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Precision Engineering 36 (2012) 546– 553

Contents lists available at SciVerse ScienceDirect

Precision Engineering

j o ur nal homep age: www.elsev ier .com/ locate /prec is ion

pplication of atmospheric plasma jet machining (PJM) for effective surfaceguring of SiC

homas Arnold ∗, Georg Böhmeibniz-Institut für Oberflächenmodifizierung (IOM), Permoserstr. 15, 04318 Leipzig, Germany

r t i c l e i n f o

rticle history:eceived 29 August 2011eceived in revised form 21 March 2012ccepted 2 April 2012vailable online 7 April 2012

a b s t r a c t

Optical and mechanical components made of SiC are widely used in ground and space based astronomicalinstruments and other scientific instrumentation. Although the manufacturing steps for SiC have beenimproved and optimized during the last decade, in some cases conventional abrasive shaping and fin-ishing techniques are not applicable, e.g. because of complex surface shapes like free forms or asphereswith strong curvatures, or very small sized components. As an alternative contactless plasma jet based

eywords:ltra-precision machininglasma jet machiningilicon carbideurface figuring

techniques can be applied for surface shaping or figure error correction on SiC surfaces. In this paper someaspects of plasma jet interaction with the surface are discussed. Furthermore, we demonstrate the capa-bility of atmospheric plasma jet machining technology to process optical and mechanical componentsmade of SiC in an effective way.

© 2012 Elsevier Inc. All rights reserved.

(((

sphere

. Introduction

Sintered silicon carbide (SiC) ceramic provides excellent phys-cal and chemical properties like high specific stiffness, highardness, low thermal susceptibility, and chemical inertness,hich makes it a material preferably used for structural and

ptical elements to construct lightweight and athermal groundnd space-based astronomical instrumentation or other scientificnstruments. SiC mirror production comprises several manufac-uring steps including conventional abrasive optical finishingrocesses, i.e. diamond tooling, lapping and polishing [1,2]. SinceiC is an extremely hard and strong material, material removal ratesf conventional shaping and finishing techniques are very timeonsuming compared to the processing of other optical materials2].

Although in the past 10 years much effort has been made toevelop effective processing chains for the manufacturing of largeigh quality SiC mirrors, difficulties still exist in the fabricationf small and medium sized mirrors (10–300 mm diameter) withomplex surface shapes like off-axis aspheres or freeforms. Theselements often exhibit large departures from flats or spheres andave steep surface gradients. With conventional diamond tooling

he accessible surface shape accuracy is limited to PV values of sev-ral microns, and subsequent polishing processes require multipleterations to achieve high quality optical surface profiles (<�/10).

∗ Corresponding author. Tel.: +49 341 235 3120; fax: +49 341 235 2595.E-mail address: thomas.arnold@iom-leipzig.de (T. Arnold).

141-6359/$ – see front matter © 2012 Elsevier Inc. All rights reserved.ttp://dx.doi.org/10.1016/j.precisioneng.2012.04.001

Even if the surface form (long spatial wavelength range) and themicro roughness (high spatial frequency range) can be brought intothe respective specifications, midspatial frequency errors cannot beaddressed by the conventional abrasive techniques. On contrary,those structures are often introduced by diamond tooling or smalltool polishing during finishing. In order to speed up the optics man-ufacturing and to increase the process convergence, an additionalprocess is required that

(i) provides sufficiently high material removal rates,ii) gives deterministic results based on metrology data,

iii) interacts locally with the substrate (subaperture tool),iv) provides flexible adjustment of tool size,(v) is insensitive to substrate geometry and mechanical loading

effects [2].

To cope with the challenges and to meet the requirements, sev-eral non-conventional technologies have been developed in thepast or are still under development. On the one hand, magne-torheological finishing (MRF) as a non-conventional deterministicpolishing method [3,4], and ion beam figuring (IBF) as a wellestablished technology for surface figure error correction on high-end optics [5,6], both provide excellent process stability and yieldhighly deterministic results, however at the expense of materialremoval rate. On the other hand, plasma assisted techniques have

been developed for a deterministic high rate material removal,e.g. chemical vaporization machining (CVM) [7,8], reactive atomplasma (RAP) [9], plasma jet machining (PJM) [10], and other tech-niques based on similar principles.

