USOO9507129B2(12) United States Patent(10) Patent No.:

Marks et al.
(54) APPARATUS COMPRISING ACOMPACT

Nov. 29, 2016(58) Field of Classification Search

CATADOPTRC TELESCOPE

None

See application file for complete search history.

(71) Applicant: Duke University. Durham, NC (US)56

(72) Inventors: Daniel Marks, Durham, NC (US);David Jones Brady, Durham, NC (US);Nathan Adrian Hagen. Durham, NC
(US)

Ref
eferences Cite
Cited

U.S. PATENT DOCUMENTS
6,449,103 B1* 9/2002 Charles .................. GO2B 13,06
359,366
2004/0080938 A1*(73) Assignee: Duke University. Durham, NC (US)(*) Notice:

US 9,507,129 B2(45) Date of Patent:

4/2004 Holman .................... F21S 8.08

362,231

2004/0228008 A1* 11, 2004 H11 .................... GO2B 21,0056

Subject to any disclaimer, the term of this359/727

patent is extended or adjusted under 35

2006/0050386 A1

3/2006 Kuthirummal ........ GO2B 17 OO

U.S.C. 154(b) by 36 days.

2010/0171866 A1* 7/2010 Brady .................. GO2B 3.0056

359,471348/340(21) Appl. No.: 14/580,001

2010/0309566 A1* 12/2010 DeWitt .................. GO2B 5,001
359,7291-1.

(22) Filed:2012/0063000 A1

Dec. 22, 2014

(65)

Prior Publication Data
US 2015/O1774.96 A1

June 25, 2015

3/2012 Batchko ................... GO2B 3.14

359,666

2014/011 1608 A1*

ck

4, 2014 Pfeil .................. HO4N 55:

2015,0177496 A1*

6, 2015 Marks ................ GO2B 13,0065

s348/335

Related U.S. Application Data
(60) Provisional application No. 61/918,788, filed on Dec.
20, 2013.
(51) Int. Cl
GO2B I3/00
GO2B I7/08* cited by examinerPrimary Examiner — Shahbaz Nazrul(74) Attorney, Agent, or Firm — Kaplan Breyer Schwarz& Ottesen, LLP(2006.01)(2006.01)(57)

ABSTRACT

H04N 5/225(2006.01)

A camera system for a mobile device includes an array ofcompact catadioptric telescopes wherein at least some of the(52) elito(2006.01)

telescopes have a portion of their aperture truncated. At least

CPC ....... G02B 13/0065 (2013.01); G02B 17/0808

S.

(2013.01); G02B 17/0856 (2013.01); G02B
23/06 (2013.01); H04N 5/2254 (2013.01)

traitsthe array are tilted

21 Claims, 9 Drawing Sheets

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1.

2
ognized that a catadioptric design is well Suited for Suchservice because the beam path through Such optics is“folded, thereby enabling a reduced profile or thickness forthe optics. In the illustrative embodiment, the catadioptric
CROSS REFERENCE TO RELATED
optics are implemented as an array of Schmidt-Cassegrain
APPLICATIONS
telescopes, which, as a consequence of the two reflections
This case priority of U.S. Pat. Appl. 61/918,788, which that occur in each telescope, enable an optical path or train
is up to three times longer than the physical thickness of
was filed Dec. 20, 2013 and is incorporated herein by thatthetelescope.
reference. This case is related to U.S. patent application Ser.
Each compact telescope in the array can have a relatively
No. 14/068,708, filed Oct. 31, 2013, which is incorporated 10 moderate
field-of-view (c.a., 25 degrees). To increase theherein by reference.
field-of-view, the axis of each of the telescopes in the arrayis tilted with respect to that of other telescopes and oriented
STATEMENT REGARDING
so that neighboring micro-cameras have overlapping fields
FEDERALLY SPONSORED RESEARCH
15 of-view. Such overlapping facilitates computationally Stitch
This invention was made with Government support under ing a single composite image from the data taken obtained
grant number NBCHC090032 awarded by the Defense from the many micro-cameras in the array.
In addition to enabling intrinsically thinner lenses, aAdvanced Research Projects Agency (DARPA). The Gov
relatively narrower field-of-view simplifies lens and mecha
ernment has certain rights in the invention.
nism design for focal adjustment, enabling a yet thinner lensassembly.
FIELD OF THE INVENTIONAPPARATUS COMPRISING ACOMPACT
CATADOPTRC TELESCOPE

