U.S. patent application number 09/747788 was filed with the patent office on 2002-08-29 for wavefront coded imaging systems.
Invention is credited to Dowski, Edward Raymond JR..
Application Number | 20020118457 09/747788 |
Document ID | / |
Family ID | 25006641 |
Filed Date | 2002-08-29 |
United States Patent
Application |
20020118457 |
Kind Code |
A1 |
Dowski, Edward Raymond JR. |
August 29, 2002 |
Wavefront coded imaging systems
Abstract
The present invention provides improved Wavefront Coding imaging
apparatus and methods composed of optics, detector, and processing
of the detected image. The optics are constructed and arranged to
have the characteristic that the transverse ray intercept curves
form substantially straight, sloped lines. The wavefront coding
corrects for known or unknown amounts of "misfocus-like"
aberrations by altering the optical transfer function of the
imaging apparatus in such a way that the altered optical transfer
function is substantially insensitive to aberrations. Post
processing then removes the effect of the coding, except for the
invariance with regard to aberrations, producing clear images.
Inventors: |
Dowski, Edward Raymond JR.;
(Lafayette, CO) |
Correspondence
Address: |
JENNIFER L. BALES
MOUNTAIN VIEW PLAZA
1520 EUCLID CIRCLE
LAFAYETTE
CO
80026-1250
US
|
Family ID: |
25006641 |
Appl. No.: |
09/747788 |
Filed: |
December 22, 2000 |
Current U.S.
Class: |
359/558 ;
359/362; 359/368; 430/5 |
Current CPC
Class: |
G02B 5/00 20130101; G02B
27/0012 20130101; G02B 27/46 20130101; G02B 27/0025 20130101 |
Class at
Publication: |
359/558 ;
359/362; 359/368; 430/5 |
International
Class: |
G03F 009/00 |
Claims
What is claimed is:
1. Imaging apparatus for imaging an object onto a detector
comprising: a lens structure; the lens structure constructed and
arranged to produce transverse ray intercept curves which are
sloped substantially straight lines; a wavefront coding element
positioned between the object and the detector; the coding element
being constructed and arranged to alter the optical transfer
function of the imaging apparatus in such a way that the altered
optical transfer function is substantially insensitive to
focus-related aberrations over a greater range of aberrations than
was provided by the unaltered optical transfer function; and means
for post processing; wherein the coding element affects said
alteration to the optical transfer function substantially by
affecting the phase of light transmitted by said wavefront coding
element.
2. The apparatus of claim 1 wherein the aberrations include one or
more of the following: misfocus; spherical aberration; petzval
curvature; astigmatism; field curvature; chromatic aberration;
temperature induced misfocus aberration; pressure induced misfocus
aberration; mechanical induced misfocus aberrations.
3. The apparatus of claim 1 wherein the coding element is formed
substantially at an aperture stop of the imaging system.
4. The apparatus of claim 1 wherein the lens structure comprises an
IR imaging system.
5. The apparatus of claim 1 wherein the post processing means
comprises a digital filter.
6. The apparatus of claim 1 wherein the lens structure comprises a
microscope objective.
7. The apparatus of claim 1 wherein the lens structure comprises a
single lens.
8. The apparatus of claim 7 wherein the coding element is formed on
the single lens.
9. The apparatus of claim 1 wherein the detector is an analog
detector.
10. The apparatus of claim 1 wherein the detector is a digital
detector.
11. A single lens imaging system for imaging an object onto a
detector comprising: a lens constructed and arranged to produce
transverse ray intercept curves which are sloped substantially
straight lines; a wavefront coding element formed on a surface of
the lens; the coding element being constructed and arranged to
alter the optical transfer function of the imaging system in such a
way that the altered optical transfer function is substantially
insensitive to focus-related aberrations over a greater range of
aberrations than was provided by the unaltered optical transfer
function; and a post processing element; wherein the coding element
affects said alteration to the optical transfer function
substantially by affecting the phase of light transmitted by said
wavefront coding element.
12. The system of claim 11, wherein the post processing element
comprises a digital filter.
