Diamond milling or turning for the
`fabrication of micro lens arrays:
`comparing different diamond
`machining technologies
`
`Scheiding, Sebastian, Yi, Allen, Gebhardt, Andreas,
`Loose, Roman, Li, Lei, et al.
`
`Sebastian Scheiding, Allen Y. Yi, Andreas Gebhardt, Roman Loose, Lei Li,
`Stefan Risse, Ramona Eberhardt, Andreas Tünnermann, "Diamond milling or
`turning for the fabrication of micro lens arrays: comparing different diamond
`machining technologies," Proc. SPIE 7927, Advanced Fabrication
`Technologies for Micro/Nano Optics and Photonics IV, 79270N (14 February
`2011); doi: 10.1117/12.874751
`Event: SPIE MOEMS-MEMS, 2011, San Francisco, California, United States
`
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`Advanced Fabrication Technologies for Micro/Nano Optics and Photonics IV, edited by Winston V. Schoenfeld,
`Jian Jim Wang, Marko Loncar, Thomas J. Suleski, Proc. of SPIE Vol. 7927, 79270N · © 2011 SPIE
`CCC code: 0277-786X/11/$18 · doi: 10.1117/12.874751
`
`Proc. of SPIE Vol. 7927 79270N-1
`
`Diamond milling or turning for the fabrication of micro lens
`arrays: comparing different diamond machining technologies
`
`Sebastian Scheiding1,3, Allen Y. Yi2, Andreas Gebhardt1, Roman Loose1, Lei Li2, Stefan
`Risse1, Ramona Eberhardt1 and Andreas Tünnermann1,3
`1 Fraunhofer IOF - Institute for Applied Optics and Precision Engineering,
`Albert-Einstein-Str. 7, D-07745 Jena, Germany;
`2 The Ohio State University, Industrial and Systems Engineering, Columbus, Ohio, USA;
`3 Friedrich Schiller University Jena, Institute of Applied Physics, Albert-Einstein-Str. 15,
`D-07745 Jena, Germany
`
`ABSTRACT
`Diamond-micro milling and ultra-precision free-form turning technologies for fabricating micro lens arrays (MLA)
`with a large number of lenslets are explained in detail and compared. Besides the programming of the toolpath,
`correction loops and cutting parameters are presented. Both technologies are compared regarding achievable form
`deviation, roughness and economic factors like machining time. The paper offers a guideline for ultra-precision
`machining of micro lens array master molds on planar substrates and curved surfaces.
`Keywords: Micro Lens Array, Diamond-Micro Milling, Free-form Machining, Fast Tool Servo, Wafer Level
`Manufacturing, Diamond Turning, Mold Insert, Micro Optics
`
`1. INTRODUCTION
`Micro lens arrays containing a large number of lenslets with aspheric shape and a precise position are used for
`beam shaping, illumination or as imaging optics in sensor devices and cameras. The geometry of micro lens
`arrays is tailored to the purpose of the optical element in the application. Depending on the size, the substrate
`material and the number of lenses in a certain area, the fabrication approaches are either based on lithographic
`technologies or machining processes with diamond tools. For each optical design, a suitable manufacturing
`strategy has to be chosen.
`Wafer scale manufacturing of small optics is a high volume fabrication method for low-cost optics. Its fundamental
`principle is the sandwich-like assembly of the light sensitive electronics and optical components such as lenses
`and mechanical components such as apertures and spacers on the wafer level. After joining all components the
`dicing results in a batch of wafer level cameras for use in cellular phones or other consumer electronic devices.
`The fabrication of mold masters for the high-volume replication is challenging due to the high demands on the
`optical quality of the relatively deep aspheres and the precise spacing on wafer sizes up to 300 mm.
`Micro lens arrays are also a centerpiece of today’s sensor products, either to raise the fill factor and collect more
`light on each pixel or to deflect the incoming beam to measure the aberrations of the wavefront, the working
`principle of the Shack-Hartmann sensor. Within illumination optics, micro lens arrays are commonly used
`for beam homogenization in projection systems. In all fields of application ranging from automotive, medical,
`consumer and industrial optics to high end sensors for space instrumentation, high quality lens arrays for direct
`use or replication have to be fabricated.