In Some embodiments, a further reduction in camera

The present invention relates to imaging optics in general, thickness is achieved by limiting the spectral regard of each
and, more particularly, to camera optics for use in cell micro-camera, thereby reducing the need for chromatic
25 aberration correction to enable a thinner lens design.
phones.
Removing the need for on-chip spectral filtering enables a
BACKGROUND OF THE INVENTION
larger numerical aperture at the pixel, which again enables
a thinner lens assembly. Full spectral imaging is achieved by
Over the past decade, integration of cameras with mobile Stitching data together from overlapping micro-camera
devices has become increasingly common. The desired 30 fields. Such overlaps are required for effective stitching, butwith spectrally diverse micro-cameras, each field point
thickness for tablets and cell phones is typically less than 1
centimeter (cm) and as thin as about 5 millimeters (mm). should be observed by three micro-cameras.
It is notable that the angular resolution need not be equal
Since the ideal camera integrated into Such devices images
normal to the device Surface, camera thickness is Subject to in all micro-cameras, that the focal state need not be thestringent constraints and is, in fact, a critical metric. That is, 35 same and that exposure values, frame sampling phase andvery low profile optics are required.
frame rate may vary from one micro-camera in the array toMarket pressures dictate that a mobile-device camera the next, enabling efficient spectral-imaging synthesis, expo
provides a large field-of-view and high resolution. These Sure and focal stacking, increased dynamic range in therequirements are, unfortunately, at odds with one another. In Stitched image and system power management. An example
particular, a large field-of-view produces large off-axis aber 40 of the use of frame-rate variation for video compression inrations that must be corrected. And to achieve high resolu the prior art is given in Mohan Shankar, Nikos P. Pitsianis,tion, a minimal-size entrance pupil is required to achieve a and David J. Brady, “Compressive video sensors using
particular angular resolution. As the number of pixels grows, multichannel imagers. Appl. Opt. 49, B9-B17 (2010).
Since the telescopes used in embodiments of the invention
more optical elements are required to correct these aberra
tions, which both become larger laterally because the 45 are wider than they are deep, their profile (i.e., height)
entrance pupil size increases. Furthermore, the axial length increases when tilted. As previously discussed, any increaseof the camera increases to accommodate the increasing in apparent camera thickness is potentially quite problematic
number of elements.
in mobile device applications. The inventors recognized that
Mobile-phone cameras are purely refractive and have an only a partial aperture of each telescope is required toentrance pupil of 2 mm or less in diameter. This limits the 50 produce the required resolution. In other words, a portion ofangular resolution to 0.015 degrees or greater, so that, for the aperture of the telescope can be removed. As a conse
example, for a 70x42 degree field-of-view camera, there are quence, when tilted, the profile of Such a partial-apertureat best 14 million resolvable pixels if the diffraction limit is telescope is reduced relative to that of a full-aperture teleachieved over the entire field.
Scope. In some embodiments, almost half of the lens is
To improve this performance, a wide entrance pupil is 55 removed.
In some embodiments, the portion of the apertureneeded, which requires wider optics as well as a longer
optical-train length.
removed reduces the profile of “tilted partial-aperture telescopes sufficiently so that they fit within a mobile device.
SUMMARY OF THE INVENTION
Regions that Suffer a resolution reduction due to partial
60 removal of the aperture are imaged by another partial
The present invention provides an optics systems system aperture telescope that provides better resolution in thathaving a wide field-of-view and that is flat enough for use in region.
a mobile device. Such as a Smartphone.
In addition to the foregoing, Some embodiments of the
In accordance with an illustrative embodiment of the
optics system include at least one and typically more of theinvention, an array of compact catadioptric (refractive and 65 following benefits:reflective) optics is used to provide a camera for a mobile
The same material is used for both the converging anddiverging elements, enabling the optics to achromatize
device (e.g., Smartphone, etc.). The present inventors recUS 9,507,129 B2
4
3
itself. Since there are relatively few optical plastics miniature cameras, each comprising a compact catadioptricavailable, this is very advantageous.
telescope. Consistent with the usage presented in U.S. Pat.
The optical train and aperture of each catadioptric tele No. 8,259,212, which is incorporated by reference herein,
scope is relatively large and flat. Therefore, tilting the each camera in the array is referred to as a “micro-camera.”camera and slicing it does not remove elements as it As used herein and in the appended claims, the termotherwise would if the optics included a relatively long “compact telescope' or "compact catadioptric telescope'narrow optical train of many elements. Rather, slicing
to a telescope having a thickness of 10 mm or less.
the catadioptric telescopes used in conjunction with the refers
FIG.
depicts prior-art camera 100, which includes
illustrative embodiment simply reduces the aperture telescope1 101
and focal plane array 126. Telescope 101,