13. The system of claim 12, wherein the digital filter comprises a
rectangularly separable filter.
14. The system of claim 11, wherein the wavefront coding element is
formed on the surface of the lens furthest from the object.
15. The system of claim 11, wherein the lens length is under 10
mm.
16. The system of claim 11, wherein the lens length is under 5
mm.
17. A microscope objective for imaging an object onto a detector
comprising: an element with optical power; the element with optical
power being constructed and arranged to produce transverse ray
intercept curves which are sloped substantially straight lines; a
wavefront coding element; the coding element being constructed and
arranged to alter the optical transfer function of the microscope
objective in such a way that the altered optical transfer function
is substantially insensitive to focus-related aberrations over a
greater range of aberrations than was provided by the unaltered
optical transfer function; and a post processing element; wherein
the coding element affects said alteration to the optical transfer
function substantially by affecting the phase of light transmitted
by said wavefront coding element.
18. The microscope objective of claim 17, wherein the post
processing element comprises a digital filter.
19. The microscope objective of claim 17, wherein the element with
optical power comprises a single lens.
20. The microscope objective of claim 19, wherein the lens is
aspheric.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] U.S. Pat. No. 5,748,371, issued May 5, 1998 and entitled
"Extended Depth of Field Optical Systems," is incorporated herein
by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] This invention relates to apparatus and methods for optical
design based on wavefront coding combined with post processing of
images.
[0004] 2. Description of the Prior Art
[0005] Traditional optical design is based on the premise that the
only major components of the imaging system are the optics and
detector. The detector can be analog (e.g. film) or a digital (
e.g. CCD, CMOS etc.) detector. Traditional image processing
techniques performed on an image are performed after the image is
formed. Examples of traditional image processing include edge
sharpening and color filter array (CFA) color interpolation.
Traditional optics are therefore designed to form images at the
detector that are sharp and clear over a range of field angles,
illumination wavelengths, temperatures, and focus positions.
Consequently, a trade off is made between forming good images,
which requires optical designs that are larger, heavier, and
contain more optical elements than are desirable, and modifying the
design in order to reduce size, weight, or the number of optical
elements, which results in loss of image quality.
[0006] A need remains in the art for improved optical designs which
produce good images with systems that are smaller, lighter, and
contain fewer elements then those based on traditional optics.
SUMMARY OF THE INVENTION
[0007] Optical design based on Wavefront Coding enables systems
that can be smaller, lighter, and contain fewer optical elements
than those based on traditional optics. Wavefront Coding systems
share the task of image formation between optics and digital
processing. Instead of the imaging system being primarily composed
of optics and the detector, Wavefront Coding imaging systems are
composed of optics, detector, and importantly, processing of the
detected image. The detector can in general be analog, such as
film, or a digital detector. Since processing of the detected image
is an integral part of the total system, the optics of Wavefront
Coded imaging systems do not need to form sharp and clear images at
the plane of the detector. It is only the images after processing
that need to be sharp and clear.
[0008] Wavefront Coding, in general, corrects for known or unknown
amounts of "misfocus-like" aberrations. These aberrations include
misfocus, spherical aberration, petzval curvature, astigmatism, and
chromatic aberration. System sensitivities to environmental
parameters such as temperature and pressure induced aberrations,
and mechanical focus related aberrations related to fabrication
error, assembly error, drift, wear, etc., are also reduced with
Wavefront Coding. Optical designs based on Wavefront Coding can
reduce the effects of these aberrations and result in simpler
designs that produce good images.
[0009] Optical system designs according to the present invention
are improved in that they have the characteristic that the
transverse ray intercept curves are substantially straight lines.
Unlike traditional optical designs, the transverse ray intercept
curves for wavefront coded systems need not have a near zero slope;
the slope, which indicates misfocus, may be substantial, because
wavefront coding allows the effects due to misfocus to be removed.
In actual systems the transverse ray intercept curves should vary
mainly in slope over wavelength, field angles, temperature, etc.
but need not be exactly straight lines. Some ripple is acceptable.
