U.S. patent application number 13/500773 was filed with the patent office on 2012-11-08 for birefringent device with application specific pupil function and optical device.
This patent application is currently assigned to SONY Corporation. Invention is credited to Daniel Buehler, Marco Hering, Markus Kamm.
Application Number | 20120281280 13/500773 |
Document ID | / |
Family ID | 43250275 |
Filed Date | 2012-11-08 |
United States Patent
Application |
20120281280 |
Kind Code |
A1 |
Buehler; Daniel ; et
al. |
November 8, 2012 |
BIREFRINGENT DEVICE WITH APPLICATION SPECIFIC PUPIL FUNCTION AND
OPTICAL DEVICE
Abstract
A birefringent device, which is configured to be mounted in an
optical path of an optical system, has an effective area in a pupil
plane. The birefringent device affects different polarization
states differently and position-dependently. The birefringent
device realizes a first pupil function assigned to a first
polarization state and a second different pupil function assigned
to a second polarization state. The pupil functions may be
optimized to achieve various specific optical properties like
extended depth of field.
Inventors: |
Buehler; Daniel; (Kirchheim,
DE) ; Kamm; Markus; (Karlsruhe, DE) ; Hering;
Marco; (Stuttgart, DE) |
Assignee: |
SONY Corporation
Tokyo
JP
|
Family ID: |
43250275 |
Appl. No.: |
13/500773 |
Filed: |
October 14, 2010 |
PCT Filed: |
October 14, 2010 |
PCT NO: |
PCT/EP2010/006296 |
371 Date: |
July 19, 2012 |
Current U.S.
Class: |
359/489.01 ;
349/194; 349/57; 977/932 |
Current CPC
Class: |
G02B 5/3083 20130101;
G02F 1/13363 20130101; G02B 27/0075 20130101; G02B 2207/129
20130101 |
Class at
Publication: |
359/489.01 ;
349/194; 349/57; 977/932 |
International
Class: |
G02B 27/28 20060101
G02B027/28; G02F 1/13363 20060101 G02F001/13363; G02F 1/13 20060101
G02F001/13 |
Foreign Application Data
Date |
Code |
Application Number |
Oct 15, 2009 |
EP |
09013046.9 |
Claims
1-36. (canceled)
37. A birefringent device configured to be arranged in an optical
path of an optical system and having an effective area to be
arranged in a pupil plane of the optical system, comprising: a
first pupil function assigned to a first polarization state; and a
second pupil function assigned to a second polarization state.
38. The birefringent device of claim 37, wherein the second
polarization state is orthogonal to the first polarization
state.
39. The birefringent device of claim 37, wherein the first pupil
function is the complex conjugate of the second pupil function.
40. The birefringent device of claim 37, wherein the slope of the
pupil functions is not zero at least in a portion of the effective
area.
41. The birefringent device of claim 37, wherein the first and
second pupil functions are determined to increase the depth of
focus of the optical system.
42. The birefringent device of claim 37, wherein the first and
second pupil functions are point-symmetric with respect to a
symmetry point of the birefringent device.
43. The birefringent device of claim 37, further comprising: a
birefringent element made of birefringent material, wherein an
orientation of an extraordinary axis of the birefringent material
changes in a plane perpendicular to an optical axis of the optical
system.
44. The birefringent device of claim 43, wherein the direction of
the extraordinary axis of the birefringent element is changing
laterally within the plane perpendicular to the optical axis of the
optical system to form a pattern defining the pupil functions for
the first and second polarization states.
45. The birefringent device of claim 43, wherein a thickness of the
birefringent element is changing laterally within the plane
perpendicular to the optical axis of the optical system to form a
pattern defining or contributing to a definition of the pupil
functions for the first and second polarization states.
46. The birefringent device of claim 43, wherein a difference
between an extraordinary and an ordinary refractive index of the
birefringent element is changing laterally within the plane
perpendicular to the optical axis of the optical system to form a
pattern defining or contributing to a definition of the pupil
functions for the first and second polarization states.
47. The birefringent device of claim 43, wherein the birefringent
element comprises a circular section and at least one annular
section encompassing the circular section, wherein the directions
of the extraordinary axes of the birefringent material in adjacent
ones of circular and annular sections change alternately.
48. The birefringent device of claim 47, wherein at least one of
the circular and annular sections does not comprise birefringent
material.
49. The birefringent device of claim 43, wherein the birefringent
material is a liquid crystal, an orientation of the liquid crystal
being aligned by an alignment layer.
50. The birefringent device of claim 43, wherein the orientation of
the alignment layer is fixed by linear photopolymerization.
51. The birefringent device of claim 43, wherein the birefringent
material is a liquid crystal polymer and the orientation of the
liquid crystal polymer is fixed by curing the polymer with UV
light.
52. The birefringent device of claim 43, wherein the birefringent
material is a nano grating formed on a surface of a substrate
having an extraordinary refractive index parallel to the
surface.
53. The birefringent device of claim 52, wherein the nano grating
is formed by a nano imprinting method.
54. The birefringent device of claim 37, further comprising: a
first and a second sub-device, wherein the first sub-device
realizes the first pupil function and the second sub-device
realizes the second pupil function.
55. The birefringent device of claim 37, wherein the birefringent
device comprises a first structure in which the refractive index
effective for the first polarization state changes with increasing
distance to the symmetry point and a second structure in which the
refractive index effective for the second polarization state
changes with increasing distance to the symmetry point.
