International Optical Design Conference 2006, edited by G. Groot Gregory,
`Joseph M. Howard, R. John Koshel, SPIE Vol. 6342, 63421F,
`© 2006 SPIE-OSA · 0277-786X/06/$15 · doi: 10.1117/12.692291
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`SPIE-OSA/ Vol. 6342 63421F-1
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`The Optics of Miniature Digital Camera Modules
`Jane Bareau and Peter P. Clark
`Flextronics Optical Technology Center, 1 Upland Road, Norwood, MA, USA 02062
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`ABSTRACT
`
`Designing lenses for cell phone cameras is different from designing for traditional imaging systems; the format poses
`unique challenges. Most of the difficulty stems from the scale of the system, which is based on the size of the sensor.
`
`Keywords: Optical design, lens design, digital cameras
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`1. INTRODUCTION
`The scale of cell phone camera systems creates particular challenges for the lens designer that are unique to this format.
`Both the size and the low-cost requirements have many implications for the design, fabrication and assembly processes.
`
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`Fig.1: This 3.6um pixel VGA camera module is 6.05 x 6.05 x 4.5 mm.
`The most critical dimension is the 4.5 mm axial length.
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`For those of us who have been involved in the design and manufacturing of consumer and commercial imaging systems
`using lens elements with diameters in the 12-40mm range, the switch to much smaller elements with diameters in the 3-
`5mm range takes some adjustment. When designing a camera module lens, it is not always helpful to begin with a
`traditional larger-scale imaging lens. Scaling down such a lens will result in a system that is unmanufacturable. If the
`design includes molded plastic optics, a scaled down system will result in element edge thicknesses shrinking to the
`point where the flow of plastic is affected. For glass elements, the edge thicknesses will become too thin to be fabricated
`without chipping. To achieve a successful design we have to modify our lens forms and adjust the proportions of the
`elements.
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`Layout drawings can be very misleading. Many times we find ourselves surprised when the mechanical layout of a lens
`barrel that looked reasonable on paper turns out to be very difficult or impossible to fabricate. Tabs on a barrel that
`appear substantial in a drawing, are found to be too flimsy to function on the actual part, “sharp” edges on molded stops
`don’t fill completely because the features are too small. The size of the lenses and mechanical details on the flanges and
`barrels affect all aspects of the manufacturing process. Diamond tools have to be redesigned to be able to generate large
`changes in angle over small areas. Handling the lenses becomes difficult even with tweezers, all inspection and
`screening has to be done with a microscope. Measuring basic dimensions and the surfaces of the lenses becomes very
`challenging. Center thickness and surface decenter measurements in particular are difficult at the high levels of accuracy
`required for current designs. The ability to fabricate accurate and robust fixtures for measurement of individual elements
`has become absolutely critical.
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`Another process that has been affected is assembly. Assembly must be done in clean conditions, with visual aids to
`ensure proper lens orientation and seating. Once an assembly is complete it needs to be tested. Testing assemblies with
`barrel outer dimensions of 6mm pose similar fixturing challenges as those in the fixturing of individual elements, with
`the additional requirement that they must be aligned with a test target for MTF or resolution testing. This target or series
`of targets must provide adequate sampling over an area representing the sensor, to characterize the lens, which could be
`anywhere from 1/10” diagonal to 1/3” diagonal. Fixturing for both MTF testing and resolution testing must minimize
`tilt of the lens barrel with respect to the target.
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`2. CMOS Focal Planes
`Development of sensors has been moving steadily towards smaller pixels and higher density formats. The initial cell
`phone cameras were based around VGA and QVGA modules with 5.6um pixels. Generally formats were between 1/7”
`and ¼” in size. Next, the sensor manufacturers began offering VGA and SXGA sensors with 3.2-3.8um pixels in 1/6-
`1/4” formats. Then the sensors moved to 2.8um pixels offered in VGA, 1.3MP and 2MP, 1/8”, ¼” and 1/3” formats
`respectively, a full 50% reduction in pixel size from the original sensors. Today we are designing for 2-3MP sensors in
`2.2um pixels, ¼” and 1/3” formats, and there are plans for 5MP sensors with 1.75um(!) pixels coming soon.
