STR/03/046/PM

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Evaluation of a Microlens Array using Optical Interferometry

S. H. Wang and I. Reading

Abstract ― In this paper, a technique based on the use of optical interferometry is employed to evaluate the surface geometry and refractive index profile of a graded-index planar microlens array. The experimental setup consists of so-dium light and He-Ne laser sources which are incorporated into a microscopy system. The two light sources can be utilized alternately for sur-face geometry and refractive index measure-ment. The Newton’s rings resulting from the so-dium and laser illumination sources are ana-lyzed by proposed algorithms combined with fringe tracking techniques. Experimental results demonstrate that the surface profile and graded-index properties of the micro-lenses can be readily obtained. Keywords: Optical interferometry, Microlens ar-ray, Surface geometry, Refractive index 1 INTRODUCTION In recent years micro-lens arrays have been widely used in applications ranging from optical computing to flat panel displays, TV projection systems, photocopiers, and micro-lithography. In particular, planar graded-index (GRIN) micro-lenses offer an alternative to the often-painstaking craft of forming/polishing a normal glass lens to the required curvature. There are a variety of means to manufacture microlens ar-rays. For example lithography can be used to create an array of resined cylinders on a sub-strate which, after the application of heat, melt to form a curved lensing surface due to the ac-tion of surface tension [1]. Graded-index mi-crolens manufacturing methods include a mo-lecular stuffing process and also ion exchange [2-3]. The ion-exchange methods have been used successfully for the fabrication of planar microlenses. In addition, optical wave-guides incorporating GRIN planar microlenses, made by ion exchange in a glass substrate, have at-tracted considerable interest recently as passive components in integrated optical circuits and telecommunications. When compared to conventional curved glass lenses, which alter the direction of light only ac-cording to the shape and smoothness of their surfaces, graded-index (GRIN) microlenses of-fer distinct advantages. By gradually varying the

index of refraction within the lens material, light rays can be smoothly and continually redirected towards an image point [4]. The internal struc-ture of this graded-index can remove the need for tightly controlled surface curvatures and re-sults in a simple, compact lens geometry, which has a flat surface to accommodate anti-reflection coatings and is easy to couple to other flat surfaces such as optical fibers. GRIN de-vices can therefore be used to reduce the spherical aberration of an optical system in comparison to a conventional homogeneous lens and thus improve the focusing power. 2 OBJECTIVE To ensure the very high quality required of a manufactured microlens array, precise knowl-edge of its focusing properties, which are indi-cated by parameters including its surface ge-ometry and refractive index, is of fundamental importance. However, because of the small di-mensions and precise alignment tolerances, measurement of these parameters is a much more complicated process than that of a normal lens. A number of different methods have been proposed to characterize microlenses [5-8]. Among these methods, interferometric testing shows most promise for this application. For example, interferometers including the Twyman-Green, Michelson and Mach-Zehnder types have been employed to inspect microlens ar-rays. However, these methods are somewhat complicated and the experimental arrangements require high quality isolation to prevent vibration. In addition, existing inspections of surface ge-ometry and internal refractive index of a mi-crolens array are separately implemented. To improve yield efficiency, an integrated method to measure the two parameters would be helpful. In this paper a direct method for measuring the surface geometry and GRIN refractive index of a microlens array using a single setup is pro-posed. 3 METHODLOGY A planar graded-index lens has an imaging area whose refractive index varies with the radial dis-tance (r) from the optical axis. The refractive-index distribution is parabolic and given by [9]:

Evaluation of a Microlens Array using Optical Interferometry

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Beam splitter

z

y θ Sample

Optical plate

B

S

Lens A

h

Lens B A

x

( )

−= 2

0 211 Arnrn (1)

where n0 is the refractive index at the optical axis and A is a constant [10-11]. Due to the lens’ parabolic refractive index profile, an incident ray which passes through the lens propagates in the form of a sine wave. The imaging and focusing properties of the GRIN lenses are determined by selecting the length/thickness of the planar microlens. An anti-reflection coating on the mi-crolens may then be applied to improve the effi-ciency of light transmission. The inspection method presented in this paper is based on the interference of light beams of equal path difference, which results in equally spaced fringes [12]. The essential idea is to form a wedge, which consists of an optical ref-erence plate and the surface of interest on the object. The basic optical setup is illustrated in Fig. 1. A light beam with wavelength λ, colli-mated by a lens A is directed at the optical (ref-erence) plate and test specimen through a beam splitter. The reflected beams from the bot-tom surface of the optical plate and surface of the test surface are captured at an image plane AB through Lens B. Due to variation in the dis-tance h within the wedge, an interference fringe pattern will be observed on the image plane. The observed intensity distribution corresponds to the interference between the two light intensi-ties I1(x,y) and I2(x,y) from the two surfaces mentioned above. These two intensities inter-fere at the image plane. The superimposed in-tensity I(x,y) at AB can be described as follows:

[ ] ),,(cos),(),(2),(),(),( 2/1

2121 yxφyxIyxIyxIyxIyxI ++= (2)

Fig. 1. Basic optical setup.

