U.S. patent number 6,011,874 [Application Number 08/945,352] was granted by the patent office on 2000-01-04 for phase contrast imaging.
This patent grant is currently assigned to Forskningscenter Riso (Danish national laboratory). Invention is credited to Jesper Gluckstad.
United States Patent |
6,011,874 |
Gluckstad |
January 4, 2000 |
**Please see images for:
( Certificate of Correction ) ** |
Phase contrast imaging
Abstract
An improved method based on a simple imaging operation with a
simple one-to-one mapping between resolution elements of a spatial
phase modulator and resolution elements of the generated intensity
pattern is provided. According to the invention a method is
provided for synthesizing an intensity pattern with low loss of
electromagnetic energy, spatial modulation of electromagnetic
radiation with a spatial phase mask for modulation of the phase of
the incident electromagnetic radiation by phasor values of
individual resolution elements of the spatial phase mask, each
phasor value being determined in such a way that the values of the
Fourier transformed phasors attain predetermined values for
predetermined spatial frequencies, and the phasor value of the
specific resolution element of the spatial phasor mask corresponds
to a distinct intensity level of the image of the resolution
element in the intensity pattern, and a spatial phase filter for
phase shifting of a part of the electromagnetic radiation, in
combination with an imaging system for generation of the intensity
pattern by interference in the image plane of the imaging system
between the part of the electromagnetic radiation that has been
phase shifted by the phase filter and the remaining part of the
electromagnetic radiation.
Inventors: |
Gluckstad; Jesper (Osaka,
JP) |
Assignee: |
Forskningscenter Riso (Danish
national laboratory) (Roskilde, DK)
|
Family
ID: |
8094340 |
Appl.
No.: |
08/945,352 |
Filed: |
December 1, 1997 |
PCT
Filed: |
April 26, 1996 |
PCT No.: |
PCT/DK96/00190 |
371
Date: |
December 01, 1997 |
102(e)
Date: |
December 01, 1997 |
PCT
Pub. No.: |
WO96/34307 |
PCT
Pub. Date: |
October 31, 1996 |
Foreign Application Priority Data
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Apr 28, 1995 [DK] |
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0506/95 |
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Current U.S.
Class: |
382/276;
359/559 |
Current CPC
Class: |
G02B
27/52 (20130101); G03H 2001/085 (20130101) |
Current International
Class: |
G02B
27/50 (20060101); G02B 27/52 (20060101); G06K
009/36 () |
Field of
Search: |
;382/276,280,294,212,100
;356/4,45 ;250/550,491.1 ;359/559 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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657760 |
|
Jun 1995 |
|
EP |
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2199716 |
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Jul 1988 |
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GB |
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Other References
Lohmann A.W. et al "Array Illuminator Based on Phase Contrast",
Applied Optics, New York, NY. vol. 27, No. 14, Jul. 15, 1988 pp.
2915-2921..
|
Primary Examiner: Couso; Yon J.
Claims
I claim:
1. A phase contrast imaging method of synthesizing an intensity
pattern I(x',y') of an image, comprising the steps of
pixellating the intensity pattern I(x',y') in accordance with the
disposition of resolution elements (x,y) of a spatial phase mask
(4, 23, 43) having
a plurality of individual resolution elements (x,y), each
resolution element (x,y) modulating the phase of electromagnetic
radiation incident upon it with a predetermined phasor value
e.sup.i.phi.(x,y),
radiating electromagnetic radiation towards the spatial phase mask
(4, 23, 43),
Fourier or Fresnel transforming the modulated electromagnetic
radiation,
phase shifting in a region of spatial frequencies comprising DC in
the Fourier or Fresnel plane, the modulated electromagnetic
radiation by a predetermined phase shift value .theta. in relation
to the remaining part of the electromagnetic radiation, and
forming the intensity pattern by Fourier or Fresnel transforming,
respectively, the phase shifted Fourier or Fresnel transformed
modulated electromagnetic radiation, whereby each resolution
element (x,y) of the phase mask (4, 23, 43) is imaged on a
corresponding resolution element (x',y') of the image,
calculating the phasor values e.sup.i.phi.(x,y) of the phase mask
(4, 23, 43) and the phase shift value .theta. in accordance
with
for selected phase shift values .theta., .alpha. being the average
of the phasors e.sup.i.phi.(x,y) of the resolution elements of the
phase mask (4, 23, 43),
selecting, for each resolution element, one of two phasor values
which represent a particular grey level, and
supplying the selected phasor values e.sup.i.phi.(x,y) to the
resolution elements (x,y) of the spatial phase mask (4, 23,
43).
2. A method according to claim 1, wherein the step of calculating
the phasor values comprises
setting the synthesized intensity of at least one resolution
element (x.sub.o ',y.sub.o ') of the intensity pattern to zero,
and
calculating the phasor values e.sup.i.phi.(x,y) of the phase mask
(4, 23, 43) in accordance with ##EQU42## for selected phase shift
values .theta., .phi..sub..alpha. being the phase of .alpha..
3. A method according to claim 2, further comprising the step of
selecting the phase shift .theta.=.pi., selecting
.vertline..alpha..vertline.=1/2, and calculating the phasor values
e.sup.i.phi.(x,y) of the phase mask (4, 23, 43) in accordance with
##EQU43## .
4. A method according to claim 1, further comprising the steps
of
moving the DC-part of the electromagnetic radiation to a second
part of the Fourier or Fresnel plane, and
phase shifting the Fourier or Fresnel transformed modulated
electromagnetic radiation at the second part of the Fourier or
Fresnel plane by .theta. in relation to the remaining part of the
electromagnetic radiation.
5. A method according to claim 4, wherein the step of moving the
DC-part of the electromagnetic radiation comprises utilization of
an optical component, such as a grating, a prism, etc, with an
appropriate carrier frequency.
6. A method according to claim 4, wherein the step of moving the
DC-part of the electromagnetic radiation comprises encoding the
function of an optical component, such as a grating, a prism, etc,
with an appropriate carrier frequency, into the spatial phase mask
(4, 23, 43).
7. A method according to claim 1, further comprising the step of
adjusting the modulus of the Fourier transform of the phasors
e.sup.i.phi.(x,y) at specific spatial frequencies in order to
control the range of intensity levels of the synthesized intensity
pattern.
8. A method according to claim 7, wherein the step of adjusting the
modulus of the Fourier transform of the phasors e.sup.i.phi.(x,y)
at specific spatial frequencies comprises at least one of the
following measures:
a) adjusting the individual phasors e.sup.i.phi.(x,y) of the
resolution elements of the phase mask (4, 23, 43) maintaining
prescribed relative intensity levels between intensities of
resolution elements of the intensity pattern,
b) adjusting the individual phasors e.sup.i.phi.(x,y) of the
resolution elements of the phase mask (4, 23, 43) by histogram
techniques,
c) spatially scaling the phasor e.sup.i.phi.(x,y) pattern of the
phase mask (4, 23, 43), and
d) utilizing half tone coding techniques.
9. A method according to claim 1, further comprising the step of
controlling power of the electromagnetic radiation in response to
the intensity range of the intensity pattern.
10. A method according to claim 1, wherein each phasor
e.sup.i.phi.(x,y) of the phase mask (4, 23, 43) is selected from a
set of two determined phasors with complementary phasor values
e.sup.i.phi.1(x,y) and e.sup.i.phi.2(x,y) in such a way that a
specific spatial frequency distribution of the intensity of the
electromagnetic radiation in the Fourier or Fresnel plane is
attained.
11. A method according to claim 10, wherein the phase .phi.(x,y) of
phasors e.sup.i.phi.(x,y) of adjacent resolution elements
alternates between the two possible complementary phasor values
e.sup.i.phi.1(x,y) and e.sup.i.phi.2(x,y).