`Requirements on the allowable shape irregularities are ranging between ±3% of the Radius of Curvature (ROC)
`for illumination optics to 200 nm (p-v) for diffraction limited imaging optics. Besides the form of an optical
`surface, its microroughness is of high importance. Scattering losses and blurred images can be avoided if the
`surface finish is adequate to the wavelength of the transmitted light. Optical elements for imaging purposes in
`the visible spectral range shall be finished with a micro roughness lower than 5 nm (rms).
`Further author information:
`Sebastian Scheiding: E-mail: sebastian.scheiding@iof.fraunhofer.de, Telephone: +49 (0)3641 807 353
`Allen Y. Yi: E-mail: yi.71@osu.edu, Telephone: +1 (614) 292-9984
`
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`Proc. of SPIE Vol. 7927 79270N-2
`
`2. LITHOGRAPHIC TECHNOLOGIES
`A variety of micro technology manufacturing methods can be used for MLA structuring. Lithographic approaches
`with a subsequent reflow process, laser lithography, UV-curing of resin droplets and step- and repeat molding
`of polymers are state of the art processes for the master manufacturing. The lithographic approach is based on
`exposing and developing resist columns on aperture stops and pedestals on a planar substrate.1 Therefore, the
`resulting profile is determined by the shape of the lens’ footprint and the volume of the resist to be melted. In
`case of the most relevant rotationally symmetric lenses, the footprint of the lens is a circle and the resulting
`geometry a sphere due to the surface tension of the liquid melt. Another method to manufacture very similar
`MLAs with spherical or slightly aspherical lenslets is to apply a number of liquid resin droplets on a substrate.
`The wetting angle, the volume of resin and the gravitation can be used to shape the lenslets. The subsequent
`UV-exposure cures the resin droplets to their final form due to volume loss from the polymerization shrinkage.
`More design freedom offers laser lithography, which is a direct writing technique that enables the generation of
`free-form profiles, not limited to spherical shapes on planar substrate surfaces.2 Here, a laser beam is scanned
`over a photo resist layer while the intensity of the beam is modulated. The height of the resulting profile at
`a given position is determined by the local dosage of the writing beam. However, the technology is limited to
`structures of several ten micrometers in height.
`All technologies of this kind have in common that a large number of lenslets can be manufactured. Lenses that
`are shaped in a liquid phase offer an excellent surface quality. On the other hand the surface figure and the
`design freedom regarding aspheric or free-form surfaces are process limited and can only be guaranteed by direct
`writing technologies such as laser lithography. Major drawbacks of the lithographic approaches are the limited
`lens depth and degree of aspherization. The shrinkage of the polymer lenslets during the curing process causes
`
`a shift of the focal length in the (cid:2) to the % range. The volume loss increases with the size of the lenslets and
`
`limits the use of lithographic or dosing technologies for imaging optics with high resolution.
`Furthermore a high fill factor with intersecting lenses is not feasible due to the minimization of surfaces of the
`resin in the liquid phase. Nevertheless, these techniques are proven tools for a wide spread field of applications.
`
`3. OVERVIEW OF THE MACHINING TECHNOLOGIES
`Besides the above mentioned technologies, precision machining of arrays or master arrays for replication is emerg-
`ing into the market for its potential to fabricating structures truly aspheric or free-form lenslets. The feasible
`geometries depend on the shape of the cutting edge of the diamond tool tip and the kinematics of the machining
`process. The smallest possible radius of curvature is a few hundred microns. The micro lens arrays can be
`very dense or even contain overlapping lenslets. The ultra-precision machining thus is an adequate addition to
`lithography for structuring three-dimensional microoptics in the mesoscopic scale.
`Either ultra-precision free-form turning technologies or diamond micro-milling (DMM) are appropriate manufac-
`turing methods to fabricating complete monolithic lens arrays. The chipping is based on cutting with a hard and
`geometrically defined diamond cutting edge, which is fed into the softer material. Both machining techniques
`employ a mono-crystalline diamond tool, whose cutting edge waviness is in the range of below 250 nm. Non
`ferrous metals such as aluminum, brass, copper and their alloys are machinable. In addition plastics and some
`crystals can be chipped with diamond tools. Differences between diamond turning and micro-milling include
`machine kinematics and the generation of the cutting speed. Whereas the cutting speed is generated from the
`rotating workpiece in turning applications, the cutting speed results from the rotating tool in micro milling.
