2013THOSS Media & DE GRUYTER
`
`DOI 10 •. 1515/aot-2012-0069 -
`
`Adv. Opt. Techn. 2013; 2(1): 13-20
`
`he modern miniature camera objective: an
`volutionary design path from the landscape lens
`
`stract: The modern miniature camera lens Is the most
`. olific design manufactured today, yet its design form
`d origins are often not well understood. This paper illu-
`. ates the ancestry of the modern.miniature camera lens
`developing the lens form from 'scratch.' Starting with
`e Wollaston meniscus of 1812, the lens is designed pro(cid:173)
`essively, employing incremental design decisions aimed
`correcting limiting aberrations at each step. The result
`monstrates an ancestry that is distinctly different than
`tofthe common large-format objective lenses.
`
`eywords: aspheric surfaces; camera objective; mobile
`one cameras; optical design; polymer.
`
`220.1000; 220.3620; 220.1250;
`
`orresponding author: Rob Bates, Fivefocal LLC, 1600 Range
`eet, Boulder, CO 80301, USA, e-mail: rob.bates@fivefocal.com
`
`Introduction
`
`e history of the camera objective, as chronicled by King(cid:173)
`e in 1989, is a fascinating look at the evolution of lens
`· gn in response to burgeoning optical materials, advances
`· manufacturing processes, and changes in design speci(cid:173)
`tions [1].· Since the completion or that work, the rise
`digital imaging and postprocessing capabilities have
`ged the modem camera and led to an expansion oflens
`to system-level design, often identified as 'computa(cid:173)
`al imaging.' These advances have resqlted in unusual
`designs, but the large-fonnat digital cameras that are
`popular use still have objective lenses that draw on an
`istakable ancestry illuminated by Kingslake's work.
`The camera objective in the compact camera module
`snot draw on the same ancestry as the common large(cid:173)
`at lens employed in digital imaging. Compared to a
`-format lens, the miniature camera objective meets
`d overcomes a different set of challenges, as described
`
`. degruyter.com/aot
`
`by a recent paper by Steinich and Blahnik [2]. Owing to the
`demand for compact track length, exploitation of optical
`grade polymers, and advances in injection molding, the
`result is a lens form that appears very different from the
`large-format lens. Figure 1 demonstrates a recent sample
`from the patent literature that is indicative of the form [3J.
`Contrasted to a typical large-format camera objective,
`like any of the double Gauss derivatives, there appears
`to be an evolutionary jump in the history of lens design
`leading to the unusual-looking modern miniature camera
`objective. However, this is not strictly the case; the double
`Gauss does not .provide the correct standard for compari(cid:173)
`son. Many modem patents from Olympus and Konica
`Minolta describe a four-element miniature camera objec(cid:173)
`tive as an inverted Ernostar. [4, 5]. When viewed from that
`perspective, the · miniature camera objective does not
`appear as unusual with . its very forward· aperture stop
`positioning, asymmetric design, and power placement.
`This tutorial seeks to build the family tree of the
`modem miniature camera objective by designing the lens
`from 'scratch,' following closely the development of forms
`identified in Kingslake's original work. We. will identify
`its ancestry along the way and demonstrate that the lens
`design form of the most widely used camera objective
`in history can be found through a logical progression of
`design choices starting from the first camera objective.
`
`2 Design specifications and
`considerations
`
`The compact camera module specifications that have been
`the driving force for change are a reduced track length and
`low cost, a motivation. clearly captured in early designs
`that were still rather traditional in form [6]. As with Kodak's
`attempts to minimize the cost in the 1950s with the Dakon
`line of lenses, the volume production of plastic elements
`became. an attractive solution for cost. Following this
`material choice, the highly aspheric, thin element shapes
`enabled by injection molded plastic elements provided an
`additional leverage to reduce the track length .
`
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`14 --- R. Bates: The modern miniature camera objective
`
`© 2013 THOSS Media & DE GRUYTER
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`Table 1 Miniature camera objective specifications.
