Mobile platform optical design
`
`Clark, Peter
`
`Peter P. Clark, "Mobile platform optical design," Proc. SPIE 9293,
`International Optical Design Conference 2014, 92931M (17 December 2014);
`doi: 10.1117/12.2076395
`Event: International Optical Design Conference, 2014, Kohala Coast, Hawaii,
`United States
`
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`PROCEEDINGS OF SPIE
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`Invited Paper
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`-9- pixel size
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`-0-- light wavelength
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`8 7 6 5 4
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`2 1 0
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`2000
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`2005
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`2010
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`2015
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`International Optical Design Conference 2014, edited by Mariana Figueiro, Scott Lerner,
`Julius Muschaweck, John Rogers, Proc. of SPIE-OSA Vol. 9293, 92931M · © 2014 SPIE
`CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2076395
`
`SPIE-OSA/ Vol. 9293 92931M-1
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`Mobile Platform Optical Design
`Peter P. Clark
`LensVector, Inc., 6 Clock Tower Place, Suite 130, Maynard, MA, USA 01754
`
`ABSTRACT
`
`Camera modules in mobile devices have become ubiquitous, and the optical design and fabrication technology behind
`them is underappreciated. We will present a basic summary of the technology and discuss some recent developments
`that may influence future camera designs.
`
`Keywords: Digital cameras, optical design
`
`
`
`1. INTRODUCTION
`Since the beginning of photography, about 170 years ago, camera design has dramatically changed. For most people,
`large assemblies of wood, leather, brass and glass have made way for the extremely miniaturized modules that are buried
`within electronic devices.1 Many millions of them are in mobile phones today, of course. At IODC-2006, Vancouver,
`Jane Bareau and I gave a similar paper,2 hoping to describe the issues encountered when designing the optics for such
`small cameras. Eight years later, there has been significant evolutionary improvement to the “conventional” mobile
`phone camera, and there are new technologies on the horizon, many based on computational optics, that may change the
`landscape.
`We said in 2006 that, compared with a 35mm film camera, the lens in a miniature camera module (MCM) is roughly an
`order of magnitude smaller in size and cost. That is probably an understatement today, and of course production
`quantities are extremely large. Successful products are manufactured by the millions per month.
`Now, there are two cameras in typical “smart” phones, and since 2006, camera lens specifications have been evolving:
`Item
`
`2006
`
`2014 primary
`2014 secondary
`Pixel size
`2.8 um
`
`1.1 to 1.4 um
`1.1 to 1.4 um
`Pixel count
`2 to 3 MP
`5 to 8 MP
`1.3 to 3 MP
`Autofocus?
`Sometimes
`yes
`
`no
`f/number
`2.8
`
`2.8-2.4
`
`2.4-2.0
`Full field of view ~60o
`~70o
`~75o
`
`
`
`2. IMAGE SENSOR DEVELOPMENTS
`
`2.1 Pixel Size
`The trend to smaller pixels has continued, although perhaps
`at a slower rate. We can see in Fig.1 how the pixel size has
`been approaching the wavelength of visible light, and there
`are sub-micron pixel designs coming in the near future.
`Developments in the silicon design, such as back side
`illumination, have improved the sensitivity and reduced
`directionality of the focal planes. This has allowed the
`implementation of smaller pixel sensors with acceptable
`low light performance, and it has somewhat relieved the
`specification requirement for chief ray angle, which helps
`the lens design.
`What is the motivation for smaller pixels? We believe there
`are three things driving pixel size down, in descending
`order of importance:
`
`
`
`Figure 1. Historically, typical pixel size has been
`decreasing, getting closer to the wavelength of visible light.
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`I
`
`Lens
`
`Exit Pupil
`
`Microlens array =
`image plane
`
`I Detector
`I array
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`I
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`1
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`40.0
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`35.0
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`. 30.0
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`S 20.0
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`15.0
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`10.0
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`CRA and field angle
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`/
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`/
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`angle
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`0.20
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`0.60
`0.40
`Relative FOV
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`0.80
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`1.00
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`SPIE-OSA/ Vol. 9293 92931M-2
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`1- Cost. The silicon detector and processor is the highest cost component of the camera module. It can represent
`nearly half of the cost, while the lens assembly is more like 15% of the camera module cost. Smaller pixels
`mean a smaller area of silicon, lowering cost.
