Is it possible to check microcomponent coatings?

Hervé Piombini,1,* Philippe Voarino,2 and Fabien Lemarchand3

1Commissariat à l’Energie Atomique et aux Energies Alternatives, DAM, LE RIPAULT, F-37260 Monts, France2Commissariat à l’Energie Atomique et aux Energies Alternatives, DRT, LITEN, F-73375 Le Bourget du Lac, France

3Institut Fresnel, Unité Mixte de Recherche 6133, Université Paul Cezanne, 13397 Marseille Cedex 20, France

*Corresponding author: herve.piombini@cea.fr

Received 30 July 2010; revised 3 January 2011; accepted 24 January 2011;posted 24 January 2011 (Doc. ID 132577); published 10 March 2011

Optical microcomponents are increasingly used in laser optical systems because of their many and novelindustrial applications. These components are coated in order to enhance their optical performance, butoptical characterizations are very difficult due to the shapes and small size. Thus, to perform this kind ofmeasurement, special devices are needed. It is difficult to check component optical responses aftermanufacturing. Thus a new method, developed by the French Atomic Energy and Alternative EnergiesCommission, is proposed to fill this gap. © 2011 Optical Society of AmericaOCIS codes: 120.1840, 120.3930, 120.3940, 120.5700, 310.1210.

1. Introduction

The controls by optical means of coatings depositedon optical components are generally made with flatwitnesses, thanks to commercial spectrophot-ometers. With flat and thin samples, spectrophot-ometers accurately measure transmittance factors,but reflectance factor measurements exhibit largeruncertainties [1]. Moreover, when the componentsare spherical or aspherical, like lenses or mirrors, thespectral response can vary because of the nonunifor-mity of thickness that is actually linked to the deposi-tion process and the component position in thecoating chamber [2]. For large radius of curvature,control can be achieved even with classical spectro-photometers. However, control becomes increasinglydifficult, and even impossible [3], when the radius ofcurvature decreases or when the optical device has acomplex shape such as slicers [4]. Thus, to performthis kind of measurement, special devices are needed[5–8]. For the optical microcomponents that are in-creasingly used in laser optical systems because oftheir numerous new industrial applications, optical

characterizations are very difficult due to their shapeand small size.

A new device [7,9] to measure reflectance has beenbuilt by the French Atomic Energy and AlternativeEnergies Commission (CEA). It can measure the re-flectance of samples even if their shapes are spheri-cal [10]. This device has a good accuracy on flatsamples [11]. Herein, we investigate samples madeof stainless steel having various curvature radii toprove the results obtained with this device are thesame, whatever the sample shape may be.

We also demonstrate that we can measure opticalmicrocomponents (mirrors and lens) thanks to thetiny size of the area analyzed by our reflectometer.Our first results on small optical components arepresented in this paper.

2. The Reflectometer Used

The reflectometer was designed to improve the accu-racy of the reflectance measurement. This device hasalready been patented [7] and presented in variousconferences and reviews [2,9–12]. This experimentalsetup is schematically drawn in Fig. 1 and summar-ized below.

This device is designed to measure the specularreflectance of mirrors over the 400 to 950nm wave-length range. The light beam is conditioned to enter

0003-6935/11/09C424-09$15.00/0© 2011 Optical Society of America

C424 APPLIED OPTICS / Vol. 50, No. 9 / 20 March 2011

the monochromator that selects the wavelength. Thesignal is spatially filtered and time modulated. Thespatial filter defines the diameter of the spot (about100 μm) on the surface of sample because the twopoints are conjugated. A set of long-pass filters heldin a wheel absorbs the parasite harmonics of themonochromator. Two lock-in amplifiers are tunedto the frequency of the chopper. They allow acquiringmodulated signals but not ambient noises. Then, thebeam is divided into two paths, one for reference andanother for measurement. The sample mounts de-pend on the form and dimension of the sample. Dif-ferent holders are put on a magnetic kinematic baseto obtain good repositioning. A magnetic mounting isfastened onto a manual goniometer, as a manual ro-tation stage is necessary to point correctly to thesample. This assemblage is fastened on a motorizedthree axes translation stage. It enables mappings tobe obtained (y and z stages) and automatically con-jugates (x stage) the photodiode with the surface ofsample using the video path. As soon as the conjuga-tion is achieved, the signals are acquired by the lock-in amplifiers for several seconds in order to make anaverage and to reject values outside the range de-fined by three times the standard deviation. By cal-culating the ratio between the measurement channeland the reference channel, problems due to the fluc-

tuations of the light source power are reduced. Thisprocedure is repeated for each wavelength. The re-flectance factor is given by