With wavefront coding optical surfaces and post processing, good
images can be produced.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 shows a single-lens miniature imaging system
according to the present invention.
[0011] FIG. 2 illustrates a series of transverse ray intercept
curves illustrating aberrations at various wavelengths, for the
system of FIG. 1 with wavefront coding removed.
[0012] FIG. 3 illustrates distortion curves for the system of FIG.
1 with wavefront coding removed.
[0013] FIG. 4 illustrates modulation transfer functions (MTF) for
the system of FIG. 1, with wavefront coding removed.
[0014] FIG. 5 illustrates modulation transfer functions (MTF) for
the system of FIG. 1, with wavefront coding, but without post
processing.
[0015] FIG. 6 illustrates modulation transfer functions (MTF) for
the system of FIG. 1, with wavefront coding, both before and after
filtering.
[0016] FIGS. 7a and 7b illustrates sampled point spread functions
(PSF) for the system of FIG. 1, with wavefront coding and after
filtering, for two object distances.
[0017] FIG. 8 shows a low cost microscope objective according to
the present invention.
[0018] FIG. 9 illustrates a series of transverse ray intercept
curves illustrating aberrations at various wavelengths, for the
system of FIG. 8 with wavefront coding removed.
[0019] FIG. 10 illustrates modulation transfer functions (MTF) for
the system of FIG. 8, without wavefront coding; with wavefront
coding; and with both wavefront coding and filtering.
[0020] FIG. 11 shows a passive athermalized IR imaging system
according to the present invention.
[0021] FIG. 12 illustrates a series of transverse ray intercept
curves illustrating aberrations at various wavelengths, for the
system of FIG. 11, without wavefront coding.
[0022] FIG. 13 illustrates modulation transfer functions (MTF) for
the system of FIG. 11, without wavefront coding.
[0023] FIG. 14 illustrates modulation transfer functions (MTF) for
the system of FIG. 11, with wavefront coding, both with and without
filtering.
[0024] FIG. 15a illustrates transverse ray intercept curves as
typically implemented in traditional imaging systems.
[0025] FIG. 15b shows MTFs for the system of FIG. 15a.
[0026] FIG. 16 illustrates an example of a one dimensional
separable filter for use as a post processing element in the
present invention.
[0027] FIG. 17 illustrates the magnitude of the transfer function
of the filter of FIG. 16.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0028] FIG. 1 shows a single-lens miniature imaging system 100
according to the present invention. Lens 102 includes wavefront
coding element 104 formed on its second surface. Detector 106 is
preceded by an IR filter 108 and cover glass 110. Post processor
112 performs processing on the images captured by detector 106.
[0029] The example single-lens imaging system (singlet) 100 is
designed to meet the following specifications:
[0030] f=2.5 mm
[0031] F/#=2.6
[0032] Length<4.5 mm
[0033] Material: PMMA
[0034] FOV=50.degree.
[0035] Focus: .infin.-30 cm
[0036] pixel size=6 .mu.m
[0037] Bayer CFA/100% fill factor
[0038] MTF>40% at 40 lp/mm
[0039] The example singlet 100, without Wavefront Coding 104, was
designed so that the aberrations that are not corrected by the
optical surfaces, namely petzval curvature and axial chromatic
aberration, are a type of misfocus. Specifically, petzval curvature
is a type of misfocus with field angle, and axial chromatic
aberration is misfocus with illumination wavelength. The effect of
these aberrations could hypothetically be corrected within small
regions of the image plane by changing the focus position. By
adding a Wavefront Coding surface, the resulting modulation
transfer functions (MTFs) and point spread functions (PSFs) will be
insensitive to the focus-like aberrations. However, the MTFs and
PSFs will not be the same as an ideal in-focus MTF or PSF from a
traditional imaging system. Image processing is required to restore
the spatial character of the image and produce a sharp and clear
image.
