metrology of thin transparent optics using shack-hartmann

Metrology of thin transparent optics usingShack-Hartmann wavefront sensing

Craig R. ForestClaude R. CanizaresMassachusetts Institute of TechnologyCenter for Space ResearchCambridge, Massachusetts 02139

Daniel R. NealWaveFront Sciences, Incorporated14810 Central SoutheastAlbuquerque, New Mexico 87123

Michael McGuirk, MEMBER SPIEMark L. Schattenburg, MEMBER SPIEMassachusetts Institute of TechnologyCenter for Space ResearchCambridge, Massachusetts 02139

Abstract. The surface topography of thin, transparent materials is ofinterest in many areas. Some examples include glass substrates forcomputer hard disks, photomasks in the semiconductor industry, flatpanel displays, and x-ray telescope optics. Some of these applicationsrequire individual foils to be manufactured with figure errors that are asmall fraction of a micron over 10- to 200-mm lengths. Accurate surfacemetrology is essential to confirm the efficacy of manufacturing and sub-strate flattening processes. Assembly of these floppy optics is also facili-tated by such a metrology tool. We report on the design and perfor-mance of a novel deep-ultraviolet (deep-UV) Shack-Hartmann surfacemetrology tool developed for this purpose. The use of deep-UV wave-lengths is particularly advantageous for studying transparent substratessuch as glass, which are virtually opaque to wavelengths below 260 nm.The system has a 1433143-mm2 field of view at the object plane. Per-formance specifications include 350-mrad angular dynamic range and0.5-mrad angular sensitivity. Surface maps over a 100 mm diam areaccurate to ,17-nm rms and repeatable to 5 nm rms. © 2004 Society ofPhoto-Optical Instrumentation Engineers. [DOI: 10.1117/1.1645256]

Subject terms: Shack-Hartmann; optical metrology; wavefront sensing; thin glassoptics.

Paper 030284 received Jun 13, 2003; revised manuscript received Sep. 23,2003; accepted for publication Sep. 23, 2003. This paper is a revision of a paperpresented at the SPIE conference on X-ray and Gamma-Ray Telescopes andInstruments for Astronomy, Waikoloa, Hawaii, August 2002. The paper presentedthere appears (unrefereed) in SPIE Proceedings Vol. 4851.

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1 Introduction

Metrology is essential for successfully shaping foil opticMetrological feedback closes the loop on the manufacing process. Quantifying figure errors permits the evaltion of process improvements. During assembly, miclevel distortions to the foil optic may occur due to gravior friction. Material thermal expansion mismatch may acause low spatial frequency distortion. Study of thesefects requires a metrology tool with a large viewing arehigh angular resolution, and large angular range.

One application for x-ray telescope foil optics requirthe accurate shaping, patterning, and assembly of thousof thin, flat grating substrates.1 Depending on the particulagrating geometry, grating substrates are generally rectalar with dimensions on the order of 140 mm and thickneranging from 0.4 to 2 mm. A variety of substrate materihave been proposed, including borosilicate glass, silicand silicon carbide. The foil specifications include a flness of 500 nm over the surface of the optic, thicknvariation of 20mm over the length, and surface roughnetolerance of,0.5 nm. These foil size specifications adriven by the telescope weight budget and assembly tenology. Flatness and surface roughness requirementsdriven by resolution goals. Here, when we use the te‘‘flatness,’’ we mean the shape of the front surface of toptic, and not the thickness variation, which is widely mused.

742 Opt. Eng. 43(3) 742–753 (March 2004) 0091-3286/2004/$15

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There are three principle functional requirements for tnon-null aspheric metrology system, as describedGreivenkamp et al.2:

• the system must be able to measure the observoutput with sufficient angular dynamic range and pcision ~angular resolution! to record the large amounof asphericity that is present

• the optic system used to create the observable oumust be designed so that no vignetting of the asphwavefront occurs

• the system must be calibrated to relate the detailsthe observable output to the surface under test.

The factory-supplied stock optic foils for our shaping prcesses typically have low spatial frequency distortions,observed with other metrology tools.~Interferometric mapsand Hartmann tests reveal about three waves per olength of 100 mm.! Stock borosilicate glass sheets~SchottGlas, model D-263! have large distortions, up to 600mmover their 100-mm lengths for 400-mm-thick foils. By com-parison, silicon wafers typically have a flatness of 3mmover a 10-mm lateral distance, or 0.3 mrad. We specifymrad as the angular range functional requirement formetrology tool. We seek to flatten these materials,0.5mm peak-to-valley ~PV! over one 100-mm-diamface. This corresponds to a measurement angular sensit

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of 50 mrad over a 10-mm lateral distance. We desiresensitivity that is five times better than the allowable, soangular sensitivity functional requirement becomesmrad.

1.1 Metrology Technology Candidates: ResearchReview

Demand for metrology of thin, transparent materials hresulted in many solutions to the problem. Here we prestechnical details of related work and discuss their relatmerits and drawbacks.

A key challenge for optical techniques is the measument of the front surface of the object without the effectthe reflection from the rear surface. We consider phshifting interferometry~PSI! methods using short coheence length sources in various configurations,3–7 math-ematically deconvolving the contributions of the two rflections using wavelength tunable sources8,9 with somemathematical manipulation,10,11 spatial separation of thetwo reflections,12,13 grating interferometers,14,15 and use ofa diode source and optical path difference~OPD! that is amultiple of the laser cavity length.16 We also consider mechanical methods, such as coatings and contact proLastly, the Shack-Hartmann technique is presented.

