Determination of Optical Field Generated by a Microlens Using Digital Holographic Method

OPTO−ELECTRONICS REVIEW 17(3), 211–216

DOI: 10.2478/s11772−009−0005−z

Determination of optical field generated by a microlens using digital holographic method

T. KOZACKI*, M. JÓZWIK, and R. JÓŹWICKI

Warsaw University of Technology, Institute of Micromechanics and Photonics, 8 Św. A. Boboli Str., 02−525 Warsaw, Poland

In the paper, application of the digital holographic method for full field characterization of the beam generated by microlenses is considered. For this goal, the laboratory setup was designed based on Mach−Zehnder interferometry with the additional reference channel. The beam generated by a microlens was imaged by an afocal system and intensity distributions or interferograms (holograms) were registered by CCD camera. The digital holography using one image allows us to deter− mine microlens parameters, i.e., focal length, aberrations, and shape. The optimum conditions to determine the surface shape of a microlens using holographic method have been found. We compare obtained results with geometrical and interferometric measurements. We show the advantage of digital holography for a shape microlens determination (improved accuracy), aberrations, and focal length (characterization facility). Through optimum refocusing, the digital holography gives more precise shape. The paper is accompanied with computer simulations and the experimental measurement data for geometrical, interferometric, and holographic methods.

Keywords: holography, interferometry, microlenses.

1. Introduction been achieved determining the field distributions of the beam generated by a microlens. It can be done by the registration of Microlenses have become important elements and are com− field distributions at various planes using the interferometric monly used in optical systems, e.g. for optical fibre coupling method or the calculation of field distributions at the same [1], measurement systems like confocal microscope [2], and planes starting from one registered field distribution with a various MEMS based devices [3]. Their small dimensions, proper diffraction formula. The software determination of wide range of focal distances, possibility of matrix arrange− field distributions belongs to the holographic method. ment opened new applications in telecommunication, optical In the paper, we first present results of microlens charac− interconnection, illumination, imaging, detection and process− terization with standard field optical methods, geometrical ing systems. These applications require high quality elements. and interferometric measurements. With these methods we To meet this demand, the surface profile and optical properties characterize microlens geometry and focal length. Such of fabricated microlenses are extensively investigated [4]. The a characterization is also performed with digital holography. standard stylus profilometer or AFM [5] can be used for the Obtained meaningful differences with both techniques are measurement of the shape and surface roughness, while the discussed with the help of extensive numerical simulation. optical interferometric methods using Twyman−Green, Mach− We show that additional numerical application of the knowl− −Zehnder or white light interferometers [6] allow determina− edge about the measured microlens into holographic process tion of the microlens surface shape or wave aberrations gener− ated by the microlens under the consideration. The same role significantly improves precision of element characterization. fulfils the digital holographic microscopy [7]. By pacing mi− crolens within immersion liquid with rotation stage and apply− 2. Experimental setup ing Optical Diffraction Tomography [8] mentioned configura− tion can be used to analyze element fabrication stresses.The all To determine microlens parameters, the Mach−Zehnder in− above mentioned methods concentrate on the microlens terferometer shown in Fig. 1 was used. All system compo− parameters. nents, including the He−Ne laser (l = 632.8 nm), were The paper subject is elaboration of the method allowing placed on the optical table isolated against external vibra− determination of all microlens parameters demanded by both tions. The linearly polarized laser beam is expanded and the producers and the users of microlenses. Such a goal has collimated by the set of the spatial filter SF and the colli− mator lens C. The beam with the highly planar wavefront is, in succession, transmitted through half−wave plate HW, re− *e−mail: [email protected] flected by mirror M1 and divided by the beam splitter BS1

Opto−Electron. Rev., 17, no. 3, 2009 T. Kozacki Determination of optical field generated by a microlens using digital holographic method

