Focusing characteristics of a 4 pi parabolic mirror light-matter interface

Lucas Alber, Martin Fischer, Marianne Bader, Klaus Mantel, Markus Sondermann, Gerd Leuchs

Background: Focusing with a 4 pi parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality. Methods: To determine these errors, we experimentally examine the focusing properties of a 4p parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single Yb-174(+) ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. Results: We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Conclusion: Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4p parabolic mirror.

Reduction of phase singularities in a speckle Michelson setup

K. Mantel, V. Nercissian

Speckle interferometry is an optical metrology technique for characterizing rough surfaces. In one application, the deformation of a specimen under a load may be determined by comparing measurements before and after the load is applied. Owing to the surface roughness, however, the results are impaired by phase singularities, leading to a strong noise in the measurement results. Usually, filtering and smoothing operations are performed to reduce the noise. However, these procedures also affect the underlying systematic phase and are therefore disadvantageous. Instead, we examine incoherent averaging, a physical procedure, to reduce the number of phase singularities in the first place. We tailor the spatial coherence of the light using extended light sources of continuous or multipoint shape, achieving smoother phase distributions. The mechanism behind the reduction process involves subtle effects like enhancing phase singularity correlations in the fields before and after the deformation takes place.

Polarization and phase shifting interferometry

Sergej Rothau, Klaus Mantel, Norbert Lindlein

This publication presents a novel interferometric method for the simultaneous measurement of the phase and state of polarization of a light wave with arbitrary, in particular locally varying elliptical polarization. The measurement strategy is based on variations of the reference wave concerning phase and polarization and processing the interference patterns so obtained. With this method, that is very similar to the classical phase shifting interferometry, a complete analysis of spatially variant states of polarization and their phase fronts can be done in one measurement cycle. Furthermore, a direct analysis of specimens under test regarding birefringence and the impact on the phase of the incoming light can be realized. The theoretical description of the investigated methods and their experimental implementation are presented.

Polarization and phase-shifting interferometry for arbitrary, locally varying polarization states

Sergej Rothau, Christine Kellermann, Simon Mayer, Klaus Mantel, Norbert Lindlein

This publication presents what we believe is a novel interferometric method for the simultaneous measurement of the phase and state of polarization of a light wave with arbitrary polarization; in particular, it can be varying elliptical. The measurement strategy is based on variations of the reference wave, concerning phase and polarization and processing the interference patterns so obtained. With this method, which is very similar to classical phase-shifting interferometry, the general analysis of spatially variant states of polarization and their phase fronts can be done in one measurement cycle. Furthermore, the analysis of different optical elements regarding the impact on the polarization and phase of the incoming light can be realized. After the theoretical description of the method and the mathematical discussion of different algorithms, the realized measurement setup is presented. Afterward, the accuracy of the method is discussed.(C) 2017 Optical Society of America

Phase retrieval from carrier frequency interferograms: reduction of the impact of space-variant disturbances

J. Schwider, V. Nercissian, K. Mantel

Phase "extraction" by using temporal phase shifting is sensitive to vibrations and drifts, producing systematic phase errors periodic with twice the fringe frequency. This error source may be avoided by evaluating only single carrier frequency interferograms, which makes the procedure immune against vibrations and drifts provided that the integration time is short enough to freeze the fringe pattern. However, the phases extracted from single interferograms in this way often show local irregularities depending on the mean phase of the interference pattern. Such local phase irregularities are caused by local disturbances in the light path like specks and dust particles on the optical components of the interferometer. Moreover, since digitized data are gathered, there is a nonlinear processing step involved which is also responsible for the generation of such irregularities. Here, it is proposed to use a set of suitably combined phase-ramped interferograms to reduce phase dependent irregularities. The proposed averaging technique also reduces edge ringing effects known from Fourier evaluation procedures. Since the imaging optics also contributes to the phase to be measured when tilted wavefronts are used, calibration is mandatory. The calibrated state is only valid if strict rules considering fringe number per diameter as well as the position of the wedge in the interferometer are maintained in the measuring process.

