Wavefront sensing by an aperiodic diffractive microlens array

Wavefront sensing by an aperiodic diffractive microlens array Lars Seifert a, Thomas Ruppel, Tobias Haist, and Wolfgang Osten a Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany ABSTRACT Shack-Hartmann sensors are commonly used wavefront sensors in a large field of applications, like adaptive optics, beam characterization and non-contact measurements. They are popular because of the ease of use and the robustness of the sensor. We introduce a new way to improve the performance of miniaturized and massproducible optical wavefront sensors for industrial inspection: A sensor design due to an aperiodic diffractive element working as microlens array allows the use of small and cost-efficient detector chips. The diffractive element was optimized using raytracing and thin element approximation (done in Zemax). As an example, we present the design and realization of a sensor for laboratory use with a measurement diameter of 20mm. We show an example measurement and results concerning dynamic range. The measurement accuracy was determined by measuring spherical waves. Keywords: Shack Hartmann Sensor, diffractive element, wavefront sensing 1. INTRODUCTION Shack-Hartmann sensors (SHS) are commonly used wavefront sensors with a wide range of applications. They consist of mainly two parts: The microlens array and a detector device (usually a CCD camera). The measurement principle is to determine the position of spots formed by the microlens array with the focal length f. The microlens array can be diffractive or refractive, static 1 or adaptive. 2 The lateral displacements x and y of the spots in reference to a plane wave are related to the derivatives of the measured wavefront Φ: [ ( ] [ Φ] = x y ) Φ = [ 1 f ( )] x y The commonly used SHS consists of a microlens array and a detector of the same size. The measurement aperture is usually limited by the detector size. Because large detectors are expensive, the measurement diameter is normally in the range of 5-15 mm. By using an aperiodic diffractive element, it is possible to design a sensor with different microlens array and detector size. This is interesting because CCD cameras with smaller detectors are much cheaper and therefore a SHS can be build at a lower price. To demonstrate this, we will present a SHS with a low cost webcam as detector device. The aim was to design a sensor for laboratory use with a sensitivity of λ /10 at a wavelength of 632.8 nm and a measurement aperture of 20 mm. (1) 2. THE SENSOR 2.1. The camera To demonstrate the concept of the aperiodic diffractive element we looked for a cheap camera. The Philips Toucam Pro II webcam is ideal for our purpose. The webcam is connected via the USB Port with the computer and costs about 60$. The specifications of the camera are listed in Table 1. To use the camera in the SHS sensor, some preparations are needed. The body, the microphone and the lens Further author information: (Send correspondence to Lars Seifert) Lars Seifert: E-mail: seifert@ito.uni-stuttgart.de Interferometry XIII: Applications, edited by Erik L. Novak, Wolfgang Osten, Christophe Gorecki, Proc. of SPIE Vol. 6293, 629302, (2006) 0277-786X/06/$15 doi: 10.1117/12.677845 Proc. of SPIE Vol. 6293 629302-1

Figure 1. The Philips Toucam II before (left) and after the modifications (right). of the camera have to be removed. The separation of the CCD-sensor from the board makes the design much more flexible. Therefore the CCD-chip must be disconnected from the circuit board and then reconnected with extension cables. On top of the CCD-chip is a glass cover. In principle the influence of the glass cover can be included in the calculation of the microlens array (see section 2.2) if all specifications like distance, thickness and material of the cover glass are known. We removed the protection cover because without cover, no additional reflections and lateral beam offsets, which could influence the measurement accuracy, can appear. The Philips webcam is a color camera. There are three channels for the colors red, green and blue with different spectral sensitivities. Therefore the camera can be used in the range of 430 700 nm. As previously mentioned, the requested measurement wavelength is 632.8 nm, so only the red channel is used in the measurement evaluation (although the green channel can be used to expand the dynamic range of the camera). The effective resolution in this spectral range is 320 200 pixel. It will turn out that even at this low resolution a useful sensor can be realized. In figure 1 the camera is shown before and after the modifications. Type Philips Toucam Pro II Sensor Interline progressive-scan 1/4 Sony CCD ICX098AK Detector size 4.60 mm 3.97 mm Pixel size 5.6m 5.6m Resolution 640 480 pixel Sensitivity < 1Lux Framerate 60 fps Table 1. Specifications of the Philips Toucam Pro II webcam 2.2. Microlens array The base component of the Shack-Hartmann sensor is the microlens array. In principle, the shape of the microlenses can be chosen freely. For example it it possible to design a microlens array with hexagonal, round or quadratic shape. The microlenses do not need to have the same size. Microlenses with different sizes can compensate non-uniform illumination. 3, 4 The effective camera resolution for green is better because of the double number of pixels. But for laboratory use a red HeNe-Laser is more common. Proc. of SPIE Vol. 6293 629302-2