`Diamond Micro-Milling processes can also be realized on the more commonly used ultra-precision turning ma-
`chines with a high-speed spindle addition. The work piece positioning and feed is realized using the polar axis as
`described in Scheiding et al.3 A comparison of free-form machining techniques in production of monolithic lens
`arrays is presented by Davis et al.4 That publication focuses on the machining of a small number of relatively
`large lenses in germanium.
`
`4. DIAMOND MICRO-MILLING
`The diamond ball end mill rotates about its axis with high speed and removes μm-sized chips. The high speed
`milling spindle used is a temperature controlled air bearing spindle with error motion in the nm range. Three
`machine axes are used to position the tool relative to the substrate and to feed the tool along its spiral tool
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`Proc. of SPIE Vol. 7927 79270N-3
`
`C-Axis
`
`X - A x i s
`
`Z-A
`xis
`
`Milling
`Spindle
`
`(a) Machine setup for micro milling of lens arrays
`
`(b) Tool radius compensation for the micro milling of an
`aspheric lenslet
`
`Figure 1. Micro milling of lens arrays
`
`path. Possible machine kinematics are a Carthesian alignment or a polar alignment of the axes. In case of a
`polar turning machine these axes are two linear axes (X, Z) and one rotational axis (C) as shown in figure 1.
`In contrast to conventional diamond turning, the rotational axis is operated discontinuously in C - axis mode.
`It can be positioned like a rotary table to arbitrary angles. Each lenslet is machined individually. Systematic
`errors resulting from a misalignment of the toolshaft to the spindle axis or the waviness of the diamond ball end
`mill can be corrected using a correction cycle. The studies were conducted on a Nanoform 250 from Precitech
`Inc. with an additional B-Axis and ISO 2.25C spindle from Professional Instruments.
`
`4.1 Programming
`Although the MLA is machined on an ultra-precision turning machine, the small off-axis lenslets are not rota-
`tionally symmetric to the center of the rotary axis. Hence the MLA has to be handled like a free-form surface
`regarding operation mode and commands. The tool center points are derived from the 3D surface information
`of the design asphere and the radius dimension of the diamond tool tip, considering the slope of the lenses. The
`programming of the numeric control is based on the calculation of nodes on a spiral tool trajectory on the as-
`pheric surface. The surface pointing vector of a central aspherical lens can be described in Cartesian coordinates
`as:
`
`⎞⎟⎟⎠
`
`x y
`
`(cid:7)
`
`R·
`
`(cid:8)
`
`1+
`
`2
`
`
`x2+y
`1−(1+κ)· x2+y2
`
`R2
`
`(cid:9) + A4 · (x2 + y2)2 + A6 · (x2 + y2)4 + A8 · (x2 + y2)6
`
`⎛⎜⎜⎝
`
`=
`
`⎞⎠
`
`x y z
`
`⎛⎝
`
`(cid:2)r =
`
`(1)
`
`(2)
`
`Here R is the radius of curvature at x = y = 0, κ is the conic constant and A4 to A8 are the aspheric
`
`∂x and ∂(cid:4)r∂y of the surface is the normal vector (cid:2)N.
`coefficients. The cross product of the partial derivatives ∂(cid:4)r
`(cid:9)
`(cid:7)
`− ∂z
`∂x− ∂z
`∂y1
`
`⎞⎠
`
`⎛⎝
`
`=
`
`(cid:2)N =
`
`∂(cid:2)r
`∂x
`
`× ∂(cid:2)r
`∂y
`
`The normal vector (cid:2)N of a surface node is used to calculate the offset for the tool radius correction as
`illustrated in figure 1(b). The command set of each lenslet contains the shifted tool center point of each node.
`The resulting machine program for the whole array sums up the cutting data of every lens in the array and
`additional information about speeds and feeds. The typical file size is around 1.5 MB per lenslet. The motion
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`Proc. of SPIE Vol. 7927 79270N-4
`
`Figure 2. Error profile of an aspheric lenslet measured with a Ultra High Accuracy 3D Profilometer UA3P by Panasonic.
