Method for holographically combining laser beams
BACKGROUND OF THE INVENTION 
     This invention relates to a novel method for holographically combining multiple laser beams into a single, combined amplitude laser beam. 
     INTRODUCTION TO THE INVENTION 
     A basic theory on holographic devices and methods for holographic recording and reconstructing, is known. Reference may be made, for example, to Goodman, J. S.: Introduction to Fourier Optics, Chap. 8, McGraw-Hill Book Company, New York, 1968; Meyer-Arendt, J. R.: Introduction to Classical and Modern Optics, Chap. 4.4, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1972; or, Collier, R. J., et al: Optical Holography, Chap 1, Academic Press, New York, 1971. 
     SUMMARY OF THE INVENTION 
     Our work is to extend and exploit the potentialities of application inherent in a theoretical elaboration of holography. To this end, we now disclose a novel method for holographically combining multiple laser beams into a single, combined amplitude laser beam. 
     The novel method of the present invention comprises the steps of: 
     1) providing an optical device comprising: 
     a) a support substrate having entrance and exit faces and comprising a monolithic device; 
     b) means providing a diffusion surface on the entrance face; and 
     c) means providing a light sensitive recording medium on the exit face comprising; 
     f the support structure and the entrance and the exit faces comprising a monolitic device; 
     2) constructing a holographic recording by simultaneously: 
     (i) directing a reference beam to the light sensitive recording medium; and 
     (ii) directing an input beam through the entrance face for interfering with the reference beam at the exit face; and 
     3) directing a plurality of conjugate reference beams to the holographic recording, thereby providing a combined conjugate output beam. 
     The method also preferably comprises a further step of selectively combining conjugate reference beams for reconstructing the input beam in accordance with predetermined intensity levels, thereby providing a digital to analog capability. 
     The method of the present invention has the advantages of realizing a laser beam combiner capability, or an optical digital to analog (DAC) capability. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is illustrated in the accompanying drawing, in which: 
     FIG. 1 shows a holographic device usable for the method of the present invention; 
     FIGS. 2A, 2B show the holographic device of the FIG. 1 used for holographic recording and reconstructing, respectively; 
     FIG. 3 shows a schematic holographic recording geometry; and 
     FIG. 4 shows a schematic holographic reconstructing geometry. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The method of the present invention preferably utilizes a holographic device of a type shown in FIG. 1 as holographic device 10. Details on the holographic device 10 are first disclosed, followed by a disclosure of the method of the present invention (FIGS. 2-4), which utilizes the holographic device 10. 
     In overview, the FIG. 1 holographic device 10 comprises a support substrate 12; a support substrate entrance face 14; and, a support substrate exit face 16 comprising a light sensitive recording medium. Individual details on the FIG. 1 holographic device 10 are now disclosed. 
     THE SUPPORT SUBSTRATE 
     The support substrate 12 may comprise a light transmissive block, for example, a glass block, or a conventional prism. We employ a prism in a preferred mode, for reasons of support stability, optical properties and economics. A typical such prism has a length from approximately 7.0 cm. to 8.0 cm.; a depth of approximately 3.0 cm. to 4.0 cm.; a width from approximately 2.5 cm. to 3.5 cm.; and, a weight from approximately 200.0 gm. to 300.0 gm., depending on its ultimate use in a particular holographic recording or reconstructing method. 
     The prism preferably functions as a deviating prism, because, as demonstrated below in the method of utility of the holographic device 10, the deviating prism refracts a reference beam at an appropriate angle. 
     A suitable prism may comprise a dove prism, although, for example, a Porro prism or a right angle prism may be used. 
     A suitable prism may be a polarizing prism. 
     The prism may comprise glass or a crystalline substrate. 
     A selection of one such particularly characterized prism depends, ultimately, on its use in a particular holographic recording or reconstructing method. 
     THE ENTRANCE FACE 
     The support substrate 12 defines the entrance face 14. A diffusion surface is provided on the entrance face 14 which may comprise a scattering medium or, alternatively, it may comprise a periodic structure. For either alternative, the diffusion surface on entrance face 14 functions so that all components of the entrance face 14 provide illumination to a common area i.e., a pupil of the exit face 16. 
     Preferably, the scattering medium comprises ground glass, that may be etched or ground by conventional techniques directly on the support substrate 12. This action creates a diffusing surface. 
     Alternatively, one may attach, for example, by way of a conventional optical cement, a discrete ground glass entity, to the support substrate 12, so as to construct a monolithic device. 
     The scattering medium may comprise an array of point scatterers, or a light sensitive recording medium, for example, a photographic film. These alternative scattering media comprise a diffusing surface that is integral to the holographic device 10. 
     As just referenced, the entrance face 14 may alternatively comprise a periodi structure, for example, an array of microlenses, or an array of pinhole apertures, or an array of diffractive optical elements. The term &#34;diffusing surface&#34; as used herein contemplates such periodic structure, as well. 
     Note that for all cases, (i.e., periodic or scattering), an index of refraction of the entrance face 14 is preferably the same as that of the support substrate 12. 
     THE EXIT FACE 
     The support substrate 12 defines the exit face 16 which is provided with a light sensitive recording medium. 
     The light sensitive recording medium may comprise a photoresistive material, or a silver halide, or a dichromated gelatin, or a photo polymer, or a thermoplastic. 
     The light sensitive recording medium may be applied to the support substrate 12 by way of a conventional coating process, which inherently adheres to the support substrate 12 so that it becomes integral to the holographic device 10, or it may be coated on a separate substrate that later adheres to the support substrate 12. 
     THE METHOD OF THE PRESENT INVENTION 
     Attention is now directed to FIGS. 2A, 2B, which illustrate a utility of the holographic device 10 in a holographic laser beam combining method of the present invention. 
     In particular, FIG. 2A illustrates an initial recording of a hologram of the diffusing surface 14. Each diffusing element of the diffusing surface 14 spreads an incident input (object) beam 18 over the whole area of the recording. A reference beam 20 is added to form an interference pattern on the recording material. 
     Note that since the light from each diffusing element is spread over the entire hologram area, upon reconstruction, each element of the hologram can reconstruct the entire diffusing area, and the beam that illuminates it. If, for example, a collimated beam is used to illuminate the diffusing surface during recording, then a collimated beam is reconstructed in a subsequent reconstructing step. This only works if an exact conjugate (time reversed) version of the original reference beam is used. 
     FIG. 2B illustrates a reconstructing step of the FIG. 2A hologram. Note, in particular, that FIG. 2B shows a step of directing a plurality of conjugate reference beams to the holographic recording. This action is that of a holographic beam combiner, whereby, for example, one can provide a laser writer generating several times the power available from a single high power diode laser. 
     Note, furthermore, that a step of selectively combining sundry of the plurality of conjugate reference beams, reconstructs the input (object) beam in accordance with predetermined intensity levels, thereby functioning as an optical digital to analog converter (i.e., an optical DAC). 
     One important feature of the present method is that it can reconstruct the exact same spatial intensity profile of the wavefront that was recorded in it, and that it is invariant to the lateral position of any of the plurality of conjugate reconstructing beams on the exit face, so long as they are within about 4° of the original reference beam angle. 
     These capabilities are now expanded upon, by way of a following mathematical disclosure. 
     HOLOGRAPHIC BEAM COMBINER/OPTICAL DAC 
     I. Recording Step 
     Assume some two-dimensional input function, in this case a plane wave with Gaussian amplitude 
     