thereof.
10 which employs catadioptric optics, was developed by some
The bokeh (defocused pattern) is highly structured since of the present inventors for a different application. See,
the aperture is highly structured. As a consequence, the Marks et al., “Wide-field Compact Catadioptric Telescopebokeh can be used to infer the amount of defocus andSpanning 0.7 to 14 um Wavelengths. Applied Optics,
obtain three-dimensional information about the scene
V52(18),
pp. 4334-4342 (Jun. 20, 2013), incorporated byfrom a single image.
Individual catadioptric telescopes in the array can differ 15 reference herein. These inventors recognized that a suitably
from one another in terms of focus, exposure, shutter modified version of telescope 101 could be used to great
speed, and the like, thereby enabling high dynamic advantage in a camera for mobile devices.
The particular catadioptric telescope depicted in FIG. 1 isrange and high depth-of-field for the optics. These
telescopes can be adjusted independently and dynami a Schmidt-Cassegrain telescope, although modified by thecally, unlike prior-art lens arrays for use with cameras. inclusion of a Mangin mirror. As will be appreciated bythose skilled in the art, the presence of the Mangin mirror
BRIEF DESCRIPTION OF THE DRAWINGS
provides additional chromatic aberration control to achievea field much wider than a typical Cassegrain telescope.
FIG. 1 depicts a schematic drawing of a cross-sectional
Telescope 101, having optical axis 103, includes front
view of a catadioptric telescopic including ray tracings. 25 optical element 102 and rear optical element 110, which
FIGS. 2A and 2B depict respective front and back views comprises annular portion 112 and central portion 118.
of a scale, solid model of the front optical element of the
In the illustrative embodiment, front optical element 102
catadioptric telescope of FIG. 1.
corrector. A Schmidt corrector is an aspheric
FIGS. 2C and 2D depict respective front and back views islensa Schmidt
thatcorrects
paths of light rays Such that the lightof a scale, solid model of the rear optical element of the 30 reflected from thethe
outerpart of the objective lens and lightcatadioptric telescope of FIG. 1.
FIG. 3A depicts a side view of a solid model of the reflected from the inner portion of the objective lens isbrought to the same focus.
catadioptric telescope of FIG. 1.
In the illustrative embodiment, annular portion 112 of rear
FIG. 3B depicts a side view of a truncated catadioptric
telescope formed by removing portions of telescope of FIG. optical element 110 is a Mangin mirror. A Mangin mirror is
35 a negative meniscus lens with the reflective Surface on the
3A, in accordance with the illustrative embodiment.
FIG. 3C depicts a front view of truncated catadioptric rear side of the glass forming a curved mirror that reflects
light without spherical aberration. Central portion 118 is atelescope of FIG. 3B.
FIG. 4A depicts a first array of truncated catadioptric field flattener, which removes astigmatism and field curva
ture.
telescopes in accordance with an illustrative embodiment.
FIG. 4B depicts a second array of truncated catadioptric 40 Front optical element 102 has power and rear opticaltelescopes in accordance with an illustrative embodiment.
element 110 has negative power, the latter canceling the
FIG. 5 depicts the field-of-view for each often cameras in positive power of the front optical element. In some embodi
a two-dimensional array, in accordance with an illustrative ments, optical elements 102 and 110 are made from the samearrangement.
Such that the dispersion of these elements cancel
FIG. 6A depicts a ray tracing through a masked catadiop 45 material.
andthechromatic
aberration is greatly reduced. Typically,
tric telescope wherein light rays arrive at the telescope in the chromatic invarianceis usually achieved using multiple
same direction as the unmasked region.
such as a flint and crown glass. The “self-cancel
FIG. 6B depicts a ray tracing through a masked catadiop materials,
property of the dispersion between the elements, intric telescope wherein the light rays arrive at the telescope in lingaccordance with embodiments of the invention, enables use
the opposite direction as the unmasked region.
FIG. 7A depicts the semicircular annular aperture of a 50 a single material in telescope 100. Most of the power istruncated catadioptric telescope in accordance with the provide by reflective elements, with the refractive elements
providing a small amount of chromatic control.
illustrative embodiment.
Each of optical elements 102 and 110 has two sides, one
FIG. 7B depicts an arrangement of micro-cameras in anarray thereof, showing the orientation of the truncated of which is closer to the object/scene being imaged and the55 other being further therefrom. Except for planar front sur
apertures of each of the micro-cameras.
FIG. 8 depicts an embodiment of a kinoform for use with face 104 of front optical element 102, each side of eacha truncated catadioptric telescope in accordance with the element includes two optical Surfaces: a center circularpresent teachings.
optical Surface and an outer annular optical Surface. In
FIG. 9 depicts an alternative embodiment of a kinoform particular:
for use with a truncated catadioptric telescope in accordance 60 Back side of element 102: includes annular optical surface
106 and the center circular optical surface 108;with the present teachings, wherein the kinoform includes
Front surface of rear optical element 110: includes annulardiffractive-achromatized prisms.
optical Surface 114 and the center circular opticalsurface 120;

