## Abstract

We demonstrated a unique monolithic integration of Fresnel elliptical zone plate (EZP) objective on a 2-axis staggered vertical comb-drive micromirror with 500μm by 800μm surface area via direct patterning of reflective binary phase modulation elements on a silicon chip. The need for focusing optics is thus obviated, simplifying the micro-endoscope assembly and improving its form factor. The design of binary phase EZP was guided by simulations based on FFT based Rayleigh-Sommerfeld diffraction model. For dual-axis scanning angles up to 9º by 9º at the image plane, the simulated diffracted Airy disks on a spatial map have been demonstrated to vary from 10.5μm to 28.6μm. Micromirrors scanning ±9º (optical) about both axes are patterned with elliptical zones designed for 7mm focal length and 20þ off-axis 635-nm illumination using 635nm laser. Videos of samples acquired with ~15μm lateral resolution over 1mm × 0.35mm field of view (FOV) at 5.0 frames/second using the device in both transmission and reflectance modes bench-top single-fiber laser scanning confocal microscope confirmed the applicability of the device to micro-endoscopy.

©2012 Optical Society of America

## 1. Introduction

In vivo optical imaging is an important tool for medical diagnosis in situations where biopsy is difficult, and for image-guided microsurgery and photodynamic therapy [1]. Cellular-level imaging enables early detection of many diseases, which is important for effective treatment and higher survival rate [2, 3]. Visualization in sensitive internal non-tubular human organs requires compact forward-imaging endoscopes, which have thus far proven to be difficult to assemble in small form factor, as opposed to sideways-imaging probes [4]. Microelectromechanical system (MEMS) technologies are uniquely positioned to provide distal beam deflection for image formation in micro-endoscopes. Vertical combdrive micromirrors have been shown to provide the large rotational torque, deflection angles and mirror surface quality for laser-scanned imaging systems [5–11], while bringing down the cost of instruments by taking its advantage of mass production compatibility with semiconductor integrated circuit industry. However, the catheter rigid length and its outer diameter are mainly limited by the focusing optics. Toward minimizing the system form factor and assembling complexity, in other literatures MEMS micromirrors with both refractive [12] and diffractive [13] lenses were fabricated for distal scanning imaging. However these techniques suffer from slow scan rates and increased optical aberrations. Micro-machined 3-D optics has also been assembled into integrated free-space systems [14], though catheter assembly becomes difficult and expensive in multi-element systems. Preliminary results of addressing these limitations were previously achieved in our lab by monolithically integrating a micro-machined Fresnel zone plate objective on the surface of the micromirror via patterning of reflective binary phase modulation elements [15]. In this paper, an FFT based Somerfield diffraction numerical simulation was conducted for the optical performance examination accompanying the quality design of the EZP. High accordance of the experimental measurements with the simulation demonstrated the feasibility of the EZP design. Both theoretical analysis and testing results proved its applicability to a novel fast-imaging handheld lens-free micro endoscope.

## 2. Methods

#### 2.1 Fresnel Zone Plate Theoretical Background

As a special form of Fresnel zone plate, the elliptical zone plate (EZP) is designed by projecting the circular zone plate annular pattern onto a plane tilted at an angle which will determine the off-axis angular position for reflection. Coherent illumination incident on the micromirror surface at that angle to the mirror normal can be concentrated at a wavelength-dependent focal distance designed according to Eq. (1):

In Fig. 1
, θ is the off-axis illumination angle, λ is the illumination wavelength, f is the focal distance, and a_{n} and a_{n}cos(θ) are the semi-major and semi-minor axes of the elliptical boundary of the n^{th} zone of the EZP. In our EZP design we have a group of 22 (n = 1,2,…22) elliptical zones and the largest semi-major and semi-minor axes are 337.37μm and 312.80 μm.. Design boundaries to prevent aberrations for circular FZPs are derived as indicated in [16]. Degradation in focal spot size due to small designed off-set angle (20°), changing illumination angle (by micromirror rotation) and illumination wavelength is negligible for optical path difference deviation of less than λ/4 from nominal value [16, 17].