1.1.1 Rear- and front-surface coatings

One method for frustrating rear-surface reflection is theplication of an appropriate index-matching coating. Omay also apply a highly reflective coating to the front sface, thereby eliminating the back reflection. Unfortunatethis impairs routine inspection of optic foils by addincomplex application and cleaning procedures. In our cacoatings induce warp on the thin optics or change thelastic behavior as well as require subsequent cleaning17

1.1.2 Partially coherent or white-light illumination forphase shifting interferometry

White light has a much shorter coherence length thamonochromatic laser, owing to the range of wavelengthat comprise it. This has been exploited in modern inferometry to eliminate ghost fringes from the back refletion of a transparent material, among other application18

This technique is limited to samples whose warp is lthan their thickness.

A Michelson interferometer has been commonly usfor white-light interferometry. In this setup, unwanted iterference fringe patterns from parallel surfaces of tramissive plates are eliminated by limiting the productioninterference fringe patterns to reference and test surfalocated at equal optical path lengths along referencetest arms. More precisely, the lengths of both arms are cfully adjusted, such that the optical path difference~OPD!is within the source’s coherence length.5–7 Well-matchedoptics are required between the reference and test awhich can be prohibitively expensive for measuring lartest plates. ADE Phase Shift~Tucson, Arizona! has devel-oped an equal path interferometer for this purpose.3 Thisinstrument features a 2- to 3-mm coherence length. Thfront or rear face of photomasks and flat panel displawhich are thicker than this, can be successfully measusince interference fringes will only be formed from onsurface.

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A white-light Fizeau interferometer reported bSchwider4 achieved similar results. Schwider combinedFabry-Perot interferometer in front of a two-beam Fizeinterferometer to obtain white-light fringes. One disadvatage to this setup is the poor light efficiency caused bylow reflectance of the Fizeau plates, and the low transpency of the Fabry-Perot interferometer averaged overfull-width half maximum~FWHM! of the interference fil-ter.

1.1.3 Wavelength-tuned phase shiftinginterferometry

de Groot, Smythe, and Deck10,11 have developed a Fizeainterferometer operating with software that mathematicaseparates the interference contributions of plane-parasurfaces. This solution is based on processing the inteence data generated with two single-mode wavelengThe cumulative interference produced by three surfacesR,T, andS ~reference, test, and rear! is measured with a firswavelengthl1 and then with a second wavelengthl2 , insequence. The sample is then flipped over with the rsurfaceS now facing the reference surfaceR, and the cu-mulative interference is again measured with the two walengthsl1 and l2 . Thus, four sets of data are generatfrom which the desired interference between the refereand the test beams may be extracted by mathematicalnipulation. The measurement of either or both parallel sfaces of a test plate therefore requires a sequence of pshift measurements and inversion of the test plate for msuring both surfaces in two opposite orientations. Tmethod requires double handling of the sample, whshould be avoided with our low stiffness foils.

A Twyman-Green interferometer has been developedOkada et al.8,9 that can obtain separate measurementssurface shapes and refractive index inhomogeneity of ocal elements using tunable-source phase shifting interometry. Separation of the interferogram from the front arear surface becomes possible, since the wavelength chis proportional to the OPD of the two arms~reference andtest!. This means that interferograms with different opticpath differences have a different amount of phase shThis device acquires 60 interference images at a sequof wavelengths and least-square fits the first-order termcalculate surface and optical thickness profiles.

A variation on this technique has been implementedDeck,19 in which a Fourier analysis of the interferencspectrum extracts the frequencies and phases of all ofsurfaces in a transparent flat. Zygo Corporation~Middle-field, CT! has successfully implemented this wavelengtuned Fourier transform PSI in a commercial product tcan measure both the front- and back-surface profiles,tical thickness variation, and index homogeneity.

1.1.4 Spatial separation of reflections

A grazing incidence interferometer by Dewa anKulawiec13 exploits the reflective surface propertiesplane-parallel plates to individually measure surfacepologies of either or both parallel surfaces of such test pin a single mounting position. Illumination at the grazinincidence laterally shears reflections of a test beam frthe two surfaces, and spatial coherence of an extended

743Optical Engineering, Vol. 43 No. 3, March 2004

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source is limited in relation to the lateral shear to prevthe formation of an undesired interference fringe pattbetween the two parallel surfaces of the plate. In additithis device provides for realigning a reference beam wthe portion of the test beam that is reflected from one ofparallel surfaces, but not the portion that is reflected frthe other surface. The realignment favors the formationan interference fringe pattern between the reference surand the one parallel test surface, to the exclusion of a slar interference pattern between the same reference suand the other parallel test surface. This technique canutilized to make the sheet appear thicker~i.e., longer thanthe illumination coherence length! for conventional PSI, orthe reflections can be spatially separated for the frontback reflection using a relatively small scanning source

Evans et al.12 has also pursued a method of spatial seration of the two reflections. In this work, a RitcheCommon configuration allows testing of flats with a sphecal wavefront. With the flat at an angle to the expandspherical wave propagation direction, a spatial shift intwo surface reflections occurs. This shift is a function of tthickness of the plate and the tilt angle. Additionally, rareflected from the rear surface will be refracted as thtraverse the front surface, producing an aberrated wavefwith focus displaced from the ideal position. Simulatioand experimentation has demonstrated that this back retion can be effectively spatially blocked with a stop.

Our application would certainly extend these techniquto their limit. Precise optical alignment will be paramounThe grazing incidence technique will also require precismachine design for a translating source and sensor. Linand angular errors will directly affect the measurementcuracy.

1.1.5 Grating interferometry

An adjustable coherence depth interferometer has bstudied by de Groot, Deck, and Lega.14,15 This geometri-cally desensitized interferometer~GDI! uses two beams adifferent incident angles to generate an interference patwith an equivalent wavelength of 5 to 20mm. Recognizingthat the coherence depth is a function of the size and shof the light source, the GDI can separate the front and breflections of transparent flats if the coherence depth isthan the sample thickness. In this work, the minimumherence length obtained is 152mm. This is just less thanhalf of the 400-mm sample thickness for our work, so thtechnique may be feasible, although back fringes willobservable, yet attenuated. From the data reported,15 theback reflection for our samples would be about 13 timweaker than the front.

