U.S. patent application number 11/886473 was filed with the patent office on 2009-03-19 for 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.
This patent application is currently assigned to CONSIGLIO NAZIONALE DELLE RICHERCHE. Invention is credited to Giuseppe Coppola, Sergio De Nicola, Pietro Ferraro, Andrea Finizio, Simonetta Grilli, Bahram Javidi, Giovanni Pierattini.
Application Number | 20090073521 11/886473 |
Document ID | / |
Family ID | 36607322 |
Filed Date | 2009-03-19 |
United States Patent
Application |
20090073521 |
Kind Code |
A1 |
Coppola; Giuseppe ; et
al. |
March 19, 2009 |
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.
Inventors: |
Coppola; Giuseppe; (Napoli,
IT) ; De Nicola; Sergio; (Pozzuoli, IT) ;
Ferraro; Pietro; (Pozzuoli, IT) ; Finizio;
Andrea; (Pozzuoli, IT) ; Grilli; Simonetta;
(Arco Felice, IT) ; Javidi; Bahram; (Arco Felice,
IT) ; Pierattini; Giovanni; (Pozzuoli, IT) |
Correspondence
Address: |
YOUNG & THOMPSON
209 Madison Street, Suite 500
ALEXANDRIA
VA
22314
US
|
Assignee: |
CONSIGLIO NAZIONALE DELLE
RICHERCHE
ROME
IT
|
Family ID: |
36607322 |
Appl. No.: |
11/886473 |
Filed: |
February 23, 2006 |
PCT Filed: |
February 23, 2006 |
PCT NO: |
PCT/IT06/00099 |
371 Date: |
October 31, 2008 |
Current U.S.
Class: |
359/9 |
Current CPC
Class: |
G03H 2001/005 20130101;
Y10S 359/90 20130101; G03H 2210/30 20130101; G03H 2001/0883
20130101; G03H 1/0866 20130101 |
Class at
Publication: |
359/9 |
International
Class: |
G03H 1/08 20060101
G03H001/08 |
Foreign Application Data
Date |
Code |
Application Number |
Mar 16, 2005 |
IT |
RM2005A000120 |
Claims
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.sub.k, with k having a value between 1
and a whole number N.sub.SD>1; C. for each distance value
d.sub.k, extracting from matrix MD a iso-level set IQd.sub.k of
corresponding bidimensional coordinate of said object or object
portion; D. for each distance value d.sub.k, reconstructing by
numerical propagation, starting from the digitalised hologram, a
bidimensional matrix IMd.sub.k of intensity values relevant to said
object or object portion; E. extracting, from each bidimensional
matrix IMd.sub.k of the method step D, a bidimensional set
IFd.sub.k of intensity values corresponding to the bidimensional
coordinates of the iso-level set IQd.sub.k extracted in method step
C; F. starting from intensity values of said IFd.sub.k sets of the
method phase E, from the coordinate bidimensional of the iso-level
set IQd.sub.k and from the relevant distance values d.sub.k, for
all values of k between 1 and N.sub.SD, reconstructing the
three-dimensional intensity image of said object or object portion;
resolution of bidimensional matrix IMd.sub.k for all values of k
between 1 and N.sub.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.sub.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.sub.e,
comprising said V.sub.r values, as well as a whole number
p=V.sub.e-V.sub.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.sub.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.sub.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.sub.r=N.sub.rM.sub.r values,
each value corresponding to a square pixel of .DELTA.x, .DELTA.y
dimensions.
53. Method according to claim 52, characterised in that hologram
reconstructed during step A.2 is represented by a rectangular
matrix of V.sub.e=N.sub.eM.sub.e values, each value corresponding
to a square pixel of .DELTA..xi.=(.lamda.d/N.sub.e .DELTA.x) and
.DELTA..eta.=(.lamda.d/M.sub.e .DELTA.y), .lamda. 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,
.DELTA..xi. and .DELTA..eta. being sample intervals of the
reconstructed holographic image.
54. Method according to claim 53, characterised in that
N.sub.e=(.lamda.d/.DELTA.x.sup.2),
M.sub.e=(.lamda.d/.DELTA.y.sup.2), .DELTA..xi.=.DELTA.x,
.DELTA..eta.=.DELTA.y.
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.sub.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.sub.k value, with k comprised between 1
and N.sub.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.sub.e.sup.k, comprising
said V.sub.r values, as well as a whole number
p.sub.k=V.sub.e.sup.k-V.sub.r>0 having constant value
corresponding to OS.sub.k, corresponding to the same number of
pixel having the same dimensions of the other ones, said whole
number p.sub.k being function of the d.sub.k distance for each
bidimensional matrix IMd.sub.k, in such a way that resolution of
each bidimensional matrix IMd.sub.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.sub.k is directly proportional to distance d.sub.k.
60. Method according to claim 58, characterised in that
Advantageously according to the invention, said constant values
p.sub.k for one or more k whole numbers between 1 and N.sub.SD are
null values (OS.sub.k=0).
61. Method according to claim 58, characterised in that said
constant values p.sub.k for one or more k whole numbers between 1
and N.sub.SD are not null values (OS.sub.k different from 0).
62. Method according to claim 58, characterised in that said
p.sub.k values are outside said V.sub.r values matrix.