RðλÞ ¼ KðλÞVMeasurementðλÞ − VMeasurement backgroundðλÞVReferenceðλÞ − VReference backgroundðλÞ

;

ð1Þ

where KðλÞ is a calibration constant, VMeasurement isthe output voltage of the measurement photodiode,VMeasurement background is the noise voltage of the mea-surement photodiode, VReference is the output voltageof the reference photodiode, VReference background is thenoise voltage of the reference photodiode, and λ is thewavelength. This procedure is repeated for each wa-velength. To calibrate the measuring system in orderto determine KðλÞ, a set of high-reflectivity dielectricmirrors is used.

The software that controls the device enables it tofocus the beam automatically on the surface of thesample at each wavelength, allowing amore accurateresult, thanks to a very good repeatability [2]. Thereproducibility of the focusing process is presentedin Fig. 2. Tomeasure it, the component was randomlypositioned, placed along the optical x axis. An auto-matic focusing procedure was done at 633nm and thelocation was recorded. This process was repeatedseveral times, and each focalization was compared

Fig. 1. (Color online) Experimental setup of CEA device.

Fig. 2. (Color online) Repeatability of self-focusing made on analuminum mirror.

Fig. 3. (Color online) Comparison spectral responses of astandard mirror between NPL and CEA’s reflectometer.

Fig. 4. (Color online) 40mm× 40mm Mapping of standardmirror at 500nm showing the heterogeneities of this one.

20 March 2011 / Vol. 50, No. 9 / APPLIED OPTICS C425

with the average position that was calculated fromall the measurements. The value, which correspondsto twice the standard deviation (σ) of the measure-ment, is 6 μm.

3. Measurement on Standard Mirror Measured byNational Physical Laboratory (NPL)

We have compared measurements made on standardmirror by NPL with ones made with our reflect-ometer onto several sites in order to highlight theresults obtained by our reflectometer. The measure-ments are given in Fig. 3 over the spectral range450 − 950nm.

The spectral curves obtained of this standard mir-ror are similar. The tiny discrepancies between thevarious measurements seem due to mirror heteroge-neities. These heterogeneities and local defects arehighlighted and measured using mappings madeat a wavelength, as in Fig. 4.

These mappings are used to evaluate the repeat-ability our measurement. Onto this mirror, two40mm× 40mm mappings are carried out at600nm (Fig. 5). Their subtraction given inFig. 6 al-lows evaluation of our measurement repeatability.The standard deviation of the difference betweenthe two mappings is 0.1%.

4. Why Can We Measure Shaped Parts WithOur Reflectometer?

The characteristic of our device is to be able to mea-sure shaped parts [10,12] because we use a smallspot (about 100 μm diameter) and a condenser lenswith very large diameter to collect all the light(see Fig. 7). Actually, if the condenser lens had smal-ler diameter, the reflected rays would be lost, for ex-ample, if the component is not normal at incidencelight. This is not the case when lenses are oversized,so the reflectance measurement of the spherical oraspherical sample becomes possible.

According to Fig. 8, we can deduce the Eq. (2) as

ρ ¼ 4hf 0

ϕOutput − ϕInput; ð2Þ

where ρ is the curvature radius sample, h is the ra-dius of the image’s spot onto the sample, f 0 is the focallength: f 0 ¼ 38:5mm, ΦInput is the diameter of en-trance beam ΦInput ¼ 16mm, and ΦOutput is theusable condenser diameter ΦOutput ¼ 46mm. Follow-ing Eq. (1), it would be possible to measure opticalcomponents having a radius as small as 1mm.

We can accept an orientation defect up to about 3°of incidence if the sample is plane. This value isfound experimentally by measuring the reflectancefactor versus the incidence for a dielectric mirrorat 633nm. Figure 9 shows that the reflectance factordecreases less than 0.1% over a range of 6°.