1.1.6 Multimode laser diode

A Fizeau interferometer that utilizes a multilongitudinamode laser as a light source for testing transparent tplate samples has been developed by Ai.16 As a result of themultimode laser operation, interference fringes are obtaionly when the optical separation between the referencetest surfaces is an integer multiple of the laser’s effectcavity length. By judicially selecting the multimode spetrum of operation and the effective cavity length of tlaser, the interferometer may be calibrated to produce in

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ference fringes at a workable optical separation betweenreference and test surfaces, without ghost fringes fromopposite surface of the thin-plate sample.

For this technology to work in our application, thewould need to be a sufficiently large number of modunder the gain curve in the power spectrum, so thatspikes in the coherence function would be very narroAccording to Ai,16 the spike width,;0.15 mm, was shortethan the glass thickness of 1 mm in his work, so there wno interference pattern between the sample’s two surfa

1.1.7 Contact metrology

A contact metrology method was also considered. In tscheme, a touch probe that uses a high-frequency resoing stylus to detect contact with a test object would be uas a displacement transducer in an application similawhat is found in many contact coordinate measurementchines ~CMMs!. The probe requires 0.1 mN of force tdetect contact. Application of this force to the center osimply supported sheet without considering gravity wouresult in a deflection of

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where the foil width w5100 mm and its thicknessh50.4 mm. The resulting maximum deflection isdmax

5170 nm. The small distortion is below the flatness tolance. However, this system would require a vertical, higprecision stage to map the foil topography. Also, througput would be restricted by the serial scanning procedur

1.1.8 Shack-Hartmann

The Shack-Hartmann technology was developed by Pand Shack20 as an improvement to the existing Hartmaconcept. Shack-Hartmann sensors do not rely on liginterference effects, but rather infer local near-field wavfront gradients by measuring a corresponding focused sposition in the far field. To do this, an array of lensletsplaced at the system image plane. This array dissectsincoming wavefront, as shown in Fig. 1. Each lensletcuses its portion of the wavefront onto the charge coupldevice ~CCD! detector array. The average wavefront tacross each lenslet aperture results in a shift of the restive focal spot. A planar wavefront produces a regular arof focal spots, while an aberrated wavefront producedistorted spot pattern. Comparing these two producemap of the wavefront slopes, and integration of these sloallows reconstruction of the test wavefront.2,20 The wave-front incident on the lenslet array can be the test wavefrdirectly ~i.e., 1:1 magnification! or it can be demagnified, along as this is accounted for in the wavefront reconstructsoftware.

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1.2 Justification for Shack-Hartmann TechnologySelection

The Shack-Hartmann technology offers a number of advtages over phase-shifting interferometry for our relativlarge-optics metrology application. In the Shack-Hartmasystem, temporally incoherent light sources can be uwhich are generally cheaper than lasers. The sensorsproduce short-duration frames either by shuttering thetector or by using a pulsed light source, thus mitigatingeffects of vibrations and turbulence by allowing manyfectively instantaneous measurements to be averag21

Shack-Hartmann sensors can function in poorly controenvironments, such as a clean room with air turbulenceacoustic noise, that would introduce errors in phase-shifinterferometry measurements or preclude th

Fig. 1 Shack-Hartmann wavefront sensing concept.

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entirely.22–24 The sensors themselves are much less coplex and expensive than sequential PSIs and can progreater angular dynamic range.

There are, of course, some drawbacks to this selectThe advantages are balanced by a reliance on the fidelitthe wavefront reconstruction algorithm, and by low spatresolution and sensitivity as compared to PSI. Accordinga study by Koch et al.,21 Shack-Hartmann sensors can mesure difference wavefronts with a fidelity approaching thof a PSI, provided an appropriate number of individumeasurements are averaged, and spatial resolution muadequate for the application. This is especially true in olarge optic application, where longer scale-length abetions ~e.g., due to mounting distortions! are important tocharacterize at full aperture, even with reduced angular ssitivity, but where high spatial frequency distortions canmeasured more easily over small subapertures.

2 System Design Overview

The optical design for our deep-UV Shack Hartmann mtrology tool is shown in Fig. 2. Collimated illumination ispectrally filtered and then focused by a beam expanlens. This light is then spatially filtered to propagate asexpanding spherical wave. The spherical wave is comated by an off-axis paraboloid, which limits the maxmum size of the object under test. The collimated light threflects from the test optic, the paraboloid again, andbeamsplitter. The optical information is then recollimatby the relay lenses, dissected by a lenslet array insidesensor, and falls onto a charge-coupled device~CCD! de-tector. From there, software interprets the image of thetic under test.

The layout is similar to a Keplerian telescope design,that collimated input from the foil optic is demagnified tocollimated output to the wavefront sensor. Unwrapping tKeplerian portion of the metrology tool yields Fig. 3. Thsystem magnification is accomplished using a large~200mm diam! off-axis parabolic mirror in conjunction withrelay lenses. The magnification of the system and thevantage of this layout can be derived from the system m

Fig. 2 Shack-Hartmann metrology tool.



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Fig. 3 Portion of the Shack-Hartmann metrology system illustrating the intrinsic Keplerian design.

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where the first lens is replaced by the parabolic mirror athe second is the relay lens. ChoosingL15 f 15755.5 mmandL25 f 2575.0 mm, the system magnificationM , givenby matrix elementD, reduces to2 f 2 / f 1 50.1. The sys-tem has no effective optical power, as indicated by theBelement. ElementC shows that the effective propagatiodistance is zero—the effects of diffraction are minimizedthe image plane. The system matrix is diagonal, reveathat position and tilt are decoupled.

3 Detailed Design

3.1 Arc Lamp

To provide the illumination for this optical metrology sytem, a 200-W broadband mercury arc lamp was selecThe photon emission is concentrated at the cathodeanode of the lamp, so-called hot-spots. A hot-spot can tbe imaged onto a pinhole.