56. An optical device comprising: a lens unit; an image sensor unit
arranged in the image plane of the lens unit; and the birefringent
device of claim 37, wherein the birefringent device is arranged
with a symmetry point of the pupil functions on an optical axis of
the optical device.
57. The optical device of claim 56, wherein the first pupil
function is assigned to a first point spread function and the
second pupil function is assigned to a second point spread
function, the first point spread function being symmetric to the
second point spread function with respect to an image plane of the
optical system.
58. The optical device of claim 56, wherein the birefringent device
comprises a plurality of spatially separated sub-devices realizing
different pupil sub-functions, the different sub-functions
resulting in the first and second pupil functions, wherein the
sub-devices are arranged in the optical path of the optical
system.
59. The optical device of claim 58, wherein the birefringent device
comprises a first sub-device realizing the first pupil function and
a second sub-device realizing the second pupil function.
60. The optical device of claim 58, wherein at least one of the
sub-devices is formed as a coating on an element of the lens
unit.
61. The optical device of claim 60, wherein the coating has a
refractive index gradient defining or contributing to a definition
of the respective pupil function.
62. The optical device of claim 60, wherein the coating has a
thickness variation gradient defining or contributing to a
definition of the respective pupil function.
63. An optical device, comprising: a lens unit; an image sensor
unit arranged in the image plane of the lens unit; and the
birefringent device of claim 43, wherein the birefringent device is
arranged with a symmetry point on an optical axis of the optical
device and comprises two carrier substrates arranged in parallel
and a liquid crystal material filling a gap between the two carrier
substrates, at least one of the carrier substrates comprising an
alignment layer for defining an alignment direction of a crystal
axis of the liquid crystal, an orientation of the alignment layers
defining or contributing to a definition of the pupil
functions.
64. The optical device of claim 63, further comprising: transparent
electrodes on at least one of the carrier substrates; and a control
unit configured to control an orientation of the crystal axis of
the liquid crystal continuously.
65. The optical device of claim 63, further comprising: transparent
electrodes on at least one of the carrier substrates; and a control
unit configured to switch an orientation of the crystal axis of the
liquid crystal between a first orientation and a second orientation
different from the first orientation.
66. The optical device of claim 63, further comprising: transparent
electrodes on at least one of the carrier substrates; and a control
unit configured to switch an orientation of the crystal axis of the
liquid crystal out of a plane parallel to surfaces of the carrier
substrates.
67. The optical device of claim 63, further comprising: transparent
electrodes on at least one of the carrier substrates; and a control
unit configured to switch an orientation of the crystal axis of the
liquid crystal parallel to a plane parallel to surfaces of the
carrier substrates.
68. An optical device comprising: a lens unit; an image sensor unit
arranged in the image plane of the lens unit; and the birefringent
device of claim 37, wherein the birefringent device is arranged
close to the aperture stop of the lens unit.
69. The optical device of claim 56, wherein the birefringent device
is formed as a coating on an element of the lens unit.
70. The optical device of claim 69, wherein the coating has a
refractive index gradient defining or contributing to a definition
of the pupil function.
71. The optical device of claim 69, wherein the coating has a
thickness variation gradient defining or contributing to a
definition of the pupil function.
72. The optical device of claim 69, wherein the coating comprises a
birefringent material, the extraordinary axis of the birefringent
material changing laterally to form a pattern defining or
contributing to a definition of the pupil function.
Description
[0001] Embodiments of the invention relate to the field of imaging
techniques, to application specific birefringent devices used in
optical imaging devices, optical systems including the birefringent
device and methods for designing and manufacturing birefringent
devices.
[0002] In optical devices like cameras for consumer, industrial or
medical applications conventional focusing techniques are based,
for example, on the use of a multitude of lenses and a focusing
device that is moved with respect to an image plane. Alternatively,
the depth of field may be extended. The various EDoF (extended
depth of field) techniques can be assigned to one of the following
approaches respectively:
[0003] In accordance with a first approach, the focus position may
be shifted across a broad range of distances during exposure. The
image is reconstructed by means of a deconvolution process in an
image post-processing unit.
[0004] A second approach is based on wavelength separation. For
example, Guichard: "Extended Depth-of-Field Using Sharpness
Transport across Color Channels"; SPIE; Proceedings of Electronic
Imaging; 2009 relies on a robust estimator that determines the
colour channel for which the object is in focus, i.e. sharply
imaged. High spatial frequencies are transported into the other
colour channels for which the object is out of focus and hence
slightly blurred.
[0005] A third approach refers to techniques providing a PSF (point
spread function) or, equivalently, a MTF (modulation transfer
function) that is sufficiently defocus-invariant, i.e. constant for
a large range of object distances. In general, these techniques
shape the pupil function of an optical system in a way to generate
the defocus-invariant PSF or MTF.
[0006] Since the pupil function is a complex function, the third
approach techniques can be assigned to one of two sub-categories
respectively. The first sub-category refers to shaping the phase of
the pupil function and the second one to shaping the amplitude of
the pupil function.
[0007] As an example of the first sub-category, Dowski and Cathey:
"Extended depth of field through wavefront coding"; Applied Optics;
Vol. 34, No. 11, 1995 and U.S. Pat. No. 5,748,371 describe a
wavefront coding technique which provides affecting only the phase
of the pupil function for avoiding intensity loss in the
transmitted light.