DETAILED DESCRIPTION
65

In accordance with the present teachings, a camera system
intended for use in mobile devices includes an array of

Rear surface of rear optical element 110: includes annular
optical Surface 116 and center circular optical Surface122.

US 9,507,129 B2
5
6
Catadioptric telescope 101 therefore includes seven optical FIG. 2B depicts backside annular surface 106 and backside
surfaces, three of which are on front optical element 102 and central surface 108 (the secondary mirror) of front opticalfour of which are on rear optical element 110. As used in this element 102.
FIGS. 2C and 2D depict respective front and back views
disclosure and the appended claims, the term “optical Sur
of a scale, solid model of rear optical element 110. FIG. 2C
face” means a surface that refracts or reflects light.
FIG. 1 also depicts a ray trace for telescope 101 showing depicts front annular surface 114 and front central surface
the path of light rays from an object (not depicted) to an 120 of rear optical element 110. FIG. 2D depicts rear annular
image thereof. Specifically:
surface 116 (the primary mirror) and backside central sur
1. Light rays are propagated from an object/scene and are face 122 of rear optical element 110.
received by and refracted through surface 104, the 10 In some embodiments, front optical element 102 and rear
optical element 110 are molded out of a plastic, such asplanar front surface of front optical element 102.
2. The rays are then refracted by surface 106, the backside E48R, available from Zeonex, Louisville, Ky. A highlyreflective coating (e.g., aluminum, etc.) is deposited onto
annular surface of front optical element 102.
3. The rays are then refracted through surface 114, the appropriate parts of the plastic to provide “mirror surfaces.
15
In some embodiments, a small region (c.a. 0.2 to 0.3 mm
front annular surface of rear optical element 110.
4. The rays are next reflected from surface 116 (the wide) at the transition Zones between the inner and outer
primary mirror), the backside annular Surface of rear surfaces of front optical element 102 and rear optical ele
ment 110 are blackened (not depicted) to reduce stray light
optical element 110.
5. The rays are then refracted, once again, through surface scattering (from these transition Zones). In some embodi
114, the front annular surface of rear optical element ments, front optical element 102 and rear optical element
110.
110 are molded with mating features (not depicted). The
6. The rays are next reflected from surface 108 (the mating features serve as an alignment feature and also
secondary mirror), the backside central surface of front simplify the process of attaching/bonding these elements toone another. Using Such mating features obviate difficult
optical element 102.
7. The rays are then refracted by field flattener 118, as 25 active-alignment steps.
Furthermore, because, in Such embodiments, elements
formed by surfaces 120 and 122, the respective front
and backside central Surfaces of rear optical element 102 and 110 are made of identical materials, the thermal
110.
expansion properties are the same and therefore the bonded
8. The rays are then propagated through sensor window components are likely to have far less image degradation
30 due to thermal expansion as all dimensions scale together
124.
9. The rays form an image on the sensor (i.e., focal plane with temperature.
FIGS. 3B and 3C depict, via respective front and sidearray 126). The focal plane array is conventional arrayof image sensors (e.g., CMOS sensors, CCD elements, views, truncated catadioptric telescope 301. FIG. 3A pro