[0040] The form of the Wavefront Coding surface used in this
example is:
S(x,y)=.SIGMA.a.sub.isign(x).vertline.x/r.sub.n.vertline..sup.b.sub.i+a.su-
b.isign(y).vertline.y/r.sub.n.vertline..sup.b.sub.i
[0041] where the sum is over the index i. Sign(x)=-1 for x<0, +1
for x.gtoreq.0. The parameter r.sub.n is a normalized radius value.
This particular Wavefront Coding surface is rectangularly separable
and allows for fast processing. Other forms of Wavefront Coding
surfaces are non-separable, and the sum of rectangularly separable
forms. One non-separable form is defined as:
S(r,.theta.)=.SIGMA.r.sup.a.sub.i
cos(b.sub.l.theta.+.phi..sub.i)
[0042] where the sum is again over the subscript i.
[0043] There are an infinite number of Wavefront Coding surface
forms. The Wavefront Coding surface for singlet 100 in this example
is placed at the stop surface (surface 104) and has the
parameterized equation:
S(x,y)=.SIGMA.a.sub.isign(x).vertline.x/r.sub.n.vertline..sup.b.sub.i+a.su-
b.isign(y).vertline.y/r.sub.n.vertline..sup.b.sub.i
[0044] and the parameter values for i=1,2,3 are:
[0045] a.sub.1=17.4171, b.sub.1=2.9911
[0046] a.sub.2=10.8895, b.sub.2=6
[0047] a.sub.3=3.8845, b.sub.3=20.1909
[0048] r.sub.n=0.459
[0049] FIGS. 2-4 illustrate the performance of system 100 with
wavefront coding element 104 removed, in order to illustrate design
requirements and performance. FIG. 5 illustrates the performance of
system 100 with wavefront coding element 104 in place, but without
post processing filter 112. FIG. 6 illustrates the performance
improvement with post processing 112. FIGS. 7a and 7b shows point
spread functions for system 100 with both wavefront coding and post
processing.
[0050] FIG. 2 illustrates a series of transverse ray intercept
curves illustrating aberrations at various wavelengths, for the
system of FIG. 1 with wavefront coding surface 104 removed for
illustrative purposes. Curves are shown for system 100 at half
field angles of 0.degree., 10.degree., 20.degree., and 25.degree.
off axis, and for illumination wavelengths of 450 nm, 550 nm, and
650 nm. A slope of zero indicates an in-focus condition. Thus
on-axis rays are nearly in focus. But, for off axis field angles,
the slopes of the transverse ray intercept curves increase
dramatically.
[0051] There are numerous traditional methods of designing lenses.
Most methods try to balance aberrations in order to improve the
off-axis imaging at the expense of on-axis imaging or system
simplicity. Traditional design methodologies do not attempt to make
the transverse ray intercept curves straight lines. Instead, the
traditional goal is to try to minimize the distance of a
substantial portion of the transverse ray intercept curves from the
horizontal axis. In most traditional systems the ray intercept
curves are very different from straight lines, but in general lie
closer to the horizontal axis than the off-axis curves shown in
FIG. 2. In other words, in traditional systems the variation from a
straight horizontal line is mainly in the straightness of the line,
rather than in its slope.
[0052] FIG. 15a (prior art) illustrates traditional transverse ray
plots. These plots are taken from "Practical Computer Aided Lens
Design", Gregory Hallick Smith, William Bell, Inc., Richmond 1998.
Note that the plot for near on axis rays do look similar to
straight horizontal lines, and thus produce an in focus image.
Refer also to FIG. 15b which shows associated MTFs for this system.
The MTFs for near on axis rays are good.
[0053] But as the rays move further off axis, the plots in FIG. 15a
quickly deviate from being straight lines. Their associated MTFs in
15b also quickly degrade.
[0054] The transverse ray intercept curves of FIG. 2 are
essentially straight lines, both on and off axis, and this is a
deliberate design goal, because the use of wavefront coding 104 and
image processing 112 can bring the captured images into focus, so
long as the curves without wavefront coding are essentially
straight lines through the origin, even if the lines are
significantly sloped. The effect of the slope is removed by adding
wavefront coding and post processing.