[0008] An example for shaping the pupil function to obtain a
desired PSF but without targeting EDoF is discussed in
Bhattacharya, Chakraborty and Ghosh: "Simulation of Effects of
Phase and Amplitude Coatings on the Lens Aperture with Polarization
Masks"; J. Opt. Soc. Am. A; Vol. 11, No. 2; February 1994, where
the effects of a pupil mask with a central portion masked by a
first polarizer having a first transmission axis and an annular
portion masked by a second polarizer having a second, different
transmission axis are simulated. As another example, Asakura and
Mishina: "Diffraction by Circular Apertures with a Ring-Shaped
.pi.-Phase Change"; Japanese Journal of Applied Physics; Vo. 9; No.
2 February 1970 deal with the three-dimensional irradiance
distribution by circular apertures with a ring-shaped it-phase
change.
[0009] Another example of shaping the phase of the pupil function
is described by Sanyal and Ghosh: "Frequency Response
Characteristics of a Birefringent Lens"; Applied Optics; Vol. 31;
No. 25; 1992. They provide a birefringent lens made of an uniaxial
crystal, whose optic axis is perpendicular to the principal axis
and which is placed between two linear polarizers for defining an
amplitude mask, a phase mask, a complex mask or a polarization
mask.
[0010] In addition, U.S. Pat. No. 7,061,693 refers to an
arrangement including an imaging lens and an optical element
configured as a phase-affecting, non-diffractive optical element,
in other words a phase mask, defining a spatially low frequency
phase transition.
[0011] As an example of a method of the second sub-category,
Welford: "Use of Annular Apertures to Increase Focal Depth"; J.
Opt. Soc. Am. A; Vol. 50; 1960 refers to a method manipulating or
shaping the amplitude of the pupil function in order to increase
the depth of field.
[0012] A fourth EDoF approach relies on polarization separation.
For example, WO2007/122615 refers to a birefringent plate, which is
configured such that a refraction index of this plate for a light
component of one polarization state passes an effective optical
path to the detector plane as if the detector is positioned in an
imaging plane corresponding to a far-field imaging condition, and a
refractive index for a light component of the other polarization
state passes through the effective optical path to the detector
plane as if the detector is positioned as required for a near-field
imaging condition. The focal planes for the two polarization states
are axially displaced to each other. An image post-processing
process is provided to restore the original image from the degraded
image received at the detector plane.
[0013] U.S. Pat. No. 7,405,883 refers to an optical low-pass filter
and describes a method of manufacturing optical components for
phase control of light by generating refractive index-change
regions in a transparent device through multi-photo absorption
processes induced by irradiation with a pulsed laser beam.
[0014] It is an object of the invention to provide optical systems
for optical devices with improved imaging characteristics. This
object is achieved by the subject-matter of the independent claims.
Further embodiments are defined in the dependent claims
respectively. Details of the invention will become more apparent
form the following description of embodiments in connection with
the accompanying drawings. Features of the different embodiments
may be combined unless they exclude each other.
[0015] FIG. 1A is a schematic view of an optical system with a
one-piece birefringent device arranged between a focusing lens unit
and an image sensor unit in accordance with an embodiment of the
invention.
[0016] FIG. 1B is a schematic view of an optical system with a
one-piece birefringent device arranged between an entrance of the
optical system and a focusing lens unit in accordance with another
embodiment of the invention.
[0017] FIG. 1C is a schematic view of an optical system with a
two-piece birefringent device arranged between a focusing lens unit
and an image sensor unit in accordance with a further embodiment of
the invention.
[0018] FIG. 1D is a schematic view of an optical system with a
birefringent device realized as a coating of an optical element of
the optical system in accordance with another embodiment of the
invention.
[0019] FIG. 2A is a schematic cross-sectional view of a one-piece
birefringent device of homogeneous thickness according to another
embodiment.
[0020] FIG. 2B is a schematic diagram illustrating the refractive
index of the birefringent device of FIG. 2A.
[0021] FIG. 3A is a schematic cross-sectional view of a two-piece
birefringent device with two structures of homogeneous thickness
according to another embodiment.
[0022] FIG. 3B is a schematic diagram showing the refractive index
of the birefringent device of FIG. 3A.
[0023] FIG. 4A is a schematic diagram showing a discretized angle
of the pupil function for a first polarization direction provided
by a birefringent device according to an embodiment.
[0024] FIG. 4B is a schematic diagram showing a discretized angle
of the pupil function for a second polarization direction provided
by the birefringent device of FIG. 4A.
[0025] FIG. 5A is a schematic cross-sectional view of a
birefringent element having a continuous impurity gradient
according to another embodiment.
[0026] FIG. 5B is a schematic cross-sectional view of a
birefringent device with a birefringent element having a stepped
thickness gradient according to another embodiment.
[0027] FIG. 5C is a schematic cross-sectional view of a
birefringent device with a birefringent element having a linear
thickness variation and a matching layer in accordance to a further
embodiment.
[0028] FIG. 5D is a schematic cross-sectional view of a
birefringent device with a birefringent element formed as a
coating.
[0029] FIG. 5E is a schematic cross-sectional view of a
birefringent device with a birefringent element formed by a liquid
crystal.
[0030] FIG. 5F is a schematic cross-sectional view of a
birefringent device with a birefringent element formed by a nano
grating.
[0031] FIG. 6 is a schematic diagram of a through focus MTF for
defining the pupil functions in accordance with embodiments of the
invention.
[0032] FIG. 7A is a schematic cross-sectional view of a
birefringent device including a circular section and an annular
section in accordance with another embodiment referring to extended
depth of field.
[0033] FIG. 7B is a schematic plan view of the birefringent device
of FIG. 7A.
[0034] FIG. 1A shows a portion of an optical system 100 of an
optical device, which may be, by way of example, an optical imaging
device like a camera for consumer, industrial, surveillance or
medical applications or an apparatus including a camera, for
example a PDA (personal digital assistant), cell phone, computer,
optical reading device, or iris recognition apparatus.
