Holographic Method With Numerical Reconstruction for Obtaining an Image of a Three-Dimensional Object Which Even Points out of the Depth of Field Are in Focus, and Holographic Apparatus Using Such a Method

Abstract

The invention concerns a holographic method with numerical reconstruction for obtaining an image of a three-dimensional object, said method employing a digitalised hologram of an object, and comprising a step A. wherein, starting from the digitalised hologram, extracting a phase image of said object corresponding to a bidimensional matrix MD of distance values; a step B. wherein a mono-dimensional subassembly SD of the distance value assembly present in matrix MD of the method step A is selected, subassembly SD containing distance values dk; a step C. wherein for each distance value dk, extracting from matrix MD a iso-level assembly IQdk corresponding to a mono-dimensional assembly of bidimensional coordinates of said object, a step D. wherein for each distance value dk, reconstructing, starting from the digitalised hologram, a bidimensional matrix IMdk of intensity values relevant to said object; a step E. wherein, from each bidimensional matrix IMdk a bidimensional matrix IFdk of intensity values is extracted corresponding to the bidimensional coordinates of the iso-level assembly IQdk; a step F. wherein, starting from intensity values IFdk from the bidimensional coordinates of the iso-level assembly IQdk and from the relevant distance values dk, reconstructing the three-dimensional intensity image of said object, and wherein the resolution of the bidimensional matrix IMdk for all values of k is identical to the resolution of matrix MD of distance values.

1 - 39 . (canceled) 
   
   
       40 . Holographic method with numerical reconstruction for obtaining an image of a three-dimensional object, said method employing a digitalised hologram of an object or of a portion of an object, and being characterised in that it comprises the following steps:
 A. starting from the digitalised hologram, extracting a phase image of said object of portion of object, the image corresponding to a matrix MD of distance values, said distance values corresponding to distances from the image plane or to the depths relevant to said object or object portion;   B. selecting a subset SD of the distance value set present in matrix MD of the method step A, subset SD containing distance values d k , with k having a value between 1 and a whole number N SD >1;   C. for each distance value d k , extracting from matrix MD a iso-level set IQd k  of corresponding bidimensional coordinate of said object or object portion;   D. for each distance value d k , reconstructing by numerical propagation, starting from the digitalised hologram, a bidimensional matrix IMd k  of intensity values relevant to said object or object portion;   E. extracting, from each bidimensional matrix IMd k  of the method step D, a bidimensional set IFd k  of intensity values corresponding to the bidimensional coordinates of the iso-level set IQd k  extracted in method step C;   F. starting from intensity values of said IFd k  sets of the method phase E, from the coordinate bidimensional of the iso-level set IQd k  and from the relevant distance values d k , for all values of k between 1 and N SD , reconstructing the three-dimensional intensity image of said object or object portion;   resolution of bidimensional matrix IMd k  for all values of k between 1 and N SD  being identical to the resolution of matrix MD of distance value.   
   
   
       41 . Method according to  claim 40 , characterised in that in step A said one phase image is obtained using two or more phase images reconstructed starting from the same digital hologram for different distance values belonging to said matrix MD. 
   
   
       42 . Method according to  claim 40 , characterised in that method step A is carried out using the convolution method. 
   
   
       43 . Method according to  claim 40 , characterised in that method step D is carried out using the convolution method. 
   
   
       44 . Method according to  claim 40 , characterised in that method A step is carried out employing Fresnel method. 
   
   
       45 . Method according to  claim 44 , characterised in that, when the digitalised hologram is comprised of a number V r  of intensity values corresponding to an equivalent number of elementary sub-images or “pixel” of the holographic image, pixel dimensions corresponding to sampling intervals of the holographic image, the method can comprise, in its step A for obtaining said one phase image, a first processing sub-step A.1 of the matrix of the digitalised hologram, and a second reconstruction sub-phase A.2 in the complex plane of the hologram starting from the digitalised hologram processed during the first sub-step A.1, the method being characterised in that the second sub-step A.2 is carried out by discrete Fresnel transform starting from a value matrix V e , comprising said V r  values, as well as a whole number p=V e −V r >0 having constant value corresponding to OS, corresponding to the same number of pixel having the same dimensions of the other ones. 
   
   
       46 . Method according to  claim 45 , characterised in that said p constant values are null values (OS=0). 
   
   
       47 . Method according to  claim 45 , characterised in that said p constant values are values different from 0 (OS not 0). 
   
   
       48 . Method according to  claim 40 , characterised in that said p values are outside said V r  value matrix. 
   
   
       49 . Method according to  claim 48 , characterised in that said p values are arranged symmetrically. 
   
   
       50 . Method according to  claim 49 , characterised in that said p values are arranged asymmetrically. 
   
   
       51 . Method according to  claim 45 , characterised in that said value V e  number is inversely proportional with respect to the pixel dimension that it is wished obtaining for said phase image MD. 
   
   
       52 . Method according to  claim 45 , characterised in that digitalised hologram is a rectangular matrix of V r =N r M r  values, each value corresponding to a square pixel of Δx, Δy dimensions. 
   
   
       53 . Method according to  claim 52 , characterised in that hologram reconstructed during step A.2 is represented by a rectangular matrix of V e =N e M e  values, each value corresponding to a square pixel of Δξ=(λd/N e  Δx) and Δη=(λd/M e  Δy), λ being the wavelength of the wave bundle impinging the object of which the hologram is registered, and d the distance between the sensing device and the object of which the hologram is registered, Δξ and Δη being sample intervals of the reconstructed holographic image. 
   