`2- Camera size. If the focal plane is smaller, the lens focal length can be smaller, reducing z-height, which is a
`critical dimension for achieving thin devices.
`3- Resolution. Higher pixel counts appear to be a lower priority, now, although there are cameras being introduced
`that are pushing beyond 10MP.
`2.2 Microlenses and focal plane directionality
`As in 2006, the CMOS image sensors use an array of microlenses, one for each of the R, B and G pixels. They are
`intended to image the exit pupil of the camera lens onto the sensitive area of the pixel, which is below the surface of the
`sensor. It is important for the lens designer to understand that the microlens array is the true image plane of the system,
`and the microlenses effectively increase the sensitive area of the pixel to nearly 100% of the pixel dimension. (See
`Fig.21)
`
`
`
`
`Figure 3. A typical plot of chief ray angle vs field (right).
`
`Figure 2. Illustrating the function of the microlens array.
`
`The incidence angle of the chief ray on the sensor must be limited by the lens design, or else there will be light loss and
`color crosstalk. The field of view specification has been growing larger since 2006. We believe this is to enable shorter
`focal length lenses, with shorter z-heights, helping to achieve shorter cameras. Corner to corner FOV’s were around 60
`degrees in 2006, and they are now often specified at 70 to 75 degrees. At the same time, chief ray angle had been
`limited to well below 25 degrees in 2006, and it is now nearly 30 degrees. (Fig.31)
`Relative illumination has been required to be no worse than cos4, approximately 50% for a 60 degree FOV, and it has
`recently been relaxing to around 40% as FOV increases – a necessary concession. Vignetting is still not allowed, since
`the lenses are always used at full aperture, unlike lenses for larger digital still cameras.
`
`
`3. LENS CONSTRUCTION
`
`3.1 Basic lens assembly construction
`Conventional lens designs are multi-element injection molded plastic lenses assembled in a plastic barrel, as they were in
`2006. There is no mechanical shutter or fixed aperture, of course, because the mechanisms would be prohibitively large
`and expensive.
`
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`M
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`1.9
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`1.8
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`1.7
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`1.6
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`1.5
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`90
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`80
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`70
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`90
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`30
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`20
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`3.2 Plastic optical materials
`Optical plastics have improved since 2006. (Fig.4)
`While optical properties have improved some, the
`dramatic improvements have been in physical
`properties. The newer materials (COP, COC and
`OKP4, for examples) are easier to mold and to
`coat. Moisture pickup is reduced. Some older
`materials, like PMMA, would absorb water over
`time, and
`refractive
`index would change
`significantly. Also, stress birefringence (a problem
`with PC)
`is
`reduced, avoiding unwanted
`aberrations from the molding process.
`3.3 Wafer level optics
`An unconventional alternative has been produced,
`called “wafer level optics,” WLO. Lenses are made in large wafers, perhaps thousands at once, and the wafers
`are stacked, with spacers and baffles, to create arrays of lens assemblies. The silicon wafer that contains the
`image sensors can be included in the assembly. This has the potential of reducing cost dramatically, but it also
`imposes constraints on the lens design. WLO designs have been produced, but they have been limited to the
`smaller, simpler cameras, so far.
`3.4 Lens construction and assembly tolerances
`In 2006, we emphasized the difficulty of controlling centering tolerances, and that is still an important issue
`today. The extremely small scale of these lenses means that centering tolerances must be proportionately small.
`Centering requirements vary with design, but can easily be below 5 microns decenter of individual surfaces and
`some lens elements. This is not easy to achieve, considering the molding process, where two halves of a large
`multi-cavity mold must maintain centration. Manufacturers control the effects of tolerances in several ways,
`from design through manufacture:
`1- Design for tolerance insensitivity. For example, multi-configuration optimization allows the designer to
`include the effects of tolerances in the design merit function.
`2- Element manufacture. Careful design and construction of manufacturing tools and processes is essential.
`3- Assembly strategies. Determination of the best combinations of cavities and assembly orientation. Also,
`sometimes active alignment is useful, for example, for tilting the lens above the sensor to correct field tilt.
`
`Figure 4. Glass map indicating plastic optical materials.
`
`
`
`4. OPTICAL DESIGN
`The designs of these MCM lenses are very different than those we are used to seeing for larger cameras. Why?
`1- Product requirements. Shortest possible length. Chief ray angle and relative illumination requirements.
`2- Plastic materials. For cost, and to allow the aspheric surfaces necessary for performance.