`
`Parameter
`
`Value
`
`Effective Focal Length (EFL)
`4.1 mm
`2.li
`f/#
`Sensor array
`3264x2448
`Pixel pitch
`1.4µm
`Sens.or format
`Bayer pattern, backside illumination
`30°, nonlinear
`Maxlmumchief ray angle
`<2%
`IDistortlonl
`>50%
`Relative illumination
`Element center and thickness >0.30 mm
`Total Track Length(TTL)
`<4.5mm
`Back Focal Length (BFL)
`>1 mm (accommodates IR-cut filter
`and cover glass)
`<45°
`
`Element surface slopes
`
`nearly 25 years before photography was invent,ed [7]. It
`took the form of a meniscus element separated·from the
`aperture stop and operated at f/15 ..
`We begin with this starting point by scaling the system
`to the 4.1-:tnm Effective Focal Length (EFL). We also shift
`immediately to plastic in place of glass, as we will be tar(cid:173)
`geting a plastic~only solution. As one of the limiting aber~
`rations in this design is lateral chromatic aberration, this
`influences the selection. For this single element lens with
`the stop fixed in the 'natural,' coma-free location, the lateral
`color can only be reduced by increasing the Abbe number.
`Thus, PMMA is selected as it represents a plastic.crown.
`An implementation of this solution with a flat tangen(cid:173)
`tial field is demonstrated in Figure 2. The spot diagram .in
`Figure 2 shows that the flat tangential field balances two
`of the limiting aberrations of this lens - the sagiUal sptead
`of the spot due to the sagittal field curvature against the
`tangential spread of the spot due to the lateral color.
`Along with the sagittal field curvature and lateral
`chromatic aberration, there are other limiting aberra(cid:173)
`tions in this lens. The third is the So/o barrel distortion.
`The fourth is unseen here because the system has been
`stopped down to f/14 to maintain a 14-µm RMS spot diam(cid:173)
`eter. As the aperture is increased, the spherical aberration
`will quickly overwhelm the other aberrations. In total, this
`is a. difficult starting point for the goals in Table 1.
`
`Figure 1 Modern f/2.8 five-plastic element miniature camera
`objective with 80° full field of view and 3.63 mm effective focal
`length .from 2012 U.S. Patent 8,189,273. The telephoto ratio Is 1.35.
`
`While cost and track length forced the change, a
`demand for a higher performance, faster lenses supporting
`larger-format imagers have accelerated the evolution of the
`miniature camera objective. In 2007, the first-generation
`· · iPhone was released with an f/2.8 camera objective paired
`with a 2-MP array. Now in 2012, the f/2.4 camera objective is a
`five-element lens paired with an 8-MP array, and the camera
`module is claimed to be 25o/o shorter than it was a year ago.
`For this tutorial, the lens will be designed to.specifications
`that are similar to the current iPhone lens with precision
`injection molding . as the manufacturing method. These
`. · specifications and design constraints are provided in Table 1.
`As the following lens design will begin with poorly
`performing origins, the design performance will first· be
`described in terms of RMS spot diameter, and the lenses
`will be designed to operate at an f/ # with a target maximum
`of 14 µm RMS spot diameter over the field, as this tends to .
`produce f-numbers similar to the original use. Only in the
`· final stage will the performance be reported using the more
`relevant MTF performance metric.
`
`3 Progressive design of modern
`camera objective
`
`3.2 Reducing track length with reversed
`meniscus
`
`3.1 Starting point: landscape lens of 1812
`
`The first photographic objective that . achieved a larger
`FOV at 60° full field was provided by Wollaston in 1812,
`
`There are several directions one could. take from the land(cid:173)
`scape lens starting point, and we choose to work on the track
`length first. This is useful at this early stage to gain an under(cid:173)
`standing of the limits of space as the design progresses.
`
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`2 Wbllaston meniscus lens with a flat tangential field. The spot diagram at the right demonstrates the trade between lateral color
`sagittal field curvature, Scale is provided by the square surroundingthe on-axis ray bundle, whkh is 10 µm on each side.
`
`\
`
`length will be reduced easily by changing to the alter(cid:173)
`form of the. landscape lens with the stop behind the
`This lens, shown in Figure 3, has a Total Track Length
`l of3.84 mm comparedto theS.15 mm before.