T. Arnold, G. Böhm / Precision Engineering 36 (2012) 546– 553 547

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-6

-5

-4

De

pth

[µ

m]

-4 -3 -2 -1 0 1 2 3 4

-11

-10 too l functi on #2

X [mm]

Fig. 2. Example of two different plasma jet tool functions (groove etchings): Toolfunction #1: VR = 0.654 mm3/h, FWHM: 1.2 mm, Tool function #2: VR = 7.34 mm3/h,

sured with a lateral resolution of 2 �m and applying an 80 �mcut-off filter to the measured profile. In some cases, roughness hasalso been evaluated using a white light interferometer (MicroMap)equipped with a 50× objective.

800

1000Bulk

Substrate #1

Substrate #2

Substrate #3

m]

SSD

200

400

600

Substrate #3

Roughness R

MS

[nm

0

200R

Fig. 1. Experimental setup for plasma jet machining.

Atmospheric plasma jet machining (PJM) presents a non-onventional surface figuring technology that has been underteady development for about 15 years. This technology is ded-cated for effective generation of surface shapes (aspheres orreeforms) and for surface error correction on optical elements.t has been successfully applied for figuring and error correctionn optical elements made of fused silica [11]. In this paper thepplication of PJM to silicon carbide is presented. We focus on thenteraction of the plasma jet with different types of SiC substratesegarding etching rate and surface roughness evolution, figuring ofspherical test structure and the midspatial frequency error cor-ection on small SiC optics and precision-mechanical components.

. Experimental details

The plasma jet machining system comprises a CNC machinequipped with 5 axes, a plasma jet source mounted as the tool andower and gas supply for the plasma generation. The plasma source

s a capacitively coupled RF plasma torch made up of a conductiveoaxial system where the inner conductor forms a coaxial tubingystem for a multi-channel gas supply. A schematic drawing of theetup is shown in Fig. 1. The coaxial system ends in a gas nozzle.y applying RF power (13.56 MHz) to the inner conductor a stablelasma jet discharge can be generated at the nozzle. The central gashannel is fed by inert gas helium ([He] = 0.5–2.0 slm). A mixture ofhe fluorine containing precursor gas CF4 and O2 is supplied eitherhrough the peripheral gas channel or the central channel as well.ypical CF4 gas flow rates range from 0.5 to 2 sccm when using theentral channel or 5–50 sccm for the peripheral gas feed. RF poweras been adjusted between 60 and 150 W.

PJM is a contactless material removal process based on chemicaltching reactions between the surface atoms of the substrate andeactive radicals in the plasma jet. The plasma jet does not exert anyignificant mechanical forces onto the surface. Material removal isccomplished by the simplified reaction scheme

iC + O∗ → SiO2 + COx (1)

iO2 + 4F∗ → SiF4 (2)

iC + F∗ → SiF4 + CFx (3)

here O* and F* are radicals formed in the plasma and SiF4 and COx

re volatile compounds desorbing from the substrate surface. Thectual mechanisms that are taking place on the surface are much

ore complex [12] and still not fully understood.The process is applied under normal environmental conditions,

hich makes this technology cost effective. Plasma jet surface fig-ring is accomplished using the dwell time method. This technique

FWHM: 2.02 mm, red dotted lines: Fit using inverse polynomial peak function. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

and all necessary mathematical algorithms are far developed [13]and widely used for the different subaperture figuring methodslike ion beam figuring, corrective polishing or MRF. The plasma jetsource moves relative to the surface on a raster or spiral path witha certain line spacing and a given local velocity that is proportionalto the local dwell time. Etching experiments have been performedon different types of sintered SiC:

• Substrate #1: round disc, no CVD coating, ground surface (sup-plied by Boostec, originating from year 1999).

• Substrate #2: round disc, with SiC-CVD coating, ground surface(Boostec, 1999).

• Substrate #3: plate, with CVD coating, mechanically polished sur-face (Boostec, 2010).

Since the production date of substrate #3 differs significantlyfrom the others, a better quality, especially that of the CVD coat-ing is expected. Surface roughness and etching rates have beendetermined using a laser autofocus surface profiler (�scan) fromgroove-like test etchings or homogeneous etchings on small areas.Rq values have been obtained from a 0.5 mm profile length mea-

0 5 10 15 20 25 30 35 40 45 50 55

Et chin g dep th [µ m]

Fig. 3. Surface roughness (Rq) on SiC samples depending on the final etching depth,measured with laser profiler.