infrared light photodetectors, etc.) that converts the vides, for comparison, catadioptric telescope 101, in which
received light into a digital representation of the 35 no portion of the aperture of the telescope is removed.
As previously discussed, to provide an adequate field-of
imaged scene.
view, catadioptric telescopes in an array thereofare tilted so
Examplethat they each provide a different field-of-view. Those fields
of-view are “stitched together to provide a composite
In an example design of catadioptric telescope 101, diam 40 image. But tilting the telescopes increases their profile (sinceeter D, of front optical element 102 (and hence telescope they are wider than they are deep). The use of truncated101) is 9.2 mm and thickness T of telescope 100 is 4.5 mm. catadioptric telescopes 301 facilitates such tilting; that is, theThe entrance pupil of telescope 101 is 8 mm and the focal truncated aperture reduces the profile of each telescope Suchlength is 5 mm. Telescope 101 images from -12.5 to 12.5 that the array of micro-cameras has a thickness that isdegrees off-axis, with design wavelengths in the range of 45 suitable for use in conjunction with mobile devices.
As depicted in FIG. 3A, even if incoming rays from a
486 to 656 nanometers (nm).
Field flattener 118 removes astigmatism and field curva scene are received at only about half of the aperture of front
ture, so that the example design achieves an f/it of 0.6. The optical element 102, the full scene is imaged through win
effective fit for illumination varies from 1.0 at the center to
dow 124 onto the focal plane array (not depicted). Therefore,
1.2 at the edge thereof. As a consequence, this design of 50 nearly one half of front optical element 102 can be removed.
telescope 101 can operate sufficiently in conditions of low Somewhat less of rear optical element 110 can be removed
light where most mobile-phone cameras operate poorly.
as is apparent from the ray tracing depicted in FIG. 1.
The image field is 2.2 mm in diameter, it is designed for
As used in this disclosure and the appended claims, thea 0.001 mm pixel CMOS sensor (an implementation of focal term “truncated,” when used in conjunction with “telescope'plane array 126). This is consistent with the recent genera 55 or “catadioptric telescope' means a telescope with a portion
tion of CMOS backside-illuminated sensors. The instantaof at least its aperture removed. That is, a portion of at least
neous field-of-view is 40 arcsec.
the front optical element (and typically the back optical
The limiting aberration of telescope 101 is lateral chro element as well) is physically removed (not simply
matic aberration, which may be corrected digitally, if “blocked'). In conjunction with the present disclosure, thosedesired, in some embodiments. Telescope 101 can be trans 60 skilled in the art will be able to determine how much of thelated by a distance of 0.031 mm to focus from infinity to 60 aperture of the telescopes can be removed and how to to do
cm distance. This is within the range of the stroke of a SO.
By way of example, assume that catadioptric telescopepiezoelectric element, so that it may be used instead of a
101 has a diameter D of 9.2 mm and a thickness T of 4.5 mm.
static power-consuming voice-coil actuator.
FIGS. 2A and 2B depict respective front and back views 65 Assume that, for truncated catadioptric telescope 301, porof a scale, solid model of front optical element 102. FIG. 2A tions of front optical element 102 and rear optical element
depicts planar front surface 104 of front optical element 102.
110 are physically removed such that front optical element