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`Over the past couple of years, pixel areas have been reduced by 75%, then 85%, soon to be 90%, compared with 5.6
`micron pixels. Lower pixel count formats (VGA and 1.3mp) have gotten correspondingly smaller, and higher resolution
`sensors (2mp and 3mp) have been introduced. The higher resolution formats have made the job of the lens designer
`extremely challenging because, while the basic imaging problem has remained the same, each reduction in pixel size
`has required an increase in lens performance,, and the overall length of the system is often required to be shorter. VGA
`systems pose different, but no less daunting problems. VGA sensors have scaled with the pixel size from ¼” with the
`original 5.6um pixels to the current 1/11” format based on a 2.2um pixel. As the pixels have shrunk, the lenses for VGA
`systems have become so small that contamination is now a major issue and the scratch/dig requirements for each lens
`surface are very tight making the lenses very difficult to manufacture.
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`3. The Problem of Scale
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`Fig.2: 3-element lens, disassembled. Barrel, three plastic
`aspheric lenses, thin sheet aperture stop and baffle.
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`It is interesting to consider the differences between these miniature camera module lenses and lenses for conventional
`photography, such as the 35 mm format. The goal is the same: Produce pleasing images of snapshot quality. However,
`the scale of the optical system is reduced by roughly a factor of ten!
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`35 mm single use
`43 mm
`37.5 mm
`11, fixed
`3.4 mm
`10 – 20 /mm
`$0.50 (est.)
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`¼” CMOS
`4.4 mm
`3.8 mm
`2.8, fixed
`1.36 mm
`50 – 100 /mm
`$1 (est.)
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`35 mm point and shoot
`43 mm
`37.5 mm
`2.8, variable
`13.4 mm
`10 – 40 /mm
`$10 (est.)
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`Film format diagonals:
`Lens EFL:
`f/number:
`Entrance pupil diam:
`Spatial frequencies:
`Cost:
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`If we were able to simply scale the 35 mm lens design by 1/10x, we would encounter a few issues:
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`1) Smaller entrance pupil: Depth of field will be much greater, but diffraction will limit performance sooner than with
`larger formats.
`2) Surface figure tolerances: Figure tolerances (fringes of irregularity, for example) will be somewhat tighter, because
`spatial frequencies of interest are higher, but because the surfaces are smaller, they will be easier to achieve in practice.
`3) Geometric tolerances: Scaling the system’s size requires linear tolerances to scale as well. So center thickness
`tolerances and surface and element decenter tolerances will be tighter by a factor of ten. This proves to be the greatest
`challenge of producing these lenses.
`4) Angular tolerances: Lens tilt tolerances do not scale down, but small defects on flanges or mounting surfaces will
`have a larger effect on tilt.
`5) Stray light considerations: An aperture or baffle feature that has an acceptably small dimension at the large scale
`should be scaled down by 1/10. However, some parts cannot be made thin enough, or they may become translucent, so
`they will cause a larger fraction of the light to scatter from their edges, resulting in flare or veiling glare.
`6) Scratch/Dig and Contamination: The smaller system is much more sensitive to defects and contamination causing
`shadowing on the image. Acceptable defect dimensions scale with the format size, and the situation is often worse in
`practice, because the back focal distance is very short and defects close to the image are more visible.
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`4. Specifications
`The following are typical lens specifications for a ¼” sensor format:
`
`
`FOV
`Image Circle
`TTL
`f/no
`Distortion
`Chief Ray Angle
`Relative Illumination
`
`60 degrees
`4.6 mm diam.
`5.0mm
`f/2.8
`<2%
`<22 degrees
`>50%
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`FOV - The field of view for these systems is typically 60 to 66 degrees across the sensor diagonal, but the design must
`include a slightly larger angle to allow for correction over the image circle.
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`Image Circle - This is the diameter of the image over which the lens has to be well corrected to allow for lateral
`displacement of the sensor relative to the optical axis. Lens to sensor centration errors are caused mostly by uncertainty
`in the placement of the sensor on its circuit board. To allow for those errors, the lens image circle is increased by at least
`0.2 mm. As sensors get smaller sensor placement accuracy must improve.
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`TTL- The total track length is the distance from the front of the barrel to the image plane, this has to be longer than the
`optical track length by at least 0.050mm in order to protect the front of the lens. This is extremely important to the cell
`phone designers because of the market pressure to produce thinner phones.