548 T. Arnold, G. Böhm / Precision Engineering 36 (2012) 546– 553

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ig. 4. Surface morphology on substrate #2: (a) ground CVD coating, initial state,oating as deposited (backside of substrate #2).

. Results and discussion

.1. Plasma jet tool function

In Fig. 2 two plasma jet tool functions are shown that have beenbtained for different sets of plasma jet parameters. The most effec-ive process parameters for adjusting the size of the tool functions RF power, working distance (distance from nozzle to substrateurface) and precursor gas flow rate. Tool function #1 can be cre-ted by using a small amount of precursor gas ([CF4] = 1 sccm) andoderate RF power (60 W) at a relatively large working distance of

mm. This small tool can be used for removing very small surfaceeatures in the range of 1 mm lateral size. The large tool functiontool function #2) is an example of a reasonably high removal rateool for effective figuring of larger substrates or generating deeptructures and steep gradients. This tool function is created by usingCF4] = 50 sccm and a RF power of 140 W. Since data of measuredool functions are too noisy to be used in deconvolution algorithmsor dwell time calculation, smoothing or fitting is necessary. It hasurned out that an inverse polynomial peak function can be used asn adequate fit function rather than a Gaussian, which is commonlyppropriate in plasma jet machining of fused silica.

.2. Roughness evaluation

Roughness development depending on the etching depth haseen determined on three SiC samples with different initial sur-ace quality. Fig. 3 shows the Rq values on ground SiC surfacesbtained from a 0.5 mm laser profiler line scan with lateral resolu-

ion of 1 �m. The initial roughness value of 800 nm for substrate #1s rather high, but the Rq value decreases sharply as etching depthncreases. A clear minimum occurs at a depth around 6 �m showingess than half that of the initial roughness value. At deeper etchings

Fig. 5. Surface morphology on substrate #3: (a) at 1 �

rface at 15 �m etching depth and (c) at 37 �m etching depth, (d) unground CVD

the roughness increases steadily. No saturation effect occurs withinthe investigated depth range. A similar smoothing effect appears forthe CVD coated substrate #2. Although the initial surface rough-ness only half that of the uncoated substrate, a significant decreaseoccurs showing a minimum at around 6 �m, which is nearly thesame position as for the uncoated sample. At increasing etchingdepth the roughness increases again slightly.

Roughness measurements on polished CVD coated substratesreveal different results. Starting with initial value of approx.Rq = 1 nm the roughness increases and shows a maximum at 5 �mdepth while for further increasing depths the Rq values decreaseslightly and remains on a constant equilibrium level of Rq = 148 nmon average for depths from 10 �m up to 60 �m. Using a light inter-ferometer, a Rq value of 50 nm has been determined. This differenceis attributed to a different lateral wavelength scale on which theroughness statistics has been calculated at both measurement sys-tems.

Surface roughness expressed as Rq values only are sometimesambiguous. Even for the same value different surface featurescan appear. Thus, the roughening effects become more instructivewhen looking at surface texture mappings. Ground surfaces of sub-strates #1 and #2 feature uniform roughness, which is shown inFig. 4(a) for substrate #2. When etching these surfaces with theplasma jet, either with or without CVD coating, reactive fluorineand oxygen particles react preferably at disturbed surface sites.Uniformly distributed subsurface damage (SSD) originating formthe grinding process presents such disturbance. When the subsur-face damage layer is removed a surface is formed that is smootherthan the initial surface. Now, the surface is in a state where bulk

structural properties become more relevant. This holds for bothground surfaces at etching depths of 5–7 �m. However, furtheretching changes surface morphology depending on the microstruc-ture of the substrate material. In the case of uncoated material

m etching depth, (b) at 60 �m etching depth.

T. Arnold, G. Böhm / Precision Engi

Table 1Parameters of the 4th degree polynomial fitted to the cross sections of the etchedasphere shapes. F gives the average factor of the etching rate with respect to theassumed rate of 7.83 mm3/h.