US 9,507,129 B2
78102 has a truncated height H' of 5.5 mm and rear opticalelement 110 has a truncated height H' of 6.2 mm. The

center of the field so that the best resolution is achieved at

the field center. This is illustrated in FIGS. 6A and 6B, in aeffect of tilting truncating catadioptric telescope 301 is

ray trace through telescope 301 of camera 300 is depicted forillustrated in FIGS. 4A and 4B.

the aforementioned scenarios.

FIG. 6A depicts the scenario in which light rays arrive at
FIG. 4A depicts an array 400A of cameras 300 including
truncated catadioptric telescopes 301 (focal plane array not the masked catadioptric telescope (equivalent to truncateddepicted) for use in a mobile device. Although depicted as catadioptric telescope 301) in the same direction as the
one-dimensional array for the sake of clarity, in an actual unmasked region (same direction as image point position).
camera system, micro-cameras 300 would be arranged in a FIG. 6B depicts the situation in which rays arrive at the
10 telescope in the opposite direction as the unmasked region
two-dimensional array.
In FIG. 4A, the outermost truncated catadioptric tele (opposite direction as image point position).
FIG. 7A depicts the semicircular annular aperture ofscopes 301 in array 400A are tilted by +27 and -27 degrees,
providing array 400A with a field-of-view of 54 degrees. If truncated catadioptric telescope 301. FIG. 7B depicts how
truncated catadioptric telescopes 301 have the dimensions aperture of each of truncated catadioptric telescope 300, in
provided in the above example, profile Pincreases to 5.5 mm 15 a plurality thereof, are arranged in array 500 to best cover thefield-of-view, as per the discussion with respect to FIGS. 6A
from 4.5 mm as a consequence of the tilt.
FIG. 4B depicts array 400B of cameras 300 including and 6B. Each aperture 730, which appears as a semicircle,
truncated catadioptric telescopes 301. In FIG. 4B, the out is oriented so that the rounded side of each aperture faces
ermost truncated catadioptric telescopes 300 in array 400A away from the center of the field-of-view. That is, theare tilted by +36 and -36 degrees, providing array 400A oppositely inclined field points toward the center of thewith a field-of-view of 72 degrees. If truncated catadioptric image. As a result, overlap regions between telescopes are
telescopes 300 have the dimensions provided in the above more likely to be better imaged by the telescope further fromexample, profile P increases to 7.4 mm from 4.5 mm as a the center of the array, where the fields are oppositely
inclined to the telescope axis.
consequence of the tilt.
FIG. 5 depicts the field-of-view for each often cameras in 25 The bokeh of the annular or semiannular aperture has aa two-dimensional array 500 in accordance with an illustra radius on the focal plane that increases with defocus. This
tive arrangement. Each camera comprises a truncated cata bokeh is useful for both finding the correct focus position in
dioptric telescopes as previously disclosed. Each circle an object, as well as estimating the three-dimensional posi
represents field-of-view FOV for one camera. Each such tion of an object in the scene. This is particularly useful
field-of-view is tilted so the array thereof covers various 30 when tracking multiple targets, such as the headlights of carsor temporary glint points from moving objects. The three
directions. In some other embodiments, the micro-camera
array includes more or fewer than ten cameras, consistent dimensional path of objects through space can thus bewith design goals (e.g., achieving a desired field-of-view, determined in a moving scene.
In an alternative embodiment, rather than tilting theetc.).
Each (micro-) camera in the array propagates the portion 35 telescope to cover larger portions of the field, a kinoform
of the scene in its field-of-view onto its respective focal may be used to tilt the beam. In some embodiments, such asplane array. The focal-plane array associated with each the illustrative embodiment depicted in FIG. 8, kinoform
telescope converts the received optical Sub-image into a 840 is patterned on front flat surface 104 of front optical
digital Sub-image of the portion of the scene. All Such digital element 102.
