freeform optical surfaces (junio 2012)

7/25/2019 Freeform Optical Surfaces (Junio 2012)

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www.osa-opn.org30| OPN Optics & Photonics News

Freeform

OpticalSurfa

ces

Kevin P. Thompson andJannick P. Rolland

A Revolution in Imaging

Optical Design


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June 2012 | 311047-6938/12/06/30/6-$15.00 OSA

n todays world, it is often difficult to separate hype from reality, even in science, particularlywhen one uses a word such as revolution. Here, this word is chosen from the perspective ofa technology that is 130 years old: the freeform optical surface. While astronomers and a few

mathematicians had developed some perspectives on mirror shapes and simple lens systems extend-ing back to the early 1600s, it was not until Abbe, Schott and Zeiss joined forces in the 1880s thatthe art of optical design, fabrication and testing began a rapid transformation into a science.

Te key to this transition was the ability to engineer the refractive index and the dispersion ofoptical glassesa technology developed by Schott. While there was earlier work in the engineer-ing of optical glass involving Stokes and Faraday and a lesser known scientist named Harcourtin the 1800s, and even earlier work by the French, Schott is the one that created a viable ongoingindustry.

Te first article in one of the first journals of sciencePhilosophical Transactionsis aboutthe development of optical glass in France, An Accompt of the Improvement of Optick Glasses(Phil. Trans.1665 1:2-3). Te optics industry, which consists of several primary and often sepa-rable functionsoptical design, fabrication, assembly and testwas fully emergent by 1900based on surfaces that were firmly founded in rotationally symmetric spheres.

Te fabrication of freeform surfaces for imaging applications using commercial equipment wasenabled only in the last decade, ahead of both optical design tools and the optical testing commu-nity. Tis revolution will change these industries and the customers they serve forever.

I

Arevolutionary

opticalsurf

aceforimagingopticaldesignisthe

resultofdevelopmentsinthe

theoryofaberrations,techniques

inopticalsystemoptim

ization,computationspeed,precision

fabricationofsurfaceswithou

tsymmetry,andextensionstothe

rangeofthesurfac

eslopes

allowedinopticaltesting.

Forbes(

2012)


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Background and definitions

In the past, the label freeform was appliedto fairly simple surface shapes, particu-larly toroidal surfaces, which only havea different radius along two orthogonal

axes. Tis labeling was convoluted by thefact that the translation of the Frenchterm for an anamorphic surface (a moregeneral form of a toroidal surface) is free-form. One of the earliest meetings to usethe title was held in 2004 in associationwith the American Society of PrecisionEngineers, where a coauthor of this article(Tompson), working with J. MichaelRodgers of Optical Research Associates(now Synopsys Inc.), presented a paper onoptical design methods for all-reflective

optical systems with anamorphic surfacestitled, Benefits of freeform mirror sur-faces in optical design.

One of the first examples of the useof a true freeform surface in imagingoptics was developed by James Bakerworking with Bil l Plummer and SteveFantone for Polaroids SX-70 camera.Prior to that, Luis W. Alvarez inventedthe variable focus lens for application inophthalmology based on arguably oneof the earliest freeform surfaces. (Here

we are ignoring the history of progres-sive ophthalmic lenses that dates backto 1954 and Maitenaz.)

Alvarez was a Nobel Prize physicistwho worked primarily on high-energyphysics. He was brought to ophthalmicswhen his fa ilure of accommodationcaused him to pause. Te day after hisinvention, he brought it to one of hisgraduate students, William Humphrey,who went on to pioneer many instru-ments in ophthalmology. Te surface

form that Alvarez introduced was,using his notation,

a t= axy2+ x3 bx+ c. (1) 3

Tis form of XY-polynomial sur-face in rectangular coordinates hasmaintained a position in the theoryand application of freeform surfaces inophthalmic and nonimaging/illumina-tion applications. In illumination, theprevalence of XY-polynomial surfaces is

type emerges first is a result of the factthat Zernike polynomials were adoptedby optical testing companies in the 1970sand as a result are integrated with theoptical analysis software environment andin some cases the imaging system optimi-

zation environment. Te demonstrationof this technology was led by Steve Patter-son, now at UNC/Charlotte, who spear-headed the creation of the Large OpticsDiamond urning Machine at LawrenceLivermore from 1987 to 1988.