[0055] The aberration petzval curvature gives rise to transverse
ray intercept curves, with slopes that are a function of field
angle. Axial chromatic aberration gives rise to ray intercept
curves with slopes that are a function of illumination wavelength.
From FIG. 2, both of these features are part of the transverse ray
intercept curves in this example design.
[0056] FIG. 3 illustrates distortion curves for system 100 of FIG.
1, with wavefront coding element 104 removed. The distortion is
less than 0.2%. If distortion was large enough then additional
digital processing might be required to reposition image points
into a non-distorted image. Table 1 lists the optical prescription
of this lens, again without the Wavefront Coding surface. Units are
in mm, and the total length is 4.1 mm. Aspheric terms describe
rotationally symmetric forms of r.sup.order with order equal to 4,
6, 8, etc.
1TABLE 1 Surface Radius Thickness Material Diameter Obj Inf Inf 0 1
2.077 1.7133 PMMA 2 Stop -2.236 0.6498 1.4 3 Inf 1.1 BK7 3.4 4 Inf
0.55 BK7 3.4 Img 0.1 3.4 Surface Conic 4.sup.th Asph. 6.sup.th
Asph. 8.sup.th Asph. Obj 0 1 -1.299 -.000375 -.010932 -.00603 Stop
-3.140 -.01049 3 0 4 0 Img
[0057] FIG. 4 illustrates modulation transfer functions (MTF) for
system 100 of FIG. 1, without wavefront coding element 104. These
MTFs correspond to the transverse ray aberration curves of FIG. 2.
The MTFs are for half field angles 0, 15, and 25 degrees with
wavelengths of 550 nm. The MTFs include the pixel MTF due to the
Bayer color filter array detector with six micron pixels and 100%
fill factor. The on-axis MTF is essentially diffraction limited.
The large drop in MTF off-axis is due to the large amount of
petzval curvature that is unavoidable in traditional single lens
designs with a large field of view. This singlet without wavefront
coding 104 does not meet the MTF specification of greater than 40%
modulation at 40 lp/mm for all field angles. But, due to its design
for Wavefront Coding, modifying the second surface with a Wavefront
Coding surface form 104 will lead to acceptable MTF modulation
values when combined with digital processing. By changing the
wavefront coding element 104 either more or less sensitivity to
misfocus aberrations can be formed.
[0058] FIG. 5 illustrates modulation transfer functions (MTF) for
system 100 of FIG. 1, with wavefront coding element 104 in place,
but without post processing 112. The system is focused at infinity.
The half field angles shown are 0, 15, and 25 degrees. The
wavelength is 550 nm. These MTFs have very little variation with
field angle due to the addition of the Wavefront Coding surface, as
compared to FIG. 4. Pixel MTF due to the Bayer CFA has again been
included. The Bayer CFA with 6 .mu.m 100% fill factor pixels has a
Nyquist spatial frequency of about 42 lp/mm. Note that there are
purposely no zeros in the MTFs below the detector's Nyquist spatial
frequency.
[0059] Since the MTFs of FIG. 5 do not match a diffraction-limited
MTF curve, a blurred image will be directly formed at the detector
by this singlet 102. Post processing is needed to correct this.
[0060] FIG. 6 illustrates modulation transfer functions (MTF) for
system 100 of FIG. 1, with wavefront coding 104 and after
processing 112. Applying a single digital filter in processing
block 112 gives the optical/digital MTFs shown in FIG. 6. The MTFs
before filtering are as shown in FIG. 5. The MTFs after processing
112 at the spatial frequency of 40 lp/mm are all above 40% as
specified by the design specifications. The level of the MTFs after
processing could further be increased beyond that of the
traditional diffraction-limited case, but possibly at the expense
of a lower signal to noise ratio of the final image.
[0061] FIGS. 7a and 7b illustrate sampled two-dimensional PSFs for
system 100 of FIG. 1, with wavefront coding 104 and after
processing 112. FIG. 7a shows the processed PSFs when the object is
at infinity. FIG. 7b shows the processed PSFs when the object is at
30 cm. These PSFs are for 550 nm wavelength and half field angles
of 0, 15, and 25 degrees. After filtering, these PSFs have nearly
ideal shapes. This singlet 100 when combined with wavefront coding
and digital filtering thus easily meets the system
specifications.