12. A method according to claim 10, wherein the phasors
e.sup.i.phi.1(x,y) and e.sup.i.phi.2(x,y) are complex
conjugated.
13. A method according to claim 1, further comprising the step of
phase shifting at selected spatial frequencies constituting a
region that is shaped to match the spatial frequency content of the
phasors e.sup.i.phi.(x,y) of the spatial phase mask (4, 23,
43).
14. A method according to claim 1, wherein modulus of the average
value .vertline..alpha..vertline. of the phasors e.sup.i.phi.(x,y)
ranges from 0.1 to 0.9.
15. A method according to claim 14, wherein modulus of the average
value .vertline..alpha..vertline. of the phasors e.sup.i.phi.(x,y)
ranges from 0.25 to 0.75.
16. A method according to claim 14, wherein modulus of the average
value .vertline..alpha..vertline. of the phasors e.sup.i.phi.(x,y)
ranges from 0.4 to 0.6.
17. A method according to claim 14, wherein modulus of the average
value .vertline..alpha..vertline. of the phasors e.sup.i.phi.(x,y)
is approximately 0.5.
18. A method according to claim 1 wherein the phase shift .theta.
ranges from .pi./4 to 7.pi./4.
19. A method according to claim 1, wherein the phase shift .theta.
ranges from .pi./2 to 3.pi./2.
20. A method according to claim 1, wherein the phase shift .theta.
ranges from 3.pi./4 to 5.pi./4.
21. A method according to claim 1, wherein the phase shift .theta.
is approximately .pi..
22. A method according to claim 1, further comprising the step of
zooming the image for scaling of the intensity pattern.
23. A method according to claim 22, wherein zooming of the image is
dynamically controllable.
24. A method according to claim 22, wherein zooming of the image is
controllable in dependence of the scaling of the phase mask (4, 23,
43).
25. A method according to claim 22, further comprising the step of
controlling power of the electromagnetic radiation in response to
the spatial scaling of the pattern in the phase mask (4, 23, 43)
and/or the zooming of the image.
26. A method according to claim 1, wherein the step of phase
shifting comprises utilization of a spatial light modulator.
27. A method according to claim 1, further comprising the step of
encoding the optical function of a Fourier-transforming lens into
the phasors e.sup.i.phi.(x,y) of the phase mask (4, 23, 43).
28. A method according to claim 1, further comprising the step of
encoding the optical function of an output lens into the phase
filter (6, 27, 45).
29. A method according to claim 1, wherein the step of radiating
electromagnetic radiation comprises radiation of electromagnetic
radiation of different wavelengths corresponding to three different
colours, such as red, green and blue, for generation of intensity
patterns of arbitrary colours.
30. A phase contrast imaging system (1) for synthesizing an
intensity pattern I(x',y') of an image, comprising
a source (2, 21, 41) of electromagnetic radiation for emission of
electromagnetic radiation,
a spatial phase mask (4, 23, 43) for phase modulation of
electromagnetic radiation and having
a plurality of individual resolution elements (x,y), each
resolution element (x,y) modulating the phase of electromagnetic
radiation incident upon it with a predetermined phasor value
e.sup.i.phi.(x,y), and being
positioned on a propagation axis of the electromagnetic
radiation,
means (5, 26, 44) for Fourier or Fresnel transforming the phase
modulated electromagnetic radiation positioned on a propagation
axis of the phase modulated radiation,
a spatial phase filter (6, 27, 45) for phase shifting in a region
of spatial frequencies comprising DC in the Fourier or Fresnel
plane, the transformed electromagnetic radiation by a predetermined
phase shift value .theta. in relation to the remaining part of the
transformed electromagnetic radiation,
means (7, 10, 26, 30, 44, 47) for forming the intensity pattern by
Fourier or Fresnel transforming, respectively, the phase shifted
Fourier or Fresnel transformed modulated electromagnetic radiation,
whereby each resolution element (x,y) of the phase mask (4, 23, 43)
is imaged on a corresponding resolution element (x',y') of the
image,
the phasor values e.sup.i.phi.(x,y) of the phase mask (4, 23, 43)
and the phase shift value .theta. substantially fulfilling that
for selected phase shift values .theta., .alpha. being the average
of the phasors e.sup.i.phi.(x,y) of the resolution elements of the
phase mask (4, 23, 43),
subject to the proviso that
if .theta.=.pi., the phase mask (4, 23, 43) is not divided into a
matrix of rows and columns of resolution elements of the same size
and shape, every fourth resolution element having the phasor value
e.sup.i.pi. and being distributed periodically and regularly across
the area of the phase mask in such a way that every second row and
every second column do not contain a resolution element with the
phasor value e.sup.i.pi., the remaining resolution elements having
the phasor value e.sup.i0, or,
if .theta.=.pi./2, the phase mask (4, 23, 43) is not divided into a
matrix of rows or columns of the same size and shape, every second
row or column having the phasor value e.sup.i.pi./2 and being
interlaced with the remaining rows or columns having the phasor
value e.sup.i0.
31. A system (1) according to claim 30, further comprising
means for pixellation of the intensity pattern I(x',y') in
accordance with the elements (x,y) of the spatial phase mask (4,
23, 43),
means for calculating the phasor values e.sup.i.phi.(x,y) of the
phase mask (4, 23, 43) and the phase shift value .theta. in
accordance with equation
means for selecting, for each resolution element, one of two phasor
values which represent a particular grey level, and
means for supplying the calculated phasor values e.sup.i.phi.(x,y)
to the elements (x,y) of the phase mask (4, 23, 43).
32. A system (1) according to claim 30, wherein the intensity is
zero for at least one resolution element (x.sub.o ',y.sub.o ') of
the intensity pattern, and wherein the phasor values
e.sup.i.phi.(x,y) of the phase mask (4, 23, 43) substantially
fulfil that ##EQU44## for selected phase shift values .theta.,
.phi..sub..alpha. being the phase of .alpha..
33. A system (1) according to claim 31, wherein the means for
calculating the phasor values is adapted to calculate the phasor
values e.sup.i.phi.(x,y) of the phase mask (4, 23, 43) in
accordance with ##EQU45## for selected phase shift values .theta.,
.phi..sub..alpha. being the phase of .alpha..
34. A system (1) according to claim 32, wherein the phase shift
.theta. is substantially equal to .pi. and .alpha. is substantially
equal to 1/2, and the phases .phi.(x,y) substantially fulfil that
##EQU46## .
35. A system (1) according to claim 33, wherein the means for
calculating the phasor values is adapted to calculate the phasor
values e.sup.i.phi.(x,y) of the phase mask (4, 23, 43) in
accordance with ##EQU47## .
36. A system (1) according to claim 30, further comprising
means for moving the region of spatial frequencies comprising DC to
a second part of the Fourier or Fresnel plane, and wherein
the phase filter (6, 27, 45) is positioned at the second part of
the Fourier or Fresnel plane for phase shifting of the transformed
modulated electromagnetic radiation at the second part of the
Fourier or Fresnel plane by .theta. in relation to the remaining
part of the electromagnetic radiation.
37. A system (1) according to claim 36, wherein the means for
moving the region of spatial frequencies comprising DC to a second
part of the Fourier or Fresnel plane comprises an optical
component, such as a grating, a prism, etc, with an appropriate
carrier frequency.
38. A system (1) according to claim 36, wherein the means for
moving the region of spatial frequencies comprising DC to a second
part of the Fourier or Fresnel plane comprises the phase mask (4,
23, 43) in which the function of an optical component, such as a
grating, a prism, etc, with an appropriate carrier frequency, has
been encoded.