Te first piece in this shape class wasan asymmetric wavefront corrector. Asecond is the family of surfaces thatfall under the heading of multicentric,radial basis function (RBF) surface s.Te key concept here, as recognized by

one of us (Rolland) in 2002 and imple-mented in an optical system designedand fabricated by Cakmakci andRolland, is the introduction of mul-ticentric functions as an added layeron an optical surface shape that couldrange from a base sphere to a Zernikesurface or the more recently developedQ-polynomial surface.

Multicentric RBFs consist of a series ofbasis form functions that, in the simpleststructure, take on the size and shape

parameters of a Gaussian (e.g., radiusand standard deviation) function. Now,however, there are multiple additive basisfunctions that are floated out acrossthe underlying parent surface where theythen take up a position determined by theneighboring functions through optimiza-tion within an application space. Teseforms are currently being explored forapplication in head worn displays.

In the nonimaging community, thesurface shape formulations that are

emerging at the leading edge are oftenbased in the non-uniform rationalB-splines (NURBS) formulation. WhileZernike formulations arose from opticaltesting, NURBS emerge from mechani-cal computer aided-design (CAD). Tereason that NURBS do not reach intothe imaging community is that they donot provide the necessary combinationof speed and accuracy simultaneously. Inaddition, the technique for parameteriza-tion is cumbersome, requiring hundreds

A simulated interferogram of the depar-

ture of a multicentric RBF freeform

surface from a w-polynomial surface.

Multicentric radial basis function(RBF) freeform surface

Rolland and Cakmakci (2009)

Waves1.0

0.5

0.0

[ ]

a consequence of many applications thathave a rectangular aperture rather thanthe circular one that is more common inimaging applications. While XY-polyno-mial surfaces are available in the imag-ing optical design environment, theyare not an enabling form. Tey are notorthonormal over the commonly circularaperture of imaging optical systems; theyare not used in optical surface testing;and they are not readily interpretable inthe context of the historical theory of theaberrations of imaging optical systems.

Here we will put forward a moderndefinition of the term freeform in thecontext of optical surfaces used predomi-nantly in imaging optical applications.Our modern definition is constructed bya definition not of what a freeform surfaceis, but, rather, by stating the technologythat has enabled this revolution.

Freeform Optical Surface,

Modern Definition (post-2000)

An optical surface that leverages a thirdindependent axis (C-axis in diamondturning terminology) during the creationprocess to create an optical surface withas-designed nonsymmetric features.

Under this formulation, the most per-vasive emerging class of freeform surfacein imaging optics is the Zernike polyno-mial surface or its derivatives. Tat this

y

x


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June 2012 | 33

or thousands of parameters that needto be variables, often with associatedconstraints for optimization. Te CADof nonimaging systems is lagging that ofimaging by roughly 10 to 15 years; a lackof a basis surface model with tractableparameterization is one of the reasons.

Conics and spheres

Historically, the first class of surface shape

is spherical and conic surfaces, whichwere the dominant shapes until about1980, particularly for large and mod-est aperture mirror systems. elescopesare the predominant optical design.Galileo is often credited for inventing thefirst telescope based on lenses, but thatappears to be a mistake. Hans Lippersheyis the current choice of historians (see,for example, H.C. King); he is believedto have developed his instrument around1610. Reflective telescopes appear in the

literature in the earliest journals of sciencewith publications of telescope forms thatstill dominate both the lexicon and theforms themselves.

While a Gregorian and Newtoniantelescope were constructed shortly afterthey were proposed, the first Cassegraintelescope was built by Ramsden in the1800s. Te conclusion from this andreports published throughout the 1700sand 1800s (see R. Smith, 1738, and D.Brewster, 1830) is that the technology

for conic mirrors existed throughout theperiod. Te Cassegrain form, with itsparabolic primary mirror, is the domi-nant type of telescope up to the HubbleSpace elescope in the 1990s. (Teprimary mirror is a defining feature,along with the convex secondary mirror,rather than the concave secondary ofGregory or the effectively plane second-ary of Newton.)