[0062] In the preferred embodiment, processor 112 is a
rectangularly separable digital filter. Rectangularly separable
filters are more computationally efficient (counting the number of
multiply and additions) than full 2D kernel filters. Separable
filtering consists of first filtering each row of the image with
the 1D row filter and forming an intermediate image. The columns of
the intermediate image are then filtered with the 1D column filter
to provide the final in-focus image. The separable filter used for
this example singlet has the same filters for rows and columns.
[0063] FIG. 16 illustrates an example of a one dimensional
separable filter 112. Coefficients are represented as real values,
but can be quantified into integer values for fixed point
computations. The sum of the filter coefficients equals
approximately 1. The coefficients were determined with a least
squares algorithm by minimizing the squared difference between the
filtered wavefront coded OTFs and a desired MTF with a value
greater than 40% at 40 lp/mm. The width of the filtered PSFs of
FIGS. 7a and 7b are also minimized with the least squares
algorithm. Changes in the filtered PSFs are minimized in regions
away from their central peaks. FIG. 17 illustrates the magnitude of
the transfer function of the filter of FIG. 16. The zero spatial
frequency value is 1.
[0064] FIG. 8 shows a low cost microscope objective 800 according
to the present invention. The magnification of objective 800 is
10X, with numerical aperture (N.A.)=0.15. Lens 802 is aspheric and
has focussing power. Aperture stop 804 includes wavefront coding
element 806. Processing is accomplished by processing block
810.
[0065] Wavefront coding microscope objective 800 is designed to
meet the following objectives:
[0066] magnification=10X
[0067] N.A.=0.15
[0068] Distortion<1%
[0069] 7 micron square pixels with 100% fill factor
[0070] VGA grayscale detector
[0071] Optical material: PMMA
[0072] The depth of field of traditional microscope objectives is
described by the numerical aperture (NA) and the imaging
wavelength. The wavefront coding objective can have a depth of
field that is independent of the NA of the objective. The depth of
field can be large enough to introduce prospective distortion to
the final images. Regions of the object that are farther from the
objective will appear smaller then regions of the object closer to
the objective. Both near and far regions can image clearly with a
large depth of field. Since the depth of field of traditional
objectives is small prospective distortion is not common with
traditional objectives, especially with high NA. Prospective
distortion can be reduced or eliminating by designing wavefront
coding objectives that are telecentric. In telecentric imaging
systems the magnification of the object is independent of the
distance to the object.
[0073] FIG. 9 illustrates a series of transverse ray intercept
curves illustrating aberrations at various wavelengths, for system
800 of FIG. 8, with wavefront coding element 806 removed. The ray
intercept curves of FIG. 9 describe the performance of the system
at wavelengths 450, 550, and 650 nm for the image field heights of
on-axis (0.0 mm), 1.2 mm, and 2.8 mm. Full scale is +/-100 microns.
Notice that each of these ray intercept curves vary mainly in
slope, as required by the present invention. I.e., the shape of the
curves are essentially the same when the slope components of the
curves are not considered. While these plots are not quite as close
to perfectly straight lines as those in FIG. 2, they can still be
considered to be sloped substantially straight lines.
[0074] The major aberration apparent in this design is axial
chromatic aberration, with a smaller amount of petzval curvature
and lateral chromatic aberration. Without Wavefront Coding this
lens would image poorly in white light, although it might produce a
reasonable image in a single color. Tables 2 and 3 give the optical
prescription for this system. Table 3 gives rotationally symmetric
aspheric terms for the system.