Assuming I1(x,y)=I2(x,y), we obtain:

=

2),(cos),(4),( 2

0yxφyxIyxI , (3)

where I(x,y) is the resultant light intensity at the image sensor, I0 is the average of I1 and I2 and

),( yxφ is the local optical phase difference be-tween I1(x,y) and I2(x,y). Since the wedge con-sists of the optically flat plate and the test sur-face, each fringe indicates the locus of constant displacement on the test surface. For a small wedge angle θ with near-normal illumination, the optical phase difference φd is given by:

kππhλπnφ kd ⋅=+= 24 (4)

where k is the fringe order number (k=1,2,3,…), n is the refractive index of the wedge, λ is the light wavelength and hk is the distance between the test surface and the optical plate. Equation (4) implies that when h takes on a value that makes φd equal to an integer multiple of 2π, then the resulting intensity based on Eq. (3) is a maximum. Applying Eq. (4) to two adjacent fringe orders, k and k+1, and subtracting them, the relative height difference ∆h between two adjacent fringes can be determined by:

nλhhh kk 2/1 =−=∆ + (5) For an air medium ( 1≈n ) and a wavelength of 589.6 nm (Sodium light) or 632.8 nm (He-Ne laser), the height difference between two adja-cent fringes, which corresponds to an optical phase difference of 2π, is 294.8 nm and 316.8 nm respectively. Based on Eqs. (4) and (5), the surface geometry of the test surface can be readily obtained. For inspection of the refractive index on a planar microlens array, the wedge consists of the front and back surfaces of the microlens array. Light beams reflected from the front and back sur-faces interfere in the image plane (AB) to form a fringe pattern as indicated by Eq. (3). In this case, the thickness (t) of the microlens array which is equivalent to the hk of the wedge is constant and Eq. (4) is expressed as follows:

kππnλ

tπφ kd ⋅=+= 24 (6)

In a similar way to recalculation of the height difference ∆h between two adjacent fringes in

Evaluation of a Microlens Array using Optical Interferometry

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250 µµµµm

Eq. (5), the difference in the refractive indices ∆n is given by:

tλn 2=∆ (7) Assuming the refractive index (n0) of the mi-crolens substrate is constant and can be prede-termined, the refractive index distribution of the microlens along an inverse radial direction may be written as:

tλknkn 2)( ⋅+= (8)

The experimental arrangement is shown in Fig. 2. Light from a monochromatic sodium light source (wavelength λ=0.5896 µm) passes through a collimating lens 1 and beam splitter 1 and is directed to lens 2 on which an adjustable aperture is mounted. The light beam emerging from lens 2 is reflected off beam splitter 3 and directed at the focal point of lens 5 mounted on a vertical axis. As lens 2 and lens 5 both have the same focal point T, light beams emerging from lens 5 are collimated. The collimated beam from lens 5 is directed at the optical plate and the specimen. To position the specimen accu-rately, the optical plate, specimen and the load cell are mounted on a 3-axis translation stage, which has a resolution of 0.01 mm. The result-ing fringe pattern is observed on the optical plate through an eyepiece and recorded by a CCD camera mounted along the vertical axis. The fringe pattern can be observed on a TV monitor and hard copies of the fringe pattern

can be obtained through a printer. Further proc-essing of the fringe pattern is carried out using a PC. It is noted that there is a very small air gap which is less than the coherence length (typical value is of the order of 10 µm for the sodium light) between the optical plate and specimen. Hence variation in profile on the test surface within a working range of 1 µm is detectable. For the refractive index inspection of the planar microlens array with a thickness of 530 µm, which is beyond the working measurement range of the sodium light, a He-Ne laser with a long coherence length is used. As shown in Fig. 2, a collimated laser through an expander (lens 3, spatial filter and lens 4) is directed onto beam splitter 1 by a mirror M1. The laser reflected off beam splitter 1 is directed onto the test speci-men along a similar optical path to that of the sodium light illumination. By alternating between the two light sources, the surface geometry and the refractive index of the test specimen may be determined. 4 RESULTS & DISCUSSION Fig. 3 shows an image of a section of a mi-crolens array obtained using a sodium light source. Figs. 4(a) and 4(b) show respectively the fringe patterns obtained from a flat surface and a microlens array using the proposed ex-perimental set-up. As can be seen, the fringes are modulated indicating an uneven surface over the array. The uneven flatness is possibly due to the ion-exchange process which is used to produce the GRIN distribution on each mi-crolens. The distortion of each fringe Fig. 4(b) is close to a quarter of a fringe pitch hence surface flatness of up to λ/8 (74 nm) can be estimated. Fig. 4(c) shows the fringe pattern on an inverted microlens array. The relatively linear fringe pat-tern indicates that the back surface is much flat-ter. It is to be noted that the bright circular areas in Figs. 4(b) and (c) are images of the aperture formed by the microlens themselves.