`Smoothed average of the profile is used to calculate the correction path for a figure correction.
`
`of the machine during the cutting process is a slow and harmonized oscillation of the linear (X) and the rotary
`(C) axis, while the linear feed-axis (Z) plunges the tool into the material.
`
`4.2 Form error correction
`Essential for achieving a form accuracy in the sub μm-range is the programming of the exact radius of the ball
`end mill and a correction of the waviness of the cutting edge as well as the kinematical behavior of the machine
`setup. In the case of a polar machine setup, the alignment of the high speed spindle to the C-axis is also of
`high importance. A distinction between a decentration in X and a height error (Y) is difficult, because the
`error characteristics are the same. Special test structures are used to analyze the Y- and X-alignment errors
`independently to achieve a tool setting accuracy in the μm-range.
`After a proper tool setting, the form deviation of an aspheric lens is in the range well below 200 nm (rms). A
`correction cycle consisting of a measurement step and a recalculation of the toolpath with respect to the occurring
`systematic errors leads to a increased form accuracy below 50 nm (rms). Interferometry or tactile profilometry
`are suitable techniques for measuring slightly aspherical lenslets. If the departure from the spherical shape is in
`the μm-range, lenslets are preferably to be measured with profilometers.
`Figure 2 shows the figure correction steps for an aspheric sample lenslet. To verify the shape and the position
`of the lenslets, a tactile measurement strategy is chosen to enter the correction loop. The measurement machine
`used is an Ultra Accuracy 3-D Profilometer (UA3P-5) from Panasonic. This tactile measurement device, with a
`measurement range of 200 mm x 200 mm x 45 mm, uses a diamond stylus tool with a tip radius size of 2 μm to
`scan the surface. The accuracy over the measurement range is 100 nm in X,Y directions, with a repeatability of
`50 nm. The probe measurement accuracy depends on the slope of the object. For slopes up to 30◦ the accuracy
`of the installed UA3P is assumed to be below 50 nm.
`The measured profiles of the aspheric lenslet are leveled, averaged and filtered. The surface nodes from the
`original tool path are interpolated on the negative smoothed average for the figure correction. Reproducible
`systematic errors, that appear in every lens can be corrected by copying the corrected cutting data in the array.
`
`4.3 Cutting Parameters for Diamond Milling
`The selection of the cutting data for the milling process depends on the material and is a trade off between
`machining time and quality regarding shape and roughness. The diamond ball end mill shall be as large as
`possible to reduce the theoretical roughness and the cutting time. Feed and spindle speed are selected to
`generate a chip thickness of 1 μm to 3 μm. The separation distance between two successive turnings of the
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`Proc. of SPIE Vol. 7927 79270N-5
`
`(a) Form deviation of a lenslet before shape correction;
`form error 133 nm (rms).
`
`(b) Form deviation of a lenslet after shape correction; form
`error 43 nm (rms).
`
`Figure 3. Form error correction of lenslets in one milling correction cycle.
`
`Archimedian spiral is 5 μm to 20 μm. Typical cutting parameters for micro milling of lenslets in an aluminum
`substrate are summarized in table 1.
`
`Table 1. Cutting parameters for diamond micro-milling of lenslets
`
`Cutting Data
`0.8 mm
`Diamond tool radius rε
`Depth of rough-cut ap,rough < 100 μm
`Depth of finish-cut ap,f inish < 10 μm
`40, 000 rpm
`Spindle speed
`40 mm/min
`Feed rate
`10 μm
`Feed per rev.
`
`The machining time for a single lenslet is in the minute range for the rough cut. The finish cut of a typical
`lenslet geometry takes 2 min to 5 min, depending on its size, the cutting tool radius and the feed. Machining
`times of more than 48 hour are typical for lens arrays containing a few hundret lenslets and more. Thus a very
`stable machine environment with an accurate temperature control is mandatory.