`The reversed landscape lens is a compromise of perfor(cid:173)
`ce for form, as was understood by those at Kodak who
`keted the solution in 1934. Compared to the specifica(cid:173)
`in Table 1, the track length requirement is now met,
`the performance is degraded. The lens must be stopped
`to f/22 to· maintain an RMS spot· diameter of 14 µm.
`lens also suffers from a pincushion distortion of 8.So/o.
`
`3.3 Reducing odd aberrationsthrough
`symmetry
`
`At this point, one could choose to achromatize the lens,
`but with the available plastics, a new achromat is not
`possible, and the old achromat will shorten the already
`troublesome Petzval · radius. In fact, such · a design will
`decrease the Petzval radius from ·2.l to-1.4 times the focal
`length. Instead, we choose to follow the path that G. S.
`Cundell took in 1844 and apply symmetry to the d~sign.
`The symmetry about the stop will correct the odd· aberra 0
`tions, ofwhichlateral color and distortion are two ofthe
`J limiting aberrations of the .current lens. This design is
`shown in Figure 4.
`
`e3 Reversed meniscus lens with a flat tangential field operat(cid:173)
`at f/22with a reduced track length at 3.84 mm.
`
`Figure 4 Symmetric meniscus lenses p.ositioned about the stop
`reduce the odd aberrations. The lens is f/12;
`
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`16 -
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`R. Bates: The modern miniature c:amera objective
`
`© 2013 THOSS Media & DE GRUYTER
`
`This step in the design process has virtually eliminated
`two of the limiting aberrations, with lateral chromatic
`aberration nearly zero and distortion at -0.4o/o. The system ·
`is now operatingatf/12 to maintain an.extreme field RMS
`· spot diameter less than 14 µm. However, increasing the
`numerical aperture further would extend the track length,
`which is already increasing beyond 4.7 mm.
`In addition to spherical aberration, the.field curvature
`is now one of the limiting aberrations in this system. The
`Petzval radius has decreased to ,1.6f, which is better than
`the achromatic solution, but worse than the reversed land(cid:173)
`scape lens. In an attempt to correct this problem, further
`optimization will tend to form the. second lens into a high,
`positive shape factor with a large displacement from the
`stop, significantly increasing the ray angles at this lens.
`Another way to reduce the Petzval sum is to increase the
`index of the second lens by changing it to PEI, but this
`greatly degrades the distortion for little• field curvature
`improvement. As the performance of this lens is decent,
`we are going to leave the correction of the field curvature
`for a while and address the issue of increasing the numeri(cid:173)
`c_al aperture of this solution.
`
`3.4 Increasing the numerical aperture
`with an achromatic doublet ·
`
`As one considers Figure 4 with plastic lenses in mind,
`there is little hesitation to apply a fourth order asphere to
`the second surface of the first element to correct spheri- ·
`cal aberration as the speed of the lens increases. As we
`are looking to develop the lens through a more traditional
`· path, and our last step was in 1844, we will, instead, apply
`an achromatic doublet at this point to help both the spher(cid:173)
`ical aberration and axial color.
`
`Although a cemented doublet is not generally used
`in high volume plastic lenses, we will begin with such an
`element knowing we will break the cemented interface
`later. We replace the first element of the symmetric menis•
`cus design with an achromat, retaining PMMA as the posi(cid:173)
`tive element and adding to it a negative SAN element. Alter•
`native achromats exist, but this provides a good balance
`of spherical aberration and distortion, while· the design'.
`is driven to f/6. The result, shown in Figure 5 with its ray
`aberration curve, is similar to the Aldis lens of 1901 [ 8].
`At this point, the f/6 lens has a maximum RMS spot
`diameter of 14 µm. The lens is 4.5 mm long, and the dis•
`tortion is -3o/o. The 0field is strongly curved, with a Petzval
`radius of -1.Sf.
`
`3.5 Increasing thenumerical aperture and
`improving performance with a triplet
`
`In order to improve the spherical aberration correction and
`gain some greater control o~r the design variables, the
`cemented doublet was broken, and the lens takes. on the
`form ofDennisTaylor's Cooke triplet from 1893. This design
`is shown in Figure 6 along with its ray fan. When compared
`to the ray fan of the Aldis lens, it is clear that there is a sig~
`nificant similarity in performance, with the broken ceme)lt
`interface enabling better spherical and color correction~
`Not indicated by the ray fan is the greatly improved distor•
`tion, which is now only 0.4o/o at its maximum.