39. A system (1) according to claim 30, wherein the modulus of the
Fourier transform of the phasors e.sup.i.phi.(x,y) at specific
spatial frequencies have been adjusted to keep the intensity levels
of the synthesized intensity pattern within a desired range.
40. A system (1) according to claim 39, wherein the modulus of the
Fourier transform of the phasors e.sup.i.phi.(x,y) at specific
spatial frequencies have been adjusted according to at least one of
the following measures:
a) adjusting the individual phasors e.sup.i.phi.(x,y) of the
resolution elements of the phase mask (4, 23, 43) maintaining
prescribed relative intensity levels between intensities of
resolution elements of the intensity pattern,
b) adjusting the individual phasors e.sup.i.phi.(x,y) of the
resolution elements of the phase mask (4, 23, 43) by histogram
techniques,
c) spatially scaling the phasor e.sup.i.phi.(x,y) pattern of the
phase mask (4, 23, 43), and
d) utilizing half tone coding techniques.
41. A system (1) according to claim 30, further comprising means
for controlling power of the electromagnetic radiation in response
to the intensity range of the intensity pattern.
42. A system (1) according to claim 30, wherein each phasor
e.sup.i.phi.(x,y) of the phase mask (4, 23, 43) is substantially
equal to a selected phasor that has been selected from a set of two
phasors with complementary phase values e.sup.i.phi.1(x,y) and
e.sup.i.phi.2(x,y) in such a way that a specific spatial frequency
distribution of the intensity of the electromagnetic radiation in
the Fourier or Fresnel plane is attained.
43. A system (1) according to claim 42, wherein the phase
.phi.(x,y) of phasors e.sup.i.phi.(x,y) of adjacent resolution
elements alternates between the two possible complementary phasor
values e.sup.i.phi.1(x,y) and e.sup.i.phi.2(x,y).
44. A system (1) according to claim 30, wherein the phase filter
(6, 27, 45) is shaped to match the spatial frequency content of the
phasors e.sup.i.phi.(x,y) of the spatial phase mask (4, 23,
43).
45. A system (1) according to claim 30, wherein modulus of the
average value .vertline..alpha..vertline. of the phasors
e.sup.i.phi.(x,y) ranges from 0.1 to 0.9.
46. A system (1) according to claim 45, wherein modulus of the
average value .vertline..alpha..vertline. of the phasors
e.sup.i.phi.(x,y) ranges from 0.25 to 0.75.
47. A system (1) according to claim 45, wherein modulus of the
average value .vertline..alpha..vertline. of the phasors
e.sup.i.phi.(x,y) ranges from 0.4 to 0.6.
48. A system (1) according to claim 45, wherein modulus of the
average value .vertline..alpha..vertline. of the phasors
e.sup.i.phi.(x,y) is approximately 0.5.
49. A system (1) according to claim 45, wherein the phase shift
.theta. ranges from .pi./4 to 7.pi./4.
50. A system (1) according to claim 45, wherein the phase shift
.theta. ranges from .pi./2 to 3.pi./2.
51. A system (1) according to claim 45, wherein the phase shift
.theta. ranges from 3.pi./4 to 5.pi./4.
52. A system (1) according to claim 30, wherein the phase shift
.theta. is approximately .pi..
53. A system (1) according to claim 30, further comprising zooming
means (10, 30, 47) for scaling of the intensity pattern.
54. A system (1) according Lo claim 30, wherein the phase filter
(6, 27, 45) comprises a spatial light modulator.
55. A system (1) according to claim 30, wherein the phase mask (4,
23, 43) is adapted to perform the optical function of a
Fourier-transforming lens by appropriate encoding of the phasors
e.sup.i.phi.(x,y) of the phase mask (4, 23, 43).
56. A system (1) according to claim 30, wherein the spatial phase
filter (6, 27, 45) is adapted to perform the optical function of an
output lens by appropriate encoding of the phase filter (6, 27,
45).
57. A system (1) according to claim 30, wherein the source (2, 21,
41) of electromagnetic radiation is adapted to radiate
electromagnetic radiation of different wavelengths corresponding to
three different colours, such as red, green and blue, for
generation of intensity patterns of arbitrary colours.
58. A system (1) according to claim 30, further comprising a first
and a second Fourier transforming lens (5, 7), the spatial phase
mask (4, 23, 43) being positioned in the front focal plane of the
first lens (5), the spatial phase filter (6, 27, 45) being
positioned at the back focal plane of the first lens (5), and the
second lens (7) being positioned so that its front focal plane is
positioned at the position of the back focal plane of the first
lens (5).
59. A system (1) according to claim 30, further comprising one
Fourier transforming lens (44), the spatial phase filter (45) being
positioned at the back focal plane of the lens (44).
60. A system (1) according to claim 30, further comprising one
imaging lens, the spatial phase filter (6, 27, 45) being positioned
in the back focal plane of the lens.
61. A system (1) according to claim 30, further comprising a
polarizing beam splitter (24) and a quarter wave plate (25) and/or
a phase filter (27) reflecting electromagnetic radiation incident
upon it.
62. A system (1) according to claim 30, wherein the spatial phase
filter (6, 27, 45) changes the phase of the radiation in the region
of spatial frequencies comprising DC and leaves the phase of the
remaining part of the radiation unchanged.
63. A system (1) according to claim 30, wherein the spatial phase
filter (6, 27, 45) do not change the phase of the radiation in the
region of spatial frequencies comprising DC and changes the phase
of the remaining part of the radiation.
64. A system (1) according to claim 30, wherein the spatial phase
filter (6, 27, 45) blocks the radiation at the region of spatial
frequencies comprising DC and leaves the remaining part of the
radiation unchanged.
65. A system (1) according to claim 30, wherein the source (2, 21,
41) of electromagnetic radiation is a Laser (2, 21, 41).
Description
FIELD OF THE INVENTION
The invention relates to a method and a system for synthesizing a
prescribed intensity pattern based on phase contrast imaging.
BACKGROUND OF THE INVENTION
It is well known to form an image on an illuminated surface of a
body by absorption or blocking of energy of an illuminating beam.
For example in an overhead projector, an over-head transparent
absorbs or blocks part of the light beam of the projector whereby a
large image of an overhead is formed on a screen. However, this
results in a loss of light intensity as part of the emitted light
from an image forming system is reflected or absorbed.
To avoid loss of energy causing, e.g. loss of light intensity of
the synthesized intensity pattern, power dissipation generating
heat in components of the system, etc., methods and systems have
been developed wherein the phase of a light beam is modulated
instead of the amplitude or intensity of the light beam, as
modulation of the phase of the light beam do not lead to loss of
energy. The phase modulation is followed by a conversion of the
phase modulation into an amplitude or intensity modulation.
A diffractive optical element, such as a holographic optical
element, may be used to generate a phase modulation. Then, the
resulting intensity modulation at each point of a picture formed by
conversion of the phase modulation into intensity modulation will
depend upon the phase modulation values at each point of the
diffractive optical element as the light intensity at each point of
the picture is formed by a coherent superposition of light received
from the entire surface of the diffractive optical element.
Diffractive optical elements are rather complex to design for
synthesis of a prescribed intensity pattern.
Imaging methods and systems may also be used in connection with
phase modulation. These methods and systems are characterized by
the fact that the intensity of a point of a picture formed by
conversion of phase modulation into intensity modulation will
depend upon the phase modulation value of one point of the phase
modulator only as this point is imaged onto the picture point in
question by the imaging system. This one-to-one relationship makes
the design of phase modulators in these systems simple. Methods and
systems of this kind are named phase contrast imaging methods and
systems.