Spherical Aberration:

Chromatic Aberration:

Off-Axis Aberration:

These conditions determine number of EZP zones and scanning angle, therefore number of resolvable points in the image. Variation in focal distance with wavelength may be utilized for axial scanning in 3D imaging systems [18].

#### 2.2 Fresnel Elliptical Zone Plate Optical Performance Simulation

As depicted in Fig. 2 , optical field diffraction of the Fresnel EZP propagates from reference plane ζ = 0 in the (ξ, η, ζ) coordinate system to reference plane z = 0 in the (x, y, z) coordinate system. The (ξ, η, ζ) coordinate system is the Fresnel EZP surface plane and the (x, y, z) coordinate system is the imaging plane, as shown in Fig. 2. To verify the optical performance, commercial software like CODE V or ZMAX typically use approaches include ray-tracing which is valid only in the geometrical optics approximation to the light propagation. In our case, ray tracing methods will not accurately predict the optical performance since its inherent approximations would affect the calculation given our comparatively large numerical aperture. Diffraction must be precisely taken into account, starting from the scalar diffraction theory to propagate the optical fields. There are some other commercial software like PARAXIA and GLAD handling scalar diffraction theory by using the Fresnel and the Fraunhofer approximations or direct integration. However, when dealing with light propagation between titled planes as in our case, all the existing software could only resort to direct numerical integration rather than adopting the Fast Fourier Transform (FFT) for calculation. Direct numerical integration could be extremely time-consuming comparing with FFT, especially when the computational window size is large. Especially for our EZP imaging, direct numerical integration does not work effectively, since the aperture size is comparatively too large as a two-dimensional integration computation window considering the imaging wavelength is only 635nm. Conditions for the Fresnel and the Fraunhofer approximations do not hold either in our case, therefore requiring a specially developed FFT based scalar diffraction integrated program. Furthermore, this program should also be compatible with tilts to calculate the optical performance for our Fresnel FZP imaging.

Conditions for the Fraunhofer approximation and the Fresnel approximation are illustrated in Eq. (5) and Eq. (6) respectively:

In Eqs. (5-6),$\text{k}=2\text{\pi}/\text{\lambda}$, λ is the imaging wavelength. In our case, the distance between the imaging plane and the micromirror is designed to be the same as the micromirror’s focal length, which is 7mm (z_{0} = f). The field size on the imaging plane is set to be the same as the size of the micromirror, which is 1mm by 1mm, and the imaging wavelength λ is 635nm. So in our case the valid range of the Fraunhofer approximation and the Fresnel approximation are z_{0} » 9.89m and z_{0} » 42.9mm, while z_{0} is truly 7mm. Therefore, conditions for Fresnel approximation illustrated in Eq. (5) and Fraunhofer approximation illustrated in Eq. (6) are not met in our occasion.

The most accurate methods for scalar treatment is the Rayleigh-Sommerfeld diffraction integral [19], the only approximation would be the ignoring of the vectorial nature of light. To understand the optical performance of the EZP model defined by Eqs. (1-4), a Rayleigh-Sommerfeld integral numeric simulation was carried out. Further, Fast Fourier Transform (FFT) based numerical simulation in MATLAB has been used to replace traditional numerical integration for efficient computation.