63. Method according to claim 62, characterised in that said
p.sub.k values are arranged symmetrically.
64. Method according to claim 62, characterised in that said
p.sub.k values are arranged asymmetrically.
65. Method according to claim 58, characterised in that said number
of V.sub.e.sup.k values is inversely proportional to the pixel
dimension of the pixel to be obtained for IMd.sub.k images
reconstructed for all values of k between 1 and N.sub.SD.
66. Method according to claim 58, characterised in that digitalised
hologram is a rectangular matrix of V.sub.r=N.sub.rM.sub.r values,
each value corresponding to a rectangular pixel having .DELTA.x,
.DELTA.y 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.sub.r.sup.k=N.sub.r.sup.kM.sub.r.sup.k values, each
value corresponding to a rectangular pixel having set constant
dimensions .DELTA..xi.=(.lamda.d/N.sub.e.sup.k .DELTA.x) and
.DELTA..eta.=(.lamda.d/M.sub.e.sup.k .DELTA.y), .lamda. being the
wavelength of the wave bundle impinging the object of which the
hologram is registered, and d.sub.k the distance between the
sensing device and the object of which the hologram is registered,
.DELTA..xi. and .DELTA..eta. being sample intervals of the
reconstructed holographic image IMd.sub.k for all k values between
1 and N.sub.SD.
68. Method according to claim 40, characterised in that
N.sub.SD>2.
69. Method according to claim 68, characterised in that N.sub.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.sub.k for each
digitalised hologram and for all values of k between 1 and
N.sub.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.
Description
[0001] The present invention relates to a holographic method with
numerical reconstruction for obtaining an image of a
three-dimensional object in which even points out of the depth of
field are in focus, and holographic apparatus using such a
method.
[0002] Particularly, method according to the present invention uses
a single image (digital hologram, from which a phase map and an
amplitude map, or an intensity map, can be obtained) obtained by
Digital Holography for numerical reconstruction of a single image
of an object, the image having many or all the "in focus points"
even if not included within the "depth of focus" or "depth of
field" of the optical system employed. The invention further
relates to a digital holography apparatus, particularly a
microscope, using the inventive method. Said method is
particularly, but not exclusively, useful in case of an optical
configuration of the image acquisition microscope type.
[0003] In the geometrical optical field, under "paraxial
approximation" conditions, it is possible stating that a thin lens
produces on a plane known as "image plane" the image corresponding
to a single plane, also known as "object plane".
[0004] The object plane can be imagined as an ideal flat surface
intersecting the volume occupied by the object.
[0005] Two planes so defined are named as "conjugate planes" and
the relevant distances of the lens from the plane are named
"conjugate distances". Conjugate distances are legate by a simple
mathematical relation depending on a parameter indicated as "focal
length" of the thin lens.
[0006] Thus, in the above-mentioned ideal case, a single
corresponding image plane is obtained for each plane of the object,
the points of which are in biunivocal correspondence with the
object plane. This means that the lens allows creating a perfectly
"in focus" image of one, and of only one, "object plane".
[0007] In a not-ideal case, optical systems usually create images
permitting focusing not a single plane of the object, but a volume
of the same.
[0008] The above property of the optical system is defined as
"field depth" or "focus depth". It depends on many intrinsic
parameters of the optical system, besides on the use conditions of
the same.
[0009] Field depth thus determines the limits of the object
portion, along the longitudinal direction, i.e. along the system
optical axis, that will be in focus on the image plane.
[0010] Points of the object out of the field depth will appear
"out-of-focus" or "non in focus". As a consequence,
three-dimensional objects the volume of which has a spatial
extension along the optical axis bigger than the field depth of the
optical system creating the image will never be completely in focus
within a single image.
[0011] In other words, once set the optical system properties, in
order to create images wherein different parts of the same object
at different distances from the optical system (e.g. in the
simplest case a converging lens) are in focus, it will be necessary
continuously varying the object-optical system distance.
[0012] In any case, only the images corresponding to the parts of
the object ideally contained within said field or focus depth will
be each time in focus.
[0013] In the optical field, a mathematical relation defining, as
first approximation, the field depth .delta.z is the following:
.delta. z = .lamda. n N . A . 2 + ne M N . A . ( 1 )
##EQU00001##
[0014] Wherein, n is the refraction index of the means (in case of
air n=1), M is the lateral enlarging, .lamda. the wavelength of the
luminous radiation employed, N.A. is the numerical aperture of the
optical system, and e is the smallest distance that can be measured
on the image plane of the optical microscope.
[0015] Thus, field depth of optical systems, being the same the
other parameters, inversely depends on its numerical aperture. On
the other hand, it is known that resolving power of a microscope is
proportionally higher with respect to its numerical aperture.
[0016] From the above, it descends that the higher is the
resolution power, and thus the magnification, the smaller is the
field depth. Thus, observing and studying three-dimensional
objects, points of the object at different distances of the
microscope objective will appear focalised at different distances.
This is a serious drawback in case of application requiring
focusing at the same time different portions of the same
three-dimensional object.
[0017] In case of objects characterised by a complex geometrical
surface, and for large magnifications, only small parts of the
object can be observed clearly and with a sufficient contrast at a
set objective-object distance. Observer is thus obliged to
continuously varying said distance in order to have a full vision,
although at different times, of the surface of the object under
examination.
