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Functional Testing of VarifocalsA wavefront sensor with enhanced measurement range based on application of micro-mirror arraysStephan Stürwald

For functional testing of optical sys-tems, typically Shack-Hartmann-based sensors consisting of a combina-tion of a micro lens matrix and a CCD/CMOS sensor are utilized. Their lateral resolution is restricted to the size of the micro-lenses, and the maximum measurable wavefront slope is usually significantly limited to avoid ambigu-ous signals on the detector. Here, we present a similar measurement method which is, however, based on a digital micro-mirror matrix for selecting sub-apertures in reflection. This leads to enhanced measurement capabilities in functional testing of optics.

Conventional wavefront systems

For measuring wavefronts, Shack-Hart-mann sensors (SHS) are typically used. Application areas for them are – besides

adaptive optics in astronomy – topo-graphy measurement, functional test-ing of optical elements, measurement of beam profiles of lasers as well as the investigation of the human eye in medi-cine. However, both the lateral resolu-tion and the measurement range for the wavefront aberration significantly limit the widespread use of these sen-sors for optical testing as many aspheric or freeform optics exceed the maximum measurable slope of this measurement principle. Therefore, a novel method for measuring wavefronts similar to the Shack-Hartmann principle is developed at the Fraunhofer IPT, allowing for an improved lateral resolution and mea-surement range compared to currently available wavefront sensors.

To circumvent the limitations of the classic setup, different modifications to the measurement principle have been suggested in research. This includes, for example, the use of an LCD as a switch-able mask in front of a single large ap-erture lens instead of microlens arrays. Through the use of LCDs, it is possible to scan different areas of the wavefront (so-called subapertures) separately. Then, a single lens serves as an imaging element

for all sub-apertures [1]. The advantage of this setup is that the number of mea-suring points as well as the available area per measurement point on the CCD are variable. In the so-called “adaptive Shack-Hartmann Sensor” (aSHS), the LCD acts as an aperture mask as well as a diffractive imaging element [2]. On the LCD for each subaperture a diffrac-tive structure in a grayscale is displayed, which is used for this subaperture as a holographic lens. However, in both methods, the number of measurement points is limited to below 1000.

Measurement principle of the scanning sensor

The novel method removes the restric-tion that the pixels have to be assigned to certain microlenses. This is possible by an explicit encoding of the subaper-tures. Innovative for this purpose is the required measurement method: Digital micro-mirrors (DMD: Digital Micro-mirror Device) – segmented surfaces that consist of more than one million micro-mirrors and that can be individu-ally controlled by electronics (± 12 ° tilt, 1920 × 1080 mirrors, 10.8 micron pixel

Fig. 1 Principle of a conventional Shack-Hartman wavefront sensor.

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Fraunhofer Institute for Production Technology IPTAachen, Germany

Fraunhofer is Europe’s largest application-oriented research organization. The Fraunhofer IPT as part of this foundation develops systems solutions for production. It focuses on the topics of process technology, production machines, mechatronics, production quality and metrology as well as tech-nology management. The department for metrology has a focus on optical testing systems comprising a variety of different measurement principles ranging from (low coherent) interferometry, holography, microscopy tech-niques, optical coherence tomography and fiber sensors.

www.ipt.fraunhofer.de

Institute

Measurement Technology

Optik&Photonik 2/2014 39© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

size, fill factor > 91%). Hence, the mirror matrix acts as a reflective, variable aper-ture element (Hartmann mask).

The current development comprises both the improvement of lateral resolu-tion as well as an extension of the dy-namic range of the sensor. This is mainly realized by utilization of a digital micro-mirror array (DMD) implemented as a switchable mask element in conjunction with a suitable detector area. Therefore, this innovative approach is based on a method which is scanning the wavefront and thus sequentially directing a por-tion of the reflected wavefront towards the detector (Fig. 3). By the selective switching of individual micro-mirrors, a single subaperture is directed towards a convective lens with a large aperture

mounted in the optical path that images the rays onto the detector. Due to the short switching times (several MHz) of the DMD, a fast scanning of the entire wavefront is possible, where the time scale is limited only by the available light intensity and the integration time of the sensor. With this system, a maximum lateral resolution can be achieved which corresponds to the number of mirror el-ements of the DMD.

Since for each measurement point the total detector area is available by the sequential processing of the individual sub-apertures (super pixels), the mea-suring range of the wavefront sensor is significantly increased and only limited by the aperture covered by the detector lens. A further advantage of the scan-

ning method is the exact one-to-one correspondence of the measured spot to the position of the respective subap-erture.

The system is calibrated with colli-mated wavefronts coupled into the sys-tem at different tilt angles (Fig. 3).

Mirror matrix induced diffraction effects

Due to the small mirror diameter of about 10 – 13 μm, different strong dif-fraction patterns are formed depend-ing on the laser wavelength used (Fig. 4), since the mirror matrix represents a three dimensional reflective diffrac-tion grating. This may falsify the de-tection of the x-y-position of the main peak on the detector for calculating the wavefront gradient, since for example; a position-sensitive diode (PSD) for the fastest possible analog readout returns solely the center of an intensity distribu-tion integrated to the x- and y-direction. Therefore, it is required to subtract the influence of the basic diffraction pattern when low-cost monochromatic light sources (lasers) are used. Additionally, an inhomogeneous (Gaussian) intensity distribution leads to errors in the entire wavefront. This is almost completely compensated by a prior calibration. By means of a calibration the correct x-y-position of the super-pixel-reflex may be, inter alia, determined by deduction of the displacement vector, which is caused by the background diffraction pattern (Fig. 5).