[0035] The optical system 100 may comprise a lens unit 120 and an
image sensor unit 130 arranged in the image plane of the lens unit
120. A birefringent device 110 is arranged in an optical axis 140
of the optical system 100. The optical system 100 guides
non-polarized or orthogonally polarized radiation, for example
visible light, to the birefringent device 110 and to the image
sensor unit 130. The birefringent device 110 is configured to be
mounted in the optical path of the optical device 100 and may have
fixing and adjustment means, for example at or near the periphery
and outside an effective area provided in the aperture (pupil) of
the optical device 110. For example, the birefringent device 110
may be arranged close to the pupil plane of the optical system.
According to an embodiment, the birefringent device 110 is arranged
close to or at an aperture stop of the lens unit 120 or the optical
system 100. The effective area of the birefringent device 110
affects the radiation (light) guided through the optical system 100
to the image sensor unit 130.
[0036] The birefringent device 110 affects different polarization
directions of the non-polarized or orthogonally polarized light
differently at different positions of a pupil plane. The
birefringent device 110 may be configured to realize a first pupil
function assigned to a first polarization direction and a second,
different pupil function assigned to a second, different
polarization direction, wherein the first and second polarization
directions may refer to orthogonal, linear polarization directions.
For example, the first polarization direction may be a horizontal
polarization and the second polarization direction a vertical
polarization. Other than a birefringent device sandwiched between
two polarizators (polarizers), the birefringent device 110 affects
more than one polarization direction.
[0037] The first and second pupil functions express the effect of
the birefringent device 110 on the phase and the amplitude of the
electromagnetic vectors associated to the two polarization
directions of the light passing through the birefringent device
110. The pupil functions are determined such that at different
positions of the birefringent device 110 light of the first
polarization direction is affected differently and light of the
second polarization direction is affected differently. Though the
pupil functions for both polarization states may be correlated,
they can be designed differently in order to improve the
performance or to extend the functionality of the optical
device.
[0038] The option of shaping two pupil functions provides
additional degrees of freedom for improving the performance of the
optical system. With regard to optical imaging devices, the pupil
functions may be shaped for extending the depth of field. The
degree of design freedom is high compared with conventional wave
front coding approaches for shaping the depth of field.
[0039] The pupil functions may be shaped by varying the orientation
of the crystal axes of the birefringent material across the pupil.
According to other embodiments, the thickness of a birefringent
layer may be varied position-dependently. Further embodiments
concern the variation of other optical properties, for example the
refractive indices for two polarization states across the
birefringent device 110.
[0040] Other embodiments may use any combination of crystal axis
distortion, thickness variation and variation of optical
properties. All these degrees of design freedom can be utilized in
an optimization procedure in order to achieve specific optical
properties. The optimization may be carried out by a simulation
model and some optimization algorithms, like for example particle
swarm optimization or damped least squares, that run on a processor
or a computer, wherein from the desired properties of the optical
imaging device an objective function is derived that defines the
target of the optimization process,
[0041] In accordance with an embodiment, the total pupil function
of the birefringent device 110 is rotationally symmetric with
respect to a symmetry point such that a rotation by an angle of
360.degree./n, n=1, 2, 3 . . . , does not change the pupil
function, wherein the birefringent device 110 is arranged with the
symmetry point on the optical axis 140. In accordance with an
embodiment, both pupil functions are point-symmetric such that a
rotation by an angle of 360.degree./(2n), n=1, 2, 3 . . . , does
not change the pupil function. For example, both pupil functions
may be circularly symmetric and are functions of the distance from
the symmetry point only.
[0042] According to an embodiment referring to extended depth of
field, the first pupil function may be the complex conjugate of the
second pupil function, wherein none of the pupil functions is
"flat" in the sense that it affects the light beams homogenously.
In other words, the slope or first derivation of the pupil function
with regard to at least one of the coordinates is not equal zero,
at least not over the whole effective area. For example, the pupil
functions are step functions where the slope is not equal zero at
the step. Providing a birefringent device with one of its pupil
functions being the complex conjugate of the other may be used in
combination with digital post-processing for image reconstruction
for extending the depth of field of an optical imaging.
[0043] These embodiments basically rely on manipulating the phase
of the pupil function for designing or shaping the modulation
transfer function in an optical path. In contrast to conventional
pupil masks, a symmetric through focus modulation transfer function
can be provided, although rotationally symmetric pupil functions
are utilized.
[0044] Provided a suitable design of the pupil functions in the
framework of the above described restrictions, an optical device
equipped with the birefringent device 110 facilitates a modulation
transfer function that exhibits extended depth of field properties.
In accordance with an embodiment, where the total pupil function of
the birefringent device 110 is point-symmetric, for example
circularly symmetric, and where the birefringent device 110 is
arranged with the symmetry point on the optical axis 140, the
birefringent device 110 avoids an unwanted displacement of high
spatial frequency structures with respect to low spatial frequency
structures, i.e. the optical transfer function is real. Point
symmetry might be referred to by p(x,y)=p(-x,-y), assuming the
symmetry point is at (0,0) and x and y are Cartesian coordinates in
a pupil plane.
[0045] The birefringent device 110 may affect both amplitude and
phase of the wavefront.