Te Hubble represents one of a fewattempts to construct a Ritchey-Chretien

form proposed in the 1920s. While thefirst generation of imaging telescopedesigns are corrected only for sphericalaberration, the Ritchey-Chretien formalso adjusts for coma, again using onlyconic mirrors, with a weakly hyperbolicprimary mirror.

Rotationally symmetric aspheres

Tis is the second class of optical surface.

In his 1899 patent, Ernst Abbe intro-duced the power series formulation fora rotationally symmetric asphere. Teseshapes occur infrequently until about2000, when fabrication and testingmethods became more advanced.

Te commercialization of MRFtechnology by QED echnology, whichhas dramatically reduced the cost of themanufacture for glass components, hasbeen significant to the introduction ofthis surface shape into mainstream optics.

At the same time, the recent prolifera-tion of cell phone cameras has drivenfurther progress. Tese cameras are madefrom plastic components squeezed intocompact spaces.

In 2008, Forbes noted that the opti-cal design community, due primarily toa thought-to-be-trivial change in inputand output formatting of optical designcodes, was suddenly submitting opticalsurfaces described by 20thorder aspheresfor MRF fabrication. He reported a new

form of aspheric surface definition that isformulated such that the coefficients thatdescribe the surface are in units of sag.

Tis change clearly illustrates that,for most optical systems, no more thantwo to three terms in a power seriesdefinition should be active or fabricated.Tis discovery led to a second era forrotationally symmetric aspheres, undera formulation that has come to be calledthe Q polynomial form, introduced inCODE V based on Forbes work.

Marin Mersenne

In 1636, a mathema-

tician in communica-

tion with Descartes

described two confo-

cal mirrors making

an afocal telescope

(originally spheres,

today associatedwith parabolas). It

is still referred to as a Mersenne.

James Gregory

He published the

original two-mirror

imaging telescope

that carries his name

(Gregorian) in 1670.

This form was used

most recently for

the Large Binocular

Telescope (LBT). It is

longer than the more common Cassegrain,but provides a real exit pupil, which is nec-

essary to effectively combine two paths.

Isaac Newton

His device is

technically a one-

mirror telescope,

with a fold mirror,

published in 1672.

It is still popular

among amateur

astronomers.

Laurent CassegrainHis telescope was described four months

after Newtons in theJournal des Savants.

It was the dominant form until the 1990s,

when the Hubble was constructed. Little

is known

about

Cassegrain,

and no

pictures of

him exist.

Whos Who in EarlyTelescope Development

Thefabricationoffreeformsurfacesfor

imagingapplicationswas

enabledonlyinthelastdecade,ahea

dofbothopticaldesigntools

andtheopticaltestingcommunity.

Wikimedia

Wikimedia

Wikimedia

Wikimedia


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XY polynomials and

off-axis conics

Te XY polynomial, the third class ofoptical surface, is a unique surface shapethat solves some specific problems. How-

ever, it is not part of the revolution thatwe are in today. It essentially adds someinteresting new degrees of freedom inone dimension. However, optical designis, in almost all cases, a two-dimensionalproblem that requires a surface of revolu-tion in 2-D.

So-called off-axis conic surfacescomprise the fourth class. Tese areconventional conic surfaces edged with alarge offset from the center of symmetry.In more extreme cases, they are fabri-cated with stressed polishing techniquesperfected during the fabrication of theKeck telescope using methods attributedmost often to J. Nelson.

What is becoming more common,however, is small-lap, computer-con-trolled polishing. insley, which is nowa division of Zygo, is often credited asan early successful developer of thistechnology. Teir polishing of thenonsymmetric conic surfaces used forthe COSAR optics of the Hubblesfirst servicing mission is evidence of

this. Off-axis conics initially appear asa result of attempts to correct the threeprimary aberrations (spherical, coma andastigmatism) for astronomical applica-tions by moving from optical systemswith two mirrors, with two conics asfree parameters for aberration correction,to those with three.

