Johannes Pfund

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.

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.

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.

Nonnull testing of rotationally symmetric aspheres: a systematic error assessment

An optical setup for the testing of rotationally symmetric aspheres without a null optic is proposed. The optical setup is able to transfer the strongly curved wave fronts that stem from the reflection of a spherical testing wave front at a rotationally symmetric asphere. By simulation it is proved that the algorithms of the Shack-Hartmann sensor that is used can cope with the steep wave-front slopes (approximately 110lambda/mm) in the detection plane. The systematic errors of the testing configuration are analyzed and separated. For all types of error, functionals are derived whose significance is proved by simulation. The maximum residual errors in the simulations are fewer than lambda/500 (peak to valley).

Expansion of the dynamic range of a Shack-Hartmann sensor by using astigmatic microlenses

The dynamic range of a Shack-Hartmann sensor is normally limited by the fact that the foci can leave their subapertures and so a definite attachment of the foci to their subapertures is difficult. One method for solving this problem is to give the focal spots a kind of label to identify them even if they leave their subaperture. We describe how the dynamic range of a Shack-Hartmann sensor can be expanded by using lenses with well-defined astigmatism. We also derive a relation between the spot displacements and the partial derivatives of the wavefront for large wavefront slopes.

Calibration of a Shack–Hartmann sensor for absolute measurements of wavefronts

We demonstrate a method with which to calibrate a Shack-Hartmann sensor for absolute wavefront measurement of collimated laser beams. Nearly perfect spherical wavefronts originating from a single-mode fiber were used as references. After the calibration, the uncertainty of the wavefront was less than lambda/100 peak to valley across a diameter of 6 mm. For example, this method allowed us to balance aberrations and prepare collimated beams with wavefronts that are plane to lambda/500 across 1 mm.

Absolute Sphericity Measurement: a Comparative Study on the Use of Interferometry and a Shack-Hartmann Sensor

The uranium samples used had been previously analysed using traditional chemical dissolution and atomic absorption spectroscopy techniques. The values found for the aluminium and iron concentrations were used as the calibration standards. These standard concentrations, when planed against the observed specual line intensity ratio of aluminium:wanium and iron:uraniwn, yielded linear relationships with best fits o f f = 0.99 in both cases. Ihe error bars shown are the 95% confidence limits for both measurement methods. The precisiodlimit of detection for both iron and aluminium w-ere found to be 9ppm142ppm and 63pymi270ppm. respectively.

Laser beam characterization by using a Shack-Hartmann sensor

Summary form only given. With the Shack-Hartmann sensor (SHS) an optical wave-front is measured by sampling it with a microlens array. The lateral spot positions produced by each microlens are detected by a CCD-camera and are interpreted as a two-dimensional derivative field of the wave-front. By LSQ-fitting to the discrete derivative fields the wave-front can be reconstructed. Our SHS utilizes a refractive microlens array with a pitch of P-0.15 mm and a focal length of f-4.5 mm. A special algorithm for the attachment of the spots to their reference points allows for the measurement of strong spherical and non-spherical wave-front aberrations. The measured wave-front has an radius of curvature of about R=30 mm the peak-to-valley value of the shown field is about 130/spl lambda/. In many industrial applications the diagnostic of laser beams is very important. The parameter K, the so-called beam propagation factor gives a measure for the cleanness of a given laser beam in the sense of a perfect Gaussian TEM/sub 00/ mode. With the SHS the determination of this parameter is possible if, in addition to the phase reconstruction, the intensity distribution of the beam, i.e., the intensity of the spots is evaluated.