[0046] In accordance with an embodiment, the birefringent device
110 exclusively affects the phase. The equations (1) and (2) refer
to such an embodiment and describe the first pupil function
P.sub.1(x) assigned to the first polarization direction and the
second pupil function P.sub.2(x) assigned to the second
polarization direction, wherein x denotes a space coordinate in the
pupil plane. The description refers only to x as one of the two
space coordinates in the pupil plane for simplicity. The first
pupil function P.sub.1(x) is designed to be the complex conjugate
of the second pupil function P.sub.2(x) such that the birefringent
device 110 acts differently for both polarization directions:
P.sub.1(x)=exp{+i(.theta.(x)+.PSI.x.sup.2)} (1)
P.sub.2(x)=exp{-i(.theta.(x)-.PSI.x.sup.2)} (2)
[0047] The one-dimensional function .theta.(x) represents the
manipulation of the angle of the complex pupil function that is
caused by the birefringent device. .PSI. represents the defocus.
.PSI. is zero for light from the focus position. For .PSI.>0,
the pupil function of a beam assigned to the first polarization
direction is the complex conjugate of the pupil function of a beam
assigned to the second polarization direction for a defocus of
-.PSI. and vice versa. Due to this kind of symmetry, the through
focus MTF becomes symmetric with respect to the focus position.
[0048] If in the optical system 100 the respective numerical
apertures are not too high, the squared modulus of the Fourier
Transform of the pupil function is a good approximation for the
intensity point spread function. It can be shown that with complex
conjugated pupil functions the point spread functions for the first
and second polarization directions simply interchange their effects
once the defocus value changes its sign. In other words, if the
first pupil function is assigned to a first point spread function
and the second pupil function is assigned to a second point spread
function, then the first point spread function is symmetric to the
second point spread function with respect to the image plane.
[0049] And since both states of polarization do not interfere with
each other, the respective point spread functions just add on an
intensity basis. Thus, for unpolarized light, in the ideal case, it
will be impossible to differentiate between positive and negative
values of defocus. In addition, the total pupil function of an
optical system comprising the birefringent device 110 exhibits an
identical shape for positive and negative values of the same
magnitude of defocus such that the through focus modulation
transfer function of the system is symmetric. Moreover, in
accordance with other embodiments, the birefringent device 110 is
utilized and designed for realizing an optical low-pass filter.
[0050] Versus a birefringent plate with only one degree of freedom
for the design of the combined PSF or OTF (optical transfer
function), namely the axial displacement as described in
WO2007/122615A2, the performance of the approach according to the
embodiments is less restricted. Other than known techniques
following the third EDoF approach discussed in the background
section, the birefringent device 110 provides both a symmetric
through focus MTF and an OTF that is real, whereas the conventional
techniques achieve either a symmetric through focus MTF or an OTF
that is real.
[0051] In other words, if the first pupil function is assigned to a
first point spread function and the second pupil function is
assigned to a second point spread function, then the first point
spread function is, in the ideal case, symmetric to the second
point spread function with respect to the image plane. However, an
asymmetry may be induced by the numerical apertures, which are not
identical if the point spread functions are considered at two
different positions along the optical axis. Since the point spread
function scales with the numerical aperture, the PSFs in front of
and behind the actual image plane may differ in size.
[0052] In the following, the differences to two different
conventional types of phase manipulation according to the third
EDoF approach will be elucidated. According to a first conventional
approach the cross-section of the phase profile through the center
of pupil exhibits the symmetry of an odd function. Then the through
focus MTF is symmetric. Hence, high and low spatial frequency
structures degrade in the same manner with increasing distance to
the focus position of the system. But the angle of the complex
optical transfer function becomes non-zero and hence spatial
structures are laterally displaced depending on their spatial
frequency and the amount of defocus. In other words, only the
magnitude of the OTF, i.e. the MTF is defocus invariant, but not
the angle of the OTF. This can lead to severe imaging artefacts
during image reconstruction.
[0053] According to a second conventional approach covered by the
third EDoF approach, the cross-section of the phase profile
exhibits the symmetry of an even function. Then the symmetry of the
phase profile does not cause any lateral displacement but it leads
to an asymmetry of the through focus MTF. Since high and low
spatial frequency structures do not degrade in the same manner with
increasing distance to the in focus position of the system, the
image looses either contrast or resolution depending on the sign of
the defocus value.
[0054] Both effects, the displacement of structures and the
non-symmetric behaviour of the through focus MTF, cannot be
compensated with a non-blind deconvolution process. With the
birefringent device 110, however, both shortcomings can be
overcome. In addition, the birefringent device 110 provides a high
degree of freedom for designing the modulation transfer function of
the optical system without using complex shaped lenses, which could
lower the production yield or increase production costs.
[0055] Summarizing, the birefringent device 110 overcomes the
following shortcomings and disadvantages of other approaches for
extending the depth of field:
[0056] Although the pupil functions may be provided rotationally
symmetric, the through focus modulation transfer function can be
provided symmetric with respect to an in focus position, if the
phase profile for the first and second polarization directions is
designed appropriately. This is typically not possible with such
state of the art techniques of pupil function engineering that
manipulate the pupil function for both polarization directions
identically.
[0057] In addition, if the birefringent device is designed to be
rotationally symmetric, the optical transfer function of the system
will be real and hence spatial structures will not be
displaced.
[0058] Regarding approaches referring to a rotationally symmetric
manipulation of the amplitude of the pupil function in a way such
that a symmetric behaviour of the through focus modulation transfer
function is achieved, a significant loss of light can be avoided
with the birefringent device 110, for example by pupil functions
manipulating the phase exclusively. Moreover, the birefringent
device 110 facilitates a greater extension of depth of field than
amplitude manipulation.