Description A (�m) B (10−6 �m−1) C (10−12 �m−3) F

Target topography −30.00 0.4800 −0.00192 1.00

instaiwb

ecmsaipbod

3

aas

z

wCFsufrygcp

hnsivvwart(iOtnm

#1: no CVD, ground −32.12 0.48117 −0.00183 1.02#2: CVD, ground −37.14 0.57946 −0.00223 1.21#3: CVD, polished −61.49 1.00399 −0.00415 2.10

ntrinsic pores which open up during etching form the high rough-ess, whereas on the CVD coating an evolution of a granulartructure occurs, which are depicted in Fig. 4(b) and (c). This struc-ure is probably caused by an etching selectivity between dropletsnd their boundaries (shown in Fig. 4(d)), which made up the orig-nal CVD coating before grinding. In Fig. 4(c) very smooth valleys

ith Rq < 2 nm (determined from 50× white light interferometer)etween high narrow ridges are visible.

The morphology of the polished surface on substrate #3 aftertching shown in Fig. 5(a) and (b) reveals that the CVD coatingonsists of arbitrarily distributed small crystallites. The Rq maxi-um at approximately 5 �m in Fig. 3 indicates the presence of a

ubsurface damage layer, where disturbances in chemical bondsre preferably attacked by the reactive particles and lead to anncreased roughness. When this layer has been removed, the bulkroperties influence the roughness structure. Etching selectivityetween the C-face and the Si-face at SiC [7,14] induces the devel-pment of crystallite facets and consequently a homogeneous andepth-independent roughness.

.3. Deep etching

The optimized plasma jet tool has been applied to machine anspherical test shape into a flat substrate. This shape can be thoughts the fictive departure from a best fit sphere. The shape is pre-cribed on a radius of 15 mm by an even polynomial of 4th degree:

= A + Br2 + Cr4 (4)

here r = (x2 + y2)0.5, A = 30 �m, B = 0.48 × 10−6 �m−1, and = −0.00192 × 10−12 �m−3. The PV value of this shape is 30 �m.ig. 6(a) shows the theoretical material removal, i.e. the inverseurface shape. The dwell time calculation has been accomplishedsing far developed deconvolution algorithms. An input toolunction determined on substrate #1 with a volume removalate of 7.83 mm3/h and a FWHM of 1.9 mm has been appliedielding a total processing time of approximately 1.5 h for theiven topography z. The resulting dwell time matrix has beenonverted to a CNC machine readable code for a line-by-line rasterath with 0.1 mm line spacing.

The three different SiC substrates (substrates #1, #2, and #3)ave been processed by this dwell time programme (one run each),ot taking into account possible differing etching rates for sub-trates #2 and #3. The etching result for substrate #1 is shownn Fig. 6(b), which reveals a rotationally symmetric shape and a PValue that is near the target value of 30 �m. The horizontal andertical cross sections of the aspheres have been plotted togetherith the theoretical targeted shape in Fig. 7. An over-etching occurs

t all substrates, which indicates a large etching rate sensitivityegarding the respective material. For a quantitative comparisonhe cross sections have been fitted using the polynomial function4). The fitting parameters are given in Table 1, where F is the scal-ng factor of the function with respect to the target topography.

bviously, the CVD coatings can be etched up to a factor of 2 faster

han the raw sintered material. This effect might be attributed toon-etchable sintering additives in the raw material inhibiting theaterial conversion to volatile compounds. The minor over-etching

neering 36 (2012) 546– 553 549

on substrate #1 is mainly caused by workpiece heating during theetching process leading to faster chemical surface reactions andthus an increase of the etching rate. Since the material removalfunction that was used in the dwell time calculation has been deter-mined from groove etchings with no significant substrate heatingthis etching rate was somewhat lower. The plasma jet machiningresults demonstrate the ability to figure deep free form shapes inSiC featuring large surface gradients and curvatures in a deter-ministic way. Further shape improvement can be achieved whenapplying more iterative processing runs.

3.4. Targeting small features

Functional SiC surfaces, either optical or mechanical, oftenrequire the application of corrective figuring methods after pre-processing (either mechanical-abrasive or PJM) to meet the givenspecifications. In this section two examples of successful figureerror correction are presented. The first example covers the manu-facturing of small strongly curved off-axis parabolic mirrors madeof uncoated sintered SiC from Boostec. The mirrors are part of thebeam angle monitoring system BAM-OMA of the GAIA satellite mis-sion [15,16]. The outer diameter of the mirrors was 20 mm, theclear aperture was only 10 mm in diameter. The main challenge forthe conventional, mechanical-abrasive fabrication of the collimatormirrors consisted in their small radius of curvature (R = 50.17 mm)and the hardness of the material. The surface form deviation fromthe mathematical prescription was specified to be 12.5 nm RMS,micro-roughness should be less than 6 nm RMS.