Equation (7) indicates the full form Rayleigh – Sommerfeld integral equation according to the coordinate system illustrated in Fig. 2:

A 1mm diameter Gaussian shape circular beam wavefront projected onto the EZP with an offset angle of 20° was modeled as input, with the consideration of phase delay due to the tilting. The offset angle was chosen considering the balancing of the fully utilizing MEMS mirror surface area, minimizing scanning imaging distortion and reserving space for large FOV. Considering the case when the diffraction propagates between two tilted planes, the focusing spots under different MEMS mirror deflection angles may deviate away from the origin point on the observation plane. Therefore there is a need to shift the focusing spot back to the center of the FFT computational window, and evaluate the impact of such deviation on focusing spot size for imaging. We applied transformation matrix and origin offset adjustment in coordinate system for the FFT algorithm [20]. The simulated focusing spot profile under different deflection angles with off-axis illumination angles of 20° are depicted in Fig. 3 . The focused Airy disk remains the center of the observation area, and little degradation of focusing profile has been observed when the scanning angle of the MEMS EZP increases. The focusing spot sizes were obtained by calculating the area size of positions where the normalized intensity is over the 1/e of the maximum intensity. The spot diagrams were shown in Fig. 3(a)-3(c), Fig. 3(d)-3(i) illustrate the Y and X axis resolutions. Y axis resolution here indicates the resolution along the semi-major axis, while X axis resolution here indicates the resolution along the semi-major axis. The equivalent diameters were then derived based on the area size.

To evaluate the focusing spot size on the full field of imaging plane, the full width half maximum (FWHM) of the simulated focusing spot profiles under different tilting angles were calculated. Figure 4 shows the resolution map with reference to different EZP X and Y axes rotational angles up to 12° by 12°. X axis here is indicating the EZP scanner rotation along the semi-major axis, while Y axis indicating the rotation along semi-minor axis. Results in Fig. 4 indicate the focusing capability varies from 10.5μm to 28.6μm when EZP scans the full field.

#### 2.3 Fabrication

The micromirror is actuated by staggered vertical comb drives fabricated by a comb self-alignment process in bonded double-SOI wafers [21, 22]. Coarse features of the stator are etched by Deep Reactive Ion Etching (DRIE) into 25μm thick SOI <100> device layer (Fig. 5 ). An oxidized <100> wafer is fusion bonded on top of the patterned wafer, and ground down to 25μm thickness with <50nm surface roughness to form the micromirror surface. Features of the elliptical zone plate objectives are patterned on the silicon surface using photolithography and RIE to quarter-wavelength depth of 160nm. Exact features of the actuators, aligned to the lower layer features, are etched into deposited silicon dioxide. DRIE-oxide RIE-DRIE etching sequence forms the self-aligned. Backside substrate DRIE and oxide RIE on both sides releases the mirror and removes remaining protective oxide. Scanning electron micrographs of the fabricated device are presented in Fig. 6 .

#### 2.4 Device characterization

The micromirror is actuated by staggered vertical comb drives fabricated by a comb self-alignment Scanning EZPs designed for 635nm wavelength with focal lengths of 7mm and off-axis illumination angles of 20° were fabricated on micromirrors of size 500μm×700μm. Two-axis beam scanning is obtained by mounting the micromirror by torsion rods within a gimbal, which is suspended by torsion rods aligned in the orthogonal direction. Rotation about each axis is driven by two sets of staggered vertical comb drives. This configuration leads to two-axis angular scanning about a single pivot point at the center of the micromirror, which reduces optical field distortions. Frequency response characteristics (Fig. 7 ) of the micromirror were tested by applying voltage of 20.0+20.0sin(ωt) volts and varying the sinusoidal frequency. The micromirror exhibits resonant out-of-plane rotation at 2280Hz and 383Hz for the inner and outer axes respectively. The static voltage deflection characteristics (Fig. 7b) were determined by applying a DC voltage to one comb drive on each axis. Static voltage deflection of ~9° (optical) was measured on application of 110 volts on both axes. Raster scan pattern was used for point-by-point image formation, employing resonant frequency operation of the inner axis for fast line scan, and non-resonant operation of outer-axis for frame scan.

Size of the focused spot of an EZP designed with 8mm focal length for 635nm illumination at 20° was profiled against micromirror rotation angle by measuring the far-field angular beam divergence (*θ*) of the Gaussian beam, and calculating the focused beam waist (*w _{f}*) using the Eq. (10).