         f.sub.1 (x,y)=A.sub.1 exp[-π(x.sup.2 +y.sup.2)/d.sup.2 ] 
    
     where x and y are spatial coordinates, and the wave is assumed to be traveling along the z axis; and A 1  is the wave amplitude; d is the beam diameter. 
     This input wave impinges on the entrance face with a complex transmission function 
     
         t.sub.1 (x,y)=exp(iφ) 
    
     where 
     φ=(2π/λ)nT is the phase; 
     λ is the wavelength; 
     n is the refractive index of the substrate; and 
     T is the thickness of the substrate. 
     The impulse response of the scatterer and media is 
     
         h.sub.1 =exp[(iπ/Tλ)(x.sup.2 +y.sup.2)]. 
    
     This is shown is FIG. 3, where S is the entrance face or input plane for the holographic recording, this is the phase scatterer, and 
     H is the recording plane; 
     R is a reference wave, and 
     R* is a conjugate reference wave. 
     This device can be modeled as a linear shift invariant system (LSI). It is linear since it abides by the principle of superposition as defined by Gaskill. (Linear Systems, Fourier Transforms and Optics by Jack D. Gaskill; John Wiley &amp; Sons, New York, 1978, pp. 137-138.) This essentially says that a linear combination of inputs or stimuli to a system result in a linear combination of outputs or responses from the system. Also understood from this is that the system is &#34;independent of the magnitude of the input.&#34; (See Gaskill previously cited, p. 139.) In the recording stage this system is also shift invariant, where shift in variance implies that the only effect caused by a spatial shift in the input is an equal spatial shift in the output. 
     It is not shift invariant in the reconstruction step, which, as will be shown, is of great advantage. The recording step can be completely characterized by this impulse response, since it is an LSI system. 
     The complex amplitude of the LSI system is the object wavefront that is recorded in the hologram at H in FIG. 3: 
     
         f.sub.2 (x,y)=f.sub.1 (x,y)t.sub.1 (x,y)*h.sub.1 
    
     where f 2  is the output and * denotes the convolution operation. The convolution operation really describes the Fresnel diffraction caused by the propagation of the original input wave through the scatterer and ensuing media. 
     The transfer function associated with Fresnel diffraction is found to be 
     