`3- Small scale. Designs are influenced by tolerance requirements, and lens elements will be relatively thicker and
`larger, when compared with the size of the image.
`4.1 Historical look at patented designs
`Looking at the patent record can give us an idea of the history and variety of these miniature digital camera lens designs.
`There are several characteristics that separate this class of lenses from more traditional wide-angle camera lens designs:
`1- Telephoto ratio is usually less than 1.3.
`2- Aperture stop is close to the front of the lens.
`3-
`f/number is between f/3 and f/2, and corner to corner FOV is 60 to 75 degrees.
`4- Extensive use of aspherics, including a large final surface, which is concave in the center and turning back
`before the edge of the surface.
`
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`.nnnNM
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`588nm
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`1. 00 RELATIVE
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`(30. 05 °)
`
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`(22. 50 °)
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`SPIE-OSA/ Vol. 9293 92931M-4
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`We might refer to them as “wide angle-aspheric field flattened” (WA-AFF) designs. This collection of patented designs
`is not exhaustive, but it does illustrate the variety of designs and give us some idea of the historical record.
`
`US 6,476,982
`
`US 7,277,238
`
`US 7,477,461
`
`US 7,408,723
`
`US 8,072,695
`
`US 8,605,367
`
`Kawakami/Casio
`2001
`
`Noda/Largan
`2005
`
`Bareau/Flextronics
`2006
`
`Lin/Hon Hai
`2007
`
`Lee/Genius
`2010
`
`1.3 MP
`f/2.85
`61.4 deg
`
`2G-2P
`LASF3-SF63-PMMA-
`PMMA
`1.29x
`
`2 MP*
`f/2.83
`69.6 deg
`
`4P*
`
`1.3 MP
`f/2.97
`62 deg
`
`3P
`
`3 to 5 MP*
`f/2.83
`64.3 deg
`
`4P
`
`407.704-PC-COP-COP COP-PC-COP
`1.13x
`1.37x
`
`COP-OKP4-COP-COP
`1.28x
`
`8 MP*
`f/2.4*
`60 deg
`
`Tsai/Largan
`2011
`
`8 MP*
`f/2.45
`66.2 deg
`
`5P
`COC-OKP4-COC-COC-
`COP
`1.25x
`A10-A10 / A10-A10 /
`A10-A10 / A10-A10 /
`A10-A10
`
`5P
`COC-OKP4-OKP4-COC-
`COC
`1.22x
`A12-A12 / A12-A12 /
`A12-A12 / A14-A16 /
`A16-A16
`
`S-S / A10-A10 /
`A10-A10 / A10-A10
`
`A10-A10 / A10-A10 /
`A10-A10
`
`A10-A10 / A10-A10 /
`A10-A10 / A10-A10
`
`SOURCE: US 6,441,971
`inventor/
`assignee Ning/Ning
`priority year 1999
`SPECS:
`pixels
`
`0.3 MP
`f/2.8
`64 deg
`
`full FOV
`DESIGN:
`
`1G-2P
`
`materials
`tele ratio
`
`SK16-PMMA-PMMA
`1.26x
`
`aspheres?
`
`S-S-S /
`S-S /
`A6-A10 / A10-A10
`A10-C / C-A10
`
`* not certain from patent information
`The earliest patented WA-AFF design that we found was from 1999. (It would be interesting to learn about earlier ones,
`if they exist.) In the chronological progression above, we see materials shifting completely to the newer types, and the
`use of high-order aspherics becoming more uninhibited. (We
`describe
`the aspheres by
`the highest order non-zero
`coefficient listed in the patent, with S for sphere and C for
`pure conic.) Glass elements were used in early designs to
`reduce Petzval sum and sometimes to correct longitudinal
`chromatic aberration. All of the designs are stop in front,
`except the fourth example (3P designs are frequently not
`stop in front.)
`4.2 Is it possible to understand how these designs work?
`If we consider small field angles, third-order aberrations
`make sense. For example, the negative last surface reduces
`Petzval sum, controlling field curvature. It cannot continue,
`though, because the chief ray angle would become much too
`large. At higher field angles, the aspheres become dominant.