2TABLE 2 Radius Surface of curv Thickness Material Diameter Conic
Obj Inf 2.45906 0.6357861 0 1 1.973107 1.415926 Acrylic 1.2
-1.680295 2 -2.882275 0.7648311 1.2 -1.029351 Stop Inf 0.1 Acrylic
0.841 0 4 Inf 25.83517 0.841 0 Img 6.173922
[0075]
3TABLE 3 Surface 4th 6th 8th 10th 12th 14th 1 0.013191 -0.22886
0.139609 -0.250285 -0.18807 0.193763 2 -0.008797 0.017236 0.007808
-0.223224 0.160689 -0.274339 Stop -0.018549 -0.010249 -0.303999
1.369745 11.245778 -59.7839958
[0076] Wavefront coding element 806 is placed at aperture stop 804,
and is given by the rectangularly separable form of:
S(x,y)=.SIGMA.a.sub.isign(x).vertline.x/r.sub.n.vertline..sup.b.sub.i+a.su-
b.isign(y).vertline.y/r.sub.n.vertline..sup.b.sub.i
[0077] and the parameter values for i=1,2 are:
[0078] a.sub.1=1.486852, b.sub.1=3.0
[0079] a.sub.2=3.221235, b.sub.2=10.0
[0080] r.sub.n=0.419
[0081] FIG. 10 illustrates modulation transfer functions (MTF) for
system 800 of FIG. 8, without wavefront coding, with wavefront
coding, and with both wavefront coding and post processing
filtering, for illumination at 450 nm. Image field heights are 0.0
mm, 1.2 mm, and 2.8 mm.
[0082] FIG. 11 shows a passive athermalized IR imaging system 1100
according to the present invention. Lens 1102 is composed of
silicon. Lens 1104 is composed of germanium. Lens 1106 is composed
of silicon. The aperture stop 1108 is at the back surface of lens
1106. Wavefront coding surface 1110 is on the back surface of lens
1106 (at aperture stop 1108). Processing block 1112 processes the
image.
[0083] Design goals are as follows:
[0084] F/2
[0085] f=100 mm
[0086] 3 deg half field of view
[0087] Illumination wavelength=10 microns
[0088] 20 micron square pixels, 100% fill factor
[0089] Silicon & germanium optics
[0090] Aluminum mounts
[0091] Temperature range of -20.degree. C. to +70.degree. C.
[0092] Combined constraints of low F/#, inexpensive mounting
material, and wide operating temperature make this design very
difficult for traditional optics. Table 4 gives the optical
prescription of system 1100.
4TABLE 4 Radius Surface of curv. Thickness Material Diameter Conic
Obj Inf Inf 0.6357861 0 1 58.6656 5.707297 Silicon 60 0 2 100.9934
22.39862 57.6 0 3 447.046 8.000028 Germanium 32.4 0 4 50.88434
17.54754 32.4 0 5 455.597 7.999977 Silicon 29.5 0 Stop -115.6064
57.9967 29.5 0 Img 6.173922
[0093] The Wavefront Coding surface for IR system 100 of this
example has the parameterized equation:
S(x,y)=.SIGMA.a.sub.isign(x).vertline.x/r.sub.n.vertline..sup.b.sub.i+a.su-
b.isign(y).vertline.y/r.sub.n.vertline..sup.b.sub.i
[0094] and the parameter values for i=1,2 are:
[0095] a.sub.1=16.196742, b.sub.1=3.172720
[0096] a.sub.2=-311.005659, b.sub.2=20.033486
[0097] r.sub.n=18.314428
[0098] FIG. 12 illustrates a series of transverse ray intercept
curves illustrating aberrations at various wavelengths, for system
1100 of FIG. 11, with wavefront coding element 1110 removed. The
ray intercept curves of FIG. 11 describe the performance of system
1100 at a wavelength of 10 microns, on axis field points for
ambient temperatures of +20.degree. C., -20.degree. C., and
+70.degree. C. Full scale is +/-100 microns. Again these plots can
be considered to be substantially straight lines. While they have
more "wiggle" than the plots of FIGS. 2 and 9, in each case, if the
plot were fitted to the closest straight line, the wiggles would
not stray far from the line.
[0099] FIG. 13 illustrates on-axis MTF curves for system 1100
without wavefront coding at three temperatures +20.degree. C.