In operation, the nearly omnidirectional output of thlamp is amplified by a spherical rear reflector. The ligthen expands from the center of the lamp to fill a colliming lens located inside the arc lamp housing. After passthrough the spectral filter, the light is focused by a positpower lens with anf number matched to the off-axis pa

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rabola. At the focus of this lens, a magnified image of tlamp is formed. The magnification is given by the ratiothe f numbers of the lenses as

arc magnification5f /#2

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where f /#1 is for the collimating lens andf /#2 is for thebeam expander lens. The original arc size of 032.2 mm2 is therefore imaged to 1.535.7 mm2. Highspherical abberation will roughly double this image sizresulting in a 3310 mm2 arc image. This image is thespatially filtered, as shown in Fig. 2.

A 266-nm pulsed laser was considered for this applition as well. The idea was rejected due to well-known prolems of high peak power per pulse in a small beam wawhich could cause a breakdown in the air. However,obvious benefits of higher power may require a revisitatof this issue in the future.

3.1.1 Arc instability

A major drawback to the arc lamp as a source is arc inbility. Although the illumination from the electrodes showgood rotational symmetry.25 there are spatial variations thacan be detected by the wavefront sensor. These changlocal tilt and intensity are caused by convection curreinside the lamp, arc migration on the electrodes, and ament temperature changes. Assuming these fluctuationsrandom with a Gaussian probability distribution, the effe

Fig. 4 Optical properties of 0.4-mm-thick borosilicate glass (SchottGlas, model D-263).

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on the metrology measurements have been mitigatedaveraging 100 successive images over a two minute tspan.

3.2 Spectral Filter

The optical properties of borosilicate glass~Schott Glas,model D-263! are shown in Fig. 4.26 From the transmissioncurve, light incident on the glass foil at wavelengths greathan 300 nm will partially transmit through the substraand reflect off its back surface. This will result in a doublset of input data to the wavefront sensor~see Fig. 5!, cor-rupting wavefront reconstruction. For example, if a longwavelength HeNe laser were used for illumination, the raof the power from the front to back reflection would be 1This would make the wavefront reconstruction erroneoTherefore, we ideally seek a filter that passes 100% ofelectromagnetic radiation below 260 nm and blocks 10above. Of course, real filters simply attenuate all walengths to varying extents. We therefore need to balanceattenuation of the visible wavelengths and the total powinput to the system. Filters considered are shown in F6.27,28As a baseline for the power measurements, the mconservative filter was installed in the system. Althouthis filter successfully blocked nearly all of the long wavlength light, only 1.1mW of power was incident on thesensor. This resulted in a very low signal-to-noise ra~SNR! with high gain. From this test, it was estimated tha signal strength increase of five times would be desira

To choose the best spectral filter from the options in F6, a simulation was created to evaluate 1. the total poincident on the detector, and 2. the power incident ondetector from the front and back reflections. This algorithmultiplies the lamp spectral irradiance by the filter tran

Fig. 5 Path of light reflected from front and back surfaces of glassinto the sensor. Back reflections (dashed line) should be avoided.

Fig. 6 Transmission curves for a range of spectral filters (ActonResearch, Omega Optical).

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mission curve to calculate the spectra incident on the goptic under test. Then, accounting for the transmission,flection, and absorptive properties of the 0.4-mm-thglass at the incident wavelengths, the spectra returnethe wavefront sensor from the front and back surfacecomputed. The lumigen-coated CCD responsivity is nconstant over the wavelength band,29 so this quantum effi-ciency is considered in the simulation as well. Integratithe resulting spectra yields the total powers returned frthe respective reflections. These values indicate the relaintensity of the front and back focal spots on the detecFrom this data, Table 1 was generated. For the 254wideband filter, a plot of the front and back reflected powinto the sensor is shown in Fig. 7. The ratio of the arunder the front reflection curve to the area under the breflection curve is 40.0, as confirmed in Table 1 for thfilter. The back reflection power is below the sensor nofloor, making the error signal negligible. Also, the 4.1-mWtotal power incident on the CCD for the 254-nm widebafilter was satisfactory. For these reasons, this filter waslected.

3.3 Spatial Filter

The spatial filter has two functions. It cleans up the illumnation from the arc lamp, reshaping the profile to an epanding spherical wave. The spatial filter also plays a krole in determining a lenslet’s focal spot size on the dettor. If the former were the sole factor, one would selectsmallest pinhole that admitted power above a SNR threold. However, the latter role of the spatial filter constraithe lower bound on the diameter.

Making the pinhole too large would do more harm thaffecting the spherical wave profile. A large pinhole woueffectively consume the dynamic range of the sensor, si

Table 1 Comparison of spectral filters for Shack-Hartmann metrol-ogy system. The total power from the front reflection returned to thesensor is shown, along with the ratio of the power from the front andback reflection, named the focal spot intensity ratio.

Spectral filter peak l (nm) 254 254 210 220 227

Filter shape narrow wide broad broad broad

Power into sensor (mW) 1.1 4.1 7.2 9.5 7.8

Focal spot intensity ratio .1000 40.0 3.9 4.6 5.5

Fig. 7 Irradiance reflected from glass sheets into wavefront sensorsas a function of wavelength for the 254-nm wideband filter. Thissimulation considers the arc lamp spectral output, spectral filtertransmission, optical properties of the borosilicate glass, and lumi-gen coating on the CCD.



748 Optical Engi

Fig. 8 Power losses throughout the optical path of the Shack-Hartmann surface metrology system.

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a lenslet’s focal spot would then cover all of the pixededicated to it. An upper bound on the pinhole size is thimposed, such that the size of the focal spot on the deteshould not exceed half of that lenslet’s pixels. For the ssor selected, there are 16 pixels/lenslet.