Reduction of phase singularities in speckle-shearing interferometry by incoherent averaging of speckle patterns

K. Mantel, Vanusch Nercissian, N. Lindlein

Speckle interferometry is a well established technique for the optical characterization of rough objects, with the quantification of deformations as one particular application of interest. Owing to its common path property, a speckle-shearing interferometer is often the natural choice as a setup. Like other speckle techniques, however, speckle-shearing interferometry suffers from the existence of phase singularities present in the speckle patterns. Phase singularities introduce ambiguities into the phase unwrapping process and make this evaluation step highly sophisticated. In this work, we attempt to reduce the number of phase singularities by physical means, i. e. by applying an incoherent averaging of multiple, mutually independent speckle intensities. The effect of the incoherent averaging on the number of phase singularities has been investigated theoretically, by computer simulations, and experimentally To obtain high contrast fringes in connection with a shearing setup, which would not be the case for a simple extended light source, a periodically structured light source with a period matched to the shear distance is applied. It turns out that the number of phase singularities may indeed be reduced, but only to a certain extent.

Incoherent averaging of phase singularities in speckle-shearing interferometry

Klaus Mantel, Vanusch Nercissian, Norbert Lindlein

Interferometric speckle techniques are plagued by the omnipresence of phase singularities, impairing the phase unwrapping process. To reduce the number of phase singularities by physical means, an incoherent averaging of multiple speckle fields may be applied. It turns out, however, that the results may strongly deviate from the expected root N behavior. Using speckle-shearing interferometry as an example, we investigate the mechanism behind the reduction of phase singularities, both by calculations and by computer simulations. Key to an understanding of the reduction mechanism during incoherent averaging is the representation of the physical averaging process in terms of certain vector fields associated with each speckle field. (C) 2014 Optical Society of America

Simultaneous measurement of phase and local orientation of linearly polarized light: implementation and measurement results

Sergej Rothau, Christine Kellermann, Vanusch Nercissian, Andreas Berger, Klaus Mantel, Norbert Lindlein

Optical components manipulating both polarization and phase of wave fields find many applications in today's optical systems. With modern lithography methods it is possible to fabricate optical elements with nanostructured surfaces from different materials capable of generating spatially varying, locally linearly polarized-light distributions, tailored to the application in question. Since such elements in general also affect the phase of the light field, the characterization of the function of such elements consists in measuring the phase and the polarization of the generated light, preferably at the same time. Here, we will present first results of an interferometric approach for a simultaneous and spatially resolved measurement of both phase and polarization, as long as the local polarization at any point is linear (e.g., for radially or azimuthally polarized light). (C) 2014 Optical Society of America

Interferometric homogeneity test using adaptive frequency comb illumination

Klaus Mantel, Johannes Schwider

The homogeneity test of glass plates in a Fizeau interferometer requires the measurement of the glass sample in reflected as well as in transmitted light. For the measurement in transmitted light, the sample has to be inserted into the ray path of a Fizeau or Twyman-Green interferometer, which leads to a nested cavity setup. To separate the interference signals from the different cavities, we illuminate a Fizeau interferometer with an adaptive frequency comb. In this way, rigid glass plates can be measured, and linear variations in the homogeneity can also be detected. The adaptive frequency comb is provided by a variable Fabry-Perot filter under broadband illumination from a superluminescence diode. Compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher. (C) 2013 Optical Society of America

Generation of a wave packet tailored to efficient free space excitation of a single atom

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, G. Leuchs

We demonstrate the generation of an optical dipole wave suitable for the process of efficiently coupling single quanta of light and matter in free space. We employ a parabolic mirror for the conversion of a transverse beam mode to a focused dipole wave and show the required spatial and temporal shaping of the mode incident onto the mirror. The results include a proof of principle correction of the parabolic mirror's aberrations. For the application of exciting an atom with a single photon pulse, we demonstrate the creation of a suitable temporal pulse envelope. We infer coupling strengths of 89% and success probabilities of up to 87% for the application of exciting a single atom for the current experimental parameters.