`At this point, we optimize the materials, driving the
`inner flint to the high index, high dispersion PEI. With thi
`material set, the Cooke triple_t form can be further pushe
`to a speed of f/4.5'with a maximum RMS spot diameter of
`14 µm and a 4.5-mm track length. In doing so, the distor~
`tion increases a little to 1.4o/o.
`
`Tangential
`
`Sagittal
`
`Fieldan·g·~-. _ .••.. ••. • ..
`
`3 0 '~
`
`21· -===I=<
`"
`
`1sµm
`
`O'
`
`Figure 5 Lens form similar to that of Aldisfrom 1901. The achromatic. doublet enables the lens to operate aU/6. Ray fan at the right is
`shown with blue, green, and red colors for wavelengths corresponding to theF, d, and C Fraunhofer lines, respectively.
`
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`THOSS Media & DE GRUYTER
`
`R. Bates: The modern miniature camera objective -
`
`17
`
`Tangential·
`
`Sagittal
`
`o·
`
`6 Cooke triplet from 1893, operating at f/ 4.5. The ray fan at the right is shown with blue, green, and red colors for wavelengths cor-
`ing to the F, d, and C Fraunhofer lines, respectively.
`·
`
`,,paths forward from this position are numerous. One
`'·. . is to move to a split triplet, though the typical split
`front element is not attractive because of the length
`"ction. We could also choose to add athick meniscus
`back of the lens.• This improves the Petzval radius
`-1.Bf to -2.Bf and is also a nicely balanced solution,
`· g the lens to be pushed to f/3.2 bi=fore reaching
`spot diameter of 13 µm. Taking this path would
`to a similar end form, butthe transitions are not as
`I.
`Instead, we. will. give up a little performance and
`e to focus on the Petzval radius by adding a negative
`.··· · flattener and moving the stop forward. In doing so,
`.~'.\ire priming the lens to be in a better position to achieve
`• ef ray angle constraint, and the Petzval radius can
`atlyimproved to 04.6f. The resulting design shown
`e?jsvery similar to the objective patented by Imai
`1, as well as the lens used for the Kodak Disc camera
`2 [9].
`,The lens is now operating at f/3.4 with a maximum
`spot diameter of 13 µm. The distortion is 2%, and the
`track length is 4.5 mm.
`
`Wi•.
`
`, Adding aspheric surfaces to increase
`the numerical aperture
`:dns point, the limiting aberration is still spherical aber·
`o if the f/# is to be driven toward f/2.4. To mitigate this
`lem, we add a single fourth-order asphere to the back
`e first element, just as Kodak did with their plastic
`element. The resulting lens is easily. pushed to f/2.4,
`gh the field performance drops off at the edge. An
`· eric · la.st element (also in line with the original lens
`
`form) enables us to improve that condition and at last
`meetthe chief ray angle requirements of Table 1, as well as
`most of the other requirements'. The lens could be pushed
`to a shorter length on par with its focal length, but we will
`keep the 4.5-mm track length in order to retain roomfciran
`additional lens. This lens is shown in Figure 8.
`The lenses in Figures 7 and 8. are difficult to clas(cid:173)
`sify. Warren Smith calls this form 'unusual' and regards
`it as a member of the wide-angle family with one nega(cid:173)
`tive outer element, a telephoto, or a triplet with a field
`corrector [10]. Both Kingslake and Imai refer to this form
`as a wide-angle telephoto. At its core, the lens is similar
`· to. an inversion of Minor's 1916 invention knowri first as
`the Ultrastigmat, a general form more famously known
`as an Ernostar [UJ. There are some examples found in
`the patent literature betweenJ940 and 1960 that are, to
`some degree, similar to the solution shown in Figure 9
`
`Figure 7 F/3.4 triplet with a field flattenerand forwarq located stop·
`improves the Petzval radius.