5. Investigation with Curved Parts

A comparison with Zeiss Co. has already been madeof an aspherical lens with antireflection (AR) coatinghaving 38mm focal length [10]. Herein, we presentthe results [13], which were obtained from severalstainless steel ball bearings having a curvature ra-dius from 22 to 7mm and therefore smaller thanthe previous aspherical lens [10].

These ball bearings are manufactured by SKF Co.The stainless steel of these balls is normally thesame, so the reflectance must follow Fresnel laws(except for scattering due to manufacturing and localdefects), whatever the diameter of the ball bearings.

Fig. 5. (Color online) 40mm× 40mm mappings at 600nm.

Fig. 6. (Color online) Difference between mappings (a) and (b).

C426 APPLIED OPTICS / Vol. 50, No. 9 / 20 March 2011

We will check and verify that our reflectometer givesresults that do not depend on the shape of themeasured sample.

A. Effect of the Incidence Angle on Measurement

Before carrying out the various measurements, theeffect of the incidence angle on the measurementis investigated.

In order to measure the ball bearings accurately,the beam must have an incidence of less than 3°.For a ball bearing having a 22mm radius, we calcu-lated, on a 3mm × 3mm square, the various beamincidences in degree onto this ball. The results aregiven in Fig. 10.

To make a correct measurement, the spot locationof the beam must be closer than 0:8mm from the topof this ball.

Before each measurement, we carry out mappingat a wavelength, for example at 633nm, to find theball top experimentally. Figure 11 shows a reflec-tance mapping on a 3mm × 3mm area for the ballhaving a radius of 22mm.

For each ball bearing, we are going to measure thespectral reflectance at a point which is located insidethe area (black square in Fig. 11) where the reflec-tance factor appears to be constant. Of course, thesize of this area depends on the ball bearingdiameter.

B. Experiment

We chose eight ball bearings; they are shown inFig. 12 with a 1€ coin. Their respective diameters

measured with a caliper rule are 44.45, 28.57,23.80, 20.63, 20.61, 19.05, 18.25, and 14:27mm.

These ball bearings have not been optically po-lished, but were machine-finished. We placed eachball bearing on a sample holder. Our software con-trols this sample holder in x, y, and z. For each ballbearing, we locate their top by using small mappingsin order to choose the site, and set it at the condenserfocus by means of our software and the motorizedstages. During the spectral measurement, translat-ing the sample holder along the optical axis for eachwavelength conserves the optical conjugation. Foreach ball bearing, we performed the measurementthree times at the same site over the spectral rangefrom 500 to 950nm. Figure 13 shows the three mea-surements obtained from the 44:45mmdiameter ballbearing.

The tiny difference between these three spectralmeasurements shows a good repeatability by the de-vice. This repeatability is identical to that obtainedwith flat samples [2,9].

The eight measurements, one for each ball bearing,are given in Fig. 14. Table 1 gives the average reflec-tance over spectral range from 500 to 950nm,presented in ascending order of the respective dia-meter of the ball bearings.

We note that the results in reflectance obtained aresimilar (average reflectance over the spectral rangefrom 500 to 950nm is 55:4� 1:4%) for the eight ball

Fig. 7. (Color online) Aim of the oversized condenser lens. If a condenser lens had aΦInput diameter, the reflected ray would be lost. That isnot the case with a condenser lens having a ΦOutput diameter.

Fig. 8. (Color online) Schema for spherical surface.Fig. 9. (Color online) Reflectance factor variation versusincidence angle.

20 March 2011 / Vol. 50, No. 9 / APPLIED OPTICS C427

bearings, even though they do not have the sameradius (from 7.13 to 22:22mm). The curves are notplaced in any particular order; they are mixed at ran-dom. This shows there is no link between the reflec-tance and the diameter of the ball bearings. As anexample, the curve of the ball bearing whose dia-meter is 19:05mm is under the curve of the 18:25mmball bearing but also is under the one whose diameteris 23:80mm. In a second example, two ball bearingsthat are close in diameter (the 20.61 and 20:63mmdiameter ball bearings) have reflection coefficientsthat are comparatively remote (56.12% and 54.38%,respectively). They all fall within an interval of 3.7%.For the shorter wavelengths, the difference is 3.7%,and for larger wavelengths, it is 2.1%.