[0018] As reported in the scientific literature, two solutions have
been suggested in order to overcome said limitation.
[0019] An approach, described in article "Extended depth of field
through front wave-front coding", E. R. Dowski, and W. T. Cathey,
Applied Optics 34, 1859 (1995) and in U.S. Pat. No. 5,748,371, is
based on the use of optical elements suitably designed and realised
to be provided in the optical apparatus.
[0020] Said optical elements are comprised of phase reticules
(named "phase optical elements") permitting extending field depth
without remarkably increasing exposure time or lighting level.
[0021] These phase optical elements, provided in the image
acquisition optical system, suitably codify the wave front coming
from the observed object so as that resulting images are as more as
possible insensible to out of focus effects aiming degrading total
visibility of the object to be studied.
[0022] A limit of this method is comprised of the fact that these
phase optical elements introduce aberration on the image
("blurring") that are partially removed by the use of specific
algorithms and software or hardware processing of the signals
arriving from a digitalised camera.
[0023] Second approach, well known in the literature, is based on
the capability of the modern microscopes of acquiring in succession
a sequence of images corresponding to different distances of the
object and on the following numeral processing of the same in order
to obtain a reconstructed image indicated as "with extended focus"
or "Extended Focus Image (EFI)".
[0024] Modern microscopes are often also provided with cameras and
electronic systems for digitalisation and presentation of the image
on analog screens and/or digital monitors. In this case too, it is
not possible observing in each one of the obtained images all the
details in-focus, since the details are at different distances from
the microscope objective and that are out of the field depth of the
system.
[0025] Furthermore, microscopes are provided with a motion system,
usually based on piezoelectric actuators, permitting varying in a
controlled manner, and with quite high accuracy and precision, the
distance between object and objective.
[0026] Particularly, said microscopes are also provided with a
control system permitting acquiring and digitalising a sequence of
the object images, each one of which corresponds to a well-defined
object-objective distance. The two registered images, i.e. the
first and the last ones of the sequence under examination, are
acquired at distances corresponding to two planes-objects such to
completely include the spatial extension along the optical axis of
the volume occupied by the object.
[0027] In this way, an image sequence is obtained, available in a
digital mode for a following numerical processing. Each digital
image is comprised of a numerical matrix of N-M elements (pixel),
each one of them having a numerical value (usually an 8 bit value),
representing its lighting intensity or its colour.
[0028] Starting from this image sequence, it is possible realising
by a numerical approach a single image (EFI) in which all
particulars of the object can be observed "in-focus" applying
numerical algorithms well known to those skilled in the art, based
on the comparison of "contrast" among sequential images, or other
algorithms (see for example R. J. Pieper and A. Korpel, "Image
processing for extended depth of field", Applied Optics, 22, 1449
(1983) e K. Itoh, A. Hayashi, and Y. Ichioka, "Digitized optical
microscopy with extended depth of field", Applied Optics, 28, 2487
(1989)). Said algorithms permit extracting from each image, in a
completely automatic way, groups of elements (pixels) corresponding
to portions of the object that are considered as in a better
in-focus condition.
[0029] However, acting on the contrast, also parts not
corresponding to the distance from the investigated observation
plane are focused.
[0030] Making reference to the example shown in FIG. 1, image EFI
is constructed reassembling in a single image all the element
groups (pixels) extracted from the whole sequence. Only those
elements (pixel) of the matrix in which portions of image
considered "in-focus" are extracted from each image of the sequence
by the numerical algorithms employed. In this way, a numerical
matrix wherein all details of the object can be observed "in-focus"
comprises EFI image obtained.
[0031] A remarkable limit of this method is that it is necessary
acquiring a sequence of images corresponding to different distances
between object and objective.
[0032] It requires an accurate and precise motion apparatus that,
however, will have a minimum pitch, e.g. determined by the
piezoelectric actuator employed.
[0033] In any case, said motion requires some time for carrying out
a complete scanning and for acquiring the corresponding images.
[0034] Furthermore, during the image scanning and digital
acquisition period, it is absolutely necessary that the object
under examination is still and does not change its shape, otherwise
it would not be possible realising the EFI image.
[0035] Now, as it was obvious in many cases when observing
organisms or biologic processes, it is not possible ensuring that
the object under examination remains still without changing its
shape. On the contrary, in many cases it is wished observing the
movements of organisms or the dynamic evolution of processes and/or
biologic interactions.
[0036] At the same way, e.g. in the technological processes for
manufacturing of micro-devices in the microelectronic field, it is
necessary and/or useful observing the dynamic behaviour of suitable
stressed structures. Further, it must be pointed out that the same
motion apparatus (either it acts on the microscope objective or on
the object bearing plate) can make the sample vibrating, thus
disturbing the acquisition procedure of the image sequence and
preventing the construction of a correct EFI image.
[0037] The same inconvenient occurs in case the microscope vibrates
due to a not optimum installation or for any other reason.
[0038] The above is not the only limit of the traditional EFI
method. In fact, it employs algorithms for construction of images
operating on a sequence of images of the object corresponding to a
series of planes focused at different distances. These algorithms
operate by procedures that can be substantially exemplified in two
different staged: recognition and reconstruction.