Three individual mirror blanks have been fixed in a special 3 in1 holder which was also made of silicon carbide. The positions ofthe individual mirrors M1 to M3 in the 3 in 1 setup can be seen inFig. 8. The whole setup has been ground by Xycarb Ceramics to aparabolic shape near the desired one. Pre-polishing was performedat TNO on a Zeeko IRP 200 7-axes polishing robot. The followingtactile measurement using a Precitech diamond turning machinewith Ultracomp tactile system revealed quite high surface shapedeviations of more than 10 �m PV (2–5 �m RMS) over an aper-ture of 12 mm for all mirrors. Fig. 9(b) exemplarily shows a Zernikepolynomial representation of the shape error of M2 incorporatinga significant tilt which results from a lateral displacement of theoptical axis in the order of more a more than 10 �m. The mountingposition of M2 is indicated by Fig. 9(a). Because of the considerableshape error, iterative corrective polishing was not an option due tothe immense processing time and uncertain outcome. Therefore,an alternative process chain including the PJM process for shapecorrection and mechanical polishing for roughness reduction hasbeen followed.

First, two consecutive cycles of high-rate PJM shape correctionand shape maintaining “cleanup-”polishing steps were applied tobring the positions of the optical axes in specification and to reducethe shape errors to a level far below 1 �m, or nearly 1% of theirinitial RMS values, respectively (step 1). After PJM correction andpolishing the surface shape was measurable on an interferome-ter setup built up at TNO. On the basis of these data two PJM finecorrections using a sub-mm tool with lower removal rates havebeen accomplished, each followed by a polishing step (step 2).Although the specified shape accuracy values had been reached,the interferometer measurements of the mirror surfaces indicatedthe appearance of periodic line structures which obviously camefrom the “cleanup”-polishing process, mainly due to an improperdressed polishing cloth and an unfavourable relation between feedand rotary speed of the polishing head (Fig. 10(a)). The Fourier anal-

ysis revealed a wavelength and amplitude of the structures of about0.33 mm and 20 nm, respectively. Since the lowest half-width of thePJM-tool used for the fine correction was about 0.65 mm no deter-ministic removal of the structures could be performed. Hence, to

550 T. Arnold, G. Böhm / Precision Engineering 36 (2012) 546– 553

Fig. 6. (a) Expected material removal for asphere etching, (b) etched aspherical shape in substrate #1.

-10

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0

5

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Subst rate #1

-15

-10

-5

0

5

Substrate #2

-20

-10

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-35

-30

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-15 -10 -5-45

-40

-35

-30

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t [µ

m]

-15 -10 -5

-70

-60

-50

-40

-30

He

igh

t [µ

m]

-15 -1 0 -5 0 5 10 15

R [mm ]

0 5 10 15

R [mm ]

0 5 10 15

R [mm ]

Fig. 7. Horizontal (red line) and vertical (black line) cross sections of etched aspherical shapes. The dotted blue line represents the theoretically prescribed asphere: (a)substrate #1, (b) substrate #2, (c) substrate #3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. (a) Off-axis parabolic mirrors fixed in a 3 in 1 setup, (b) individual mirror (images by courtesy of G. Gubbels, TNO).

Fig. 9. (a) Position of the mirrors in the 3 in 1 holder and (b) surface error of M2 after grinding and pre-polishing (Zernike representation of the tactile measurement resultover a diameter of 18 mm).

T. Arnold, G. Böhm / Precision Engineering 36 (2012) 546– 553 551

Fig. 10. (a) Intermediate states of M2 after PJM fine correction followed by an unfavourable “cleanup”-polishing step leading to significant periodic line structures, and (b)after the necessary high-removal polishing step with improved parameters.

r the fi

eicftpotprd

Ft

Fig. 11. Surface shape error of M2 (a) before and (b) afte

liminate them it was necessary to conduct a high-removal pol-shing run with modified parameters, which unfortunately led to aonsiderable increase of the shape error as illustrated in Fig. 10(b)or the M2 mirror (step 3). Nevertheless, starting from this situa-ion with a very smooth shape deviation the remarkable correctionotential of the PJM process could be demonstrated. Within onlyne PJM step the shape errors could be reduced again by 80–90%o RMS values being well below the specification (step 4). A final

olishing step that worked well as indicated by Fig. 11(a) and (b)educed the roughness below the specified Rq value (step 5). Theiagrams shown in Fig. 12 summarize the development of the shape