Phase contrast imaging methods were originally developed within the
field of microscopy. Many objects of interest in microscopy are
largely transparent, thus absorbing little or no light. When light
passes through such an object, the predominant effect is the
generation of a spatially varying phase shift which can not be seen
by a human as the eye of a human responds to light intensity and
colour and does not respond to the phase of light.
In 1935, Fritz Zernik proposed a phase contrast technique which
rests on spatial-filtering principles and has the advantage that
the observed intensity is linearly related to the phase shift
introduced by the object.
Suppose that a transparent object with amplitude transmittance
is coherently illuminated in an image-forming system. For
simplicity, a magnification of unity is assumed and the finite
extent of the exit and entrance pupils of the system is neglected.
Further, a necessary condition to achieve linearity between phase
shift and intensity is that the phase shift .phi. be less than 1
radian, in which case the amplitude transmittance can be
approximated by
The terms of order .phi..sup.2 and higher are neglected in this
approximation. It is seen that the first term of (2) leads to a
strong wave component that passes through the sample without
change, while the second term generates weaker diffracted light
that is deflected away from the axis of the system.
The image produced by a conventional microscope can be written
where the term .phi..sup.2 has been approximated by zero. It is
seen that the diffracted light is not observable because it is in
phase quadrature with the strong background. As Zernik recognized
that the background is brought to a focus on-axis in the focal
plane while the diffracted light--containing higher spatial
frequencies--is spread away from the focal point, he proposed that
a phase-changing plate be inserted in the focal plane to modify the
phase relation between focused and diffracted light.
The phase-changing plate can consist of a glass substrate on which
a small transparent dielectric dot has been coated. The dot is
placed at the center of the focal plane and has a thickness and
index of refraction such that it retards the phase of the focused
light by either .pi./2 radians or 3.pi./2 radians relative to the
phase retardation of the diffracted light. In the former case the
intensity in the image plane becomes
while in the latter case
Thus, the image intensity has become linearly related to the phase
shift .phi.. When the phase of the background is retarded by
.pi./2, the result is known as positive phase contrast, while a
3.pi./2 retardation is said to yield negative phase contrast.
It is seen that the method described above leads to a phase
contrast imaging method that provides a small phase signal that is
superimposed on a large DC-component. This leads to an important
disadvantage of the method because, typically, it will be necessary
to attenuate the DC-component to enhance the information contained
in the phase modulated signal. However, the attenuation of the
DC-component leads to loss of energy. This kind of filtering is
usually denoted Dark Field Filtering.
It is another disadvantage of the phase contrast imaging method
described above that it is based on the assumption that the phase
shift .phi. is less than 1 radian which is very often not fulfilled
in practical real-life applications. However, the theory is still
applied to such applications, disregarding the fact that the basic
assumption is not fulfilled, and this leads to non-optimized
technical solutions.
In EP 0 657 760 a phase contrast imaging system is disclosed in
which an image simulation and projection system is based on the
Texas Instrument flexure beam digital mirror device (DMD). The
flexure beam DMD is used for analog phase modulation of reflected
light and the phase modulation is converted to amplitude modulation
utilizing a phase contrast imaging method. The flexure beam DMD
provides a flicker-free modulated wave and accordingly, optical
image sensor synchronization is not needed. The system disclosed
operates according to the Zernike method and, thus, includes the
corresponding disadvantages described above.
Another example of a phase contrast imaging system is disclosed in
GB 2 199 716, wherein an optical guide-beam projector for a missile
guidance system is disclosed that provides a spatially intensity
modulated guide-beam. A spatial phase modulator is used to generate
the guide-beam. The phase encoding of the spatial phase modulator
constitutes a periodic square-wave modulation (50% duty cycle) of
two phase values 0 and .pi./2. The phase modulation is converted
into an amplitude modulation by Fourier transforming lenses and a
phase plate providing a phase shift of the background signal by
.pi./2. A method for synthesizing the specific intensity pattern of
the optical guide-beam based on phase contrast imaging is not
disclosed in this document.
A similar example of a phase contrast imaging system is disclosed
in "Array illuminator based on phase contrast", Applied Optics Vol.
27, No. 14, pp. 2915-2921 (1988). A method is disclosed of
converting a wide beam of uniform intensity into an array of bright
spots without losses. The input spatial phase mask constitutes a
periodic array of phase dots with the phase value .pi., the
remaining area of the phase mask having the phase value 0. The
phase modulation is converted into an amplitude modulation by
Fourier transforming lenses and a phase plate providing a phase
shift of the background signal by .pi.. The method is limited to
the implementation of periodic array configurations with the binary
phase values 0 and .pi..
It is well-known to use so-called "radiation focusators", i.e.
computer generated holographic optical elements, for spatial phase
modulation of a light beam, e.g as disclosed in Special Issue on
Computer Optics in the USSR, Optics and Lasers in Engineering, Vol.
15, no. 5 1991. However, such elements are complicated to
synthesize. Typically, they are synthesized in such a way that the
desired image is formed in the Fresnel region or the Frauenhofer
region. Thus, the intensity of a resolution element in the
generated image is a function of several, typically all, phase
values of the resolution elements of the holographic optical
element. Obviously, this complicates the design of a general
purpose holographic optical element and advanced, very time
consuming algorithms have to be applied. Further, the complicated
design of the holographic optical elements renders it almost
impossible to implement dynamically changeable spatial phase
modulators with such elements.
It is a further disadvantage of holographic optical elements that a
carrier frequency is needed to separate diffracted light from
non-diffracted light resulting in an off-axis system geometry and a
need for a diffractive medium that can support these high frequency
terms.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide an apparatus of
the above kind which apparatus is robust, compact, simple to design
and relatively cheap to manufacture.
It is another object of the present invention to provide an
improved method and apparatus for phase contrast imaging that take
all terms of the Taylor's series: ##EQU1## into account and, thus,
is not based on the assumption that the phase shift .phi. is less
than 1 radian. It is important to note that each term of the
Taylor's series contribute to the DC-value of the function t(x,y).
This fact is not recognized in the art as the DC-value has until
now been believed to be represented by numeral 1 in equation
(2).
It is still another object of the present invention to provide an
improved method and apparatus for phase contrast imaging without
the need of attenuating the DC-component of the signal to enhance
the information contained in the phase modulated signal.
It is yet another object of the present invention to provide an
improved method based on a simple imaging operation with a simple
one-to-one mapping between resolution elements of a spatial phase
modulator and resolution elements of the generated intensity
pattern.
According to the invention a method is provided for synthesizing an
intensity pattern with low loss of electromagnetic energy,
comprising spatial modulation of electromagnetic radiation with a
spatial phase mask for modulation of the phase of the incident
electromagnetic radiation by phasor values of individual resolution
elements of the spatial phase mask, each phasor value being
determined in such a way that
1) the values of the Fourier transformed phasors attains
predetermined values for predetermined spatial frequencies, and
2) the phasor value of a specific resolution element of the spatial
phase mask corresponds to a distinct intensity level of the image
of the resolution element in the intensity pattern,
and a spatial phase filter for phase shifting of a part of the
electromagnetic radiation, in combination with an imaging system
for generation of the intensity pattern by interference in the
image plane of the imaging system between the part of the
electromagnetic radiation that has been phase shifted by the phase
filter and the remaining part of the electromagnetic radiation.
Although, the present method is related to encoding of spatial
phase masks in two spatial dimensions (planar encoding), the
principles of the method may be utilized for phase encoding in one
to three spatial dimensions and/or in the temporal dimension.
The electromagnetic radiation may be of any frequency range of the
electromagnetic spectrum, i.e. the gamma frequency range, the
ultraviolet range, the visible range, the infrared range, the far
infrared range, the X-ray range, the microwave range, the HF (high
frequency) range, etc. The present method is also applicable to
particle radiation, such as electron radiation, neutron radiation,
etc.