`
`4.4 Results of the diamond micro-milling
`The form error correction, which is conducted on one sample lens is used to generate the NC-code for the whole
`array. Eliminating all the systematic errors from the misalignment of the tool, the cutting edge waviness and the
`3 @ 633 nm can be achieved. Figure 3 shows the shape deviation
`machine kinematics a figure error of less than λ
`of an aspheric lenslet with a sag hight of 137 μm, an aperture of 1 mm and an maximum edge slope of 30◦ before
`(a) and after form correction (b).
`The surface finish strongly depends on the material used. In general the micro-roughness is comparable to the
`surface finish in diamond turning. In case of the brass micro lens array containing 1310 lenslets for wafer scale
`manufacturing, that is shown in figure 1(a) during the machining process, the achieved micro roughness is 7 nm
`(rms). The corresponding surface texture measured with white light interferometry is shown in figure 4(b). Still
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`:I3@O P:OOe7
`
`Proc. of SPIE Vol. 7927 79270N-6
`
`(a) SEM image of overlapping diamond micro-milled
`lenslets
`
`(b) Surface finish of a diamond micro-milled lenslet
`measured with white light interferometry
`
`Figure 4. Surface quality of diamond micro-milled Lenses
`
`visible is the theoretical roughness coming form the successive turnings of the Archimedian spiral of the tool on
`the surface. Furthermore high frequency concentric circles are noticeable, that might be the result of a slightly
`wear of the cutting edge or chips that are drawn over the optical surface. Figure 4(a) is an scanning electron
`microscopy (SEM) image of a very dense lens array with overlapping lenses. Visible are the sharp edges between
`two lenslets. The small μm-sized burr occurs only in one direction and can be removed by molding of the lenslets
`using a polymer.
`The lens-to-lens registration accuracy is critical for a wide variety of applications such as wafer level manufac-
`turing or coupling of light. The precision of lens-to-lens registration is inherent to the machine accuracy and
`the thermal stability of the environment. Typical values achieved are a position accuracy of ±5 μm over the
`entire substrate. A further enhancement can only be expected if the machines environment is controlled with an
`accuracy below 1 K and a temperature drift of less than 0.1 K/h.
`
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`Proc. of SPIE Vol. 7927 79270N-7
`
`5. ULTRA-PRECISION FREE-FORM TURNING
`Ultra-precision turning machines are used to fabricate optics with a center of symmetry. Since 3D structures
`show no rotational symmetry, but rather high frequency asymmetric features, they are treated as be free-form
`geometries. The deviations from the rotationally symmetric reference features such as a sphere range from a
`few μm to mm or higher are manufactured on an ultra-precision lathe with additional strokes of the machining
`tool. The stroke of the diamond tool is synchronized to the angular position of the free-form surface in the
`machine’s workpiece spindle. The forward and reverse motion is achieved either by the mechanical feed axis
`itself (Slow Tool Servo - STS), or an additional kinematic tool holder of low inertia (Fast Tool Servo - FTS). For
`high-frequency free-form geometries the FTS technology is generally preferred.
`To show the potential of micro-optics manufacturing with the free-form manufacturing technique, we have chosen
`a micro-lens array design with a high frequency asymmetric portion. The lens array design shown in Figure 5
`is a mold insert for an injection molding tool. The molded plastic lens array is used later as a 3D microoptical
`imaging element to transfer features from a 3D mask onto a curved substrate using lithographic process.5 The
`mold insert contains 1,219 single spherical lenslets whose vertices are arranged on a spherical surface with a
`radius of 11 mm. The outer diameter of the array is 9.5 mm.
`For the conducted studies of MLA manufacturing a Nanotech 450 UPL machine with an additional NFTS-6000,
`from Moore Nanotechnology Systems, LLC was used. The stroke of the FTS is ±3 mm. The integrated linear
`scale encoder with sub- nm resolution is in a closed control loop with a voice coil actuator, that positions the air
`bearing slide. With a maximum acceleration of 49.1 m/s2, the NFTS is able to precisely follow an amplitude of
`100 μm at 160 Hz.6
`
`Figure 5. Geometry of the machined free form array containing 1,219 spherical lenslets on a hemisphere
`
`5.1 Programming
`The programming of the FTS can either be accomplished using commercial CAM-Tools such as NanoCAM 3D or
`proprietary software solutions. Although commercial software solutions are well developed for a wide variety of
`standard free-form machining applications, major drawbacks are the limited number of data points and possible
`approximation errors coming from the spline interpolation of high frequency free-form surfaces. The limitations
`of data points leads to an increased distance between the control points for the tool motion and consequently to
`a high shape deviation of high frequency free-forms. Typical spline interpolation errors are transitions between
`piecewise differentiable surfaces where spline-ringing may occur.