[0059] With regard to approaches using colour channels, utilizing
the birefringent device 110 does not necessarily require estimators
for blind image convolution in an image post-processing unit.
Hence, the whole image post-processing required for image
reconstruction is robust, since no wrong decisions of an estimator
can cause erroneous results.
[0060] Returning to FIG. 1A, the birefringent device 110 may have a
position-dependent first refractive index effective for the first
polarization state and a position-dependent second refractive index
effective for the second polarization state, wherein each of the
first and second refractive indices takes at least two different
values. The gradients of the first and second refractive indices
may be point-symmetric, for example circularly symmetric, with
respect to a symmetry point positioned on the optical axis 140 of
the optical system 100. In accordance with an embodiment, the
gradient of the second refractive index is the complex conjugate of
the gradient of the first refractive index such that the depth of
field is significantly increased.
[0061] In accordance with another embodiment, the birefringent
device 110 includes a birefringent element of one or more
birefringent materials, wherein an orientation of an extraordinary
axis of the birefringent material is position-dependent and varies
across the birefringent element in a plane perpendicular to the
optical axis of the optical system 100. According to an embodiment,
the direction of the extraordinary axis changes laterally, for
example radially, within the plane perpendicular to the optical
axis 140 to form a pattern defining the pupil functions for the
first and second polarization states completely. According to
another embodiment, a pattern formed by the lateral change of the
extraordinary axis contributes to the pupil functions for the first
and second polarization states. The variation may be
point-symmetric, for example circularly symmetric.
[0062] According to a further embodiment a thickness of one or more
birefringent materials of the birefringent element may be
position-dependent and may vary across the birefringent element
within a plane perpendicular to the optical axis (140) to form a
pattern that defines or contributes to the definition of the pupil
functions. For example, a thickness gradient of the at least one
birefringent material may be point-symmetric, for example
circularly symmetric.
[0063] Other embodiments may combine at least two or all of
refractive index variation, crystal axis distortion and thickness
variation for shaping the pupil functions in order to obtain an
objective function representing the desired functionality.
[0064] FIG. 1B shows another optical system 100, where a
birefringent device 110 is a one-piece device arranged between an
entrance of the optical system 100 and a lens unit 120 focusing the
incoming light on an image sensor unit 130. An effective area of
the birefringent device 110 is within the aperture of the optical
system 100.
[0065] The birefringent device 110 may be a non-lensing device
which does neither converge nor diverge light beams passing through
the birefringent device. According to other embodiments, the
birefringent device may be additionally configured to correct
aberrations caused elsewhere in the optical system 100, for example
in the lens unit 120.
[0066] According to an embodiment, both pupil functions may be
rotational symmetric, for example point-symmetric or circularly
symmetric. The birefringent device 110 may be a one-piece device
merging both pupil functions. According to further embodiments, the
lens unit 120 may comprise more than one element, and the
birefringent device 110 may be arranged between two lens unit
elements.
[0067] FIG. 1C refers to further embodiments providing the
birefringent device 110 as a plurality of spatially separated
sub-devices realizing different pupil sub-functions, wherein the
sum of the different sub-functions result in the sum of the first
and second pupil functions. For example, as illustrated in FIG. 1C,
the birefringent device 110 may be a two-piece device, wherein a
first sub-device 112 may realize the first pupil function and a
second sub-device 114 may realize the second pupil function. All
sub-devices 112, 114 are arranged between the entrance of the
optical device 100 and the image plane. For example, according to
the illustrated embodiment, all (both) sub-devices 112, 114 may be
arranged between the lens unit 120 and the image sensor unit 130.
According to other embodiments, all (both) or at least one of the
sub-devices 112, 114 may be arranged between the entrance of the
optical device 100 and the lens unit 120.
[0068] FIG. 1D refers to embodiments providing at least a portion
112, 114 of the birefringent device 110 as a coating. The coating
may me provided at any transparent element arranged in the optical
path of the optical system 100, for example on one element or more
elements of the lens unit 120. The pupil function may be realized
by locally varying a refractive index, for example by varying
physical and/or chemical properties of the coating over the
effective area. In accordance with another embodiment, the coating
has a thickness gradient in conformity with the respective pupil
function. According to other embodiments, the pupil function of the
coating results from a combination of thickness and refractive
index variations.
[0069] According to an embodiment, the coating is a liquid crystal
that is aligned and fixed during manufacturing. According to
another embodiment, the birefringent device is realized by a liquid
crystal layer which orientation of the extraordinary axis is
controllable by a control unit 180. For example, the orientation of
the liquid crystal can be switched between two different
directions. The control unit 180 may activate and deactivate an
extended depth of field feature of the optical system 100 without
requiring any movable mechanical components. Moreover, a liquid
crystal coating may also allow continuously changing the
birefringent pupil function.
[0070] FIG. 2A illustrates a one-piece birefringent device 110
comprising a birefringent element 111 of homogenous thickness. The
material of the birefringent element 111 may be any suitable
material showing birefringence, for example YVO.sub.4, calcite,
MgF.sub.2, SiO.sub.2, a liquid crystal or stretched polymers.
According to an embodiment the material of the birefringent element
111 is a liquid crystal or a plastics like polycarbonate. The
thickness of the birefringent element 111 is at least 0.3 .mu.m and
at most 200 .mu.m, for example at least 1.5 .mu.m and at most 55
.mu.m in connection with birefringence values from 0.01 to 0.3 and
a phase change of n for radiation having a wavelength of 530
nm.