Preferably, the electromagnetic radiation is monochromatic or
quasi-monochromatic so that the energy of the electromagnetic
radiation is concentrated in a narrow frequency bandwidth. As the
intensity pattern is synthesized by interference of two
electromagnetic waves emitted from a common source of
electromagnetic radiation but the phases of which have been changed
differently, it is required that the frequency range of the emitted
electromagnetic radiation is sufficiently narrow to ensure that the
two waves of electromagnetic radiation are coherent so that their
superposition generates the desired intensity pattern. If the
frequency range is too broad, the two waves will be incoherent and
the phase information will be lost as superposition of non-coherent
waves results in a summation of the intensities of the two waves.
It is required that the difference between individual delays of
electromagnetic radiation to be superpositioned is less than the
wavelength of the radiation. This is a relaxed requirement that
allows the electromagnetic radiation to be relatively broad-banded.
For example in the visible range a Xe-lamp or a Hg-lamp can be used
as a light source in a system according to the present invention
with the advantage compared to a laser light source that the
speckle noise is reduced. The requirements of the spatial coherence
of the electromagnetic radiation depend upon the space bandwith
product of the corresponding system and how close the required
system performance is to the theoretically obtainable performance
of the system.
Preferably, the electromagnetic radiation is generated by a
coherent source of electromagnetic radiation, such as a laser, a
maser, a phase-locked laser diode array, etc. However a high
pressure arc lamp, such as a Hg lamp, a Xe lamp, etc, may also be
used and even an incandescent lamp may be used as a source of
electromagnetic radiation in a low performance system.
A spatial phase mask is a component that changes the phase of an
electromagnetic wave incident upon it. The spatial phase mask may
transmit or reflect the incident electromagnetic wave. Typically,
the spatial phase mask is divided into a number of resolution
elements each of which modulates the incident electromagnetic wave
by changing its phase by a specific predetermined value. The
predetermined values are assigned to each resolution element in
different ways depending upon the technology applied in the
component. For example in spatial light modulators, each resolution
element may be addressed either optically or electrically. The
electrical addressing technique resembles the addressing technique
of solid-state memories in that each resolution element can be
addressed through electronic circuitry to receive a control signal
corresponding to the phase change to be generated by the addressed
resolution element. The optical addressing technique addresses each
resolution element by pointing a light beam on it, the intensity of
the light beam corresponding to the phase change to be generated by
the resolution element illuminated by the light beam.
Spatial phase masks may be realized utilizing fixed phase masks,
devices comprising liquid crystals and being based on liquid
crystal display technology, dynamic mirror devices, digital
micromirror arrays, deformable mirror devices, membrane spatial
light modulators, laser diode arrays (integrated light source and
phase modulator), smart pixel arrays, etc.
A spatial phase filter is typically a fixed phase mask, such as an
optically flat glass plate coated with a dielectric layer at
specific positions of the glass plate. However, the spatial phase
masks mentioned in the previous section may also be used for
spatial phase filters.
The imaging system maps the phase modulating resolution elements of
the spatial phase mask on the target surface of the synthesized
intensity pattern. It may comprise a 4f-lens configuration (two
Fourier transforming lenses utilizing transmission of light or one
Fourier transforming lens utilizing reflection of light) or a
single imaging lens. However, any optical imaging system providing
a filtering plane for the spatial phase filter may be applied in a
phase contrast imaging system.
In the method according to the present invention, the synthesized
intensity pattern is generated by superposition of two
electromagnetic waves in the image plane of the imaging system. The
spatial phase mask changes the phase values of an electromagnetic
wave incident upon it and the imaging system directs the
electromagnetic wave with changed phases reflected from or
transmitted through the spatial phase mask towards the spatial
phase filter. The phase filter phase shifts a part of the
electromagnetic radiation and the imaging system is adapted to
superimpose in the image plane the phase shifted part of the
electromagnetic radiation with the part of the electromagnetic
radiation that is not phase shifted by the spatial phase
filter.
According to a preferred embodiment of the invention, the spatial
phase mask is positioned at the front focal plane of a lens while
the spatial phase filter is positioned in the back focal plane of
the lens, whereby a first electromagnetic field at the phase mask
is Fourier transformed by the lens into a second electromagnetic
field at the phase filter. Thus, specific spatial frequencies of
the first electromagnetic field will be transmitted through the
spatial phase filter at specific positions of the phase filter. For
instance, the energy of the electromagnetic radiation at zero
frequency (DC) is transmitted through the phase filter at the
intersecting point of the Fourier plane and the optical axis of the
lens also denoted the zero-order diffraction region.
It is presently preferred that the spatial phase filter is adapted
to phase shift the DC-part of the electromagnetic radiation and to
leave the remaining part of the electromagnetic radiation unchanged
or, alternatively, to leave the DC-part of the electromagnetic
radiation unchanged and to phase shift the remaining part of the
electromagnetic radiation. The last alternative is preferred when
the energy level of the DC-part of the electromagnetic radiation is
so high that the phase shifting part of the phase filter will be
destroyed by it. For example in laser cutting, the DC level of the
laser beam can be so high that a phase shifting dot positioned at
the intersecting point of the DC part of the laser beam at the
phase filter would evaporate. It is also possible to block the
electromagnetic radiation (no transmittance) in the zero-order
diffraction region, however, the DC energy of the radiation is then
lost.
Below, an expression of the intensity of the synthesized intensity
pattern as a function of the phasor values .phi.(x,y) of the phase
mask, when the DC-part of the electromagnetic radiation is phase
shifted, is deduced.
Electromagnetic radiation incident on the spatial phase mask can be
described by a function A(x,y), where A(x,y) is a complex number
(amplitude and phase) of the incident field on the point (x,y) of
the spatial phase mask. At the point (x,y), the spatial phase mask
modulates the phase of the incident radiation with a value
.phi.(x,y) so that the field after reflection by or transmission
through the spatial phase mask may be described by the function
A(x,y)*e.sup.i.phi.(x,y), e.sup.i.phi.(x,y) being the phasor value
of the point (x,y) of the spatial phase mask. As A(x,y) preferably
is a constant value over the entire surface of the spatial phase
mask, the term is left out of the following equations for
simplicity.
The expression of the electromagnetic radiation incident on the
spatial phase filter may now be separated into an AC-term and a
DC-term. If the DC-term of the field is denoted .alpha., the
AC-term of the field is given by the term e.sup.i.alpha.(x,y)
-.alpha.. As the spatial phase filter changes the phase of the
DC-part of the electromagnetic radiation by .theta., the intensity
of the synthesized intensity pattern at the image plane of the
imaging system is given by:
wherein (x',y') is the coordinates of the image of the point (x,y)
of the spatial phase mask formed by the imaging system in the image
plane.
It should be noted that the second term of the equation is a
complex number that adds to the phasors e.sup.i.phi.(x,y) of the
spatial phase mask and may be interpreted as a contrast control
parameter for the synthesized intensity pattern I(x',y').
According to a preferred embodiment of the invention, the average
value of the phasors is adjusted in order to control the range of
intensity levels.
Instead of phase shifting the DC-part of the electromagnetic
radiation, it is also possible to synthesize a prescribed intensity
pattern by phase shifting other parts of the electromagnetic
radiation by adapting the spatial phase filter to phase shift
electromagnetic radiation incident upon one or more arbitrary
regions of the phase filter and leaving the phase of the remaining
part of the electromagnetic radiation unchanged and then
superimposing the two parts of the electromagnetic radiation. The
corresponding mathematics and the corresponding design procedures
for the spatial phase mask and spatial phase filter will of course
be more complicated than for the method described in the previous
section.