`The representation of free-form data in the control of the FTS-System is a look up table of tool center points of
`the diamond tool in a polar coordinates. The streaming of data into this look up table allows the computing of
`large point cloud files containing some millions tool center nodes.
`To transfer the 3D surface data with the high-frequency free-form features into a numerical code for machining,
`the piecewise differentiable surface is calculated in 25.2· 106 supporting points in a polar mesh. Based on this
`point cloud, the tool radius correction is made to account for the cutting-edge geometry. Characteristic for any
`turning applications is the tool radius correction only in the radial direction. The cutting edge radius of the
`diamond tool tip in the angular direction is in the range of 10 Å − 20 Å can be neglected.
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`Proc. of SPIE Vol. 7927 79270N-8
`
`design surface
`
`tool center trajectory
`
`surface normals
`
`1.8
`
`2
`
`2.2
`
`2.4
`r/mm
`
`2.6
`
`2.8
`
`3
`
`11.3
`
`11.2
`
`11.1
`
`11
`
`10.9
`
`10.8
`
`10.7
`
`10.6
`
`10.5
`
`z/mm
`
`(a) Tool radius compensation of the diamond tool tip in the radial
`direction
`
`(b) Asymmetric portion of the toolpath as input
`parameter for the look up table for the FTS
`control
`
`Figure 6. Form error correction of lenslets in one milling correction cycle.
`
`Figure 6 (a) shows the tool radius correction for one of the 12, 600 lines. Due to the discontinuities in the slope
`of the profile, the radius compensation is not defined in the transition area between the spheres. The missing
`points are calculated with a spline based interpolation. The resulting free-form portion of the tool center points
`are shown in figure 6 (b). Superimposed with the curved trajectory of the rotationally symmetric portion the
`geometric information for the production of this microoptical component is established.
`
`5.2 Cutting Parameters for Free-form Machining
`The total FTS-stroke needed to fabricate the lens array is 18 μm. According to the frequency response speci-
`fication of the manufacturer, the FTS is able to operate at more than 200 Hz at this amplitude. Assuming a
`constant spindle speed, the highest necessary frequency of the FTS is expected on the outer diameter. Here
`109 lenslets are machined on a common reference circle. The possible speed of 110 rpm is reduced to 25 rpm,
`because the excitation of 18 μm does not follow a sinusoidal motion. To achieve a reasonable smooth surface,
`the feed per revolution is adjusted to be in the micron range. The cutting data are summarized in table 2. The
`machining time for the whole array is 80 min. The material used is a high strength aluminum alloy as mold
`inserts for injection molding.
`
`Table 2. Cutting parameter for the free-form machining of the lens array
`
`Cutting Data
`0.470 mm
`Diamond tool radius rε
`Depth of rough-cut ap,rough < 18 μm
`25 rpm
`Spindle speed
`0.125 mm/min
`Feed rate
`5 μm
`Feed per rev.
`
`5.3 Results of the Free-Form Machining
`The free-form micro lens array is machined in a two-tool process. The first diamond tool is used for rough cutting
`of the sphere and the reference surfaces, the second tool is mounted on the FTS and is used for the cutting of
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`Proc. of SPIE Vol. 7927 79270N-9
`
`(a) Micro roughness of the aluminum surface
`inside a lenslet is 4 nm (rms) measured
`with white light interferometry.
`
`(b) Form deviation of the free-form machined micro lens
`array 1.37 μm (rms)
`
`Figure 7. Quality in terms of shape and roughness of the free-form machined micro lens array on a curved surface.
`
`the hemisphere with the spherical lenslets. After diamond servo turning, the micro lens array is cleaned and
`inspected.
