An innovative and efficient method to control the shape of push-pull membrane deformable mirror

Polo, Alessandro; Haber, Aleksandar; Pereira, S. F.; Verhaegen, Michel; Urbach, H. P.

doi:10.1364/oe.20.027922

Cited by 28 publications

(22 citation statements)

References 23 publications

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“…The theoretical predictions were validated with our experiment, performed using a deformable mirror to induce known aberrations in a spherical lens (0.1 NA) [16]. The wavelength of the experiment was λ 638 nm.…”

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confidence: 69%

Theoretical analysis for best defocus measurement plane for robust phase retrieval

2013

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We study the phase retrieval (PR) technique using through-focus intensity measurements and explain the dependence of PR on the defocus distance. An optimal measurement plane in the out-of-focus region is identified where the intensity distribution on the optical axis drops to the first minimum after focus. Experimental results confirm the theoretical predictions and are in good agreement with an independent phase measurement. © 2013 Optical Society of America OCIS codes: 220.1080, 120.5050, 100.5070.Phase retrieval (PR) concerns all the types of nonlinear algorithms for recovering phase information when only the intensity of a complex field is known [1][2][3]. PR has widely been applied in the last 20 years to determine the phase aberrations in the exit pupil of an optical system. PR methods that use through-focus (PRTF) intensity images show advantages over standard interferometric techniques [4,5], such as low demand on the temporal coherence requirement and system mechanical stability. Nevertheless, one of the main disadvantages of PRTF is the need for several through-focus measurements, which leads to a heavy computation load. With the recent developments in high-performance computing systems and graphic processing units, PRTF has the potential to be used as a real-time phase measuring technique for application where fast phase measurements are needed, such as adaptive optics systems [6,7] or beam-shaping probing. However, when more than one measurement plane is used to retrieve the phase, uncertainties in the relative distance between two adjacent measurement planes are introduced into the system. In order to minimize the contribution of these uncertainties in the measurement results, it would be attractive to perform the PRTF using only one intensity measurement plane, added to some a priori knowledge of the optical system, such as numerical aperture (NA) and finite support of the pupil [8]. Lee et al.[9] introduced a statistical analysis in order to find the optimal defocus distance based on the Cramer-Rao lower bound. In this Letter, we show that in the limit of small aberrations [10] one can derive an analytical model that identifies the optimum measurement plane to achieve accurate PR. Simulations are carried out, and experimental results verify the predictions. The PR algorithm, considered in this Letter, is based on a nonlinear optimization with respect to the Zernike coefficients [11] that describes the phase-only distribution within the exit pupil of an optical system. A detailed description of the algorithm can be found in [6,12,13]. As an example, we show the performance of this algorithm for four different random phase distributions consisting of 36 Zernike coefficients with the total RMS 0.04λ [ Fig. 1(a)] in an optical system with NA 0

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confidence: 69%

Theoretical analysis for best defocus measurement plane for robust phase retrieval

2013

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“…The vector u(k) ∈ R 48 will be called the control input. We identified M using the identification procedure explained in [30,31]. The total wavefront y(k), that is measured by the S-H WFS, is a sum of the wavefronts produced by the two DMs:…”

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confidence: 99%

Predictive control of thermally induced wavefront aberrations

et al. 2013

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Abstract:In this paper we experimentally demonstrate the proof of concept for predictive control of thermally induced wavefront aberrations in optical systems. On the basis of the model of thermally induced wavefront aberrations and using only past wavefront measurements, the proposed adaptive optics controller is able to predict and to compensate the future aberrations. Furthermore, the proposed controller is able to correct wavefront aberrations even when some parameters of the prediction model are unknown. The proposed control strategy can be used in high power optical systems, such as optical lithography machines, where the predictive correction of thermally induced wavefront aberrations is a crucial issue. Baik, "Lens heating impact analysis and controls for critical device layers by computational method," Proc. SPIE 8683, Optical Microlithography

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“…The benefits of the ILC algorithm for correcting wavefront aberrations were first demonstrated in [15]. However, in [15] the ILC algorithm only penalizes the differences between the voltages of two consecutive control iterations.…”

Section: Introductionmentioning

confidence: 99%

“…However, in [15] the ILC algorithm only penalizes the differences between the voltages of two consecutive control iterations. Although this approach enables us to control the convergence rate of the ILC algorithm, in some situations the steady-state voltages can still saturate.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control of a membrane deformable mirror for optimal wavefront correction

et al. 2013

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We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature.

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An innovative and efficient method to control the shape of push-pull membrane deformable mirror

Cited by 28 publications

References 23 publications

Theoretical analysis for best defocus measurement plane for robust phase retrieval

Theoretical analysis for best defocus measurement plane for robust phase retrieval

Predictive control of thermally induced wavefront aberrations

Iterative learning control of a membrane deformable mirror for optimal wavefront correction

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