`
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`18 ....... R. Bates: The modern miniature camera objective
`
`© 2013 THOSS Media & DE GRUYTE1
`
`3.8 Optimizing to the final design form
`
`At last, the design is ready to take on its final form. W
`increase the field, split.the third element, and aspheriz
`all surfaces to improve the performance. This design i
`shown in Figure 9;
`The design meets the specifications from Tablelwit
`a 4.1-mm EFL, 70° full field of view, 4.5 mm track lengtl
`and 1 mm back focal length, which allows room for focw
`an IR cut filter, and sensor cover glass; All edge and centE
`thickness constraints are met, and element surface slope
`are minimized. The chief ray angles are less than 30° c
`the sensor, and the relative illumination.at the edge ofth
`field is 59o/o. As shown in Figure 10, the distortion range
`from -2o/o to 2o/o.
`For the performance, it is more relevant at this poir
`to present an MTF metric. The MTF shown in Figure l
`demonstrates that the lens has been optimized. for goo
`nominal performance. A nearby solution designed for llig
`
`35
`
`-5.0
`
`-2.5
`2.5
`0
`Distortion(%)
`
`5.0
`
`Figure 8 Inverted Ernostar objective o.perating at f/2.4. The second
`surface of the first element has a fourth-order asphere, and the last
`element is described by the fourth- and sixth-.order asp heres on
`both surfaces.
`
`and its variants, but too superficial to claim a more direct
`relationship [12-15].
`The lens is now f/2.4 wi.th a maximum RMS spot diam(cid:173)
`eter of 14 µm. The track length is 4.5 mm, and the chief ray
`. angle constraint, aswell as the surface slope constraints,
`is met. The distortion ranges from ·2o/o to 2o/o.
`
`.
`Figure 10 Distortion plot for five-plastk element miniature camerc
`objective.
`
`~.)
`
`'
`
`1;0
`0.9
`0.8
`0.7
`C: 0.6
`0
`Zl
`.ill 0.5
`::,
`"O
`0 0.4
`:ii:
`0.3
`0.2
`0.1
`
`Figure9 The final f/2.4 five-plastic element design meeting the
`specifications with a 4.1-mm effective focal length ancf 70° full field ·
`of view. All surfaces are aspheric of varying order, upto the 14th
`order. The telephoto ratio is 1.1.
`
`Figure 11 MTF for five-plastic element miniature camera objective,
`The fields are defined by their relativll heights out to the 35° field
`angle. The tangential MTFis indkated by solid lines, the sagittaf
`MTF is indicated. by dashed lines.
`
`40
`
`80
`
`120 160 200 240 280 320
`Spatial frequency (cy/mm)
`
`.360
`
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`ER
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`· © 2013 THOSS Media & DE GRUYTER
`
`R. Bates: The modern miniature camera objective -
`
`19
`
`Ne
`ize
`is
`
`:th
`:h,
`lS,
`:er
`es
`at
`Ile
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`nt
`11
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`
`F/15 Wolla',Ston meniscus, 1P
`
`. Fl2.4Minor Ultrastigmat, 4P F/2 4 Miniature
`(inverted with aspherlcs)
`ca~era lens 5p
`F/4,5 Taylor triplet, 3P
`'
`
`1800
`
`2000
`
`F/12Cundall
`symmetric menisci, 2P F/6 Aldis lens, 3P
`
`F/3.4lmai lens, 4P
`
`Figure 12 The modern miniature camera lens progressive design
`timeline. F-numbers are attributed according to the resultantdesign
`. in this study and do not necessarily correlate to. the original use.
`The number of plastic elements is indicated after the .lens name.
`
`yield would have been optimized to trade Httle nominal
`performance, in order to make the solutionas robust to
`manufacturing errors as possible, as demonstrated.previ(cid:173)
`ously by the author [16].