`
`5.3.1 Surface micro roughness
`For characterizing the micro roughness, a Zygo White Light Interferometer NewView 600 with a 50x objective
`lens is used. To distinguish between form error and roughness profile a spherical surface with the design radius
`is subtracted from the surface data. The surface texture is shown in figure 7 (a). The finish of 4 nm (rms) is
`similar to ultra-precision diamond turning of aluminum alloys. The influence of the redundant kinematics of the
`FTS system is visible in the high frequent residuals in two direction.
`
`5.3.2 Surface figure
`The shape deviation of the complete free-form surface is measured with the tactile 3D-profilometer UA3P-5 from
`Panasonic. Since the piecewise differentiable surface topology is not programmable in the UA3P proprietary
`software, the profilometer is used to scan the surface only. The exported point cloud, representing the center
`points of the contact probe with a radius of 2.02 μm on the surface, is fitted and recalculated to obtain the
`shape error image as shown in figure 7 (b). The surface slopes for the radius correction of the diamond stylus
`are calculated using the design data of the free-form lens array.
`The shape of this high frequency free-form surface deviates well below ±1.5 μm (p-v) over a wide area from the
`design surface. Visible is a slight radius error of the overall sphere, whose origin is an inaccuracy of the radius
`value during the tool setting. An overshooting in the transition area between two lenslets, can not be discovered.
`The cutting speeds and feeds can be further increased to reduce the cutting time.
`
`APPL-1039 / IPR2020-00896 / Page 10 of 12
`APPLE INC v. COREPHOTONICS LTD.
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`Proc. of SPIE Vol. 7927 79270N-10
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`Figure 8. Free-form lens array mold insert containing 1,219 single spherical lenslets whose vertices are arranged on a
`hemisphere
`
`6. CONCLUSION
`Each of the introduced processes produced micro lens arrays in metal substrates to a level of quality that could
`be considered functional for replication for imaging or illumination optics. The diamond micro-milling process
`offers the opportunity to machine truly aspheric shapes and correct the residual shape errors to achieve form
`deviations down to 40 nm (rms) / 200 nm (p-v) required for imaging optics in the infrared to visible wavelengths.
`Also the micro roughness ranging around 7 nm (rms) complies to these spectral ranges. For shorter wavelengths,
`the micro roughness has to be improved to reduce scattering losses of the optical surface.
`The design freedom regarding possible shapes of the lenslets is very high. Edge slopes up to 60◦and more are
`feasible and a high fill factor with intersecting lenslets is possible. A drawback and cost driver is the increased
`production time of diamond micro-milled lens arrays. Besides the time for the tool setting, the cutting time of
`an array containing thousand lenslets and more can be up to several days continuous machining.
`Nevertheless, the ability to manufacture deep lenslets with sag-heights up to several hundred μm with truly
`aspheric shapes on arbitrary positions on large substrates offers an additional degree of freedom for the design of
`micro lens arrays, either directly structured or as master for replication. These achievements show the potential
`application of this technology for fabricating micro imaging systems on the wafer level for cellular phones or
`sensor devices.
`
`Free-form machining using a FTS is more demanding regarding the tool path programming, but shorter
`machining times can be expected. The FTS used is expedient for machining high frequency free-form surfaces
`with a size smaller than ∅ 50 mm. The reason for this drawback is the amount of data necessary to describe the
`array in the look up table. An uniform polar meshing with a sufficiently dense point spacing of less than 10 μm
`raises the computing and loading times significantly.
`The processing time of only 80 minutes for the machining of the described high strength Aluminum alloy injection-
`mold insert and the surface quality of 4 nm (rms) show the good applicability of the free-form machining process
`for structuring of these small free-form optics. The shape deviation in the μm-range could be considered func-
`tional for infrared imaging optics and for a broad spectrum of illumination optics. Correction cycles to improve
`the shape of the optical element after a metrology step are not targeted for high frequency free-form surfaces,
`because contributions to the shape irregularities are caused by the inertia of the FTS system and inconsistent
`cutting conditions over the diameter of the workpiece.
`Feasible geometries are mainly limited by the diamond cutting tool geometry with a clearance angle up to 40◦ and
`the radius of the diamond tool used. Replication by