To determine the size range for the pinhole, a few cculations need to be performed. A focal spot on the deteshould cover at least 10 pixels for accurate centroidingthe diameter of the spot should therefore be at leastpixels. Diffraction effects from the lenslet array will increase the focal spot size. A collimated input to a lenswill have a focal spot diameter due to diffraction, given

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Using the peak transmitted wavelengthl of 253.7 nm, thelenslet parameters diameterdlenslet of 224mm, and the focallength atl, f lenslet, of 17.904 mm, the focal spot diametedue to diffraction is 40.6mm.

Next, we need to consider the demagnified pinhole ctribution. This demagnification is given by the ratio of thfocal lengths of the lenslet array and the relay optic. Tother lenses do not contribute to the demagnification sia conjugate 1:1 magnification of the pinhole occurstween the beamsplitter and the relay lenses, as shown2. Therefore, the diameter of the pinhole image on thetector is given by

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With f lenslet given before andf relay optic575.0 mm, the pin-hole diameter on the CCD is 0.239dlenslet. Hereafter,mwill denote the pinhole magnification of 0.239.

These two effects, diffraction and pinhole demagncation, are combined by convolution. This is approximatthe same as addition in this case, yielding a total focal ssize on the detector of 40.6mm10.239dpinhole. This focalspot diameter must cover at least 3.6 pixels for sensitivas previously mentioned, but not more than (1/2)58 pixels for dynamic range. Since the pixel size is 14mm,we have

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To satisfy this inequality, the pinhole diameter must be btween 41 and 299mm in size. To admit as much power apossible, a 250-mm-diam pinhole was selected.

3.4 Power Considerations

Making sure that enough irradiance would reflect from tinefficient glass and return to the sensor for a succesmeasurement was a prime consideration in the design.diance from the source is lost at many locations alongoptical path, as illustrated in Fig. 8. To keep track of tpower remaining for imaging, we need to calculate tpower into the system and the power lost. This procstarts with the arc lamp inside of the lamp housing. To fithe total power coming out of this lamp, the spectral filtbandwidth ~FWHM! is multiplied by the average powefrom the lamp spectral irradiance curve over this banwidth. From Fig. 6, the FWHM is 40 nm. The average flufrom the lamp over this bandwidth is 35 mW/m2-nm.25 Sothe flux from the lamp is 1400 mW/m2.

Three multiplicative factors next affect this power: thspectral filter transmittance, lamp housing rear reflecand the housing itself. The filter transmittance at FWHMapproximately 20%, again obtained from Fig. 6. The lamhousing rear reflector acts as an amplifier, yielding a 16boost.25 The housing itself is naturally very lossy, since thomnidirectional irradiance is mostly wasted, excluding tcontribution from the rear reflector. The housing factor ismere 5%.25 So in the exit tube of the lamp housing, whave 1400 mW/m230.231.630.05522.4 mW/m2.

The antireflection-coated fused-silica beam-expanlens at the end of the condenser~exit tube! transmits 99.8%of incident light. So the image of the arc formed at tspatial filter contains 22.4 mW30.998522.34 mW/m2. Asmentioned in Sec. 3.1, this image size is 30 mm2. About40% of this power is lost in a ‘‘halo’’ around the imagefurther reducing our available power to 13.4 mW. Next, wspatially filter with a 250-mm pinhole, as described in Se3.3. The ratio of the area of this pinhole to the area ofimage is 0.16%, so a mere 21mW makes it through.

This light then goes through a veritable pinball machiof mirrors and lenses until it is incident on the CCD dete

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tor inside of the wavefront sensor. The percentage transted or reflected by each component in normal operatiosummarized in Table 2.30–34 These data were compilefrom intensity graphs as cited. Intensity data can be usince power is proportional to intensity. So the final powincident on the CCD detector is 21mW from the spatialfilter multiplied by 15.6% for the optical elements dowstream. This theoretical calculation gives roughly 3.3mWof power centered at 254 nm to excite electrons inCCD. This light is then divided unevenly by the lensleover the 102431024-pixel CCD. Is this enough? Teststhe measurable power threshold for this instrument indicthat 500 nW is detectable, but 1mW is needed for a lowergain, higher SNR measurement. An experimentally incidpower of 4.1mW, as shown in Table 1, is therefore satfactory. There is good agreement between the theoreticcalculated power of 3.3mW and the measured 4.1mW.

3.5 Wavefront Sensor

There were a number of tradeoffs considered in the setion of this device, as identified by Greivenkamp et al.2 Thespot displacement on the detector is equal to the wavefslope times the focal length of the lenslet. A limitationthe maximum allowable wavefront slope, or dynamrange, is imposed by the detector area allocated tolenslet. This is primarily a software-based limitation. Theis no inherent requirement that a spot remain within theof pixels associated with its lenslet. Spots can translateeral cells as long as the one-to-one correspondence betthe spots and the lenslets can be mapped or identified.2 Forthe same detector, a lenslet array with a shorter focal lenwill have greater dynamic range with reduced sensitivOn the other hand, a longer focal length lenslet will allogreater accuracy in determining the average incident wafront slope, since a given slope produces a greaterdisplacement. So there is a tradeoff of sensitivity andnamic range associated with the lenslet focal length.

The size versus number of lenslets is another importradeoff. As the number of lenslets is increased for a givarea, spatial sampling and spatial resolution are increaThis results in less averaging of the wavefront slope othe lenslet aperture, but reduces the number of detepixels that are available behind each lenslet to make

Table 2 Optical element transmission (T) and reflection (R) per-centages from spatial filter to CCD detector. The items are listed inthe order that the light ‘‘sees’’ them. Repeated items are seen twice.High transmission percentages are due to antireflection coatings.