[0071] The diagram in FIG. 2B illustrates an example for a first
refractive index gradient n.sub.1(r,.phi.) effective for the first
polarization direction and a second refractive index gradient
n.sub.2(r,.phi.) effective for the second polarization direction.
The refractive index gradients n.sub.1(r,.phi.), n.sub.2(r,.phi.)
are non-flat, i.e. the slopes (also "first derivations") of the
refractive index gradients are not equal zero at least in a portion
of the effective area defined by the exit or entrance pupil of the
respective optical system. Apart from this requirement, the actual
refractive index gradients of n.sub.1(r,.phi.), n.sub.2(r,.phi.)
may be adapted to the respective application. However, regardless
of the respective application, the refractive index gradients
n.sub.1(r,.phi.), n.sub.2(r,.phi.) of the birefringent element 111
are characterized in that they lead to pupil functions that are
conjugate complex for the different polarizations.
[0072] The refractive index gradients may be rotational-symmetric
to a symmetry point, which may be the center point of the effective
area of the birefringent element 111. Typically, the effective area
of the birefringent element 111 is a circle area. One of the
refractive index gradients may monotonically increase either in
steps or continuously with increasing distance to the center point.
According to other embodiments, one of the refractive index
gradients may strictly monotonically increase with increasing
distance to the center point or may increase exponentially, either
continuously or in discrete steps. According to other embodiments,
the refractive index gradients may have one or more maxima or
minima between the center point and the outer periphery of the
effective area.
[0073] FIGS. 3A and 3B refer to an embodiment where the
birefringent device 110 comprises a first structure 121 in which
the refractive index effective for the first polarization state
changes with increasing distance to the symmetry point and a second
structure 122 in which the refractive index effective for the
second polarization state changes with increasing distance to the
symmetry point. In accordance with the illustrated embodiment, the
refractive indices n.sub.1(r,.phi.), n.sub.2(r,.phi.) change in
discrete steps.
[0074] FIG. 4A is a schematic diagram showing a discretized angle
of the pupil function for a first polarization state provided by a
birefringent device according to an embodiment. The discretized
phase angle of the pupil function is circularly symmetric and
strictly monotonic increasing with increasing distance to a center
point of the birefringent device. The phase angle is flat and low
in a central portion up to about 85% of the radius R, is flat and
high in an annular portion of the effective area, and has a steep
transition between the two portions.
[0075] FIG. 4B shows the corresponding discretized angle of the
pupil function for the second polarization state provided by the
same birefringent device. A modulation transfer function for
unpolarized light resulting from these pupil functions is almost
constant up to three values of defocus in units of the Rayleigh
depth of field. In addition, the MTF shows a pronounced drop such
that the birefringent device fulfilling the described requirements
can also be used for an optical low-pass filter for avoiding
aliasing. In this case, the MTF should stay rather high for a range
of spatial frequencies up to the Nyquist frequency of the image
sensor and then drop steeply to zero. In accordance with further
embodiments of the invention, the birefringent device provides
pupil functions that facilitate both optical low-pass filtering and
extended depth of field.
[0076] FIG. 5A refers to a sub-device 112 of a birefringent device
with a birefringent element 111 formed as a transparent plate
having a continuous refractive index gradient according to another
embodiment. The continuous refractive index gradient may be
generated by varying locally an impurity concentration in the
transparent plate 111, by way of example. The impurity
concentration may increase or decrease with increasing distance to
a center point.
[0077] Another birefringent device 110 is illustrated in FIG. 5B.
The birefringent device 110 may comprise a transparent substrate
119 and a birefringent element formed by birefringent material 116
arranged on the transparent substrate 119. The thickness of the
birefringent material 116 varies in a staggered manner, wherein the
thickness changes in steps. The varying thickness of the
birefringent material 116 varies the optical path length for the
first and second polarization directions. A compensation layer 118
may be provided which may have the negative thickness gradient of
the birefringent material and which compensates for the optical
path length differences. For example, the compensation layer 118
may have a refractive index that is half the sum of the
extraordinary index of refraction n.sub.e and the ordinary index of
refraction n.sub.o of the birefringent material 116. Other
embodiments of the birefringent device 110 may be provided without
a transparent substrate 119.
[0078] The birefringent device 110 illustrated in FIG. 5C provides
a transparent substrate 119 as a carrier for a birefringent element
111 showing a linear thickness variation from a center point to a
perimeter. In addition, the birefringent device 110 comprises a
compensation layer 117 compensating for optical path length
differences between the two polarization directions.
[0079] FIG. 5D refers to a birefringent element 111 provided as a
coating 116 on one of the optic elements 102 of an optical system
100. The coating 116 may include at least two different portions
116a, 116b, 116c for realizing one or two or all of refractive
index variation, crystal axis distortion and thickness variation
for shaping the pupil functions. According to other embodiments,
the refractive index variation, crystal axis distortion and/or
thickness variation change gradually.
[0080] FIG. 5E shows a birefringent device 110 including a liquid
crystal 155 as birefringent element. The birefringent device 110
may further comprise two carrier substrates 152, 158 arranged in
parallel, wherein the liquid crystal 155 fills a gap between the
two carrier substrates 152, 158. One or both of the carrier
substrates 152, 158 may include an alignment layer 154, 156 that
align the liquid crystal molecules of the liquid crystal 155 in a
predefined alignment direction. The alignment direction may be
position-dependent, for example may vary circularly symmetric to a
centre point. The predefined alignment directions may define the
pupil functions completely or may at least contribute to the
definition of the pupil functions.
[0081] According to an embodiment, the alignment layers are based
on polymers and the orientation of at least one of the alignment
layers 154, 156 may be fixed by linear photopolymerization.