Fig. 3. Image of a region of the microlens array.

Lens 5

Lens 2

3-axis translation-stage

Optical-plate

Specimen

T

Beam splitter 3

Aperture

Lens 1 Eyepiece

Beam Splitter 2

Sodiumlight

Monitor

CCD

Printer

Computer

Lens 3

Lens 4 Spatial filter M1

Beam splitter 1

Fig. 2. Experimental set-up.

Evaluation of a Microlens Array using Optical Interferometry

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nm

X in pixel Y in pixel

Radial distance across the microlens r (µµµµm)

1.53

1.535

1.54

1.545

1.55

1.555

1.56

-150 -100 -50 0 50 100 150

Refractive index n

(a)

(b)

(c)

250 µµµµm

Fig. 4. (a) A fringe pattern obtained on a flat sub-strate. (b) Fringe pattern on the front surface of a microlens array. (c) Fringe pattern on the back sur-face of a microlens array. Fig. 5 shows plots of the microlens array profile. As can be seen in Fig. 5 the front surface of the microlens array is concave. Hence the surface curvature could affect the focusing and imaging properties. However, the curvature is relatively small (less than 100 nm) compared with the di-ameter (250 µm) and thickness (0.53 mm) of the microlens, it would therefore not have significant influence on the focusing and imaging proper-ties. Fig. 5. 3D plot on the front surface of a microlens ar-ray. Fig. 6 shows the fringe patterns on the mi-crolens illuminated by a He-Ne laser. As can be seen, the fringe density increases radially from

the center of the microlens. It indicates that the refractive index is decreasing along the radial direction of the microlens. By fringe tracking, in terms of Eq. (7), and knowing the substrate re-fractive index of 1.5356, a cross-sectional index distribution can be plotted, see Fig. 7. The rela-tionship between the index (n) and the radius (r) of the microlens may be curve fitted using the following empirical equation:

5571.1102102 526 +×−×−= −− DDn (9) with a correlation coefficient of 99.8%.

Fig. 6. Fringe pattern on the front surface of the mi-crolens array using a He-Ne laser at 20× magnifica-tion. As can be seen in Fig. 7, the maximum GRIN difference (∆n) is about 2.15% to make the pla-nar GRIN microlenses have the required light focusing function. This typical cross-sectional distribution is close to parabolic as a function of distance from the apex of the convex distribu-tion, which corresponds to the optical axis, as expected from Eq. (1). Fig. 7. Refractive index distribution across a mi-crolens.

Evaluation of a Microlens Array using Optical Interferometry

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5 CONCLUSION In this work, an effective and simple method for measuring the surface geometry and the refrac-tive index profile of a microlens array has been studied. In this method two light sources (so-dium light and a He-Ne laser) have been inte-grated to meet the requirement for different co-herence lengths for the measurement of the pro-file and refractive index properties of a mi-crolens array. The proposed method is capable of providing accuracy in the nanometer range and is based on a relatively simple optical set-up. The refractive index profile obtained for the microlens shows the expected near-parabolic distribution. The application of this method for microlens array measurement thus appears fea-sible. 6 INDUSTRIAL SIGNIFICANCE The work presented in this report has demon-strated a possible technique for the high-speed automation of the inspection of graded-index microlens surface and refractive index structure. With further verification it could form the basis for a manufacturing inspection technique. REFERENCES [1] P.H. Nussbaum, R. Volke, H.P. Herzig, M.

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[5] S. Horst, Falkenstorfer, Lindlein and J. Schwider, “Characterization of microlenses using a phase shifting shearing interferome-ter”, Opt. Eng., Vol. 33, pp. 2680-2686, (1994).

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[7] F.M.E. Sladen, D.N. Payne and M.J. Ad-ams, “Determination of optical fiber refrac-tive index profiles by a near-field scanning technique”, Appl. Phys. Lett., Vol. 28, pp. 255-258, (1976).

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[9] F.C. Allard, Fiber optics handbook for Engi-neers and scientists, McGraw-Hill, New York, (1989).

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