   
       54 . Method according to  claim 53 , characterised in that N e =(λd/Δx 2 ), M e =(λd/Δy 2 ), Δξ=Δx, Δη=Δy. 
   
   
       55 . Method according to one of the  claim 45 , characterised in that after a second sub-step A.2, if each sample interval of the holographic image is not equal or lower to a set threshold, number of values p added to the digitalised hologram matrix is increased, and the second step is again carried out. 
   
   
       56 . Method according to  claim 55 , characterised in that said threshold is set in function of the signal/noise ratio of the holographic image. 
   
   
       57 . Method according to  claim 45 , characterised in that method step D is carried out employing Fresnel method. 
   
   
       58 . Method according to  claim 57 , characterised in that, when the digitalised hologram is comprised of a number V r  of intensity values corresponding to an equivalent number of elementary sub-images or “pixel” of the holographic image, pixel dimensions corresponding to sampling intervals of the holographic image, the method step D comprises a first processing sub-step D.1 of the matrix of the digitalised hologram, and a second reconstruction sub-phase D.2 for each d k  value, with k comprised between 1 and N SD , in the complex plane of the hologram starting from the digitalised hologram processed during the first sub-step D.1, the second sub-step D.2 being carried out by discrete Fresnel transform starting from a value matrix V e   k , comprising said V r  values, as well as a whole number p k =V e   k −V r >0 having constant value corresponding to OS k , corresponding to the same number of pixel having the same dimensions of the other ones, said whole number p k  being function of the d k  distance for each bidimensional matrix IMd k , in such a way that resolution of each bidimensional matrix IMd k , is identical to the resolution of the MD matrix of distance values. 
   
   
       59 . Method according to  claim 58 , characterised in that said whole number p k  is directly proportional to distance d k . 
   
   
       60 . Method according to  claim 58 , characterised in that Advantageously according to the invention, said constant values p k  for one or more k whole numbers between 1 and N SD  are null values (OS k =0). 
   
   
       61 . Method according to  claim 58 , characterised in that said constant values p k  for one or more k whole numbers between 1 and N SD  are not null values (OS k  different from 0). 
   
   
       62 . Method according to  claim 58 , characterised in that said p k  values are outside said V r  values matrix. 
   
   
       63 . Method according to  claim 62 , characterised in that said p k  values are arranged symmetrically. 
   
   
       64 . Method according to  claim 62 , characterised in that said p k  values are arranged asymmetrically. 
   
   
       65 . Method according to  claim 58 , characterised in that said number of V e   k  values is inversely proportional to the pixel dimension of the pixel to be obtained for IMd k  images reconstructed for all values of k between 1 and N SD . 
   
   
       66 . Method according to  claim 58 , characterised in that digitalised hologram is a rectangular matrix of V r =N r ·M r  values, each value corresponding to a rectangular pixel having Δx, Δy dimensions. 
   
   
       67 . Method according to  claim 66 , characterised in that hologram reconstructed in second sub-step D.2 is represented by a square matrix of V r   k =N r   k ·M r   k  values, each value corresponding to a rectangular pixel having set constant dimensions Δξ=(λd/N e   k  Δx) and Δη=(λd/M e   k  Δy), λ being the wavelength of the wave bundle impinging the object of which the hologram is registered, and d k  the distance between the sensing device and the object of which the hologram is registered, Δξ and Δη being sample intervals of the reconstructed holographic image IMd k  for all k values between 1 and N SD . 
   
   
       68 . Method according to  claim 40 , characterised in that N SD >2. 
   
   
       69 . Method according to  claim 68 , characterised in that N SD  is set on the basis of the minimum resolution of the holographic apparatus by which the digitalised hologram is obtained. 
   
   
       70 . Method according to  claim 40 , characterised in that aberrations have beforehand eliminated from said digitalised hologram by numerical processing. 
   
   
       71 . Method according to  claim 40 , characterised in that a reference-digitalised hologram has been beforehand subtracted from said digitalised hologram. 
   
   
       72 . Method according to  claim 71 , characterised in that said reference digitalised hologram is the hologram of a flat surface registered under the same conditions of registration of the hologram of said at least one object portion. 
   
   
       73 . Method according to  claim 40 , characterised in that method is carried out simultaneously for more than one object portion. 
   
   
       74 . Method according to  claim 73 , characterised in that resolution of MD matrix of at least one of said more than one portion is different from at least one of the resolutions of the other corresponding MD matrixes. 
   
   
       75 . Method according to  claim 40 , characterised in that A, B, C, D, E, F, method steps are repeated for more than one wavelength of the light used for obtaining digitalised hologram, or equivalently for two or more digitalised hologram obtained at different wavelengths, resolution of all bidimensional matrix IMd k  for each digitalised hologram and for all values of k between 1 and N SD , being identical to the MD matrix resolution of distance values, MD matrix being extracted starting from at least one of the digitalised holograms corresponding to said different wavelengths, three-dimensional intensity images of said object or of said object portion being the juxtaposition of the three-dimensional images reconstructed starting from said more than one digitalised holograms. 
   
   
       76 . Computer program characterised in that it comprises code means arranged to execute, when operating on a processor, method according to  claim 40 . 
   
   
       77 . Memory support readable by a processor, having a program memorised, characterised in that the program is the computer program according to  claim 76 . 
   
   
       78 . Apparatus for revealing holographic images, particularly a holographic microscope, comprising a unit for processing the digitalised hologram, characterised in that the processing unit processes data revealed employing the method according to  claim 40 .