Sub-images are transmitted to a processor. The processor 40 Kinoform 840 comprises a periodic array of prisms 842 ofcomputationally Stitches the digital Sub-images together via refractive index n, with n usually being the same refractive
known algorithms, thereby forming a composite digital index of the substrate (i.e., front optical element 102).
Kinoform prisms 842 have a height Helsin 0 and deviate
image of the entire scene.
There is overlap between the fields-of-view FOV to the light beam by a deviation angle=0(n-1) in radians (in thefacilitate the Stitching process. A hexagonal coverage pattern 45 Small angle approximation). Because refractive index inmaximizes overlap and minimizes the number of catadiop depends on wavelength w, the deviation angle also depends
tric telescopes needed for coverage. Because there is overlap on the wavelength, and the image is blurred. To minimize
between fields-of-view, as the panorama is acquired, objects this effect, in some embodiments, each of prisms 842 inare viewed in the overlap regions between telescopes. Par kinoform 840 is achromatized by superimposing a diffrac
allax in these two regions may be used to infer the range to 50 tion grating on each prism to set the deviation the same at
objects, as well as help remove the parallax artifacts from two wavelengths w and W, while achieving a nominal
deviation C. at wavelength W. Kinoform 940 including
the Stitched panorama.
In an illustrative embodiment, each telescope provides a diffractive-achromatized prisms 942 is depicted in FIG. 9.
field-of-view of 24 degrees and the spacing between centers Typically, wavelengths W. W., and w are the commonof each telescope is 18 degrees. This provides array 500 with 55 Abbe-defined wavelengths 486, 656, and 587 nm. Solving
a field-of-view X-Y of 54x31 degrees. The 31 degree for the period A of the grating in the Small angle approxi
mation (large period):
field-of-view is calculated as: 18x2xcos(30 deg).
The modulation transfer function for a masked aperture(to simulate a truncated aperture) was calculated. BecauseDsymmetry is broken by blocking half of the aperture, sepa 60
a == 86(no - 1)) ++ - rate MTF plots were prepared for the field angles that areA.
A.
inclined in the same direction as the unmasked region, and9(ne - 1) + i = 0(ne-1)+
the field angles that are oppositely inclined. Due to vignett
ing, the oppositely inclined angles form a better image witha MTF very similar to an unmasked telescope. As a conse 65
quence, in preferred embodiments, the apertures arearranged Such that oppositely inclined rays point toward theUS 9,507,129 B2
10
14. The system of claim 1 wherein each telescope in the-continued
array is a compact telescope.
C- F
15. The system of claim 1 wherein the system comprises
A np - 1 T. A
acamerasystem for a mobile device, wherein the camera
D
C - F.
5 system includes:a – = voan array of micro-cameras, each micro-camera compris
A = Vn(D(C -- E)F) ++ Ding one of the catadioptric telescopes and a focal planeCarray, wherein light within a field-of-view of eachmicro-camera is propagated to the micro-camera's
As an example of a design for kinoform 940, for plastic 10
focal plane array, the light defining an optical Sub
image, and wherein the focal plane array generates a
E48R (n=1.531, V 56.04), AC-00101 mm radians, so
digital Sub-image from the optical Sub-image.
that for 6 degrees (0.104 radians), the period A=0.0971 mm
and 0=10.6 degrees. The exact solution requires the non
16. The system of claim 15 wherein at least some of theparaxial Solution, which can be found using a ray-tracing micro-cameras have at least one controllable setting that isprogram.
15 independently and dynamically adjustable, wherein the con
It is to be understood that the disclosure teaches just one trollable setting is selected from the group consisting of
example of the illustrative embodiment and that many focus, exposure, gain, magnification, and dynamic range.
variations of the invention can easily be devised by those
17. A system comprising an array of catadioptric teleskilled in the art after reading this disclosure and that the Scopes, the system having a system optical axis, wherein:(a) each catadioptric telescope comprises:
scope of the present invention is to be determined by thefollowing claims.
(i) a front optical element comprising an aspheric lens;(a-AliWhat is claimed is:

1. A system comprising an array of catadioptric tele
Scopes, the system having a system optical axis, wherein:(a) at least Some of the telescopes in the array are 25
truncated; andand(ii) a rear optical element comprising an outer annularportion and an inner circular portion, wherein theouter annular portion is a negative meniscus lens andthe inner circular portion is a field flattener;(b) at least Some of the catadioptric telescopes are trun(b) an optical axis of at least Some of the telescopes in thearray are tilted with respect to the system optical axis.
cated; and(c) the catadioptric telescopes are oriented so that neigh
2. The system of claim 1 wherein the catadioptric tele30
boring catadioptric telescopes have overlapping fields
Scopes consists essentially of seven optical Surfaces.
of-view.
3. The system of claim 1 wherein the catadioptric telescope is a Schmidt-Cassegrain telescope.
18. The system of claim 17 wherein an optical axis of at
4. The system of claim 1 wherein the catadioptric tele least some of the catadioptric telescopes are tilted with
Scopes comprises a front optical element and a rear optical respect to the system optical axis, and wherein at least someelement.
35 of catadioptric telescopes are tilted by a different amount
5. The system of claim 4 wherein the front optical element than other catadioptric telescopes in the array.
consists essentially of three optical Surfaces and the rear
19. The system of claim 17 wherein a kinoform is
optical element consists essentially of four optical Surfaces. disposed on a front surface of the front optical element of at
6. The system of claim 4 wherein the front optical element least some of the catadioptric telescopes in the array.
is a Schmidt corrector and the rear optical element com 40 20. A system comprising an array of compact catadioptric
telescopes, the system having a system optical axis, wherein:prises a Mangin mirror and a field flattener.
(a) each catadioptric telescope in the array comprises:
7. The system of claim 4 wherein a back side of the front
optical element consists essentially of an annular optical(i) a front optical element having a front and back anda rear optical element having a front and a back, theSurface and a center circular optical Surface disposed within
front being closer to an object being imaged;
the annular optical Surface, wherein the center circular 45(ii) the front of the front optical element comprising a
optical Surface is a mirror.
planar surface and the back of the front optical
8. The system of claim 4 wherein a front side and a backelement comprising an positive refractive lens in aside of the rear optical element each consist essentially of anannular optical Surface and a center circular optical Surface
first annular region and a mirror in a central circular50
region within the first annular region;
disposed within the annular optical Surface.
(iii) the front of the rear optical element comprising a
9. The system of claim 4 wherein the front optical element
negative meniscus lens in an second annular region
and the rear optical element comprise the same material.
and a first Surface of a field flattening lens in a central
10. The system of claim 1 wherein a field-of-view of eachcatadioptric telescope in the array overlaps a field-of-view ofcircular region within the second annular region;55
at least three other catadioptric telescopes in the array.
(iv) the back of the rear optical element comprising a
11. The system of claim 1 wherein all telescopes in the
primary mirror in a third annular region and a second
array are truncated, each telescope having an aperture withsurfaced of the field flattening lens in a central
circular region within the third annular region;a rounded side and a flat side as a consequence of the(b) at least Some of the catadioptric telescopes are trun
truncation, wherein the aperture of each telescope is oriented
cated;
so that the rounded side thereof faces away from a center of 60(c) an optical axis of at least Some of the catadioptrica field-of-view of the array.
telescopes in the array are tilted with respect to the
12. The system of claim 1 wherein an optical axis of all
system optical axis.
telescopes in the array are tilted with respect to the system
optical axis.
21. The system of claim 20 wherein, truncated catadiop
13. The system of claim 1 wherein each telescope in the 65 tric telescopes have removed portions of the front opticalarray provides a field-of-view of 24 degrees and wherein element and rear optical element that are bounded by a planespacing between centers of each telescope is 18 degrees.
intersecting the front and rear optical elements but notUS 9,507,129 B2
11intersection the image formed by truncated catadioptric
telescope, wherein portions not removed are on a side of theplane containing the image formed by the truncated cata
dioptric telescope.

12