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`f/number – Although most camera module customers specify f/2.8, it is not uncommon to see lenses at f/3.0 and f/3.3
`when the increased fno has a significant effect on performance or manufacturability. However, smaller pixel sensors
`have less light gathering capability and will suffer at slower f/numbers.
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`Distortion – The usual distortion requirement is <2% optical distortion or <1% TV distortion. Although this sounds like
`a much more stringent requirement than the 4% typically allowed in traditional 35mm camera lenses, the distortion
`curve can vary significantly from assembly to assembly due to build tolerances. In fact the approximate effect of
`tolerances is to add positive or negative slope to the nominal distortion curve.
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`a) Distortion: Nominal Design
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`c) Distortion: Toleranced Build #2
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`b) Distortion: Toleranced Build #1
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`d) Distortion: Toleranced Build #3
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`Fig.3: a) Nominal design distortion curve, b) Distortion curve for a simulated toleranced build,
`displaying moderate tilt, c) Another sample of a simulated build with induced tilt in the distortion
`curve, d) Distortion curve representing the simulated build with the maximum amount of tilt
`generated for this design.
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`As demonstrated in fig.3, a nominal design with distortion < 0.3% can easily generate distortion >1% when fabricated.
`An even more critical factor in ensuring good performance is to limit the slope and rate of change of slope of the
`distortion curve. The added tilt due to tolerances applied to a fast changing distortion curve can result in extremely steep
`slopes that are objectionable in an image.
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`a) Distortion: Nominal Design
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`Fig.4: a) Nominal design distortion is low in magnitude but fast changing over the field, b) Distortion
`curve for simulated build displaying unacceptable tilt and variation in slope as a result of build tolerances.
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`Even though absolute distortion values may be low, large changes in slope over a small area will be noticeable in an
`image. For this reason it is important to control both the shape and the magnitude of the distortion curve.
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`Chief Ray Angle (CRA)– The CRA is the incidence angle of the chief ray at the image plane for any field point. The
`CRA is usually specified as a maximum value that cannot be exceeded anywhere in the field. Most camera module lens
`CRA curves increase monotonically with field to a maximum value and then drop off at the edge of the image, because
`of pupil aberrations. See fig.5.
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`Chief Ray Angle, 1.3MP 1/4"
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`CRA
`microlenses
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`25
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`20
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`15
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`10
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`05
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`Degrees
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`0
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`0.2
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`0.6
`0.4
`Relative Field
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`0.8
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`1
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`Fig.5: Chief Ray Angle and Microlens Optimum Acceptance Angle as a Function of Relative Field
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`To better illustrate the source of this requirement, let’s first take a closer look at the structure of the focal plane. The
`CMOS sensor array is an array of sensors with color filters integrated, to produce the standard Bayer pattern of red,
`green and blue detectors:
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`b) Distortion: Toleranced Build
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`SPIE-OSA/ Vol. 6342 63421F-6
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`Fig.6: Photomicrograph of a portion of a Bayer pattern sensor. 2.8um pixels.
`Note the specular highlights from microlens surfaces.
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`The surface of the detectors is not uniformly sensitive, though. Circuitry integrated with the sensor reduces the active
`area significantly. To improve sensitivity, an array of microlenses is applied to the top of the sensor:
`
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`Fig.7: Microlenses located above active area of sensor, are positioned relative to pixel location
`based on expected incident angle and enhance the sensor’s light collecting ability by magnifying
`the effective area of each pixel. [Highly schematic drawing, not to scale.]
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`These lenses act as condensors, relaying the sensor image to the exit pupil of the lens. This increases the apparent size
`of the detectors, improving sensitivity, because the diameter of the microlens becomes the apparent size of the detectors.
`The plane of microlenses is effectively the image plane of the system. The microlensed detectors now have limited
`angular response; if the exit pupil of the taking lens is increased beyond the size of the detector image, system
`sensitivity does NOT increase. In practice, the microlenses are not perfectly formed, so their imaging is crude, but they
`do improve performance.