         H.sub.1 (ξ,η)=F{h.sub.1 (x,y)} 
    
     (where ξ and η represent spatial frequencies in the x and y directions). This describes the propagation of plane wave components from the input plane to output plane when the Fresnel approximations are valid. 
     
         F.sub.2 (ξ,η)=F.sub.1 (ξ,η)*T.sub.1 (ξ,η)H.sub.1 
    
     represents the distribution of plane wave components in the output plane. 
     To record the hologram at plane H, a plane reference wavefront is combined with the object wavefront F 2  (ξ,η). This is represented as a complex amplitude 
     
         R(x,y)=A.sub.2 exp(i2πxξ.sub.r) 
    
     where ξ r  =(sinθ)/λ), and 
     where θ is an angle the reference beam makes at the hologram plane H. In frequency space this could be written as 
     
         R(ξ,η)=A.sub.2 δ(ξ-ξ.sub.r). 
    
     The recording medium linearly records the intensity in the resulting interference pattern. This intensity is represented as ##EQU1## 
     II. Reconstruction Step 
     Assume that the transmittance function of the hologram is proportional to the intensity in the recording interference pattern. Reconstruction of the hologram is achieved by illuminating the hologram with the conjugate of the original reference beam R*(ξ,η). 
     This results in the following wavefront (see FIG. 4). 
     In accordance with FIG. 4, we develop the following relationships: ##EQU2## where the first term, |F 2  (ξ,η)| 2  R*(ξ,η) represents the intensity of the diffracted object wavefront combined with a background conjugate reconstruction wave. 
     The second term, |R(ξ,η)| 2  R*(ξ,η) is the intensity of the reference wave with a DC reconstruction beam component. 
     The third term, F 2  (ξ,η)|R*(ξ,η)| 2  is the diverging virtual image of the diffracted object wavefront plus conjugate reference intensity. 
     The fourth term, F 2  *(ξ,η)|R(ξ,η)| 2  is the conjugate object wavefront which converges to the plane of the scatterer along with background reference wave intensity. 
     Diffraction from the hologram back toward the plane of the scatterer is simply the reverse process of when the hologram was recorded, so complex conjugates of the original terms are used, i.e., 
     
         F.sub.2 *(ξ,η)=F.sub.1 *(ξ,η)*T.sub.1 *(ξ,η)H.sub.1 *. 
    
     Inverse Fourier transforming thus becomes 
     
         f.sup.-1 {F.sub.2 *(ξ,η)}=f.sub.1 *(x,y)t.sub.1 *(x,y)*h.sub.1 * 
    
     where fhu -1 denotes an inverse Fourier transform. Next, we substitute the conjugates of the original functions 
     
         f.sub.1 *(x,y)t.sub.1 *(x,y)*h.sub.1 *=A.sub.1 exp[π(x.sup.2 +y.sup.2)/d.sup.2 ]exp(-iφ)*exp([(-iπ/Tλ)(x.sup.2 +y.sup.2)]. 
    
     When this is recombined with the original phase scatterer the transmittance functions cancel. The impulse response of the system will also cancel the initial recorded impulse response. This leaves only the conjugate of the original Gaussian wave function 
     
         A.sub.1 exp[π(x.sup.2 +y.sup.2)/d.sup.2 ]exp(-iφ)exp(iφ)*exp([(-iπ/Tλ)(x.sup.2 +y.sup.2)]exp([(iπ/Tλ)(x.sup.2 +y.sup.2)]=A.sub.1 exp[π(x.sup.2 +y.sup.2)/d.sup.2 ]. 
    
     The conjugate of the original wavefront emerges from the system in a time reverse manner. It should be noted that in the reconstruction or end use stage of this device, it still behaves in a linear manner, yet is not shift invariant; i.e. a change in the angle of incidence of the reconstruction beam (the conjugate of the reference) or in its size or position on the recorded hologram surface, will not effect similar changes in the reconstructed wavefront. The conjugate output is invariant to the position of the reconstructing wavefront(s) in the sense that the output is constant in spatial profile.