A simple example of phase shifting a part of the electromagnetic
radiation of a spatial frequency different from the zero frequency
is provided by moving the DC-part of the electromagnetic radiation
to another spatial frequency in the Fourier plane (identical to the
plane of the spatial phase filter) utilizing an optical component
with an appropriate carrier frequency (i.e. a grating or a prism)
or, preferably, encoding the function of a grating or a prism into
the spatial phase mask, and adapting the spatial phase filter to
change the phase of the electromagnetic radiation at this spatial
frequency and to leave the phase of the remaining part of the
electromagnetic radiation unchanged.
According to another preferred embodiment of the invention, the
phase mask is not positioned in the back focal plane of the lens
but in the Fresnel region of the lens instead. In this case, the
electromagnetic field at the phase filter will be given by a
Fresnel transformation of the electromagnetic field at the spatial
phase mask. This further complicates the mathematics and the design
procedures, for example the term .alpha. in equation (7) has to be
substituted by the value of the Fresnel transformation at the
point(s) of phase changes of the phase filter. However, the Fresnel
transformation may be calculated from a Fourier transformation by
multiplication of the phasor values of the spatial phase mask by a
quadratic phase factor followed by a Fourier transformation.
It is an important aspect of the present invention that each
intensity level of the synthesized intensity pattern for each
resolution element may be generated by at least two different
phasor values of a resolution element of the spatial phase
mask.
For example, when the spatial phase filter phase shifts the DC-part
of the electromagnetic radiation, it will be shown later that,
advantageously, the average .alpha. of the phasors of the
resolution elements of the phase mask should be equal to 1/2 and
the value of the phase shift .theta. should be equal to .pi.. In
this case, the intensity of the synthesized image pattern at the
image (x',y') of the resolution element (x,y) will be given by:
It is seen that complex conjugate phasors (values of .phi. of
opposite sign) result in identical intensity levels I(x',y'). It
can be shown that for any value of the modulus of the average of
the phasors .vertline..alpha..vertline., two phasors exist that
will generate identical intensity levels of the synthesized
intensity pattern.
Further, if the spatial phase filter phase shifts parts of the
electromagnetic radiation different from the DC-part, the phasor
value that generates a specific intensity level will depend on the
position of the resolution element in question, i.e. the phasor
value and the position of the resolution element with that phasor
value together define the intensity level at the image of the
resolution element in the synthesized intensity pattern. Still, it
is true that for each resolution element of the spatial phase mask,
each intensity level of the synthesized intensity pattern may be
represented by one of two different phasors of complementary phase
values.
This freedom of being able to select, for each intensity level to
be generated and for each resolution element of the spatial phase
mask, one of two phasors is used to control the phase of the
Fourier transform of the phasors at specific spatial frequencies by
selection of phasors with appropriate phase values to ensure two
intervals of biunique functional dependence between phasor values
and corresponding intensity values.
This freedom of choice of phasors may be utilized to select phasors
of neighbouring resolution elements of the spatial phase mask with
a maximum difference between them, thereby generating an
electromagnetic radiation emitted from the phase mask with a
maximum content of high spatial frequencies which will generate a
good separation of the DC part of the electromagnetic radiation
from its AC part. However, any other strategy of selecting between
two possible phasor values of each resolution element may be chosen
to generate a desired spatial frequency content of the
electromagnetic radiation.
Preferably, the phase of the Fourier transform of the phasors at
specific spatial frequencies is adjusted in order to control
whether the relation between each phasor and the corresponding
intensity level is a monotonic increasing or a monotonic decreasing
function.
Below, a set of different methods are described that are provided
according to the present invention for adjustment of the modulus of
the Fourier transform of the phasors at specific spatial
frequencies to attain a prescribed value. If convenient, the
methods may be combined.
According to one of the methods, the individual phasors of the
resolution elements of the phase mask are adjusted by a constant
value until the desired value of the modulus of the Fourier
transform of the phasors at specific spatial frequencies is
attained while maintaining prescribed relative intensity levels
between intensities of resolution elements of the intensity
pattern, i.e. iteratively.
According to another method, the individual phasors of the
resolution elements of the phase mask are adjusted utilizing
histogram techniques known from image processing. A histogram is a
bar chart showing the number of resolution elements of the
synthesized intensity pattern with a specific intensity value as a
function of the intensity value. Any histogram technique, such as
histogram equalization, adapting the histogram to a predetermined
distribution, etc., may be used iteratively until the modulus of
the Fourier transform of the phasors at specific spatial
frequencies attain the prescribed value.
According to yet another method, the phasor pattern of the phase
mask is spatially scaled in order to adjust the modulus of the
Fourier transform of the phasors at specific spatial
frequencies.
According to still another method, the modulus of the Fourier
transform of the phasors at specific spatial frequencies is
adjusted utilizing half tone coding techniques, such as raster
techniques, area ratio modulation, spot diameter modulation,
etc.
It is seen from the description above that the intensity levels may
differ from one synthesized intensity pattern to the next as a
consequence of the adjustments of the modulus of the Fourier
transform of the phasors at specific spatial frequencies. Thus, it
is preferred to control the power of the radiation source in
dependence of the intensity range of the intensity pattern so that
a sequence of different intensity patterns show uniform intensity
levels.
According to a preferred embodiment of the invention, the shape of
the phase filter is adapted to match the spatial frequency content
of the phasors of the spatial phase mask, e.g. to optimize the
desired separation of the part of the electromagnetic radiation to
be phase filtered from the remaining part of the electromagnetic
radiation.
It is within the scope of the present invention that the imaging
system further comprises zooming means for variable scaling of the
synthesized intensity pattern. The zooming of the imaging system
may be dynamically controllable, e.g. in response to the scaling of
the pattern of phasor values of the phase mask.
According to the present invention, the power of the radiation
source may be controllable in response to the spatial scaling of
the pattern in the phase mask and/or the zooming of the focusing
system.
In order to provide a compact and integrated system according to
the present invention, the optical function of a
Fourier-transforming lens is encoded into the phasors of the
spatial phase mask. The Fourier transforming lens may be
refractively or diffractively encoded into the phase mask.
Similarly, the optical function of an output lens may be encoded
into the phase filter either refractively or diffractively.
Further, a compensation may be encoded into the phasor values of
the spatial phase mask so that part of the electromagnetic
radiation modulated by the phase mask has a substantially flat
intensity profile in the image plane. Without this compensation,
part of the electromagnetic radiation modulated by the phase mask
will have a flat profile with perturbations resulting from the
phase filtering superpositioned upon it. This may cause "ringings"
(oscillations) at the edges of the synthesized intensity
pattern.
According to another preferred embodiment of the invention, the
source of electromagnetic radiation comprises one or more light
sources of different wavelengths corresponding to three different
colours, such as red, green and blue, for generation of intensity
patterns of arbitrary colours. Further, several independent systems
each one illuminated by its own wavelength can be combined into a
single multi-wavelength system.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a 4f optical system for phase contrast imaging,
FIG. 2 shows a 2f optical system for phase contrast imaging,
FIG. 3 shows a if optical system for phase contrast imaging,
FIG. 4 shows (A) off-axis read-out of reflective SLM and (B)
on-axis read-out of reflective SLM.
FIG. 5 shows schematically an example of a prescribed intensity
pattern in 1D.