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`The CRA curve illustrated in fig.5 represents a lens designed for a maximum CRA value of 20 degrees. The purpose of
`the CRA constraint is to maximize the light collection efficiency of the microlenses. Instead of centering each microlens
`on its pixel, the sensor manufacturers have offset the center of each microlens in order to compensate for the incidence
`angle of chief rays. Ideally the microlens distribution would exactly match the CRA variation of the lens it was to be
`used with, but this is not generally seen in practice. Typically the microlens offsets vary linearly with radial position
`from the center of the sensor, and are designed to minimize CRA/microlens mismatch based on expected lens CRA
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`curves. The effect of mismatch is a drop in light collection efficiency or decreased relative illumination at the image, or
`cross-talk between microlenses and adjacent pixels, resulting in false coloration.
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`Today, maximum CRA specifications for different sensor formats are readily available in the <12 degree to <26 degree
`range, with the larger CRA allowances corresponding to smaller VGA formats (2.2um, 3.6um). The demand for shorter
`TTL’s is putting pressure on sensor manufacturers to increase their maximum allowable CRA values. Added constraints
`and fewer elements are lessening the lens designer’s ability to deliver good image quality performance and low CRA’s.
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`Relative Illumination – The relative illumination is the level of light energy incident at the image plane for a given field
`point relative to that at the center of the image.
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`Relative Illumination vs Field Angle
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` Rel. Ill.
`cos^4
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`0
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`5
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`20
`15
`10
`Field Angle (degrees)
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`25
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`30
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`1.1
`1
`0.9
`0.8
`0.7
`0.6
`0.5
`0.4
`0.3
`0.2
`0.1
`0
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`Relative Illumination
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`Fig.8: Relative Illumination and Cos^4 as a Function of Field Angle
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`The blue curve in fig.8 is a typical relative illumination plot. Lens specifications usually require a value greater than
`50% at the edge of the field. This corresponds roughly to cos^4, so there is rarely enough corner illumination to allow
`vignetting for aberration control. If relative illumination meets the requirements, the final image is corrected
`electronically. Also, it’s important that the drop in the relative illumination curve is not precipitous towards full field, or
`a slight decenter of the sensor relative to the optical axis will cause one corner of an image to appear noticeably dark.
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`5. Designing
`When first beginning a lens design, it is not obvious how many elements to use or which materials. The biggest
`challenge in designing these systems is to create a lens that is insensitive to tolerances and will perform well when built.
`Each additional element adds tolerances that will degrade the as-built performance. But each element also adds
`variables that can be used to increase nominal performance while meeting system and manufacturing constraints.
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`Fig.9: A typical 3-plastic element (3p) imaging system.
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`The three-element form is very common (fig.9), and a good place to start. Just about every camera module lens
`manufacturer has a lens of this form in their offerings. Designs tend not to be stop-symmetric. The aperture stop is
`usually towards the front of the lens, often before the first element, which helps CRA and TTL. The majority of these
`lenses are all-plastic although some incorporate one glass element (usually the front element) for the advantages of
`high-index refraction and color correction. Plastic elements are almost always bi-aspheric, and frequently the aspheres
`are not subtle! The shape of the last lens surface in the design above is typical. Four element systems provide high
`performance, but are only viable when the TTL is relatively large (>6.0mm), otherwise the performance degradation
`due to tolerances cancels out the nominal gain. Four element systems are mostly found in cameras with ¼” sensor
`formats or larger, though they are becoming less common. Likewise, the effectiveness of a 3-element approach
`decreases to the point that a 2-element system becomes more practical when the TTL is less than 4 mm.
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`Part of the selection process, when considering materials, is the cost of satisfying the manufacturing constraints. Plastic
`injection molded optics have minimum edge thicknesses, minimum center thickness and a range of acceptability for
`their center to edge thickness ratio that must be met in order that they can be molded. Additionally, the maximum slope
`that can be diamond-turned in mold inserts and measured in either the lens or the mold is around 45 degrees. One big
`advantage of plastic is that flanges with mechanical details can be molded that eliminate the need for spacers and allow
`for mechanically driven centering of one element to another. One disadvantage is that there are very few plastic
`materials that lend themselves to precision optical molding with stability over large ranges of temperature and humidity,
`so the choices are limited.
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`Traditional glass lenses have similar types of requirements but with different values, based on their own manufacturing
`processes. The inability of lens manufacturers to accurately center the outer dimension of these elements on the optical
`axis, makes precise mounting very difficult. The benefits of traditional glass is reduced as the TTL requirements
`become shorter.