-20.degree. C., and +70.degree. C.). Performance is nearly
diffraction limited at +20.degree., but drops dramatically with
changes in temperature.
[0100] FIG. 14 illustrates MTFs for system 1100 of FIG. 11, with
wavefront coding, both with and without filtering by processing
block 1112. The illumination wavelength is 10 microns. The MTFs
without filtering are significantly different from diffraction
limited MTFs, but vary little with temperature. Thus, processing
block 1112 is able to correct the images. The MTFs after filtering
are near diffraction limited for all three temperatures
(+20.degree., -20.degree., and +70.degree.). Filtered MTFs extend
only to the Nyquist frequency of the 20 micron detector, or 25
lp/mm.
[0101] The best way to define what constitutes a transverse ray
intercept curve which is a "substantially straight line" is to look
at the MTFs over the entire useful range of the system with
wavefront coding applied. These curves must be very close to each
other, in order for the post processing to be able to move all the
the MTFs to the desired performance level. Compare the MTFs of FIG.
4 (no wavefront coding) to those of FIG. 5 (wavefront coding) The
FIG. 5 MTF curves are very close together. In FIG. 6, post
processing has moved the MTFs to an acceptable level (more
sophisticated post processing could improve the MTFs much further,
to nearly diffraction limited performance, so long as the
preprocessing curves are close enough together). Post processing
could not accomplish this goal with the curves of FIG. 4, because
they are not at all close together.
[0102] FIG. 10 also illustrates this concept. The MTF curves
without wavefront coding do not track each other. The curves with
wavefront coding are very close together. Thus, the the curves with
wavefront coding after post processing are very good.
[0103] Finally, in FIGS. 13 and 14, the MTF curves without
wavefront coding are far apart, but the MTF curves with wavefront
coding are so close together that the post processing curves are
nearly all diffraction limited.
[0104] In FIG. 13, it can be seen that the on-axis MTF (at
+20.degree. C., meaning essentially no temperature related
misfocus) is essentially diffraction limited. This is the best case
traditional MTF for this system. The MTFs at other temperatures,
though, have greatly reduced performance due to temperature related
effects.
[0105] Now consider the upper set of MTFs of FIG. 14, with
wavefront coding and after processing. The MTFs are nearly
identical. Thus the associated transverse ray intercept curves can
be considered to be substantially straight lines, since they are
close enough to straight to give essentially ideal MTFs.
[0106] For other systems, a lower level of performance may be
acceptable, and consequently the deviation of the transverse ray
intercept curves from a straight line may be larger. Such a
situation would result if a fast lens (say F/2) is used with a
digital detector, with, say, 10 micron pixels. In 500 nm
illumination, the diffraction limited MTF for the optical system
would extend to 1000 lp/mm, but the highest spatial frequency that
could be measured by the detector would be only 50 lp/mm. Thus,
aberrations that alter the highest spatial frequencies of the
optics are of no consequence, because they will not be measured by
the detector. Note that while the transverse ray intercept curves
may have noticeable deviations from a straight line (corresponding
to the higher spatial frequencies), the transverse ray intercept
curves are still "substantially straight lines" according to our
definition, because the MTFs with wavefront coding are very close
together. The MTFs under consideration are those that correspond to
the useful range of the particular system being considered.
[0107] Compare the MTFs of FIGS. 6, 10, and 14 with wavefront
coding (useful range MTFs for embodiments of the present invention)
with the MTFs resulting from traditional design of FIG. 15b. These
traditional MTFs are quite far apart, so post processing could
never give adequate performance. These curves are generally 50% or
more apart, whereas the wavefront coding curves in FIGS. 6, 10, and
14, are within an average of 20% of each other over the useful
range of the system, and in the case of FIG. 10, are within an
average of 10% of each other over the useful range of the
system.
[0108] The major aberration apparent in the design of FIG. 11 is
temperature related misfocus. Without Wavefront Coding, this lens
would image poorly over a range of temperatures, although it would
image well at a single temperature.
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