Optical element T,R % Reference

Beamsplitter T 50 30

Parabola R 87 31

Test optic (Si or glass) R 50 32

Parabola R 87 31

Beamsplitter R 50 30

Relay optic 1 T 99.8 33

Relay optic 2 T 99.8 33

Lenslet array T 95 34

Total 15.6

-

-

t

t

-n

-t

t

.

r

measurement. Selecting larger lenslets will allow a msensitive measurement of slowly varying wavefronts, bmay not sufficiently sample high spatial frequency wavfronts, producing artificially smooth surface maps.

Pixel size on the detector and the lensletf number arealso related. The spot size produced by each lenslet musufficiently large~covering at least 10 pixels in area! toobtain a good centroid calculation, while separation btween spots from adjacent lenslets must be maintaineensure dynamic range. As a general rule, the spot sizeameter should not cover more than half of the numberpixels dedicated to a lenslet’s diameter for a reasonabalance of sensitivity and dynamic range. The spot sscales linearly with the wavelength and lensletf number, sothe lenslet diameter and focal length should be selecwisely.

3.5.1 SMD 1M15 instrument

Wavefront Sciences~Albuquerque, New Mexico! providedthe SMD 1M15 wavefront sensor for our application.35 Theinstrument features a 64364 lithographically etched, fusedsilica lenslet array. Table 3 displays a summary of thetable physical characteristics of the instrument’s lensletray and detector, along with some system magnificatioThe CCD detector was coated with lumigen by SpecInstruments36 ~Tucson, Arizona! to increase its quantum efficiency. The lumigen coating is 30 to 40% efficient in asorbing the incident light at 250 nm and up-converting500 nm.~The lumigen coating is actually 60 to 80% efficient in absorbing the incident light at 250 nm and uconverting to 500 nm. However, the lumigen is a thin layon top of the CCD, so half of the photons are emittedeach direction, thus you lose 50% is lost from the directioality!. In selecting this unit, its ability to meet our func

Table 3 Wavefront sensor lenslet array, detector, and system mag-nification summary.

System

Operating wavelength l 254 nm

System magnification M 20.1

Pinhole magnification m 0.239

Pinhole diameter dp 250 mm

Lenslet

Lenslet diameter dl 0.224 mm

Lenslet focal length at l f l 17.904 mm

Nominal sag 1.378 mm

Active number of lenslets X Nl 64

Active number of lenslets Y Nl 64

Total number of lenslets X 72

Total number of lenslets Y 72

Total aperture X D 16.128 mm

Total aperture Y D 16.128 mm

Detector

Pixel size X p 14 mm

Pixel size Y p 14 mm

Number of pixels X Np 1024

Number of pixels Y Np 1024


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tional requirements for sensitivity and dynamic angurange were paramount. These goals, described in Sec. 110 mrad and 0.3 mrad, respectively.

The dynamic range of measurement is limited bydetector area allocated to each lenslet~named the area-ofinterest or AOI!. When the focal spot behind a lenslet ecroaches on the edge of its AOI, crosstalk occurs and wafront reconstruction is compromised. This limitationfocal spot shift is depicted in Fig. 9. The angular rangethis instrument can be geometrically estimated fromlenslet diameter of 0.224 mm and operating focal length17.904 mm to be approximately66 mrad. Taking the system magnification into account allows one to estimatemeasurable dynamic range at the object plane tou20.136 mradu50.6 mrad. To make a more accurate cculation, we need to consider the focal spot size. The fospot radius on the CCD at the 254-nm operating walength,r spot,254, is given by

r spot,2545f ll

dl1

mdp

2. ~8!

From the values in Table 3, the spot size is 50.2mm. Thiswill effectively reduce the lenslet diameter. So the actdynamic range, considering the magnification, will be

dynamic range5MF S dl

22r spot,254D

f l

G , ~9!

which gives a value of 0.35 mrad. This instrument wtherefore meet the dynamic range requirement of 0.3 mat the object plane. This angular range is the same forlenslet or the set of lenslets. For one lenslet with a diamof 224 mm, which corresponds to 2.24 mm at the objeplane, a wavefront tilt of 0.78mm can be measured. SincNl564, the maximum measurable object tilt over the enlenslet array is 0.78mm364550.18mm over a 143.3-mmlateral distance.

Estimating the instrument’s sensitivity is a bit more dficult. We need to calculate the noise floor after algorithmwavefront reconstruction. This analysis requires expmental data for the centroid estimation error as well

Fig. 9 The high tilt of the incident wavefront results in a focal spotshift to the edge of the lenslet’s AOI. This is the extent of the instru-ment’s angular range.


re

-

l

r

knowledge about the digital signal processing used formerical reconstruction of the wavefront shape. We startby calculating the centroid estimation error at the operatwavelength,e254. As a baseline, the manufacturer htested the centroid estimation error for a similar instrumat 633 nm, yieldinge63350.0025 pixels. To extrapolate ouestimate, we need to scale by the square of the diffractlimited spot half widths at this baseline wavelength andoperating wavelength. The square is used to realize ancontribution from a length measurement.

e2545e633F f l~254 nm!

dl

f b~633 nm!

db

G 2

. ~10!

For the baseline sensor tested at 633 nm,f b anddb are itslenslet focal length and diameter, respectively, which givf b(633 nm)/db536.0mm. The resulting e254

50.0079 pixels. Now we must use this information to cculate our instrument’s rms angular noise floor. This isfunction of the angle to the edge of a pixel and centroestimation error. Including the magnification will translaus to the object plane. The noise floor is therefore

u rms5M S pe254

f lD , ~11!

resulting in u rms50.61mrad. The minimum measurablvariation from flatness, or noise floor, is influenced by tnumerical reconstruction algorithm as follows:

noise floor5ANldu rms. ~12!

The lenslet diameter is included to compute the ‘‘per lelet’’ noise floor. A factor of the square root of the numberlenslets is introduced to effectively account for the errorandom walk over the lenslet array. Equation~12! thereforegives the final numerically reconstructed noise floor, PThis minimum measurable deviation from flatness is eqto 1.1 nm. This could occur over a lateral distance as shas 2.24 mm~one lenslet’s diameter magnified!. So, thissensitivity corresponds to an angular resolution of 0.5mradfor one lenslet. As greater lateral distances are considethe angular resolution improves, so the sensitivity funtional requirement of 10mrad is always met.

