element (6) according to any one of the claims 1-19 and an optical source (2,4) configured for generating said first electromagnetic field (DOB), and wherein said first electromagnetic field (DOB) has a wavelength and said diffractive optical element (6) is formed by a plurality of aperiodic regions, each aperiodic region having a respective maximum size that is smaller than half of said wavelength.

27. Optical system comprising a diffractive optical element (60) of the holographic type and an optical processing element (14;40) between a phase plate and a fork hologram, said optical system being configured in a manner such that:

- when the diffractive optical element is illuminated by an input electromagnetic field lacking orbital angular momentum, it generates an output electromagnetic field having a non-zero orbital angular momentum and adapted to form an image substantially lacking noise; and

- when the diffractive optical element is illuminated by an electromagnetic field having non-zero orbital angular momentum, it generates an output electromagnetic field adapted to form a noisy image.

28. Method for obtaining a diffractive optical element (6) according to any one of the claims from 1 to 19.

29. Diffractive optical element according to any one of the claims from 1 to 8 when obtained as stated in any one of the claims from 9 to 19.