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`Another option becoming more readily available is molded glass, allowing the advantages of both high index and
`aspheric correction. Some current issues with molded glass are the small number of flint-type glasses available for
`molding, surfaces with inflections can only be used under very limited circumstances and flanges can only be formed in
`a restricted range of shapes, no sharp corners or abrupt changes in slope are allowed. Cost and manufacturing capacity
`also limit the use of molded glass elements today. Nevertheless molded glass can be the lens type of choice when the
`goal is stability over extreme ranges of conditions, or great lengths of time.
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`6. Performance Requirements
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`Lens performance for digital sensors is commonly expressed in terms of MTF at spatial frequencies between Nyquist/2
`(Ny/2), and Nyquist/4 (Ny/4). The Nyquist frequency is 1/(2*(pixel size)), so for 5.6um pixels Ny/2 is 45 lp/mm and
`Ny/4 is 22.5 lp/mm; for 1.75 pixels Ny/2 is 143 lp/mm, Ny/4 is 71.4 lp/mm.
`
`Initially, when pixel sizes were relatively large (5.6um), cell phone manufacturers would specify MTF performance for
`Ny/2 and even Ny. This was because Ny/2 was still a relatively low frequency, so the requirements were possible to
`meet. As pixels became smaller (3.6-2.8um), the specifications gravitated to significant response at Ny/4 and Ny/2.
`These requirements were more challenging, but the size was allowed to grow to help satisfy the MTF requirements. At
`the same time the tooling capability of manufacturers was increasing so that build tolerances could be decreased,
`improving performance. The combination of these factors allowed delivery of high performance camera modules. And
`then the drive to reduce TTL began.
`
` As cell phone manufacturers began demanding smaller and smaller camera modules to be able to offer extremely thin
`cell phones, image quality became secondary to size. Today most cell phone manufacturers understand that imposing
`severe size restrictions will significantly compromise image quality, and they are willing to accept worse performance
`based on Ny/2 and Ny/4 MTF response than with previous camera modules. This means that the image quality of 2MP
`camera modules are not all alike; as the pixels get smaller the image quality will be worse, and even newer, thinner
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`versions of cameras based on the same sensor will have worse performance. The opposing requirements of good image
`quality and short TTLs coupled with the shrinking size of pixels are rapidly running into the limitations of physics.
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`7. Tolerance-limited Design
`The lens designer must consider manufacturing tolerances at the optimization stage, compromising nominal
`performance to achieve improved as-built performance. Nevertheless, manufacturing processes are not always available
`to achieve the necessary tolerances. One of the most challenging aspects of designing lenses for camera modules is
`desensitizing the system. If sensitivity to manufacturing tolerances is not built into the merit function, then the lens will
`not be manufacturable.
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`a) Nominal Design - Lens A
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`b) Nominal Design - Lens B
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`c) 50th Percentile Build - Lens A
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`d) 50th Percentile Build - Lens B
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`Fig.10: a) and b) Nominal MTF curves for two lens designs, lens B has been desensitized to the effects
`of manufacturing tolerances, lens A has not; c) and d) 50th percentile MTF curves representing a typical
`manufactured lens, based on simulated builds. The manufacturable MTF performance of lens A is
`greatly deteriorated from the nominal, the performance of lens B holds up much better when
`manufacturing tolerances are applied.
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`Fig.10 illustrates the impact of including desensitization in the optimization process. As the MTF curves clearly
`illustrate, a desensitized lens generally has slightly lower performance than a lens that has not been desensitized, but the
`benefit in the performance stability of manufactured systems more than offsets this difference, improving the overall
`performance of the manufactured lens population.
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`Due to the significant risk that an unfortunate combination of build tolerances will produce a lens with unacceptable
`performance, most lenses for miniature camera modules are 100% tested for image quality, usually with commercially
`available test systems that measure through-focus MTF. Performance is judged at representative points across the field,
`usually at one or two spatial frequencies. Evaluating MTF in two defocused planes can quickly expose field tilt or
`curvature problems.
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`The vast majority of systems are built in threaded barrels and focused at assembly, with no other alignments performed.