FIG. 6 shows schematically the resulting phase encoding
corresponding to FIG. 5.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
FIG. 1 shows a 4f phase contrast imaging system (1). A laser (2)
emits a light beam which is expanded by a beam expander (3) into a
plane light wave of uniform intensity and directs it towards a
spatial phase mask (4). The light beam is transmitted through the
spatial phase mask (4) and a Fourier transforming lens (5). The
spatial phase mask is positioned in the front focal plane of the
lens (5) and a spatial phase filter (6) is positioned in the back
focal plane of the lens (5) that is also the front focal plane of a
lens (7). The Fourier transforming lenses (5, 7) need not have
identical focal lengths. Different focal lengths lead to a
magnification ratio different from one. The phase filter (6) phase
shifts the zero order diffraction part (8) of the light phase
modulated by the spatial phase mask (4). The synthesized intensity
pattern is generated in the back focal plane (9) of the lens (7)
and a dynamic focusing system (10) images the synthesized intensity
pattern onto a focusing plane (11).
The optical system is controlled by a computer (12). The computer
(12) comprises interface means for addressing each of the
resolution elements of the phase filter (4) and transmitting a
phasor value to the addressed resolution element. Further, the
computer (12) comprises laser control means for controlling the
power of the laser (2) and imaging control means for controlling
the focusing and the image ratio of the dynamic focusing system
(10). The computer (12) also comprises input means, such as a
keyboard, a diskette drive, an optical disc drive, a network
interface, a modem, etc, for receiving an image pattern to be
synthesized by the system (1). From the received image pattern, the
computer is adapted to calculate phasor values to be transmitted to
the resolution elements of the phase mask, e.g. based on a
histogram technique as described herein. Optionally, the phase
shift of the phase filter (6) is adjustable and controllable by
optional phase control means of the computer (12) which may be
further adapted to adjust the phase shift, e.g. utilizing equation
(18).
FIG. 2 shows a 2f phase contrast imaging system (20). A laser (21)
emits a light beam which is expanded by a beam expander (22) into a
plane light wave of uniform intensity and directs it towards a
spatial phase mask (23) and a polarization beam splitter (24) and a
quarter-wave plate (25). The polarization beam splitter (24) and
the quarter-wave plate (25) allows beam-splitting of light of a
specific linear polarization without the power loss associated with
conventional beam-splitters due to splitting of the beam in both
directions of transmission through the beam-splitter. After
transmission through the polarization beam splitter (24) and the
quarter-wave plate (25), the light beam is transmitted through a
Fourier transforming lens (26) and is reflected from a spatial
phase filter (27). The spatial phase mask (23) is positioned in the
front focal plane of the lens (26) and the spatial phase filter
(27) is positioned in the back focal plane of the lens (26). The
phase filter (27) phase shifts the zero order diffraction part (28)
of the light that is phase encoded by the spatial phase mask (23).
The synthesized intensity pattern is generated in the back focal
plane (29) of the lens (26) and a dynamic focusing system (30)
images the synthesized intensity pattern onto a focusing plane
(31). As described for the system shown in FIG. 1, the system (20)
is controlled by a computer (32).
FIG. 3 shows a if phase contrast imaging system (40). A laser (41)
emits a light beam which is expanded by a beam expander (42) into a
plane light wave of uniform intensity and directs it towards a
spatial phase mask (43). The light beam is transmitted through the
spatial phase mask (43) and an image forming lens (44). A phase
filter (45) positioned in the back focal plane of the lens (44)
phase shifts the zero order diffraction part of the light phase
encoded by the spatial phase mask (43). The synthesized intensity
pattern is generated in the image plane (46) of the lens (44) and a
dynamic focusing system (47) images the synthesized intensity
pattern onto a focusing plane (48). As described for the system
shown in FIG. 1, the system (40) is controlled by a computer
(49).
FIG. 4 shows details of (A) an off-axis read-out of a reflective
phase mask (50) (or a spatial light modulator) and of (B) an
on-axis read-out of a reflective phase mask (51) with a beam
splitter (52). Both configurations (A, B) may be utilized in the
systems shown in FIGS. 1-3.
Phase Encoding For DC Phase Filtering
In the following an example of encoding a spatial phase mask and a
spatial phase filter will be given based on a system filtering in
the DC-frequency range. The system chosen in this example is based
on a 4-f lens configuration as shown in FIG. 1 and illuminated by
electromagnetic radiation in the visible frequency domain,
hereafter simply denoted as light radiation.
Assuming that the illuminating light is monochromatic and has a
substantially flat amplitude profile we obtain the following
spatial amplitude distribution emitted from the spatial phase mask:
##EQU2## where .alpha.(x,y) =exp(i.phi.(x,y)) represent the
spatially encoded phasor values and .DELTA.x.DELTA.y is the area of
the input phase modulating spatial light modulator.
It turns out to be convenient to separate .alpha.(x,y) into two
terms describing a spatially invariant DC-value, .alpha., and a
spatially varying AC-contribution .DELTA..alpha.(x,y). The DC-value
can be found as: ##EQU3##
Subsequently the AC-term is expressed by: ##EQU4##
The separation of .alpha.(x,y) into a spatially invariant DC-term
and a spatially varying AC-term is an important point and will be
used throughout the remaining part of this example, especially in
the description of the spatial filtering procedure.
The spatial filter utilized in this example is chosen as a circular
phase contrast filter (different transverse shapes can also be
used) centered around origo in the the spatial frequency domain,
denoted by coordinates (f.sub.x,f.sub.y): ##EQU5## where f.sub.x
=.sqroot.f.sub.x.sup.2 +f.sub.y.sup.2 denotes radial spatial
frequency and .DELTA.f.sub.x describes the size of the circular
(circ) phase filter.
In the spatial frequency domain (the filtering plane) the Fourier
transformation (.Fourier.) of the spatially modulated light
radiation from the spatial phase mask is present. The filtering
operation on the Fourier transformed light radiation performed by
the spatial phase contrast filter can be expressed as a simple
point-by-point multiplication procedure. Subsequently the spatially
filtered light is inverse Fourier transformed (.Fourier..sup.-1) by
the second Fourier lens (Fourier transformation and reflected
output coordinates) and the resulting spatial amplitude
distribution in the image plane (with coordinates (x',y')) can
accordingly be written as: ##EQU6##
Within the illumination-region, (x',y').di-elect cons.', outlined
by ##EQU7## one obtains: ##EQU8##
Requiring that .vertline.o(x.sub.o ',y.sub.o ').vertline..sup.2
.tbd.0 corresponding to complete darkness as the lowest intensity
level in regions (x.sub.o ',y.sub.o ').di-elect cons..sub.o '
implies: ##EQU9## where the abbreviation .phi..sub.0 =.phi.(x.sub.o
',y.sub.o ') has been used.
The solutions to Eq. (15) are given by: ##EQU10##
The requirement o<.vertline..alpha..vertline.<1 implies that:
##EQU11## leading to ##EQU12## where the +sign is for
.theta.-values in the interval: ##EQU13## and the -sign is for
.theta.-values: ##EQU14##
The corresponding interval for (.phi..sub..alpha. -.phi..sub.o) is:
##EQU15##
Inserting the expression for .vertline..alpha..vertline., one
obtains the simple intensity expression: ##EQU16## where
##EQU17##
The phase-only transformations imply that energy is conserved:
##EQU18##
A special case:
The most convenient choice for .alpha. is: .alpha.=1/2 (implying
that .theta.=.pi.+P.sub.even 2.pi.), so that the output intensity
can be described as:
In this case the phaseointensity mapping is described by the
intervals [0;.pi.].fwdarw.[0;4].
By setting .alpha.=1/2 one obtains the following requirement to the
phase function .phi.(x,y): ##EQU19##
Inserting the expression for .vertline.o(x',y').vertline..sup.2 in
Eq. (24) yields: ##EQU20## in accordance with the first of the
integral expressions in Eq. (26). Encoding procedure:
A given intensity distribution (image)
.vertline.o(x',y').vertline..sup.2 is desired at the output side of
the optical setup.