Operation for aspheric testing

To demonstrate the measurement capa-bility as well as for closer examination of the conformity of measurement and simulation, direction and magnitude of the tilt angle are evaluated separately for a progressive lens (freeform optics,

Fig. 3 2D and 3D illustration of the measurement principle for wavefront sensing.

Fig. 4 Left: Diffraction patterns at selected wavelengths λ for mirror sizes at 10.6 µm and a superpixel size of 30 × 30 pixel mir-rors. Right: Sketch of a one dimensional approximation of the mirror matrix grating with specification of geometric parameters.

Fig. 2 Illustration of the micromechanics (a) and photo of a digital micro mirror array (DMD) with a sketch of the mirror arrangement used for scanning a wavefront.

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diameter: 60 mm, 2 diopters). This cor-responds to the representation of the local normal vectors in polar coordi-nates. In Figure 6 (top), the magnitude of the angular orientation (or φ); in the figure below, the magnitude of the an-gular distribution (or θ ) is shown. The evaluation of the calculated wavefront by means of optics simulation is located on the left, the measured wavefront (for a rough sampling with 15 × 15 micro-mirrors super pixel size) respectively on the right side. Both methods each have a clearly recognizable agreement between simulation and measurement. In this case, the remaining deviations can mainly be attributed to a deviation of the simulation model as well as the topography measurements of the dem-onstrator device under test from the real structure. The deviations are typi-cally 400 nm regionally, globally up to a maximum of about 1.4 microns in the edge region, and are primarily due to a non-ideal positioning of the measuring

system with respect to the wavefront. An additive residual error also results from the use of a PSD. For robust mea-surement with higher repeatability of about λ/20 RMS but longer measure-ment time (> 6 seconds at a lateral reso-lution of the specimen of about < 1 mm) it is preferred to use a camera, since a parallel or subsequent analysis via im-age processing algorithms (inter alia also Hough and Radon transform) a highly accurate, sub-pixel precise deter-mination of the local super pixel reflex can be realized. The main disadvantage resides then – depending on the camera and computer used – in the increase of measurement time by a factor of 5 – 10.

Conclusion and outlook

The presented measuring principle for scanning measurement of wavefronts by a digital mirror array (DMD) allows ef-fectively an extension of the measuring range of up to about ± 5 ° with respect to conventional wavefront sensor that has been shown also by simulations, al-though the measurement range shows a strong dependence on the designed op-tical imaging system. Depending on the required wavelength of the used light in the test system and thus depending on the deviation from the theoretical blazed grating condition, the diffraction pat-tern of a sub-aperture of the mirror array and the wavefront on the detector varies.

For robust and flexible evaluation of the wavefront gradient, the use of a camera with image processing is advantageous, which limits the measurement time per sub-aperture especially to the frame rate of the camera (in this case 75 fps). The inno-vative measuring principle enables a full-surface form and function measurement even of sophisticated optical components such as strong aspheric or freeform sur-faces with high lateral resolution in trans-mission and reflection geometry.

The measurement procedure which is currently developed further is improved by the use of optimized hardware com-ponents such as a high-speed camera, a speckle reducing moving diffuse optics (speckle reducer), a highly sensitive posi-tion-sensitive detectors based on photo-transistors with 100 kHz readout speed as well as an alternative telescope and detec-tor optics design. A demonstrator of the measurement system is also shown at the trade fair Optatec in Frankfurt from 20th until 22nd of May at the Fraunhofer booth.

Acknowledgements

This research is funded by the BMBF project “VariScan”. The author gratefully acknowledges the support of the alliance partners Iris Erichsen and Felix Hahne of Trioptics and Mr. Hornauer by Carl Zeiss Vision for providing the samples.

[1] S. Olivier, V. Laude and J.-P. Huignard: Liq-uid crystal Hartmann wave-front scanner, Appl. Opt. 39, 3838 (2000)

[2] J. Liesener, L. Seifert, H. J. Tiziani and W. Osten: Active wavefront sensing and wave-front control with SLMs, Proc. ff SPIE Vol. 5532, 147 (2004)

DOI: 10.1002/opph.201400047

Fig. 5 Determination of a corrected x-y-position of a superpixel reflex mainly based on a subtraction of the dis-placement vector caused by the background diffraction pattern and determined by a previous calibration.

Fig. 6 Angular orientation and angular distribution of the simulated wavefront (left) and the measured wave front (right).

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Author

Stephan Stürwald is leading the group for micro- & nano metrol-ogy at the Fraunhofer IPT since 2010. He specialized on optical technologies mainly for biomedical appli-cations and optical

testing. Stürwald holds a Diploma in phys-ics and a Master in mathematics from the University of Münster and currently finished his works on his second doctoral thesis.

Dr. Stephan Stürwald, Fraunhofer IPT, Steinbachstrasse 17, 52074 Aachen, Germany, Tel.: +49-241-8904-439, E-mail: stephan.stuer-wald@ipt.fraunhofer.de