`Lateral chromatic aberration, distortion, field curvature, and
`astigmatism, in particular, are corrected by the interaction of
`multiple high-order aspheric surfaces, see Figs. 5 and 6. This
`is remarkable, because the front stop designs get no help
`from stop symmetry in the correction of distortion and lateral
`chromatic aberration, and the plastic material choices are
`limited. This observer cannot come up with a simple
`explanation for it. [J. Sasian discusses the use of aspheres to
`correct field curvature in another paper at this conference,
`though.] We would expect that the very strong aspherics and
`high ray incidence angles increase alignment tolerance
`sensitivities, making the practical success of these lenses
`even more impressive.
`
`Figure 5. Field aberrations, USP 8,605,367.
`
`Figure 6. Transverse ray aberrations, USP 8,072,695.
`
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`Nikon 28mm f/2.8
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`1
`0.9
`0.8
`0.7
`0.6
`0.5
`0.4
`0.3
`0.2
`0.1
`o
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`o
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`10
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`15
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`20
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`25
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`-10 c /mm Sag - - - 10 c /mm Tan - 30 c /mm Sag - - - 30 c /mm Tan
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`- Sag 10c /mm - - - Tan 10& /mm -Sag 30c/mm - - - Tan 300mm
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`4.3 Design performance comparison
`Can we compare these WA-AFF designs to other camera lenses? One might think that because of their small scale, these
`lenses don’t need to perform as well, geometrically, as those for larger formats. To attempt a fair comparison, we took
`one of the best patent designs, USP 8,605,367, and scaled it up to match the 35mm format. We can find MTF data for
`some commercial lenses for 35mm. So, to match the diagonal of the 35mm format, the patent EFL (4.35mm) was scaled
`to 31.48mm, f/2.8. Nikon publishes MTF data for some of its DSLR lenses, and their 28mm f/2.8 product is close in
`specification to our scaled miniature lens. It is built with six glass elements, all spherical surfaces. The high-order
`aspheric terms of the patent design were slightly reoptimized, to correct for errors in the patent data (probably precision
`limitations).
`
`
`
`Figure 7. MTF data from a wide angle lens for 35mm photography3 (left), and a WF-AFF design, scaled to the 35mm format.
`The scaled lens stands up well in comparison. Corner MTFs are surprisingly high, and its mid-field tangential MTF
`could probably be improved with more careful optimization. This comparison is not strictly fair, though; we don’t know
`the conditions of Nikon’s MTF data (is it design only, design plus tolerances, or measured from samples?) and the patent
`lens evaluation does not include tolerances. Of course, it is NOT reasonable to conclude that the plastic patent lens could
`actually be built at that large scale, we were just curious to compare the geometrical performance of the design.
`
`
`5. AUTOFOCUS
`As an example of the issues presented to miniature camera designers, providing automatic focus adjustment (AF) at such
`a small scale and low cost is not as easy as one might think. Early MCMs were fixed focus, acceptable for general
`photography, relying on large depth of field that comes with small entrance pupils and low digital resolution. Now,
`though, the need for focusing from infinity to 10 cm is driven by barcode reading and document scanning.
`A camera of modest specifications (5MP, 1.4 micron pixels, f/2.6, 70o FOV) has an EFL of 3.24 mm and EPD of 1.25
`mm. If our focus error limit is 1 Airy disc diameter (2.4 pixels), the hyperfocal distance is 1.16 meters, and there are 5.8
`focus “zones” between infinity and 10cm. AF is certainly required.
`Furthermore, plastic lenses have large changes of refractive index with temperature. Focal length can change
`significantly, and AF systems can correct that error.
`Implementing AF sounds simple, but there are challenges: Cost, size, speed (minimize shutter lag), and reliability goals
`must be met while maintaining acceptable image quality.
`5.1 Classes of AF solutions
`1- No physical change to the lens.
`a. Fixed focus – limited close focus distance.
`b. Extended depth of field (EDOF). This is a computational optics method. The classic idea is to build a
`“pre-aberrated” lens, which will produce a known point spread function that changes minimally with
`
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`object distance. The earliest work on EDOF that we know was by Dowski and Cathey4, in the ‘90s.
`EDOF has been used in consumer cameras. Special processing is used to restore sharpness to the
`image. It is a challenge to build the aberrated lens precisely. The two big benefits are high reliability
`because there are no moving parts, and zero shutter lag.
`2- Axial lens motion.
`a. Unit focusing – Move the entire taking lens. This is the classic way to focus a camera, and it dominates
`the MCM market now. Voice coil motors (VCM) are used to move the lens, which is suspended on
`very compliant flexures. VCM assemblies add cost and moving parts. It is a challenge to move the lens
`without tilting it, and going towards even smaller assemblies is difficult. Nevertheless, performance
`can be excellent.