Pixellation of the image, that is generally represented in the
greyscale range: [0;gmax], provides the relation: ##EQU21## The
histogram for the desired image .vertline.o(i,j).vertline..sup.2 is
adjusted (adj) within the greyscale range [0;gmax], so that the
previous point is fulfilled:
The phase values can now be calculated as: ##EQU22## As before
pixellation provides the relation: ##EQU23## The previous point can
now be fulfilled by complex conjugating half the input pixels
having the same phase value in the phase histogram.
The phase conjugate phase flipping provides a valuable tool (an
extra degree of freedom) for manipulating the spatial frequency
content in order to optimize the separation of low and high
frequency terms at the filter plane.
The scheme is robust to constant phase errors across the input
spatial phase modulator, since Eq. (22) is a function of the
difference: .phi..sub..alpha. -.phi.(i,j), only. Furthermore, small
variations in the individual pixel phase values do not introduce
any detrimental effects because the average value .alpha., is a
result of a very large phasor sum.
If the desired intensity distribution is too small to include all
energy, that is, the histogram is scaled to maximum and the left
hand side of Eq. (24) is still smaller than the right hand side,
then the input phase object can be scaled until Eq. (24) is
fulfilled. In order to obtain a scale invariant output intensity
level a dynamic focusing system is needed. Similarly, intensity
invariance can be obtained by controlling the radiated power from
the light source. Alternatively, one can ignore the residual
background illumination and obtain intensity levels with a gain
factor of 9.sup.- (background constant equal to 1.sup.-) for narrow
generally shaped line structures (e.g. Eq. (14)).
EXAMPLE 1
A very simple example illustrating the individual steps in the
above procedure will be given below. To simplify the example it
will be considered in one dimension only. The starting point for
encoding the spatial phase mask in this example is based on the
following parameters: ##EQU24##
Consider the pixellated 3-step function shown in FIG. 5 to be
synthesized in the image plane as an intensity distribution. From
the above choices of parameters one obtains the simple relation
between phase values in the spatial phase mask and the image
intensity values:
To proceed from here it necessary to calculate the accumulated
intensity ##EQU25## in the image to be synthesized. The accumulated
intensity is easily calculated from an image histogram where the
x-axis represents greylevel value and the y-axis represents the
amount of pixels in the image at a given greylevel value. By use of
a histogram ##EQU26## is simply found as the weighted sum of all
greylevel values (x-axis) multiplied by their pixel counting
(y-axis). This describes, so to speak, the "weight" of the image.
In this simple example histogram calculations are not needed since
we only have 3 greylevels with well-defined separations.
The value for the accumulated intensity has to obey the equality:
##EQU27##
From FIG. 5 we obtain: ##EQU28##
So that the value for max can be estimated to be: 7
The corresponding adjusted intensity levels,
.vertline.o(i).sub.adj.sup.2, are therefore: 7/4, 7/8 and 0. These
values can now be utilized to calculate the phase values of the
spatial phase mask from the relation: ##EQU29## where from we
obtain the three phase values: 1.45 rad. 0.97 rad. and 0 rad.
The last step needed in order to encode the spatial phase mask is
that the following equality is fulfilled: ##EQU30##
Since we have the choice to use complex conjugate phasor values
(two phasors giving the same intensity level) many approaches can
be taken from here. A simple approach is to flip every second
phasor with its complex conjugate value as shown in FIG. 6. The
final phase values used in the phase masks are accordingly:
.+-.1.45 rad. .+-.0.97 rad. and 0 rad.
As the last step we can check whether the criteria: .alpha.=1/2, is
actually fulfilled with the chosen phasor encoding: ##EQU31##
General Phase Correction Procedure Integrated With the Phase
Encoding
In Eq. (14) we obtained an analytic relation between the phase
values in the spatial phase mask and the resulting intensity
distribution, within the region (x',y').di-elect cons.':
##EQU32##
The analysis leading to the above relation was based on the
assumption that .vertline..alpha..vertline. is a constant value
within the '-domain. In other words, the following approximation
was applied: ##EQU33##
However, for certain spatial filter parameters the lefthand side of
this expression will not be a space invariant constant value
throughout the whole '-domain but will instead manifest slowly
variations/oscillations. This will introduce small errors in the
final superposition between the phase filtered DC-value and the
direct propagated AC-signal. In order to circumvent this problem a
technique is needed that can counteract the distortions by use of
phase-only encoding in the components already present in the
system. In what follows a procedure for integrating predistortion
that counteracts the above mentioned distortions will be described
that is purely based on modifying the phasor values in the spatial
phase mask at the input side of the system. The method can also
counteract other types of distortions inherent in a practical
implementation of the system. Furthermore, the method can be
applied in systems filtering at other spatial frequencies than
DC.
Procedure:
When encoding the input phase function it is helpful to have a
reverse equation, expressing the input phase distribution as a
function of an adjusted (electronic) image grey-level distribution,
I.sub.slm, addressing the input spatial light modulator: ##EQU34##
where it has been taken into account that .alpha.(x',y') is not
considered as a constant but manifests a smooth oscillating
behaviour within the optical image domain. The maximum value of
I.sub.slm is denoted gmax.
Now, one can derive a formula for the grey-level correction,
.DELTA.I.sub.slm (x',y'), that one needs to apply in order to
encode a phase function that compensates for the spatial variation
of the average phase value .alpha.(x',y'): ##EQU35## where the
second relation has been derived from the first by setting
.alpha.=1/2 and .theta.=.pi..
By inserting the second relation in the first expression one gets:
##EQU36##
This formula is however not directly useful because it is related
to the histogram adjusted grey-level distribution denoted by
I.sub.slm.
One needs a formula that relates the above correction term to the
original input grey-level distribution I(x,y) that has not been
modified by histogram adjustments. This is important since the
effect of the grey-level corrections also have to be incorporated
in the procedure of histogram adjustments.
The histogram scaling gives: ##EQU37## where I.sub.max and
I.sub.slm,max are the maximum grey-level values occurring in the
original and the adjusted electronic grey-level distributions
respectively.
Similarly, one can apply this relation to the intensity correction
term .DELTA.I.sub.slm and obtain: ##EQU38## resulting in:
##EQU39##
In order to have enough dynamic range in grey-levels for the
correction term one can derive an inequality from the above
relation by using the fact that I.sub.max .ltoreq.gmax:
##EQU40##
Since the first term is the dominating term in the expression for
the intensity correction it will in practice be sufficient just to
have the much simpler corrections: ##EQU41## Proposed Applications:
Laser machining, marking, branding, trimming, hardening, scribing,
labeling, welding and cutting on two- and three-dimensional
surfaces especially by use of CO.sub.2 and Nd:YAG laser based
systems. The main advantage is that energy is not absorbed in the
system (thereby preventing damage of the optical hardware) and this
nonabsorbed energy is instead utilized to increase the intensity
level of the desired light distribution in the image plane. High
power can be delivered to selected regions on a work piece
simultanously.
Efficient and dynamic spot-array generators based on phase contrast
imaging. In order to provide bias or holding beams for arrays of
optoelectronic elements, such as bistable elements, photonic
switches and smart pixels.
Generation of structured light (lossless) for machine vision
applications. E.g. periodic and skew periodic mesh grid
illumination that can be updated in parallel.
Photolithographic applications (laser 3D direct writing in parallel
without the need for sequential scanning). E.g. high power laser
direct writing of waveguides in Ge-doped silica.
Spatial light intensity modulation in general by use of pure phase
modulation (radiation focusators).
Laser beam shapinq (dynamic).
Highly efficient parallel image projection without the need for a
laser scanning device.
Dynamic Infrared Scene Projection (DIRSP).
Exposure device for grating and mask production.
LIDAR applications.
Laserprinting in parallel.
Lasershow applications.
Atmosphere research.
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