According to another embodiment, the liquid crystal 155 is a liquid
crystal polymer and the orientation of the liquid crystal polymer
is fixed by curing the polymer with UV light.
[0082] According to another embodiment, the birefringent device 110
may further comprise one or more transparent electrodes 159
arranged at least on one of the carrier substrates 152, 158. A
control unit 180 may be connected with the transparent electrodes
159 and may control the orientation of the crystal axis of the
liquid crystal 155 by applying suitable voltages to the transparent
electrodes 155. Separately controllable sections 159a, 159b, 159c
of at least one of the transparent electrodes 159 may be assigned
to different regions of the liquid crystal 155, for example to a
circular region and one or more annular regions surrounding the
circular region.
[0083] In accordance with an embodiment, the control unit 180 is
configured to control the orientation of the crystal axis
contiguously such that the orientation of the complete liquid
crystal 155 or a section of the liquid crystal 155 can be adjusted
to an arbitrary angle between a minimum and a maximum value.
According to another embodiment the control unit 180 controls the
orientation in steps. According to a further embodiment, the
control unit 180 switches the orientation of the crystal axis of
the liquid crystal 155 between a first orientation and a second
orientation differing from the first orientation.
[0084] For example, the control unit 180 may switch the orientation
of the crystal axis of the liquid crystal 155 out of a plane
parallel to surfaces of the carrier substrates 152, 158 and/or
parallel to the plane parallel to the surfaces of the carrier
substrates 152, 158.
[0085] FIG. 5F refers to an embodiment with a birefringent element
formed as a nano grating 165 on a surface of a substrate 161 having
an extraordinary refractive index parallel to the substrate
surface. The nano grating can be formed by nano imprinting
techniques. The pattern of the nano grating may vary continuously
or in steps.
[0086] FIG. 6 shows an example for a through focus MTF for one
particular spatial frequency and which may be realized with a
birefringent device according to the invention.
[0087] FIG. 7A illustrates a further one-piece birefringent device
110 comprising a transparent element 119 and a birefringent element
111 of homogenous thickness disposed on one side of the transparent
element 119. The birefringent element 111 has an inner circular
zone (section) 171 and an outer annular zone (section) 172 directly
adjacent to the inner circular zone 171. The material of both zones
171, 172 may be the same birefringent material. In the annular zone
172 the birefringence axes of the birefringent material are rotated
against that in the circular section 171 by 90 degrees such that
the two birefringence axes are interchanged. According to other
embodiments, the birefringent device 110 may include more than one
annular zone with differing orientation of the birefringence axes.
Other embodiments may provide a circular zone and/or one or more
annular zones without birefringence, for example in addition to at
least two zones with differing orientation of the extraordinary
axes.
[0088] The arrows depicted in FIG. 7B indicate for both zones 171,
172 that polarization direction which is affected by the ordinary
index of refraction n.sub.o and that polarization direction which
is affected by the extraordinary index of refraction n.sub.e.
[0089] A crystal axis of the birefringent material is aligned in an
xy-plane that is perpendicular to an optical axis 140 of an image
device in which the birefringent device 110 is arranged. The
orientation of the crystal axis of the birefringent material
changes by 90 degrees for the different zones 171, 172. Since in
both zones 171, 172 the crystal axis is perpendicular to the
optical axis 140, the birefringent device 110 can be considered to
be an a-plate type wave plate. In accordance with other
embodiments, the orientation of the crystal axis may continuously
change between the centre point and the perimeter, for example in
an annular region.
[0090] The material of the birefringent element 111 may be any
suitable material showing birefringence, for example YVO.sub.4,
calcite, MgF.sub.2, SiO.sub.2, a liquid crystal or a plastics like
polycarbonate. For example, the birefringent material of the
circular section 171 has a refractive index n.sub.o for the
ordinary beam and a refractive index n.sub.e for the extraordinary
beam which differs from n.sub.o. For example n.sub.e may be about
1.662 and n.sub.o about 1.582. The difference An at a wavelength of
530 nm may be 0.08. Then the annular section 172, which is from the
same material but which is rotated by 90 degrees, has an n.sub.o of
about 1.662 and an n.sub.e of about 1.582. In order to achieve an
optical path difference of about .lamda./2 at a wavelength of 530
nm, the thickness of the birefringent element may be about 3.3
.mu.m. The birefringent device 110 as described here may provide
the phase profile as illustrated in FIGS. 4A, 4B.
[0091] As shown in FIG. 7B, the ratio between the radius of the
circular section 171 and the width of the annular section 172 may
be about 4:1. The total diameter of the birefringent element 111
may be in the range of 0.5 mm and 2 mm.
[0092] According to an embodiment, a method of manufacturing an
optical system comprises defining an application specific symmetric
MTF or a real OTF. Then, from the MTF or the OTF a set of two
complex conjugate pupil functions is derived. A birefringent device
is formed realizing the two complex conjugate pupil functions.
[0093] According to another embodiment first an objective function
(target function) is defined that represents a desired
functionality, wherein the target function may be a PSF, MTF, OTF,
by way of example. Using a simulation model running on a digital
processing unit. Position-dependent parameters of a birefringent
device are determined to realize the target function, wherein the
parameters are such that they influence different polarization
states differently, like crystal axes orientation, optical material
properties and material thickness. Further, the simulation model
may output parameters for an image restoration program for
restoring the original image from the detected image.
[0094] In accordance with further embodiments, the optical devices
include a processor unit configured to restore an original image
from an image as detected at the image sensor unit.
* * * * *