Because the designated sensor should be all-purpose, we chose to use microlenses with the same size and with quadratic shape. The quadratic shape of the microlens makes the integration of the measured wavefront during the reconstruction process simpler 5. The number of microlenses is identical to the number of slope measurements Figure 2. Adding a convex lens between the microlens array and detector results in a larger minimal diffractive structure needed for the microlens array. over the aperture. Common SHS use often about 400 microlenses. Due to the low resolution of the chosen camera, the number of the microlenses is limited to about 200 lenses. A detector area for a single spot of 40 40 pixel leads to a 16 12 grid of microlenses. This is a good choice as all pixels of the detector are used. A standard microlens array can not be used. The CCD chip is much smaller than the measurement area. The spots have to be tilted, so that they are focused on the detector. Due to the different tilts the microlenses of the array will have different phase functions. Therefore, the manufacturing of a diffractive element is more suitable. Unfortunately diffractive microlenses with high tilt angles need small diffractive structures. For example a minimal diffractive structure of 5 µm leads to a minimal distance between microlens array and detector of 20cm. A sensor with such a long focal length is very sensitive, but has a low dynamic range. A compact sensor with a broad application range can not be realized with such a setup. For this reason we add a biconvex lens between microlens array and detector. This setup is shown in figure 2. The result is an increase of the minimal diffractive structure of the microlens array because most of the refraction power is transfered to the lens. A compact sensor size canberealized. Weusealens with a focal length of f =30.3mm (BK7, r 1 =24.406 mm, r 2 = 24.406 mm, thickness 7 mm). As a result of the additional lens, equation 1 is no longer valid. The aberrations of the lens can be corrected by the microlens array. The measurement aperture of the sensor is circular but the detector area is rectangular. Because all pixels of the detector should be used, the assignment from microlens to spot position can not be uniform 6.Forthedesignof the 192 microlenses in a circular shape only one quadrant needs to be considered. There are a lot of possible remappings between microlens and spot area on the CCD ship. According to equation 1 the path length between the microlens and the spot position is important for the dynamic range and the accuracy of the slope measurement. Because all microlenses should have the same dynamic range, the path length for all microlenses should be the same. Only then the optimal measurement accuracy is available. Therefore we chose a remapping in which the path length variation over all microlenses is minimal. By assigning different path lengths to different microlenses it is possible to obtain an improved aberration detection if the type of aberration is known in advance. Figure 3 shows this remapping on the basis of a quadrant of the microlens array. The deviation of the average optical path length is shown in figure 4. It is less than 1.2mm for the chosen remapping. This has to be regarded in relation to the edge length of a microlens (1.23 mm), the edge length of the designated detector area (0.22 mm) and the lateral distance between the border of the CCD to the border of the microlens array (8.52 mm). The calculation of the microlens array is done in the optical design program ZEMAX. Depending on the position Proc. of SPIE Vol. 6293 629302-3

w!cwieu2 saga CCDCP!b Figure 3. The remapping between microlenses and the spot area at the CCD-chip. Absolute deviation of average optical path length [mm] Figure 4. The deviation of the average optical path length is less than 1.2 mm for the chosen remapping between the microlenses of one quadrant and the detector area. of the microlens and the position of the designated detector area, the phase structure of every microlens in a quadrant of the microlens is different. The phase structure Φ(x, y) is expressed by a polynomial: Φ(x, y) = N A i x mi y ni (m i + n i N) (2) i=1 The highest order is N = 4, which means that there are 14 coefficients A i. The calculation is done in an optimization process. The merit function is defined by the spot position on the detector and a maximal spot size of 2 µm. Another sensor parameter is the distance between the additional lens and the CCD-chip. The distance has an influence to the minimal structure size of the DOE. After the simulation of different distances between lens and Proc. of SPIE Vol. 6293 629302-4