Initially, Meinel and Shack, andastronomers such as Rumsey, introducedthree-mirror anastigmats, typically withlarge obscurations. One of the earliest

public documents that illustrates the useof off-axis conic mirrors is a 1972 patentby Offner. It only reveals afocal forms,leading one to hypothesize that the focalforms were investigated, but not pub-lished at that time. Offner is best knownas the optical designer of an all-reflectivespherical mirror system that used anoffset field, a concept that may have origi-nated with Rod Scott of Perkin-Elmer.

In the 1980s, the advent of theStrategic Defense Initiativemore

aberration theory (NA) in 1977. Tiswas then expanded from a concept to acomplete theory of the aberration fieldsthrough 5th order of nonsymmetricoptical systems. Tis work was com-pleted in 1979, but only recently made

its way to the literature.In the context of modern freeform

optical surfaces, NA reported to date,with one exception, requires that thesurfaces under study be sections of rota-tionally symmetric conics or aspheres.An important development was theintroduction of the full field displayanew optical system analysis feature thatprovides a visualization of the nodalfield properties of specific aberrationterms in terms of the FRINGE Zernike

polynomial characterization of the aber-rations published at the 1985 opticaldesign conference. Tis feature, whichhad a compute time of more than 30minutes when introduced, can now fullycharacterize even the James Webb Spaceelescopes NIRSPEC camera in sec-onds. In August 2011, Sagem completedfour aggressively configured MAs in achain on NIRSPEC.

Shacks discovery of the nodal aber-ration field property of optical systems

without symmetry was based on afundamental concept by Buchroeder.It will become a key enabler for theoptical design of the coming generationof freeform optical surfaces. A recentdiscovery by K. Fuerschbach, workingin collaboration with us, has removedthe limitation that NA could only beapplied to intrinsically rotationally sym-metric surfaces.

Tis last fundamental discovery,which has been 35 years in the making,

leaves the optical design communityfully prepared to develop the necessaryoptical design and analysis environmentto successfully exploit the new opti-cal design degrees of freedom broughtforward by the modern definition offreeform surfaces. Tis work is essentialin order to avoid becoming disorientedby all of the apparently new parameterspaces. What used to be simply a radiusand a conic constant has become a myr-iad of surface description parameters to

Bauer and Rolland (2011)

Fuerschbach, Thompson and Rolland (2011)

Tilted sphericalmirror

With RBFadded

Coma & astigmatism

[ Multicentric radial basis functions ]

[ w-polynomial surfaces ]

Secondary

Primary

Tertiary25 mm

Coma

commonly known as the Star Wars pro-gramsparked the design communitys

interest in the unobscured telescopeform based on fundamentally off-axisconic mirrors to reduce stray light. LacyCook working at what was then Hughespatented a number of forms, includingthe one most often referred to as theCook reflecting triplet three-mirroranastigmat (MA). (Tis was a coinci-dental parallel to the ubiquitous Cookerefractive triplet of the late 1800s,which was patented by Dennis aylorwhile working for Cooke.) In 1990,

Figoski published an early report of asuccessfully built MA. At this point,optical alignment and testing began toemerge as a limiting factor in advancingthe technology.

While Cook was using somewhatconventional optical design methods onan internal software package (Hexagon),simultaneously, one of us (Tompson)was developing methods for the opticaldesign of a nonsymmetric optical systembased on R.V. Shacks discovery of nodal


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June 2012 | 35

Whatusedtobesimplyaradiusanda

conicconstanthasbecome

amyriadofsurfacedescriptionpara

meterstobesuccessfully

managedbythedesignerandhisorh

eroptimizationtools.

be successfully managed by the designerand his or her optimization tools.

o some extent, the two mirrortelescopes that were discovered in the1670s were perfected in the later part ofthe 1900s. Tree mirror anastigmats,on the other hand, were invented inthe 1960 to 1985 timeframe. Tey werefirst shown in public as a subscale levelin a prototype in 1990 in the paper by

Figoski. Te most significant challengesin perfecting this technology in the endwere related to aligning and testing theoff-axis components in the MA.