[0039] First numerical phase is dedicated at processing and
identification in each image of sequences of different portions of
the object that are in a best "in-focus" condition.
[0040] Second construction phase is instead dedicated at extraction
of said image portions (pixel groups) and at their assembling for
realising EFI image.
[0041] More complex and problematic phase is the first one,
relevant to recognition of "in-focus" zones, since recognition of a
portion of an image in-focus highly depends on the algorithm
employed and on the kind of image. In fact, in-focus definition is
not univocally determined under the numerical-mathematical point of
view.
[0042] It is object of the invention that of providing a
holographic method with numerical reconstruction permitting
overcoming the drawbacks and solving the problems of the prior
art.
[0043] It is further object of the present invention that of
providing apparatuses and instruments necessary for carrying out
the method according to the invention.
[0044] Furthermore, it is specific object of the present invention
a holographic apparatus, particularly a microscope, employing the
method according to the invention.
[0045] It is therefore specific object of the present invention a
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:
[0046] A. starting from the digitalised hologram, extracting an
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;
[0047] 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.sub.k, with k having a value between 1 and a whole number
N.sub.SD>1;
[0048] C. for each distance value d.sub.k, extracting from matrix
MD an iso-level set IQd.sub.k of corresponding bidimensional
coordinate of said object or object portion;
[0049] D. for each distance value d.sub.k, reconstructing, starting
from the digitalised hologram, a bidimensional matrix IMd.sub.k of
intensity values relevant to said object or object portion;
[0050] E. extracting, from each bidimensional matrix IMd.sub.k of
the method step D, a bidimensional IFd.sub.k of intensity values
corresponding to the bidimensional coordinates of the iso-level set
IQd.sub.k extracted in method step C;
[0051] F. starting from intensity values of said IFd.sub.k sets of
the method phase E, from the coordinate bidimensional of the
iso-level set IQd.sub.k and from the relevant distance values
d.sub.k, for all values of k between 1 and N.sub.SD, reconstructing
the three-dimensional intensity image of said object or object
portion;
[0052] resolution of bidimensional matrix IMd.sub.k for all values
of k between 1 and N.sub.SD being identical to the resolution of
matrix MD of distance value.
[0053] According to the invention, in step A said one-phase image
can be obtained using two or more phase images reconstructed
starting from the same digital hologram for different distance
values.
[0054] According to the invention, method step A can be carried out
using the convolution method.
[0055] According to the invention, the method step D can be carried
out using the convolution method.
[0056] According to the invention, method A step can be carried out
employing Fresnel method.
[0057] According to the invention, when the digitalised hologram is
comprised of a number V.sub.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.sub.e, comprising said V, values, as
well as a whole number p=V.sub.e-V.sub.r>0 having constant value
corresponding to OS, corresponding to the same number of pixel
having the same dimensions of the other ones.
[0058] Preferably, according to the invention, said p constant
values are null values (OS=0).
[0059] Preferably, according to the invention, said p constant
values are values different from 0 (OS not 0).
[0060] Advantageously according to the opinion, said p values are
outside said V.sub.r value matrix.
[0061] Advantageously according to the opinion, said p values are
arranged symmetrically.
[0062] Advantageously according to the opinion, said p values are
arranged asymmetrically.
[0063] Preferably, according to the invention, said value V.sub.e
number is inversely proportional with respect to the pixel
dimension that it is wished obtaining for said phase image MD.
[0064] Preferably, according to the invention, digitalised hologram
is a rectangular matrix of V.sub.r=N.sub.rM.sub.r values, each
value corresponding to a square pixel of .DELTA.x, .DELTA.y
dimensions.
[0065] Preferably, according to the invention, hologram
reconstructed during step A.2 is represented by a rectangular
matrix of V.sub.e=N.sub.eM.sub.e values, each value corresponding
to a square pixel of .DELTA..xi.=(.lamda.d/N.sub.e .DELTA.x) and
.DELTA..eta.=(.lamda.d/M.sub.e .DELTA.y), .lamda. 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,
.DELTA..xi. and .DELTA..eta. being sample intervals of the
reconstructed holographic image.
[0066] Advantageously, according the invention
N.sub.e=(.lamda.d/.DELTA.x.sup.2),
M.sub.e=(.lamda.d/.DELTA.y.sup.2), .DELTA..xi.=.DELTA.x,
.DELTA..eta.=.DELTA.y.
[0067] Advantageously, according to the invention, 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.
[0068] Advantageously, according to the invention, said threshold
is set in function of the signal/noise ratio of the holographic
image.
[0069] Preferably, according to the invention, method step D is
carried out employing Fresnel method.
[0070] Preferably, according to the invention, when the digitalised
hologram is comprised of a number V.sub.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.sub.k value, with k comprised between 1 and N.sub.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.sub.e.sup.k, comprising said V.sub.r
values, as well as a whole number
p.sub.k=V.sub.e.sup.k-V.sub.r>0 having constant value
corresponding to OS.sub.k, corresponding to the same number of
pixel having the same dimensions of the other ones, said whole
number p.sub.k being function of the d.sub.k distance for each
bidimensional matrix IMd.sub.k, in such a way that resolution of
each bidimensional matrix IMd.sub.k, is identical to the resolution
of the MD matrix of distance values.