Fig. 1. Scheme of a measurement system. on the object and reference channels. The reference channel optical field generated by a microlens. The optical imaging is composed of linear polarizer POL, half−wave plate HW, system (MO + IL) is designed in such a manner, that the CCD mirror M2 and plane−parallel plate PP, while within the ob− detector plane coincides with the image focal plane of the im− ject one we have mirror M3, diaphragm D, the microlens aging lens IL. It means that the object plane of the micro− O under the test, high quality microscope objective MO, and scope objective MO, coinciding simultaneously with its ob− imaging lens IL. The microscope objective with the infinity ject focal plane, is imaged on the detector plane. Therefore tube length is a Nikon Plan having flat field optical correc− displacing the microlens along the optical axis, various opti− tion (10x, NA = 0.25, WD = 10.5 mm). The rotating polar− cal field cross sections can be registered by CCD camera. ization elements (HW, POL) serve to get maximal inter− ferometric fringe contrast adjusting both the polarization 3. Geometrical measurements states and the intensity values of the interfering beams. Both waves propagating in both channels are joined by the beam The problem concerns the determination of the plane posi− splitter BS2. The result of the superposition (interference) is tion with the maximal intensity concentration of the beam registered by CCD camera. The CCD camera was CV−A1 (physical focus) generated by the microlens. p JAI Corp (1/2”, CCD sensor with a pixel size of 4.65 × Let MO and FMO denote the object plane and the object 4.65 μm). The object field of a view is 640 × 480 μm and the focus of the microscope objective MO (Fig. 2), respectively. p transverse resolution of the applied system 0.47 μm. If by O the plane with the maximum intensity concentra− The optical field generated by the microlens is imaged tion is denoted, then displacing the microlens O along the D p p on the CCD detector by the afocal system consisting of the distance z between the planes MO and O is changing. In microscope objective MO and the imaging lens IL. The use this manner, different intensity distributions at the object p of the afocal system introduces the essential advantages fa− plane MO can be registered for various positions of the cilitating our analyses. First, the lateral magnification of this microlens O. Displacing the microlens to a plane where the b =- ¢¢=- x ¢ ¢ system afff IL MO 10. 2 , where f IL and f MO are image of its surface m on the PC monitor is observed, the the focal lengths of the imaging lens and the microscope ob− physical focal front distance sFO for the aperture angle uMO jective, respectively, is constant and independent of the ob− can be determined. Inverting the microlens O, the focal dis− ject plane position. Next, field distributions defined on tance s’FO is found, which for the paraxial relations equals a plane perpendicular to the optical axis in the object space the focal length f’ of the microlens. Additionally, assuming are imaged on a suitable plane perpendicular to the optical the homogenous medium of the microlens and the planar axis too without any phase corrections. surface m, the radius of the microlens can be found. As the measured object O, one microlens was applied Decreasing the numerical aperture of the objective MO chosen among the microlens array (5×5 microlenses). The by the truncation of its exit pupil, the positions of physical mentioned array was fabricated in FEMTO−ST (Université foci will be determined for various aperture zones. The no− de Franche−Comté, Besançon, France) using replication in tion of the physical focus takes into consideration the micro− PMMA by hot embossing technology. The sample con− lens aberrations and the diffraction phenomena. sisted of 25 technically identical microlenses. Their diame− It is worth emphasizing that the thickness ds of the ter equals 190 μm and the measured back focal length f ¢ = microlens substrate is much larger than the thickness d of 280+/–10 mm. The lens was designed as spherical with a the sole microlens and actually the focus F is virtual. In fact, radius of curvature 132 μm. the beam focusing into fibers, e.g., is realized for the invert As it was mentioned, the proposed interferometric and microlens position with regard to the position shown in holographic methods allow the registration of the complex Fig. 2. Because one of the paper goal is the measurement of

212 Opto−Electron. Rev., 17, no. 3, 2009 © 2009 SEP, Warsaw Fig. 2. Mutual position of the microlens O and the microscope objective MO. the microlens surface shape, the choice of the microlens po− sition in the paper was the result of smaller spherical aberra− tion, what decreases measurement errors.