10 p y y 8 \& 6 4, 'y'r*r4 2 s 0 tlijij" ' L }A%i'r 'rk -4 C 91o 4 02 4 6 '1 8 10 Figure 5. Profile of the microlens layout. detector, we determined a distance of 13.3 mm as a good compromise between sensor dynamic, sensitivity and minimal structure size of the DOE. Figure 5 shows the resulting microlens array in a phase diagram (without wrapping). The arrows are the normal vectors of the microlenses. Cleary visible is the tilt in the phase function of the microlenses. Our first manufactured microlens array (figure 6) has some manufacturing defects. These defects can influence the spot quality of concerned microlenses. In our case only one spot is deformed and the effect on the sensor accuracy can be neglected. The complete design of the sensor with all distances is shown in figure 7. 2.3. Evaluation Because of the added lens in the sensor, the relation between spot position and wavefront gradient is not as simple as in equation 1. With the help of a raytracing program it is possible to calculate the influence of the lens. The simulation includes the propagation of wavefronts with different tilts and calculates the position of the spots for every microlens. The results for the upper right quadrant of the microlens array are shown in figure 8. A red rectangle defines the designated area on the detector for the spot of one microlens. The blue dots mark the position of the spot for different wavefront gradients with a maximal gradient of ±0.3 o in x and y-direction. No spot leaves the designated detector area for this maximal gradient and a tilt in only one direction leads as a first approximation to a linear movement of the spot. A closer examination shows that the microlenses at the border of the microlens Proc. of SPIE Vol. 6293 629302-5

Figure 6. A microscopic picture of a quarter of the manufactured microlens array with visible defects. array have apparently less dynamic range and the spots move non-linear for large wavefront gradients. Therefore, every microlens in a quadrant of the array needs its own calibration function to calculate the wavefront tilt from the spot position. This function is computed by fitting a polynom of third order to the simulation data. The error in the fitting process is smaller than 1.7 10 7 rad which is equivalent to an error of λ/200 (λ = 632.8 nm, entry aperture 20 mm). Due to the additional lens the adjustment of the sensor components are more complicated. The determination and removal of tilts and rotation of elements can not be done by the same methods 7 which prove useful for the conventional sensor. In principle, the best calibration can be achieved by measuring wavefronts with known gradients and a subsequent adaption of the calibration function for every microlens. For the first measurements we will use the simulated spot movement function and calibrate only the home position of the spots when using a plane wave. The next chapter will show, that this is sufficient for the target accuracy. Because of the cheap CCD-sensor, the noise is quite high. In our experiments the spot position error is about 0.5 pixel. This is sufficient for a live picture evaluation, but not for a precise measurement. An average over 100 pictures can lower the spot position error due to noise to a value of 0.03 pixel, which is sufficient for the target requirements. Because of the higher signal-to-noise ratio, the error of the spots from the middle of the microlens array is smaller when measuring a beam with a Gaussian intensity distribution. An array with different microlens sizes could compensate this behavior. The calculation of the slope depending on the spot position is identical to the conventional sensor 1, 5, 8, 9.Therefore we do not go into detail here. Proc. of SPIE Vol. 6293 629302-6

Figure 7. Complete design of the sensor. 3. FIRST MEASUREMENT A known reference wave is needed for the determination of the sensor accuracy. The simplest wavefront for this task is a spherical wave. The experimental setup is shown in figure 9. A laser with a pinhole is used to create spherical waves. The radius of the spherical wave is defined by the distance between pinhole and sensor. After the measurement with the SHS the reconstructed wave can be compared with the theoretical data. The minimal distance between sensor and pinhole can be calculated. As mentioned in section 2.3, the maximal measurable wavefront gradient is 0.3 o. With the sensor radius r = 10 mm, the minimal distance R is: 10 mm R = 2m (3) sin 0.3o With this minimal distance between sensor and pinhole, small additional tilts between the sensor and the optical axis of the laser-pinhole system can lead to spots leaving the detector area. Therefore we chose a distance of about 5 m as measurement distance. Then the sensor can be tilted against the optical axis up to 0.18 o before the dynamic range is exceeded. During the measurement the distance is varied between 4600 mm and 5300 mm in an interval of 100 mm. The position of the sensor is determined with a laser distance measurement device (SICK DME 2000) with an accuracy of 3mm. The comparison between the real distance and the distance according to the measurement with the sensor is shown in Figure 10. The phase error between the measurement with the sensor R 1 and the real distance to the pinhole R is: λ 1 λ (R ) ( ) R 2 r 2 R 1 R1 2 r2 (4) This phase error is shown in figure 11. According to the figure the average phase error is 0.06 λ. This error meets the sensor demands. The measurement error due to the laser distance measurement device is less than 0.01 λ and can be neglected. Proc. of SPIE Vol. 6293 629302-7