[0071] Preferably, according to the invention, said whole number
p.sub.k is directly proportional to distance d.sub.k.
[0072] Advantageously according to the invention, said constant
values p.sub.k for one or more k whole numbers between 1 and
N.sub.SD are null values (OS.sub.k=0).
[0073] Advantageously, according to the invention, said constant
values p.sub.k for one or more k whole numbers between 1 and
N.sub.SD are not null values (OS.sub.k different from 0).
[0074] Advantageously, according to the invention, said p.sub.k
values are outside said V.sub.r values matrix.
[0075] Advantageously, according to the invention, said p.sub.k
values are arranged symmetrically.
[0076] Advantageously, according to the invention, said p.sub.k
values are arranged asymmetrically.
[0077] Preferably, according to the invention, said number of
V.sub.e.sup.k values is inversely proportional to the pixel
dimension of the pixel to be obtained for IMd.sub.k images
reconstructed for all values of k between 1 and N.sub.SD.
[0078] Preferably, according to the invention, digitalised hologram
is a rectangular matrix of V.sub.r=N.sub.rM.sub.r values, each
value corresponding to a rectangular pixel having .DELTA.x,
.DELTA.y dimensions.
[0079] Preferably, according to the invention, hologram
reconstructed in second sub-step D.2 is represented by a square
matrix of V.sub.r.sup.k=N.sub.r.sup.kM.sub.r.sup.k values, each
value corresponding to a rectangular pixel having set constant
dimensions .DELTA..xi.=(.lamda.d/N.sub.e.sup.k .DELTA.x) and
.DELTA..eta.=(.lamda.d/M.sub.e.sup.k .DELTA.y), .lamda. being the
wavelength of the wave bundle impinging the object of which the
hologram is registered, and d.sub.k the distance between the
sensing device and the object of which the hologram is registered,
.DELTA..xi. and .DELTA..eta. being sample intervals of the
reconstructed holographic image IMd.sub.k for all k values between
1 and N.sub.SD.
[0080] Preferably, according to the invention, N.sub.SD>2.
[0081] Preferably, according to the invention, N.sub.SD is set on
the basis of the minimum resolution of the holographic apparatus by
which the digitalised hologram is obtained.
[0082] Advantageously, according to the invention, aberrations have
beforehand eliminated from said digitalised hologram by numerical
processing.
[0083] Advantageously, according to the invention, a
reference-digitalised hologram has been beforehand subtracted from
said digitalised hologram.
[0084] Preferably, according to the invention, 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.
[0085] Advantageously, according to the invention, method is
carried out simultaneously for more than one object portion.
[0086] Advantageously, according to the invention, 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.
[0087] Preferably, according to the invention, 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.sub.k for each
digitalised hologram and for all values of k between 1 and
N.sub.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.
[0088] Juxtaposition can be realised employing an RGB technique or
a wavelet technique, as described in article "Three-dimensional
image fusion by use of multi wave length digital holography", B.
Javidi, P. Ferraro, S. Hong, S. De Nicola, A. Finizio, D. Alfieri,
G. Pierattini, 144 Optics Letters/Vol. 30, No. 2/Jan. 15, 2005.
[0089] It is further specific object of the present invention a
computer program characterised in that it comprises code means
suitable to execute, when operating on a processor, method
according to the invention.
[0090] It is still specific object of the present invention a
memory support readable by a processor, having a program memorised,
characterised in that the program is the computer program according
to the invention.
[0091] Furthermore, it is specific object of the present invention
an 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 the
invention.
[0092] The present invention will be now described, for
illustrative but not limitative purposes, according to its
preferred embodiments, with particular reference to the figures of
the enclosed drawings, wherein:
[0093] FIG. 1 shows the method steps for reconstruction of an
object observed by a microscope according to standard EFI
technique;
[0094] FIG. 2 shows a hybrid block diagram and flow chart of the
traditional holographic reconstruction method;
[0095] FIG. 3 shows a flow chart of the holographic method with
numerical reconstruction according to the invention;
[0096] FIG. 4 shows the flow-chart of the method according to the
invention with images taken from a particular reconstruction
example.
[0097] Interferometric technique permitting recording and
reconstructing the reflected complex field (amplitude and phase),
transmitted and/or diffused by an object is usually named in the
scientific literature as "Digital Holography", that in the
following will be indicated by acronym DH (see for example articles
"Controlling image size as a function of distance and wavelength in
Fresnel-transform reconstruction of digital holograms", P. Ferraro,
S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G.
Pierattini, Optics Letters 29, 854-856 (2004); "A digital
holographic microscope for complete characterization of
microelectromechanical systems", G. Coppola, P. Ferraro, M. Iodice,
S. De Nicola, A. Finizio, and S. Grilli, Measurement Science and
Technology 15, 529-539 (2004); "Controlling images parameters in
the reconstruction process of digital holograms, P. Ferraro, G.
Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini,
IEEE Journal of Selected Topics in Quantum Electronics 10, 829-839
(2004); "Recovering image resolution in reconstructing digital
off-axis holograms by Fresnel-transform method", P. Ferraro, S. De
Nicola, A. Finizio, G. Pierattini, and G. Coppola, Applied Physics
Letters 85, 2709-2711 (2004)).
[0098] It is indicated as "Digital Holography" an interference
figure recorder by an integrated matrix of radiation sensors.