`Accurate, tight threads are difficult to produce, and they present measurement and contamination problems. Alternatives
`that allow alignments for lens to sensor centration and tilt are being implemented. As pixel counts get higher and sensor
`dimensions get smaller, these alignments are becoming more critical.
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`The problem of communication of quality between lens manufacturers and their customers is important. Manufacturers
`usually produce their own designs, and they are unwilling to share design data with customers. Also, actual
`manufacturing tolerance capability is not usually available, so it is not possible to verify the manufacturability of a new
`design. Standard methods of predicting production quality are needed to avoid unpleasant surprises during volume
`manufacturing.
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`8. TTL and Desensitization
`The ability of the designer to desensitize a lens is directly tied to the TTL and, for shorter forms, the BFL constraints.
`For instance, the 2MP 2.8um sensor required a lens with good performance over a large format. We were able to
`produce a lens that consistently delivers good image quality only because the TTL for this system was allowed to
`increase to as large as 7.8mm. The longer the TTL, the more modest the refraction needed at each surface, the weaker
`each lens can be and the less sensitive the performance of the system is to build tolerances. The more constrained the
`lens system in length, the more refractive power is needed at each surface, and the more sensitive the lens becomes to
`tolerance-induced image degradation.
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`a) Nominal Design - Lens A (TTL=7.5 mm)
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`b) Nominal Design - Lens B (TTL=6.5 mm)
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`c) 90th Percentile Build - Lens A (TTL=7.5 mm)
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`d) 90th Percentile Build - Lens B (TTL=6.5 mm)
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`Fig.11: a) and b) Nominal MTF curves for two 4-element lens designs constrained by different TTLs, the
`performance is essentially identical; c) and d) MTF curves representing 90th percentile performance
`based on simulated builds. The longer TTL results in more consistently high performance.
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`The MTF curves in fig.11 illustrate the effect of TTL on desensitization. The additional constraint of conforming to a
`shorter TTL increases the difficulty of designing a manufacturable lens with acceptable performance and reasonable
`yields. Although this exercise was performed using a relatively long TTL lens (an older design), the same concept
`applies to today’s shorter TTL designs for systems with three elements or more.
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`Two-element systems often naturally adopt forms with short TTL’s, but desensitization to tolerances can require a
`relatively short BFL. Positioning the IR filter in such a system can be challenging. It is important for the back surface of
`the filter to be as far as possible from the sensor to ensure small surface defects and contamination are adequately out of
`focus. The closer to the sensor, the more restrictive the acceptability requirements on defect size. An IR filter positioned
`too close to the sensor could require such a tight scratch dig specification as to make it prohibitively costly or
`unmanufacturable.
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`The primary focus in recent camera module development has shifted from image quality to size and lens designers are
`being pressured to design lenses with shorter and shorter TTLs. Recent lenses for ¼” formats are being held to
`TTLs<5.0mm and there are plans for new lenses for the same format to be even shorter. Of course the pixels are
`smaller, so Ny/2 is higher (113.6 lp/mmfor 2.2um pixels, 142.9 lp/mm for 1.75um pixels) making the problem even
`more difficult.
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`9. Future Prospects
`We believe that the race for smaller pixels is slowing, because Moore’s law cannot shorten the wavelength of visible
`light, or increase the brightness of photographic subjects. Pixels whose dimensions are under 2 um have limited light-
`collection ability, and much faster f/number lenses are unlikely to be developed. The continuing pressure to design with
`very short TTL’s both for packaging and cost considerations suggests that in the near term the customer can expect
`worse image quality from camera modules using sensors with these very small pixels. Perhaps the market will split, to
`allow a choice between low cost/very small/modest quality cameras, and more costly/larger cameras that can rival
`today’s digital still cameras.
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`The path to sharpness improvement most likely involves a hybrid solution incorporating a desensitized lens design
`combined with improved build tolerances, active alignment at lens and camera assembly, image processing for
`improved depth of field, or all three. There are companies currently developing image processing methods to improve
`image quality and depth of field in digital images. These methods may allow us to build simplified, desensitized lens
`systems whose performance is corrected by digital image processing. There are, of course, tradeoffs to be made between
`sharpness, noise levels and electronic complexity. In each case there will be added costs; it will interesting to see what
`cost/image quality balance cell phone manufacturers finally select to offer their customers in the next generation of cell
`phone cameras products.
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