4. Interferometric measurements The proposed optical system (Fig. 1) is applied to recon− struct optical field distribution at a chosen plane in a vicinity of the microlens. The first interferometric measurement was p accomplished focusing the imaging system on the plane i coincided with the microlens edge (Fig. 2), what facilitates p p the focusing procedure. In this case, the planes MO and i are coincident. Interferometric fringe pattern received for this microlens position is shown in Fig. 3. The region with− p out fringes seen in the figure is the result of the smaller nu− Fig. 3. Fringe pattern registered for the microlens plane i. merical aperture of the microscope objective (NA = sin uMO = 0.25) with comparison to NA = sin uO = 0.32 of the microlens (see Fig. 2). The registration of the fringe pattern 5. Holographic measurements is accomplished using the temporal phase shift method with five−frames algorithm. The phase shifting control is realized The digital holography allows determination of optical inclining precisely the plane−parallel plane PP in relation to fields at any arbitrary localized plane using known diffrac− the optical axis (Fig. 1). The calculated phase distribution tion formulae. The knowledge of these fields can be a base gives a shape function of the lens presented as a grey−level to determine demanded features of an optical system gener− map and its cross section A−A in Fig. 4. ating the mentioned fields, focal length or microlens surface

Fig. 4. Obtained shape function of a lens microlens area (a) and in its cross section A−A (b).

Opto−Electron. Rev., 17, no. 3, 2009 T. Kozacki 213 Determination of optical field generated by a microlens using digital holographic method shape. However, for a given optical system configuration, shown in Fig. 5(b). In the reconstruction process, the limi− the choice of the plane conjugated with the hologram plane tation of the spatial harmonics introduced by the micro− p scope objective MO (see Fig. 2) and the CCD detector fea− (plane MO conjugated with CCD detectors, see Fig. 2) al− lowing the determination of mentioned features influences tures were taken into account. The dimensions of Fig. 5(b) the measurement precision. In order to optimize experimen− correspond adequately to the CCD detector dimensions. tal holographic setup, the simulation of the holographic It is worth emphasizing that the whole area of Fig. 5(b) measurement process is accomplished. Namely, first the op− participates in the registration and reconstruction timization of the holographic steps (registration and recon− processes. struction) is achieved, next the optimal plane to measure the One of the paper goals is the measurement of the shape microlens surface shape is found. of the microlens surface. This is usually performed apply− The simulation of the holographic registration process ing linear dependence between a phase of an optical field p consists in the interference of two waves, the reference at the measurement plane i (Fig. 5) and an element shape. wave and the object one received by the propagation of the As it was mentioned, the choice of measurement plane is a plane wave through microlens (see Fig. 1). The object wave major source of error. Such an error is presented in Fig. 6. scattering by the microlens is a demanding task for a com− The graphs are obtained for various axial position dzrec. puter simulation. It cannot be solved with either ray optics It is clear that shape at central part can be obtained with the or rigorous methods. We have applied composition of two highest accuracy (P−V error 0.1 mm) for dzrec =30μm. methods. The Born approximation method of scattered field In this area, the object height 30–40.3 mmforr <51mmis at dielectric interface [9] is applied to simulate light propa− obtained. The element growth in a range 20–30 mm(51

S p Fig. 5. Simulation of propagation through a microlens of the plane wave (a) and its reconstruction at the plane MO.

6. Conclusions

In the paper, optical methods for full field characterization of the beam generated by microlenses were considered. These methods allow the determination of microlens geo− metrical parameters (focal length and surface shape) as well as complex field distributions of the beam generated by a microlens. Such an approach allows the use of the measure− ment results by both the producers and the users of mi− crolenses. The beam measurements were performed using geometrical, interferometric, and holographic methods. The geometrical measurements are the simplest and sufficient to find the focal plane position and the foci intensity distribu− tion. The most general method is the holographic one allow− ing the determination of all demanded parameters. For this goal, one registered interferogram is sufficient and the field distributions at other planes can be calculated using diffrac− tion formulae. However, the hologram registration plane Fig. 7. Reconstructed field amplitude at a microlens physical foci has to be chosen carefully. plane with digital holography. Special attention was devoted to the determination of the microlens surface shape. It was done calculating the field propagation through the microlens. It was shown, that the choice of the reference plane allowing the surface shape de− termination using simple phase shift influences the mea− surement accuracy. It was proved by extensive numerical applications. At the end it is worth to emphasize, that the knowledge about the measured microlens into the holo− graphic process significantly improves precision of the element characterization.

Acknowledgements

The work was supported by the Ministry of Science and Higher Education in the project No 3T 10C 00120 and the statutory activity founds.

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