[0099] Different methods exit permitting numerical reconstruction
of the complex field starting from the hologram and particularly
"convolution" method and "Fresnel" method.
[0100] As it is known, particularly, in Fresnel method, spatial
resolution of the complex field (comprising amplitude and phase) is
determined by some parameters. Some of these parameters are
determined by the features of the integrated matrix of radiation
sensors and particularly of the number of elements comprising the
matrix and of the dimension of the single element. Instead, other
parameters are reconstruction distance, determined by the d
distance of the object (or points of its surface or volume) and the
.lamda. wavelength of the lighting source employed for creating the
hologram.
[0101] Usually, in the literature, spatial resolution defined by
the "reconstruction pixel" indicated as a wavelength and that will
be indicated in the following by the acronym PR. Dimensions of
bidimensional PR, .DELTA..xi. along axis x and .DELTA..eta. along
axis y depend on the above mentioned parameter by the following
mathematical relations:
.DELTA. .xi. = .lamda. d N .DELTA. x .DELTA. .eta. = .lamda. d M
.DELTA. y formula ( 2 ) ##EQU00002##
[0102] Wherein, M is the number of pixels acquired (by an image
acquisition device) along axis x, N is the number of pixels along
axis y, .DELTA.x and .DELTA.y are dimensions of pixels according to
the two directions of axes x and y.
[0103] From the above relation, it is well evident that the complex
field at different distances, being the other parameters the same,
will have a PR value different, and particularly PR dimension will
increase when the reconstruction distance increases. In this case,
spatial resolution, by which complex field has been reconstructed,
will have a lower spatial resolution. On the contrary, spatial
resolution will be higher at a lower reconstruction distance, since
in this case PR dimension diminishes.
[0104] For example, in case of objects observed under reflection,
having a three-dimensional profile, when reconstructing amplitude
(or intensity) obtained from hologram will not appear completely
"in-focus", since reconstruction occurs along a single plane at a d
distance from the hologram recording opto-electronic sensor
(typically a CCD camera).
[0105] According to the invention, it is instead possible numerical
reconstruction of the whole volume within which the object lies
starting from a single image (digital hologram). This is possible
constructing hologram for different distances within which all the
object points are included, and using the phase map obtained at a
single distance, for extracting the three-dimensional profile fully
in-focus. It must be pointed out that to this end it is sufficient
using a single-phase map for extracting the three-dimensional
profile fully in-focus. In fact, although the phase map has been
reconstructed at a single distance, it in any case describes a
sufficiently precise three-dimensional profile of the object.
[0106] In any case, it is also possible, if necessary, employing
more than one phase maps obtained at different distances or
combinations of the same in order to obtain a more accurate
definition of the profile. By "combination" it is for example meant
an average of a plurality of maps, or the juxtaposition of map
portions reconstructed at different distances, choosing each time
portions having a better definition.
[0107] In order to reconstructing the intensity figure at different
distances, it can be used a reconstruction method known as
"convolution method", described in the literature by the scientific
publication "Whole optical wave fields reconstruction by digital
holography", S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G.
Pierattini, and R. Meucci, Optics Express 9, 294-302 (2001); object
amplitude or intensity images reconstructed at different distances
have the same dimension.
[0108] As an alternative, according to the invention, it is
possible employing the above-mentioned Fresnel method, having a
more general application and many advantages.
[0109] In Fresnel method, making reference to FIG. 2, a preparation
unit for the hologram acquisition conditions or "set-up" 2 collects
radiation 4 arriving from a source 1 and lightens by radiation 5
the object 3 under examination. Further, said set-up 2 provides a
device for creating a reflected ray 6, transmitted or diffused by
the object 3, an object beam O and a device for creating a
reference beam R. object beam O and reference beam R are combined
within set-up 2 so as to create an interference distribution 7
along a plane. Said interference creates a hologram 8 of the object
under examination.
[0110] Here it is necessary specifying that, since Fresnel approach
interests only the wavelength of the radiation impinging on the
object, method according to the present invention is not limited to
the optical field and can be applied for numerical reconstruction
of holograms registered by every kind of electromagnetic radiation
(e.g. X rays) and not electromagnetic radiation (e.g. electron
beams and/or acoustic waves). Particularly, source 1 could be
constructed by a combination of two or more wavelengths. Due to the
above reason, nature, wavelength and coherence of source 1 could be
of any kind.
[0111] Hologram 8 is acquired, digitalised and memorised by an
acquisition method 9. each kind of image acquisition system
existing or that will be developed in the future can be used to
this end.
[0112] Inside the acquisition system 9 it is provided a device for
digitalisation and memorisation on a computer of the acquired image
8. Digitalised image is named "digital hologram" 10 and it is
described by a matrix H(n.DELTA.x, m.DELTA.y) of NM numbers,
obtained by the spatial bidimensional sampling of hologram 8
H(x,y).
[0113] For a perfect reconstruction of the object image, it is
necessary that the digitalisation process satisfies the sampling
theorem. Particularly, it must be satisfied condition that spacing
between fringes of the interference distribution 7 is higher than
at least two pixels of the acquisition system 9. Thus, sampling
theorem imposes minimum resolution that it is possible obtaining by
an experimental datum 2.