To explain the discrepancies observed, we in-spected the ball bearings using Normaski interfer-ence optical microscopy (Leica/DMRME microscope,Germany), and found that they have a few local de-fects and scratches (Fig. 15).

As SKF Co. specifies on their web site [14] that ballroughness is about 10nm, we calculated the total in-tegrated scattering (TIS) to estimate the level of thescattered light by the ball bearings due to theirvarious roughnesses. The TIS is defined accordingto [15]

TIS ¼ diffuse reflectancespecularþ diffuse reflectance

; ð3Þ

where the diffuse reflectance is the fraction of the in-cident beam that is reflected off-specular direction,and the specular reflectance is the fraction of theincident beam that is reflected into the specular di-rection. The relation between TIS [15] and rmsroughness for a reflecting surface is given by

TIS ¼�4πδλ

�2; ð4Þ

where δ is the rms roughness of the surface and λ, theilluminating wavelength. Equation (4) is for normalincidence illumination.

We calculate the fraction of scattered light varia-tion versus wavelength over the spectral range(500–950nm) by our ball bearings (average value)for four roughness values (5, 7, 10, and 12nm). Theresults are given in Fig. 16.

The tiny differences can be explained by the localdefects, the various scratches, the various rough-nesses, and a local variation of composition, whichhave been observed by the Normaski optical micro-scope. If the ball bearings were optically polished,our results would be closer.

So we can conclude the reflectance measured withour device does not depend on the curvature radius ofthe sample. In fact, the size of the beam that is re-flected by the sample is so small (about 100 μm) thatthe surface lit by the spot can be considered as flat.Therefore, we can say our reflectometer is able to

Fig. 11. (Color online) Reflectance factor mapping at 633nm forthe ball bearing having a radius of 22mm.

Fig. 12. (Color online) Photograph of our eight ball bearings.

Fig. 10. (Color online) Incidence mapping versus a ðx; yÞ spotlocation. The incidence is less than 3° inside the black square.

Fig. 13. (Color online) Three measurements made on the44:45mm diameter ball bearing.

C428 APPLIED OPTICS / Vol. 50, No. 9 / 20 March 2011

determine the reflectance of pieces in form havingcurvature radii greater than to 7mm.

6. First Measurement of Micro-Optical Components

Before this paper, our reflectometer has been used tomeasure many components (substrates, mirrors, ARcoatings), but these components had an area of a fewcm2. Now, we present the first measurements carriedout on small optical components.

Fig. 14. (Color online) Measurement of the eight ball bearingswith our reflectometer.

Table 1. Average Reflectance Versus Ball Bearing Diameter

Sorting Average Reflectance (%) Ball Bearing Diameter (mm)

1 54.00 44.452 54.38 20.633 54.97 19.054 55.16 14.275 55.75 23.806 56.01 28.577 56.12 20.618 56.68 18.25

Fig. 15. (Color online) Photograph of a ball bearing by aNormaski microscope.

Fig. 16. (Color online) Scattered light versus wavelength for fourroughness values (5, 7, 10, and 12nm).

Fig. 17. (Color online) Photograph of micromirror on its holder.

Fig. 18. (Color online) Three spectral responses and theassociated fit of the measured micromirror.

Fig. 19. (Color online) Photograph of the measured microlens.

20 March 2011 / Vol. 50, No. 9 / APPLIED OPTICS C429

A. Plane Component, Like a Micromirror

The small size of the spot on the tested component,about 100 μm diameter, enables us to easily measurecomponent heterogeneity [2], local defects [2,9], andsmall mirrors with our measuring system. This po-tential use is highlighted by the measurements onthree various sites of a protected metallic mirror.The measured micromirror, which is 2mm diameter,has been bonded on a metallic rod (shown in Fig. 17)and based on our adjustable holder. The mirror sur-face has been put at the collecting lens focus of ourreflectometer by using motorized stages and our im-age processing.

The curves obtained, in Fig. 18 ,are similar forthese three measurements. These curves have beenfitted with a model compound by a metallic layer anda dielectric layer. The best fit corresponds to an alu-minum layer coated by a silica film having a thick-ness of 146nm. So, we can characterize coatings onsmall optical components.