Evaluation algorithms for multistep measurement of spatially varying linear polarization and phase

Andreas Berger, Vanusch Nercissian, Klaus Mantel, Irina Harder

Optical components manipulating both polarization and phase of wave fields find more and more applications in today's optical systems. In particular, the polarization orientation may vary across the aperture. New measurement techniques and evaluation algorithms are needed to simultaneously characterize the properties of such elements. In this Letter, a general measurement algorithm for locally linear polarization distributions is presented, extending the methods of phase shifting interferometry to the simultaneous determination of polarization and phase. A class of evaluation algorithms is derived, and some example algorithms are described and tested for their resilience against systematic and stochastic stepping errors. (C) 2012 Optical Society of America

Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light

Vanusch Nercissian, Irina Harder, Klaus Mantel, Andreas Berger, Gerd Leuchs, Norbert Lindlein, Johannes Schwider

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution. (c) 2011 Optical Society of America

Perfect imaging of hypersurfaces via transformation optics

Klaus Mantel, Dustin Bachstein, Ulf Peschel

Conventional optical imaging systems suffer from the presence of many imperfections, such as spherical aberrations, astigmatism, or coma. If the imaging system is corrected for spherical aberrations and fulfills the Abbe sine condition, perfect imaging is guaranteed between two parallel planes but only in a small neighborhood of the optical axis. It is therefore worth asking for optical systems that would allow for perfect imaging between arbitrary smooth surfaces without restrictions in shape or extension. In this Letter, we describe the application of transformation optics to design refractive index distributions that allow perfect, aberration-free imaging for various imaging configurations in R(n). A special case is the imaging between two extended parallel lines in R(2), which leads to the well-known hyperbolic secant index distribution that is used for the fabrication of gradient index lenses. (C) 2011 Optical Society of America

Adaptive frequency comb illumination for interferometry in the case of nested two-beam cavities

Irina Harder, Gerd Leuchs, Klaus Mantel, Johannes Schwider

The homogeneity test of glass plates in a Fizeau interferometer is hampered by the superposition of multiple interference signals coming from the surfaces of the glass plate as well as the empty Fizeau cavity. To evaluate interferograms resulting from such nested cavities, various approaches such as the use of broadband light sources have been applied. In this paper, we propose an adaptive frequency comb interferometer to accomplish the cavity selection. An adjustable Fabry-Perot resonator is used to generate a variable frequency comb that can be matched to the length of the desired cavity. Owing to its flexibility, the number of measurements needed for the homogeneity test can be reduced to four. Furthermore, compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher if a Fabry-Perot filter is applied. (C) 2011 Optical Society of America

Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy

Peng Gao, Irina Harder, Vanusch Nercissian, Klaus Mantel, Baoli Yao

A new common-path and in-line point-diffraction interferometer for quantitative phase microscopy is proposed. The interferometer is constructed by introducing a grating pair into the point-diffraction interferometer, thus forming a common-path and in-line configuration for object and reference waves. Achromatic phase shifting is implemented by linearly moving one of the two gratings in its grating vector direction. The feasibility of the proposed configuration is demonstrated by theoretical analysis and experiments. (C) 2010 Optical Society of America

Interferometric quasi-absolute tests for aspherics using a radial shear position

Klaus Mantel, Eduard Geist, Irina Harder, Norbert Lindlein, Gerd Leuchs

Increasing accuracy requirements in aspheric metrology make the development of absolute testing procedures for aspheric surfaces important. One strategy is transferring the standard practice three-position test for spheres to aspherics. The three-position test, however, involves a cat's eye position and therefore has certain drawbacks. We propose an absolute testing method for rotationally symmetric aspherics where the cat's eye position is replaced with a radially sheared position. Together with rotational movements of the specimen, the surface deviations can be obtained in an absolute manner. To demonstrate the validity of the procedure, we present a measurement result for a sphere and compare it with a result obtained by the standard three-position test. (C) 2009 Optical Society of America