Norbert Lindlein

Phase-shift extraction for generalized phase-shifting interferometry

A simple algorithm for blind extraction of phase shifts is proposed for generalized phase-shifting interferometry from only three interferograms. Based on the statistical property of the object wave, the algorithm calculates approximately the involved phase shifts as initial values. The extraction is further improved by an iterative method, considering the fact that the closer the phase shifts approach their real values, the more uniform the reconstructed reference wave will become. The feasibility of this algorithm is demonstrated by both simulation and experiment.

Design of a mode converter for efficient light-atom coupling in free space

In this article, we describe how to develop a mode converter that transforms a plane electromagnetic wave into an inward-moving dipole wave. The latter one is intended to bring a single atom or ion from its ground state to an excited state by absorption of a single photon wave packet with near-100% efficiency.

Dynamic range expansion of a Shack–Hartmann sensor by use of a modified unwrapping algorithm

An algorithm for expanding the dynamic range of Shack--Hartmann sensors is proposed. The distribution of the spot dislocations is treated with a modified unwrapping algorithm that is widely used in interferometry. The algorithm unwraps the spot dislocations and assigns the spots to their original subapertures, leading to a huge expansion of the dynamic range. For the proposed algorithm there remains a limitation on the maximum wave-front curvature instead of on the maximum wave-front slope. Examples are given that show spot fields that were wrapped four times; the measured wave front had a peak-to-valley value of 116 lambda .

ABSOLUTE SPHERICITY MEASUREMENT : A COMPARATIVE STUDY OF THE USE OF INTERFEROMETRY AND A SHACK-HARTMANN SENSOR

A comparison of absolute sphericity measurements with a ShackHartmann sensor and a TwymanGreen interferometer is presented. The absolute deviations of a test sphere from its ideal shape were calculated in both cases from the measured wave aberrations of three different positions. Very good qualitative and quantitative agreement of the results was achieved. The difference of the root-mean-square values of the two methods was 1/1000 of a wavelength.

Characterization of microlenses using a phase-shifting shearing interferometer

A shearing interferometer is proposed for the characterization of microlenses. The optical configuration of the test system enables the measurement of the wave aberrations, the focal length, and the deviations of the lens surface from an ideal sphere. In addition, a quantitative evaluation method is given that enables the calculation of the wave aberrations (e.g., the phase function) from the shearing interferometer data.

Algorithm for expanding the dynamic range of a Shack-Hartmann sensor by using a spatial light modulator array

Normally, the dynamic range of a Shack-Hartmann sensor is limited by the foci leaving their respective subapertures, thus a definite attachment of the foci to their subapertures is difficult. By using an array of spatial light modulators in front of the microlenses of the sensor to switch on and off the subapertures, a definite assignment of the spots to their subapertures is possible. We present a coding algorithm that needs only log2N+1 frames to assign N spots unequivocal to their subapertures.

Simulation of micro-optical systems including microlens arrays

The simulation of micro-optical systems, especially those including microlens arrays, is still a challenging task. There are of course traditional methods which can be applied under certain circumstances. This paper will discuss several geometrical optical and diffraction-based methods for the simulation of micro-optical systems. A simple paraxial geometrical optical matrix theory will be extended to the simulation of off-axis optical elements. Ray tracing will be used to model incoherent micro-optical systems. The propagation of Gaussian beams through off-axis optical systems using differential ray tracing will be discussed. The angular spectrum of plane waves will be used to propagate a scalar complex wave amplitude in free space simulating non-paraxial diffraction effects. Finally, a model will be proposed which combines ray tracing and wave propagation methods by converting a complex wave amplitude into rays and vice versa. In the case of wavefront warping a decomposition of the wave into elementary waves has to be performed. This combined model can take into account non-paraxial effects such as aberrations of optical elements and also diffraction effects.

Misalignment effects of the Shack–Hartmann sensor

The Shack-Hartmann sensor uses a microlens array and a CCD camera for wave-front measurements. To obtain wave-front measurements with high accuracy, an accurate relative alignment of both is essential. The different states of misalignment of the Shack-Hartmann sensor are divided into groups and are treated theoretically and experimentally. Their effect on the accuracy of wave-front measurements is evaluated. In addition, a practical method for proper alignment of the Shack-Hartmann sensor is proposed.

Wave-front reconstruction with a Shack–Hartmann sensor with an iterative spline fitting method

One limitation of the conventional Shack-Hartmann sensor is that the spots of each microlens have to remain in their respective subapertures. We present an algorithm that assigns the spots to their reference points unequivocally even if they are situated far outside their subaperture. For this assignment a spline function is extrapolated in successive steps of the iterative algorithm. The proposed method works in a single-shot technique and does not need any aid from mechanical devices. The reconstruction of a simulated steep aspherical wave front (approximately 100 lambda/mm slope) is described as well as experimental results of the measurement of a spherical wave front with a huge peak-to-valley value (approximately 400 lambda). The performance of the method is compared with the unwrapping method, which has been published before.

Confocal microscopy with a refractive microlens–pinhole array

The stable setup of a confocal arrangement consisting of a combination of a refractive microlens and a pinhole array is presented. The focal plane of the microlenses lies at the rear surface of the substrate in the pinhole plane. By using a microscope objective one can image the stop array onto the object at a reduced size. Surface profiles of refractive and diffractive optical elements were measured with the help of this confocal microscope.