B. Curved Component, Like a Lens

This measured microlens is supplied by Thorlabs Co.under the item name C440TME-B [16] and is shownin Fig. 19. This mounted lens is made from ECO-500,a glass with similar optical properties to C-0550, butnot containing hazardous materials. Its focal lengthis 2:95mm, thickness 4:06mm, and its diameter is4:70mm. Both faces are aspherical. It is broad-

band-AR coated from 600nm to 1050nm accordingto the supplier (see green curve in Fig. 20).

Its housing is mounted onto an adaptor plate,which is based on our adjustable holder. The frontface is put at the condenser lens focus of our reflect-ometer by using motorized stages and our imageprocessing. We measure. three times, the coating re-sponse over the spectral range (400–950nm) onto asame site. These results are presented in Fig. 21.

Our spectral responses are slightly different fromthe curve promised by the supplier (Fig. 20), but theyseem similar to another AR coating of this supplier(Fig. 22).

In order to translate our spectral measurements totheoretical values, we consider the twomost probablespectral responses (the green spectrum in Fig. 20,here called spectrum 1 and Fig. 22, here called spec-trum 2) provided by the supplier. Clearly, as the ARband and the number ofminima are different, the twospectra are derived from different designs. We thenuse a reverse engineering program to determinethe number of layers, the index of materials, andthe thicknesses for both configurations. This home-made thin-film software uses a global optimizationprocedurederived fromT.Csendes [17].nþ 2variableparameters are required, where the number “n”

Fig. 21. (Color online) Spectral response of C440TME-B lensmeasured by our reflectometer.

Fig. 22. (Color online) 600–1050nm AR-coated calcite accordingto Thorlabs Co. [16].

Fig. 23. (Color online) Spectrum 1 (gray triangle, supplier data)and theoretical response from reverse engineering (solid curve).Insertion: design 1a corresponding to theoretical curve.

Fig. 20. (Color online) Molded aspherical broadband AR coating,according to Thorlabs Co. [16]. (A) 350–700nm, (B) 650–1050nm,(C) 1050–1620nm.

C430 APPLIED OPTICS / Vol. 50, No. 9 / 20 March 2011

corresponds to the layers thicknesses and “2” corre-sponds to two different refractive indexes that aresupposed to be nondispersive.We also try tominimizethe number of layers since the number of solutions in-crease if one considers a large number of layers. A rea-listic solution corresponding to spectrum 1 is plottedon Fig. 23, with a four-layer design (design 1a) with1:45=2:25 as refractive index values. Using the sameprocedure, design 2a—corresponding to spectrum2—is determined (Fig. 24) with a five-layer design alsohaving 1:45=2:25 as index values.

We then propose to make a refinement procedurefrom experimental data, taking into account possiblerefractive index dependence on wavelength. It is wellknown that high-index materials present a largerdispersion; we use a high index material dispersionlaw nh ¼ a0 þ a1=λ2, whereas nl ¼ b0 is considered tobe constant over the spectral range ½400; 950nm�.Using design 1a and design 2a as initial solutions,we then refine the two designs with spectral mea-

surements as target. Results (called design 1b anddesign 2b) are plotted on Figs. 25 and 26.

Clearly, the spectral fit is better for design 2 thanfor design 1. We can also observe that thicknesses ofdesign 2b are very similar to those of design 2a. Clas-sically, we can expect a 3% error thickness toleranceand a 0.02 index variation from nominal values, com-patible with our analysis. Thus agreement betweenour experimental results and the supplier data(spectrum 2) is ensured.

7. Conclusions

After having validated our reflectometer onto the flatsample and compared our measurements with theNPL, we have carried out measurements on severalcurved parts and microcomponents.

The results obtained for the balls show that themeasured reflectance does not depend on the radiuscurvature of the sample when the curvature radius isgreater than 7mm. Our device provides access to anew metrology over a spectral range from 400nmto 950nm on complex components, which was notavailable a few years ago.

The small size of the spot’s reflectometer enablesmeasurement of small optical components.

We highlight the fact that we can also measure theAR coating on certain microlenses. Nevertheless, wemust assess the limits of our device for this kind ofcomponent with help from a manufacturer. In addi-tion to the curvature radius, we investigated the in-fluence of component thickness. In the future, wecould reduce the focal length of our collection lensin order to decrease the spot diameter and the depthof focus, so as to measure smaller and thinner com-ponents.

We would like to acknowledge the SKF Companyfor supplying the ball bearings used in these experi-ments, Xavier Le Borgne for photographs, and AlanGates and Annette Stansfeld for their help.