[0114] One of the remarkable advantages obtained by the digital
holography is that it is possible acting directly on the
digitalised hologram of object 3, in order to carrying out
operation on the acquired information.
[0115] The above means that it is possible making different
processing on the digitalised hologram for processing the images
11. by said processing it is for example possible eliminating the
zero diffraction order of the hologram reconstruction, or
eliminating one "phase aberration" induced by the optical system
employed.
[0116] By the "phase aberration" it is meant a deformation of the
front wave travelling through the hologram creation and
registration system. Phase aberration correction compensates said
deformations permitting obtaining a correct reconstruction of the
observed object.
[0117] Object numerical reconstruction process 13 under observation
is based on two steps. During first step, "processed" digitalised
hologram H(n,m) 12 must be multiplied for a digitalised replica of
the reference beam R, obtaining a field distribution F(n, m) from
which it is possible obtaining the image of the object under
examination.
[0118] Second step of the propagation process is the propagation of
the field distribution F(n, m) from the plane on which the camera
is provided to the observation plane or image plane. This process
brings to the reconstructed image 14.
[0119] Reconstructed image 14 can be an amplitude image 14' and/or
a phase image 14'' (obtained both with convolution and Fresnel
method).
[0120] Phase image 14'' shows the object profile, and thus provides
all data relevant to the distances of the various points of the
object from the observation plane.
[0121] In fact, Digital Holography (DH) is able providing map (or
three-dimensional profile) of an object, for example by reflection,
through the reconstruction of optical phase as described in the
following scientific publications: "Surface topography of
microstructures in lithium niobate by digital holographic
microscopy", S. De Nicola, P. Ferraro, A. Finizio, S. Grilli, G.
Coppola, M. lodice, P. De Natale, and M. Chiarini, Measurement
Science and Technology 15, 961-968 (2004); "A digital holographic
microscope for complete characterization of microelectromechanical
systems", G. Coppola, P. Ferraro, M. lodice, S. De Nicola, A.
Finizio, and S. Grilli, Measurement Science and Technology 15,
529-539 (2004).
[0122] Phase map can be thus obtained or by a single digital
hologram by the procedures indicated in article "Compensation of
the inherent wave front curvature in digital holographic coherent
microscopy for quantitative phase-contrast imaging, P. Ferraro, S.
De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G.
Pierattini Applied Optics 42, 1938-1946 (2003), or by
reconstruction of two digital holograms by the holographic
interferometry.
[0123] In fact, in some applications, Digital Holography (DH) is
used in order to analyse variations of the object under observation
caused by an outer action (for example force, pressure, and
temperature variation). Variations are measured according to a
quantitative mode subtracting the phase maps of two holograms
registered with the object in two different conditions (for example
before and after the outer perturbation action). This technique is
named Digital Holographic Interferometry.
[0124] In the Digital Holographic Interferometry applied in order
to obtain the 3D profile of the object, a flat surface hologram
registered under the same circumstances of the object hologram is
used as reference hologram (see for example article "Compensation
of the inherent wave front curvature in digital holographic
coherent microscopy for quantitative phase-contrast imaging P.
Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro,
and G. Pierattini Applied Optics 42, 1938-1946 (2003)).
[0125] From the above phase map 14'' it is possible obtaining
distance map of the different points of the object d (x, y) by the
simple relation:
d(x,y)=.phi.(x,y)*.lamda./4.pi.
[0126] wherein phase is obtained by:
.phi.(x,y)=(4.pi./.lamda.)OPD(x,y)
[0127] and wherein OPD is the "Optical Path Difference" with
respect to an arbitrary reference plane.
[0128] Now, it is possible knowing which are the different planes
in which the different points of the object are.
[0129] Method according to the invention employs the information
about the distances of the various points of the object from the
observation point.
[0130] Making reference to FIG. 3, by the method according to the
invention it is possible obtaining an image wherein also points of
the revealed object are in-focus that are beyond the focus
depth.
[0131] In fact, once obtained phase map 14'', different method
steps are carried out, bringing to this result. An example of
succession of method steps according to the invention is
illustrated in the following.
[0132] First, in step 15 according to the invention, various d
reconstruction distances are extracted on the basis of the object
as obtained in phase map 14'', along with the iso-level coordinate
set for each distance.
[0133] Now, distance d.sub.k from the observation plane is set in a
following step 16, within the limit obtained from the above phase
map 14'', and set distance d.sub.k image is reconstructed in a
subsequent phase 17, using the method controlling dimension (and/or
resolution) described in scientific article "Controlling images
parameters in the reconstruction process of digital holograms", P.
Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G.
Pierattini, IEEE Journal of Selected Topics in Quantum Electronics
10, 829-839 (2004) and in the International Patent Application
PCT/IT04/000380.
[0134] The above procedure is repeated for different distances (k
included between 1 and N.sub.SD>1) from the observation plane,
thus obtaining a "stack" 18 of images reconstructed at different
distances and having comparable dimensions. This stack represents
all or part of the volume wherein the object is contained, and thus
it is possible, if wished, going beyond the field depth.
[0135] In other words, once carried out the reconstruction
according to the invention starting from a single digital hologram,
a series of object images are available, said object being
reconstructed at different distances d of the same object from the
observation plane.