Comparing these calculated values back to the futional requirements, for a 10-mm lateral distance in tobject plane, we have theoretically measurable PV heof 63.5mm with a resolution of61 nm.

4 Performance Evaluation

4.1 Test Optic Surface Mapping

The Shack-Hartmann surface metrology instrument, shoin Fig. 10, has been successfully used to generate surmaps of large l/30 reference flats, 0.45-mm-thic3100-mm-diam polished silicon wafers as are commoused in semiconductor industry, and 100314030.4-mm3

glass sheets. The system can provide both angular de

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tions from flatness and absolute PV measurements.former are critical to telescope resolution, while the latare of immediate use in polishing and shaping.

Measurement of a 0.4-mm-thick borosilicate glass shis shown in Fig. 11. Results from glass metrology showindication of back reflections in the raw data. The arrayfocal spots is regular and the frequency of spots is aspected, one per AOI. Large warp in prefigured stock glsheets makes their entire surface unmeasurable; howsubset regions have been successfully measured.

4.2 Repeatability and Accuracy

The repeatability of the measurements has been primalimited by random variations in the arc lamp caused bymigration on the electrodes and convection currents insthe lamp.25 Averaging 100 successive images has mitigathe effects of these variations, reducing the range ofsurface maps to 5.0 nm rms! over a minimum 100-mm-diam object size while the setup is unchanged. To demine the repeatability of the instrument for a human-in-th

Fig. 10 Shack-Hartmann metrology system hardware in a class1000 cleanroom environment at the MIT Space NanotechnologyLaboratory.

e

t

-

r,

loop environment, specimens were measured, physicremoved from the metrology station, replaced, and remsured. Both the reference surface and the silicon waspecimens were studied; results were similar. Repeatabmeasurements ranged 35.6-nm PV with a 13.2-nm standeviation. The rms surface variations ranged 14.0 nm wa 5.1-nm standard deviation.

The accuracy of the system is difficult to quantify, sinaberrations in the lenses will contribute different anguerrors to measurements at different spatial locations.roughly estimate the overall accuracy of the system, tflats with factory-provided interferograms were measurThese interferograms reveal nonflatnesses of 2.6-nmand 4.9-nm rms, respectively. Comparing the two flats wthe Shack-Hartmann system shows an average rms sudifference of 17.6 nm. Overlapping the interferograms,rms deviation can be estimated to beA2.6214.92

55.5 nm. The difference between the Shack-Hartmanninterferometric data provides a crude estimation of thecuracy of the tool. Assuming root-sum-squared~RSS!stacking of errors, a conservative estimate of the accuryields A17.6225.52516.7-nm rms. Several factors contribute to the difference between the interferograms aShack-Hartmann measurements. The mirrors are subjeto different temperatures and mounting forces betweeninstruments. Additionally, the uncertainty in the interfermetric measurements is estimated to bel/50'13-nm PV.

In operation, the user will make a reference image wa flat, then substitute the optic under test. Based onearlier analysis, the test measurement will be accurat,17 nm and repeatable to;5 nm rms. These results arsummarized in Table 4.

5 Conclusions

A Shack-Hartmann surface metrology tool is developthat permits metrological feedback of transparent or opaoptic foils. This instrument can be used to determine isurface meets the 500-nm global flatness manufacturingquirement. The surface mapping data is accurate,17-nm and repeatable to;5 nm rms. Nonflat figures can

Fig. 11 Raw data (left) is collected on the CCD array in the wavefront sensor. Comparison with areference image, regular array focal spots from a l/30 flat mirror, enable the wavefront reconstruction(right), which is equivalent to a surface map at the object plane. The intensity scale (center) indicatesthe relative energy density incident on the CCD in 21254096 discrete values.


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also be studied up to a dynamic range of6350mrad at theobject plane. The 1433143-mm2 square viewing range caaccommodate the proposed 1403100-mm2 foil optic sur-face area.

Acknowledgments

We gratefully acknowledge the assistance of our colleagat WaveFront Sciences, Incorported. The support of thedents, staff, and facilities from the Space NanotechnolLaboratory are much appreciated. This work is supporby NASA Grants NAG5-5271 and NCC5-633 and the Ntional Science Foundation.

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Konkola, J. Przbylowski, Y. Sun, J. You, S. M. Kahn, and D. Goli‘‘Precision shaping, assembly and metrology of foil optics for x-rreflection gratings,’’Proc. SPIE4851, 538–548~2002!.

2. J. E. Greivenkamp, D. G. Smith, R. O. Gappinger, and G. A. Willi‘‘Optical testing using Shack-Hartmann wavefront sensors,’’Proc.SPIE4416, 260–263~2001!.

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system for fault location in optical waveguide devices based oninterferometric technique,’’Appl. Opt.26, 1603–1606~1987!.

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15. P. de Groot, ‘‘Grating interferometer for metrology of transparflats,’’ Opt. Fabrication Testing6, 28–30~1996!.

Table 4 Shack-Hartmann surface metrology system performanceresults.

Setup Statistic PV (nm) rms (nm)

Static

Repeated Range 5.0 0.5

measurements

Repeatability Range 35.6 14.0

Removed and

replaced object Standard deviation 13.2 5.1

Accuracy

Compared two Average - ,16.7

known surfaces


s-

-

-

16. C. Ai, ‘‘Multimode laser fizeau interferometer for measuring the sface of a thin transparent plate,’’Appl. Opt. 36, 8135–8138~Nov.1997!.