`b. Group focusing – Move a subsection of the lens, maybe one lens element. This may require shorter
`motion than unit focusing, but it may also need tighter control of tilt and decenter. Aberration balance
`of the lens will change. It has been implemented with MEMS structures providing suspensions.
`3- Tunable optical power.
`Create a lens element whose optical power can be tuned electrically, with essentially no moving parts. It
`can be mounted near the aperture stop of a fixed-focus camera module and its optical power is weak, so
`integration is simple. z-height of the module is increased by the thickness of the element, but x and y can be
`small. The tunable part affects aberration balance. Image sharpness will be reduced at close focus. There are
`three technologies that have been demonstrated:
`a. Deformable lens. Typically, a flexible lens is squeezed or stretched to change its shape.
`b. Electrowetting5. Two immiscible liquids in a cell. They have different refractive indices, and the
`boundary between them changes shape with electrical signal.
`c. Liquid crystal lens6. Cells of birefringent liquid crystal material form a variable gradient index lens.
`
`6. ZOOM AND IMAGE STABILIZATION
`These two lens features that are found in many digital still cameras have not yet become commonplace in MCMs.
`Optical zoom is made very difficult by the size and cost constraints of mobile devices. There are high-end solutions that
`enable digital “zoom” by using a very high resolution sensor and taking lens.
`Optical image stabilization can provide a valuable improvement in low light performance, by reducing the effect of
`camera shake at long exposure times. There are some cameras that implement it with VCMs moving the lens or sensor in
`x and y, using data provided by miniature gyroscopic sensors. In the future, this might be accomplished with tunable
`prisms, or perhaps with computational methods.
`
`
`7. UNCONVENTIONAL DESIGN ALTERNATIVES
`Lightfield photography,6 where light from the pupil is divided into an array of subpupils, which are recorded separately,
`could have future utility in MCMs. With post-exposure computation, it enables focus tuning, extended depth of field,
`and other capabilities. It is hard to imagine the small entrance pupils being reduced even further without penalty in MTF
`due to diffraction, though.
`Array cameras are also being considered.7 Replacing the traditional MCM with an array of much smaller cameras can
`significantly reduce system z-height (a big motivating factor), and gives us a broad menu of post-exposure possibilities
`for computational image recovery, similar to lightfield photography.
`Any computational imaging scheme raises questions of reduced signal to noise ratio and of digital artifacts in the final
`image, but it also presents the opportunity for innovative new capabilities, transforming the camera from an image
`recorder to a more general data collection device.
`
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`Exhibit 2032
`Page 7
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`SPIE-OSA/ Vol. 9293 92931M-7
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`8. CONCLUSIONS
`The optics in today’s miniature camera modules are a remarkable technical achievement. Steady progress continues to be
`made, and the performance of the extremely small, low cost lenses has become surprisingly good.
`The asphere-dominated design form that has developed for these products appears to have been known for less than
`twenty years. It deserves recognition – and maybe even a name of its own (WA-AFF, perhaps?).
`Radically different camera designs are being considered for these products, to reduce size and cost and to provide new
`capabilities. Optical designers must be part of that process, bringing their experience to the conversation.
`
`
`9. ACKNOWLEDGMENTS
`Thanks to the CRC Press for permission to use figures 2 and 3, from reference [1]. Thanks also to Scott Lerner and the
`IODC-14 committee for suggesting this talk.
`
`REFERENCES
`
`[1] Galstian, T. V., [Smart Mini Cameras], CRC Press, Boca Raton, FL, (2014).
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`[3] http://www.nikonusa.com/en/Nikon-Products/Product/Camera-Lenses/AF-Nikkor-28mm-f%252F2.8D.html#!
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`[5] “Liquid lens based on electrowetting: A new adaptive component for imaging applications in consumer electronics,”
`J Crassous, C Gabay, G Liogier, B Berge, Proc. SPIE 5639 (2004).
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`[7] “Digital Light Field Photography,” R Ng, PhD Dissertation, Stanford University (www.lytro.com/renng-thesis.pdf)
`[8] “PiCam: An ultra-thin high performance monolithic camera array,” K Venkataraman, et al, ACM Transactions on
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`APPLE V COREPHOTONICS
`IPR2020-00906
`Exhibit 2032
`Page 8
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