[0136] It must be noted that, contrary to the case when different
images are acquired by a mechanical motion of the shooting
apparatus (for example by a microscope), the only limit to the
number of distances at which the image is reconstructed (and thus
of the number of final images) is given by the minimum resolution
that can be obtained by a single holographic apparatus, since it is
only a numerical reconstruction.
[0137] After having used the above image dimension and/resolution
control and/or modification method, it is possible applying the
method usually employed for construction of an EFI image, i.e.
selection of a region in-focus of the object for every image of the
stack obtained, and the subsequent reconstruction of the final
image of the object having all the points "in-focus".
[0138] In the above two cases it is evident the great advantage of
the method suggested according to the present invention: it is
possible making the reconstruction of an EFI image of an object
without making any scanning (thus it is not necessary making an
acquisition of a sequence of images with well evident advantages),
but making a series of numerical reconstructions starting from a
single image (digital hologram).
[0139] In other words, the image sequence is obtained from which
the EFI image is extracted by an only numerical procedure
exploiting the reconstruction properties at different distances of
the digital hologram. In this way, it is possible avoiding every
mechanical scanning for varying the object-objective distance from
the microscope, thus reducing observation time and permitting
obtaining EFI images also for objects suffer dynamic variations and
thus not permitting recording an image sequence during e mechanical
scanning.
[0140] As already said, it is also possible using two starting
holograms in the method according to the invention. This is not
necessary, but advantageous in order to eliminate aberrations, this
being also possible also numerically starting from a single
hologram.
[0141] It is also possible another embodiment of the method
according to the invention.
[0142] In fact, it must be put into evidence that holographic phase
map 14'' comprises a three-dimensional profile of the object under
examination.
[0143] In this way, having a three-dimensional profile for
construction of EFI image it is possible making volume within which
object is included, said volume being comprised of the stack of
amplitude images reconstructed at different distances, intersecting
in step 19 with the profile map, or selecting amplitude values for
each image of the stack corresponding to the above bidimensional
coordinate iso-level sets.
[0144] EFI image is thus obtained constructing a single image
comprised of the pixel set of the amplitude images intersecting
object three-dimensional phase profile. Obviously, EFI image will
be as more accurate as the amplitude images reconstructed at
different distances.
[0145] It is clear that direct intersection is possible only among
images having the same resolution and dimension. This is the reason
why it is employed the resolution modification method according to
International Patent Application no PCT/IT04/000380 and in the
Italian Patent Application RM2003A000398 (particularly in step 17
of FIG. 3).
[0146] It must be still noted an advantage of the method according
to the present invention, i.e. possibility (not possible in the
traditional EFI method) of increasing the resolution on single
portions of the revealed object, thanks to the selective use of the
dimension and/or resolution control method mentioned in the
above.
[0147] Two embodiments of the method according to the invention are
shown in FIG. 4, for reconstruction of a microscopic object having
a ramp shape along one deformation.
[0148] An object hologram is acquired by apparatus e1. Starting
from digitalised hologram e2 of the object and possibly a reference
hologram e3 of the object (digitalised hologram of the reference
plane), it is obtained stack of amplitude images e6, varying the
reconstruction distance and controlling dimension of images.
[0149] Thus, from stack e6 it is possible passing to the
bidimensional reconstruction e8 of the in-focus object.
[0150] As an alternative, or in addition, it is possible employing
object phase map e4 for extracting the three-dimensional profile e5
of the same object.
[0151] Then, stack e6 is intersected with profile e5 in order to
obtain the three-dimensional image e9 fully in-focus.
[0152] As already seen, method described in the present invention
permits passing the limitations of the two methods according to the
prior art described in the above.
[0153] In fact, by the present method, it is possible
reconstructing an EFI image starting from a single acquired image
of a single digital hologram (or, at most, for advantageously
improving precision, two images of two digital holograms), thus
avoiding making an acquisition of an image sequence at different
distances. Method can further be applied without the needing of
designing, realising and using suitable optical elements.
[0154] EFI image obtained by the method according to the invention
is three-dimensional. An important difference with respect to the
image obtained by the traditional EFI image is that the latter is
reconstructed starting from few known distances of the observation
plane from the observed object, thus requiring an interpolation
jeopardising precision and quality; on the contrary, method
according to the invention permits employing such a high number of
distances making it not necessary an interpolation, thus being the
image obtained by the method according to the invention highly
precise and with a very high quality.
[0155] Method is applied by the reconstruction of digital holograms
registered by a digital holographic interferometer with a
microscope configuration.
[0156] More particularly, method according to the present invention
permits, by the digital registration on one or at most two images
on the plane of a bi-dimensional matrix of optical sensors.
[0157] Method according to the present invention can be applied in
all the industrial and technological fields providing the use of
optical instruments and for which it is necessary obtaining in a
single image many, or all details of an object, visible and
in-focus, even if said details are not in the "focus depth" or
"field depth" of the optical system employed.
[0158] It must be clear that the method can be applied also to the
sole points included in the field depth with a remarkable
improvement of the image quality with respect to what can be
obtained by the traditional methods.
[0159] The present invention has been described for illustrative
but not limitative purposes, according to its preferred
embodiments, but it is to be understood that modifications and/or
changes can be introduced by those skilled in the art without
departing from the relevant scope as defined in the enclosed
claims.
* * * * *