`
`4 Conclusions
`
`The modern, miniature camera objective can be devel(cid:173)
`oped using incremental steps between forms created over
`· the last 200 years of lens design, producing a time line as
`shown in Figure 12. ·
`In developing .the form of the modem miniature
`camera objective, we started with the Wollaston menis(cid:173)
`cus lens of 1812 and reduced the length of the lens by
`reversing its placement with the aperture stop. Odd
`aberrations were corrected through the introduction of a
`second lens, which provided symmetry about the aperture
`
`· stop, in the fashion of Cundell. Spherical aberration was
`improved through the introduction of a doublet, enabling
`the system to take on a higher numerical aperture in the
`form of Aldis lens. The achromatic doublet was split to
`achieve the Taylor triplet and allow a better control over
`allSeidel aberrations to reduce the f/# further. A field flat(cid:173)
`tener was added to improve the Petzval radius, resulting
`in a solution similar to Imai's. Aspheric surfaces enabled
`independent correction of sphericalaberration as well as
`a better control of the field curves and distortion while
`meeting the constraints of the chief ray angle ofincidence :
`at the sensor. This culminated in meeting the goal of f/2.4
`operation with a lens similar to an inversion of Minor's
`Ultrastigmat The final !eris performance was optimized
`while meetin~ the design constraints through the intro(cid:173)
`duction of aspheric surfaces throughout.
`The design process. demonstrates how a lens of pre(cid:173)
`sumably unusual design may be conceived and also gives·
`rise to a kind offamily tree. In this development, we find
`that the modem miniature camera lens extends from the
`Cooke triplet on a different path than thatofthe common
`large-format objective. The large-format objective lens
`follows from the triplet along the lines of the split triplet,
`Emostar, Sonnar, Tessar, and double Gauss. forms. Owing
`to its space consttaints, the miniature camera objective .
`follows from the triplet as a compact wide-angle telephoto
`that is most closely related to an inverted Ernostar from
`1916 or Imai's patent from 1979.
`·
`
`Received November 13, 2012; accepted December 13, 2012
`
`References
`
`[ll R. Kings!ake, 'A History of the Photographic Lens' (Academic
`Press, London, 1989).
`(2) T. Stelnich and V'. Blahnik, Adv. Opt, Techn. 1, 51-58 (2012).
`[3) S. Noda, 'Imaging Lens Assembly', U.S. Patent 8,189,273 B2
`(2012).
`[4] Y. Kamo, 'Image formation optical system and imaging system
`incorporating the same', U.S. Patent 7,206,143 B2 (2007).
`[5) M. Sato, 'Image pkkup lens, image pickup apparatus, and
`mobile terminal provided with image pickup apparatus', U.S.
`Patent 7,215,492 B2 (2007).
`[61 H. Yamada, 'Imaging lens\U.S; Patent 5,940,219 (1999).
`[7] W. H. Wollaston. Phil. Mag. 41,124 (1813).
`[8) H. Aldis, 'Photographic lens', U.S. Patent 682,017 (1901).
`
`[9] T. Imai, 'Photographic lens system', U.S. Patent 4,303,313
`(1981).
`[10] W .. Smlth, 'Modern Lens Design' (McGraw-Hill, U.S., 2005).
`[11] C. Minor, 'Photographic objective', U.S. Patent 1,360,667
`(1920).
`[12] F. Altman, .'Lens', U.S. Patent 2,343,629 (1942).
`[13] W. Orser, 'Optical scanning objective lens system for
`inspection devices', U.S. Patent 2,747,466 (1956).
`[14) I. Sand back, 'Optical objective', U.S. Patent 3,011,401 (1961).
`[15] W. Johnson, 'Optical objective', U5. Patent 3,011,402 (1961).
`[16] R. Bates, Proc. SPIE 7793, 779302 (2010). Available l:lt
`http:// proceed! n gs. spied igitallib rary. org /proceeding.
`aspx?articleid=1347508.
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`APPL-1040 / Page 7 of 8
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`DE GRUYTER
`
`2013 · VOLUME 2 · NUMBER 1
`ISSN 2192-8576 · e-lSSN 2192-8584
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`ADVANCED
`OPTICAL
`TECHNOLOGIES
`
`EDITOR-IN-CHIEF
`Michael Pfejfer
`
`European Oplical Society
`
`Col1erence ior Europe
`
`www.degruyter.com/aot
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`APPL-1040 / Page 8 of 8
`APPLE INC v. COREPHOTONICS LTD.
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