Sagems success in developing MAsfor the James Webb telescope, underthe leadership of R. Geyl, completes theevolution for this class of optical surfaceshape. All aspects of the design, fabrica-tion, test and assembly have been success-fully demonstrated in a cost-/profit-drivenenvironmenta good working definitionof a mature technology.

Rotationally nonsymmetric

polynomial aspheres

Te fifth class of optical surfaces, whichis a subclass of a freeform surface, arerotationally nonsymmetric polynomialaspheres, or more specifically w-polyno-mial aspheres; Zernike polynomials area significant subcategory. o trace theevolution of this form, we must look tothe optical component fabrication com-

munity for the initiation of the relevanceof this surface to optical systems.

Te key development comes with theintroduction of slow servo (also called5-axis, and C-axis) in the commercialdiamond turning community around2002. Tis actively emerging tech-nology is going to change the world,and quickly. It will lead to aggressive

Te most significant impediment toprogress is the optical testing of thesesurfaces. Te preferred method forimaging optics is interferometry, whichlimits the maximum slope that a surfacecan contain. Fundamentally, the opticalsurface is imaged onto a digital camerathat restricts the density of fringes. woindependent solutions emerged recently(Zygos Verifire and QEDs ASI) thatexpand the surface slope that is allowed,but further dynamic range is needed.

At the same time, each and everycommunity along the supply chain mustlearn new concepts and develop newtools to leverage these revolutionaryshapes. It is a new dawn. t

Kevin Thompson([email protected]) is agroup director of R&D at Synopsys Inc., U.S.A.Jannick Rollandis the Brian J. Thompsonprofessor of optical engineering at the Institute

of Optics at the University of Rochester,N.Y., U.S.A.Member

ONLINE EXTRA:Visit www.osa-opn.org for a complete list of references for this article.

OSA Incubator Meetings

This article provides a historical context

that will inform next months feature

summarizing work presented at OSAs

recent Incubator meeting on freeform

optics. OSA recently initiated this new

form of meeting to provide unique and

focused experiences, giving research-

ers in niche fields an opportunity to

discuss advances, challenges and

opportunities regarding their research.

Jannick Rolland is leading the develop-

ment of this exciting program.

OSA Incubator meetings:

c Target emerging topics and fields.

c Further interest and support of

promising topic areas.

c Encourage extensive formal and

informal discussion while estab-

lishing a sense of community.

c Offer a valuable means of dissemi-

nating information and ideas.

For more information, visit www.osa.

org/Meetings/Incubator_Meetings.

innovation in optical design, fabrica-tion and particularly optical testing.One of the first full cycle pathfindersystems is based on a design by Fuersch-bach and Rolland. It is expected to becompleted as a prototype demonstratorof all aspects of the technology, similarto the Figoski MA prototype of 1990,in 2012/13. No other optical system hasbeen successful in placing the key opti-cal parameter of a surface, the center ofcurvature, significantly away from theoptical axis. Tis important packagingdegree of freedom is fully enabled byw-polynomial surfaces.

Tis is a true revolution. Until thesesurfaces became feasible, there was noindependent control of the three Seidelaberrationsspherical, coma and astig-matismthat fundamentally limit thefield of view and f/number coverage thatcan be achieved with any particular opti-cal form. Tis is manifested by the factthat the amount of coma and astigma-tism in a design was directly related tothe amount of spherical aberration intro-duced at a surface. Particularly for theimportant class of off-axis, a ll-reflective,unobscured systems, which are a key tothe future of optical lithography, thiscondition has locked EUV technology ina box well short of what is commerciallyfeasible for over 15 years.

Freeform surfaces described by w-poly-nomials are under active development

and integration in all aspectsopticaldesign, optical fabrication, optical com-ponent testing, optical system alignmentand optical system testing. Te currentfocus is to move the wavelength at whichthese surfaces are diffraction-limiteddown from the current region, arguably1 m, all the way to 13 nm (for EUVlithography) and beyond.

freeform optical surfaces (junio 2012)

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