IEEE 0.6 0.4 0.2 1 H 1HHHHHL1HHH HH 0 2 a4 a as i 1.2 1.4 1.6 mm Figure 8. Simulation of the spot movement depending of the gradient of the wavefront to be measured. Only the first quadrant of the microlens array is shown. Figure 9. Experimental setup for the determination of the sensor accuracy. 4. CONCLUSIONS We have shown that it is possible to design a Shack-Hartmann sensor with a small and cheap CCD-sensor. This SHS is able to measure a wavefront with a comparative large aperture. The sensor was designed with the specifications of section 1. First measurements have shown that these specifications were achieved. The concept of an aperiodic microlens array together with a positive lens is the basis for this sensor. Therefore the use of a webcam with a small CCD-chip as the detector device is possible. A webcam is cheap and the connection to the computer via USB-port is very easy and comfortable. With an averaged image acquisition, the noise of the webcam can be compensated. Because of the new sensor concept, the simple equation between wavefront gradient and spot position is not valid Proc. of SPIE Vol. 6293 629302-8

5400 theoretical measurement Figure 10. Measurement results for the determination of the spherical waves. 0.2 wul6_ 0.1.............. a 0.06.... U I I I I I I 4600 4600 4700 4800 4900 6000 6100 6200 6300 distance between sensor and pinhole [mm] + Figure 11. Phase error for eight measurements with different distances between pinhole and sensor. anymore. We have simulated the spot movement dependent on the wavefront tilt and confirmed the correctness in an experiment. With a very basic calibration method the actual sensor achieves a measurement accuracy of about 0.1 λ which is sufficient for daily laboratory use. In the future we want to use not only a simulated calibration function but want to calibrate the sensor with real wavefronts in order to enhance the sensor accuracy. REFERENCES 1. D. Malacara, Optical Shop testing, John Wiley & Sons, ISBN 0-471-52232-5, 1992. 2. L. Seifert, J. Liesener, and H. Tiziani, The adaptive Shack-Hartmann sensor, Optics Communications 216, pp. 311 319, 2003. 3. D. Neal, M. Warren, J. Gruetzner, T. Smith, and R. Rosenthal, A multi-tiered wavefront sensor using binary optics, Proc. SPIE 2201, pp. 574 585, 1994. 4. J. Rha, D. Voelz, and M. Giles, Reconfigurable Shack-Hartmann wavefront sensor, Opt. Eng. 1, pp. 251 56, 2004. 5. L. Seifert, H. Tiziani, and W. Osten, Wavefront reconstruction with the adaptive Shack-Hartmann sensor, Optics Communications 245, pp. 255 269, 2005. 6. D. Neal, J. Mansell, J. Gruetzner, R. Morgan, and M. Warren, Specialized wavefront sensor for adaptive optics, Proc. SPIE 2534, pp. 338 348, 1995. 7. J. Pfund, N. Lindlein, and J. Schwider, Missalignment effects of the Shack-Hartmann sensor, Appl. Optics 37, pp. 22 27, 1998. Proc. of SPIE Vol. 6293 629302-9

8. M. Montoya-Hernandez, M. Servin, D. Malacara-Hernandez, and G. Paez, Wavefront fitting using Gaussian functions, Opt. Comm. 163, pp. 259 269, 1999. 9. S. Groening, B. Sick, K. Donner, J. Pfund, N. Lindlein, and J. Schwider, Wavefront reconstruction with a Shack-Hartmann sensor with an iterative spline fitting method, Appl. Opt. 39(4), pp. 561 567, 2000. Proc. of SPIE Vol. 6293 629302-10