10000,0(a) (

100,0

1000,0

M3

M2

M1

1,0

10,0

Pre-polished

(no

Optical axes

corrected

Shape in

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Improved

polishing

Final PJM

(step 4)

Finally

polished

Sh

ap

e e

rro

r R

MS

in

nm

processing) (ste p 1 )

(step 2)

(ste p 3 ) (ste p 5 )

ig. 12. (a) Convergence behaviour of surface shape error and (b) surface roughness over ahe specifications for shape (12.5 nm rms) and roughness (Rq = 6 nm).

nal properly working shape maintaining polishing step.

errors and the surface roughness values for the three mirrors dur-ing the iterations step 1 to 5. In summary, it can be said that PJMand mechanical polishing have successfully combined to a benefi-cial outcome. The fabrication of such strongly curved small sizedsurface shapes solely by (chemical-)mechanical abrasive methods,although feasible, would have exceed the time frame significantly.

The second example is connected to the first one. The SiC mir-rors of the GAIA BAM are mounted on a full SiC optical bench using

shims. A flat mirror and the shim comprise a monolithic construc-tion as shown in Fig. 13(a). During the alignment procedure of theoptical system it became necessary to adjust the three bearing faces

30,0b)

15,0

20,0

25,0 M2

M1

0,0

5,0

10,0

Pre-polished

(no

Optical axes

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Shape in

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Improved

polishing

Final PJM

(step 4)

Finally

polished

Su

rface r

ou

gh

ness R

q in

nm

processing) (ste p 1 )

(step 2)

(ste p 3 ) (ste p 5 )

M3

diameter of 12 mm depending on the manufacturing step. The dotted lines indicate

552 T. Arnold, G. Böhm / Precision Engineering 36 (2012) 546– 553

F V hasp

(tciofiiosn

iFaetmT

Fs

ig. 13. (a) SiC shim with flat mirror, (b) Sketch of the shim. A wedge with 5 �m Patch surfaces.

patches) of the shim in such a manner that the bearing plane andhe mirror surface plane include a defined angle. In this particularase an accurate alignment of the optical path and a vibration-nsensitive mechanical connection was crucial for the performancef the whole optical system. As the mirror itself had already benished and coated by an anti-reflective layer, mechanical pol-

shing of the bearing faces was not an option due to the dangerf contamination of the mirror surface with polishing slurry. Con-equently, a non-contact process like PJM providing a sufficientlyarrow material removal function came into play.

For a test, a wedge with an angle of 90 �rad was required, result-ng in a 5 �m wedge-like material removal. This is illustrated inig. 13(b). The outer diameter of the ring shaped patches was 9 mmnd the inner diameter was 6 mm. During PJM the mirror wasncased in a sealed housing to prevent contamination or etching ofhe anti-reflective coating. The result after one run of PJM (approxi-

ately 1 h processing time) is shown as an interferogram in Fig. 14.he expected wedge of 5 �m PV has been achieved.

ig. 14. (a) Interferogram of flat mirror and tilted patches after etching, (b) crossection as indicated in (a).

to be etched to maintain an angle of 90 �rad between the mirror surface and the

4. Conclusion

Atmospheric plasma jet machining provides in some casesadvantages over conventional abrasive machining of SiC. Thismethod is especially suitable for figuring and error correction ofsmall sized surfaces with strong curvatures. During etching a sur-face roughness increase is observed in most cases. This effect ismainly due to the pure chemical attack of the reactive radicals.The roughness evolution and the resulting morphology dependsstrongly on the type of material, and on the respective pre-machining procedures (and thus sub-surface damage structure). Ithas been shown that PJM can be applied for deterministic figuringof an aspheric shape. Furthermore, a successful error correction onstrongly curved off-axis parabolic SiC mirrors as well as on precisionmechanical surfaces has been accomplished.

Acknowledgements

The authors would like to acknowledge the fruitful collabora-tion with Guido Gubbels and Fred Kamphues from TNO science andindustry.

Financial support by the German Federal Ministry of Educationand Research (BMBF) within the framework of the InnoProfile ini-tiative ‘Ultra-precision manufacturing using atomic particle beams’is gratefully acknowledged.

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[

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