Fig. 25. (Color online) Spectral response of C440TME-B lensmeasured by our reflectometer (gray triangle) and theoreticalone with a refinement procedure starting with design 1a (solidcurve). Insertion: design 1b corresponding to refined structure.

Fig. 26. (Color online) Spectral response of C440TME-B lensmeasured by our reflectometer (gray triangle) and theoreticalone with a refinement procedure starting with design 2a (solidcurve). Insertion: design 2b corresponding to refined structure.

Fig. 24. (Color online) Spectrum 2 (gray triangle, supplier data)and theoretical response from reverse engineering (solid curve).Insertion: design 2a corresponding to theoretical curve.

20 March 2011 / Vol. 50, No. 9 / APPLIED OPTICS C431

References1. Facilities http://www.nist.gov/pml/div685/grp03/spectrophoto

metry_transfer.cfm.2. Ph. Voarino, H. Piombini, F. Sabary, D. Marteau, J. Dubard, J.

Hameury, and J. R. Filtz, “High-accuracy measurements of thenormalspecular reflectance,”Appl.Opt.47,C303–C309 (2008).

3. G. J. Kopec, “Colorimetry as diagnostic tool in manufacture ofantireflection coatings,” Proc. SPIE 4517, 236–241 (2001).

4. J. Schmoll, D. J. Robertson, C. M. Dubbeldam, F. Bortoletto, L.Pina, R. Hudec, E. Prieto, C. Norrie, and S. Ramsay-Howat,“Optical replication techniques for image slicers,”NewAstron.Rev. 50, 263–266 (2006).

5. R.Grunwald,S.Nerreter,J.W.Tomm,S.Schwirzke-Schaaf,andF. Dörfel, “Automated high-accuracy measuring system forspecular micro-reflectivity,” Proc. SPIE 4449, 111–118 (2001).

6. J. Sancho-Parramon, A. Abdolvand, A. Podlipensky, G. Seifert,H. Graener, and F. Syrowatka, "Modeling of optical propertiesof silver-doped nanocomposite glasses modified by electric-field-assisted dissolution of nanoparticles," Appl. Opt. 45,8874–8881 (2006).

7. H. Piombini and Ph. Voarino, “Device and process for measur-ing the characterisation by reflectometry,” U.S. patent7,773,208 (6 December 2007).

8. X. Zheng, Z. Wang, and Y. Zhao, “An apparatus for the mea-surement of spectral specular reflectance of spot area incurved surfaces,” Proc. SPIE 7156, 71560B (2008).

9. H. Piombini and Ph. Voarino, “Apparatus designed for veryaccurate measurement of the optical reflection,” Appl. Opt.46, 8609–8618 (2007).

10. H. Piombini, S. Bruynooghe, and Ph. Voarino, “Spectralmeasurement in reflection on steeply aspheric surfaces,” Proc.SPIE 7102, 71021C (2008).

11. J. Dubard, J. Hameury, J.-R. Filtz, D. Soler, P. Voarino, and H.Piombini, “Normal reflectancemeasurement based on high re-flectivity dielectric mirrors reference standard,” presented atNewrad, Daejeon, South Korea, 13–15 Oct., 2008.

12. H. Piombini, D. Soler, and Ph. Voarino, “New device tomeasure the reflectivity on steeply curved surface,” Proc.SPIE 7018, 70181B (2008).

13. H. Piombini and L. Caillon, “Reflectance measurement ofspherical samples,” Opt. Rev. 16, 571–574 (2009).

14. http://www.skf.com/skf/support/html/dictionary/dictionary.jsp?lang=en&site=CH.

15. J. M. Elson, J. P. Rahn, and J. M. Bennett, “Relationship of thetotal integrated scattering from multilayer-coated optics toangle of incidence, polarization, correlation length, and rough-ness cross-correlation properties,” Appl. Opt. 22, 3207–3219(1983).

16. Thorlabs catalog, Vol. 20, pp. 626, 630, 764 (2009).17. T. Csendes, “Nonlinear parameter estimation by global

optimization—Efficiency and reliability,” Acta Cybernetica8, 361–370 (1988).

C432 APPLIED OPTICS / Vol. 50, No. 9 / 20 March 2011