17. R. K. Heilmann, G. P. Monnelly, O. Mongrard, N. Butler, C. G. CheL. M. Cohen, C. C. Cook, L. M. Goldman, P. T. Konkola, MMcGuirk, G. R. Ricker, and M. L. Schattenburg, ‘‘Novel methods fshaping thin-foil optics for x-ray astronomy,’’Proc. SPIE 4496,62–72~2002!.

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25. The Book of Photon Tools, Oriel Instruments, 150 Long Beach BlvdStratford, CT 06615~2001!.

26. SCHOTT Corporation, 3 Odell Plaza, Yonkers, NY 10701.27. Acton Research Corporation, 15 Discovery Way, Acton, MA 017228. Omega Optical, Inc., 210 Main Street, Brattleboro, VT 05301.29. Seishin Trading Co., LTD., 2-1, 1-chome Sannomiya-cho, Chuo

Kobe, 650-0021 Japan.30. OptoSigma, 2001 Deere Avenue, Santa Ana, CA 92705.31. Space Optics Research Labs., 7 Stuart Road, Chelmsford, MA 0132. Handbook of Optical Constants of Solids, E. D. Palik, Ed., Academic

Press, San Diego, CA~1985!.33. Lambda Research Optics, Inc., 1695 W. MacArthur Blvd., Co

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NM 87123-3905.36. Spectral Instruments, 420 North Bonita Avenue, Tucson, AZ 8574

Craig R. Forest is currently a PhD candi-date in the Department of Mechanical En-gineering at the Massachusetts Institute ofTechnology in the research group of A.Slocum. He received a BS in mechanicalengineering in 2001 from the Georgia Insti-tute of Technology, and MS in mechanicalengineering in 2003 from the Massachu-setts Institute of Technology. His current re-search interests include MEMS, optics, andprecision machine design. His recent re-

search efforts have focused on providing metrology and assemblytechnology for NASA’s next generation x-ray telescope, as well asoptical MEMS sensors.

Claude R. Canizares is Associate Provostand the Bruno Rossi Professor of Experi-mental Physics at MIT and is a professor atthe Center for Space Research. He is aprincipal investigator on NASA’s ChandraX-ray Observatory, leading the develop-ment of the high resolution transmissiongrating spectrometer for this major spaceobservatory, and is Associate Director ofthe Chandra X-Ray Observatory Center.He has also worked on several other space

astronomy missions, including as coinvestigator on the Einstein Ob-servatory (HEAO-2). His main research interests are high resolutionspectroscopy and plasma diagnostics of supernova remnants andclusters of galaxies, cooling flows in galaxies and clusters, x-raystudies of dark matter, x-ray properties of quasars and active galac-tic nuclei, and gravitational lenses. He is a member of the Board of


Trustees of the Associated Universities Incorporated, the Board onPhysics and Astronomy of the National Research Council, and theAir Force Scientific Advisory Board. He served on the NASA Advi-sory Council and was chair of the Space Studies Board of the Na-tional Research Council and NASA’s Space Science Advisory Com-mittee. He received the BA, MA, and PhD in physics from HarvardUniversity. He came to MIT as a postdoctoral fellow in 1971 andjoined the faculty in 1974, progressing to professor of physics in1984. He is a member of the National Academy of Sciences, a fellowof the American Physical Society, a member of the InternationalAcademy of Astronautics, and a fellow of the American Associationfor the Advancement of Science. He has authored or coauthoredmore than 170 scientific papers.

Daniel R. Neal obtained his Bachelors ofScience from the University of Texas inaerospace engineering in 1980, and hisPhD from Stanford University in aeronau-tics and astronautics and applied physicsin 1984. For 13 years he worked at SandiaNational Laboratories developing high-energy laser systems. During that time, hedeveloped numerous laser diagnostic in-struments, adaptive optics, laser resona-tors, and micro-optics systems. He also de-

signed a series of increasingly sophisticated instruments formeasuring aberrations in lasers and optics. The early film-basedHartmann sensing evolved to a 1-D, all electronic Shack-Hartmannsensor, which was used for wind-tunnel, tomographic and hyper-sonic diagnostics and other applications. In 1995, in conjunctionwith business partner T. Turner, he founded WaveFront Sciences,Incorporated, to commercialize the Shack-Hartmann and micro-optics technologies. Since then, he has developed many differentwavefront sensor configurations and instruments, including applica-tions to optic, laser beam, silicon wafer, and ophthalmic testing.

Michael McGuirk: Biography and photograph not available.

Mark L. Schattenburg is a Principal Re-search Scientist in the MIT Center forSpace Research. He is Director of theSpace Nanotechnology Laboratory, Associ-ate Director of the NanoStructures Labora-tory and Senior Research Affiliate with theMicrosystems Technology Laboratories.His principal work has been in the area ofmicro/nanofabrication technology, opticaland x-ray interferometry, advanced lithog-raphy including x-ray and electron beam,

nanometrology, x-ray optics and instrumentation, x-ray astronomy,high-resolution x-ray spectroscopy, and space physics instrumenta-tion utilizing nanotechnology. He is a member of the NASA ChandraScience and Instrument Development Teams, the Constellation-XFacility Science Team, the Micro-Arcsecond X-Ray Imaging Mission(MAXIM) Study Team, and the NASA/ESA Laser InterferometerSpace Antenna (LISA) Study Team. He is also a member of thesteering committee of the International Conference on Electron, Ionand Photon Beam Technology and Nanofabrication, serving as pro-gram chair in 2003. He received a BS degree in physics from theUniversity of Hawaii in 1978, and a PhD in physics from MIT in 1984.He was appointed postdoctoral associate at MIT in 1984, progress-ing to Principal Research Scientist in 1996. He has published morethan 120 papers and holds six patents. He is a member of the Op-tical Society of America, the American Vacuum Society, DPIE, theInstitute of Electrical and Electronic Engineers, and the AmericanSociety for Precision Engineering. He was awarded the 2003 BA-CUS Prize by SPIE.


metrology of thin transparent optics using shack-hartmann

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