The measured focused spot size shows little degradation (Fig. 8 ) for micromirror scanning angles up to 10° (optical) about both axes. When comparing with the simulation results predicted in Fig. 4, the measured esults shows a similar resolution range, while the spot size 2-D distribution is different in certain areas. The simulated resolution map has the minimum and maximum values of 10.5μm and 28.6μm, while the measured resolution ranges from 12 to 24μm. The small difference may come from fabrication defects and measurement errors. In simulated resolution map, the worst resolution happens when both the horizontal and vertical axes reach the maximum deflection angles. The reason for this could be longer diffraction distance for the laser beam to propagate from the micromirror to the imaging plane when the deflection angles are larger, therefore deviating from the value of the focal length designed for Fresnel EZP. However in measurement, worst resolution happens when there is largest horizontal axis deflection with a small vertical deflection.

## 3. Imaging results

#### 3.1 Transmission imaging using EZP micromirror

Preliminary testing of image-formation capabilities of the device was performed in a simple transmission-mode experiment, depicted in Fig. 9 . A sample with spatially-varying transmission was placed in the focal plane of a scanning EZP, and transmitted light was concentrated into a photo-detector using two collection lenses. Mylar transparencies printed with longhorn logos and numbers were imaged (Fig. 10 ) using the system at 5 frames/second. Comparison with images obtained from an Olympus BX51 microscope using 10X objective indicated an estimated field of view of 1mm × 0.35mm at approximately 15μm resolution.

#### 3.2 EZP Micromirror-Based Reflectance Confocal Imaging

The devices were then incorporated into a portable bench-top single-fiber laser-scanning reflectance confocal microscope (Fig. 11 ) that is better suited to eventual use in in vivo imaging applications. Polarized light from a 635nm semiconductor laser diode is launched into a single-mode polarization-maintaining fiber, aligned to the fiber slow axis. After collimation into a beam matched to the size of the EZP, the linearly polarized light is converted into circularly polarized light by a quarter-wave plate (QWP) before being simultaneously focused and scanned across the sample by our device. Reflected light from the sample maintains some component of circularly polarized light, which is converted into light linearly polarized along the fiber fast axis, orthogonal to the incident illumination. This allows the walk-off polarizer to separate the sample reflection from laser illumination and direct it to an avalanche photo-detector. Images using this system of a USAF1951 resolution target obtained are depicted in Fig. 12 .

Field of view of 1mm × 0.35mm and lateral resolution of 15μm are estimated based on calculating the line width of the resolvable features in the resolution target images. The nonlinear asymmetric distortion of the field of view as shown is due to the dynamic deformation of the micromirror plate when scanning. While the novel concept of Fresnel EZP applied in confocal imaging is demonstrated, further improvements on imaging quality are expected to be achieved in combination with more robust scanner architecture design.

## 4. Conclusions

Novel monolithic integration of reflective binary-phase modulation elements on two-axis MEMS scanning micromirrors is demonstrated for simultaneous beam scanning and focusing in a compact single-chip solution. Focusing capability varying from 10.5μm to 28.6μm with reference to different EZP deflection angles were predicted by a FFT based Rayleigh-Sommerfeld scalar integral simulation, and afterwards experimentally determined to be around 15μm. This approach can potentially eliminate the need for focusing optics in a micro-endoscopes catheter, thus simplifying assembly and improving form factor. Elliptical zone plates integrated on two-axis self-aligned staggered vertical comb driven micromirrors, incorporated into a lasers canning reflectance confocal microscope experiment, were shown to provide the cellular-level resolution required in micro-endoscopes without complex multi-element assembly.

## Acknowledgments

This research is sponsored by National Science Foundation Grant# 99150 through UT Austin and NanoLite Systems, Inc. The authors wish to thank Microelectronics Research Center (MRC) at UT Austin for providing facilities for micro-device fabrication and characterization.

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