Interferometric grazing incidence test of rough steep convex aspherics: full 3D reconstruction of the object

A grazing incidence interferometric measurement procedure is applied to test rough convex steep rotationally symmetric aspherics. The measurement of rough surfaces is possible; i.e., without the need to polish the surfaces, due to the large effective wavelength (λ_eff=10µm) of the test. One measurement step using diffractive beam splitters and phase-shifting techniques delivers the surface information along one meridian. The full surface description can be stitched together from several phase results combined with appropriate object rotations. This publication includes, besides the short recapitulation of the measurement principle and experimental setup, a presentation of the simulated and measured data of an aspherical object under test. The data analysis of each meridian is focused on the elimination of the misalignment aberrations caused by specimen displacements. Finally, the stitching of multiple meridian regions to a 3D surface map of the specimen is shown.

Interferometric grazing incidence test of rough steep convex spherics: experimental data analysis

Grazing incidence interferometry has been applied to plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, in a first step towards measuring aspherics, we demonstrate that also rough convex steep rotationally symmetric spherics can be measured along one meridian in a single step using diffractive beam splitters and phase shifting techniques. The measurement of rough surfaces is possible, i.e., without the need to polish the surfaces, due to the large effective wavelength (λ_eff≈10µm) of the test. We include, besides the short recapitulation of the measurement principle and experimental setup, a presentation of the measured data of one small meridian region for the special case of spherical objects under test. The subsequent data analysis combined with suitable simulations focuses on elimination of the misalignment aberrations from the results caused by specimen displacements in the setup.

Interferometric grazing incidence test of rough steep convex spherical and aspherical surfaces: first simulations and experimental proof of principle

In the past, grazing incidence interferometry has been applied for rough plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, we demonstrate that also rough convex steep rotational symmetric spherical or aspherical surfaces can be measured along one meridian in a single step using diffractive beam splitters and phase-shifting techniques. The extension to the whole surface can be attained by successive meridional measurements of the surface under test by azimuthal adjustments. The principle of the method is given and for a spherical ball lens as an extremely curved surface simulated, and experimental data are presented. The features of the interferogram are discussed, and the experimental evaluation of a single meridian including the unwrapped phase data is shown.

Concentric ring metal grating for generating radially polarized light

A subwavelength concentric ring metal grating for visible light (λ=632.8 nm) is designed and fabricated by electron-beam lithography to transform circularly polarized light into radially polarized light. Experimental results are compared to theoretical predictions and the advantages and disadvantages of the element with alternative methods are discussed.

Absolute testing of the reference surface of a Fizeau interferometer through even/odd decompositions

Absolute testing of spherical surfaces is a technological necessity because of increased accuracy requirements. In a Fizeau setup, the main part of the interferometer deviations thereby comes from the reference surface. We demonstrate the validity of an absolute testing procedure for the reference surface that has been proposed earlier. The procedure relies on the decomposition of the surface deviations into odd and even parts and could be used in partially coherent illumination. The odd deviations are obtained from a basic and a 180 degree-rotated position of an auxiliary sphere, and the even deviations can be measured with the help of a cat's eye position in double pass using an opaque half screen in the interferometer aperture.

High numerical aperture imaging with different polarization patterns

The modulation transfer function (MTF) is calculated for imaging with linearly, circularly and radially polarized light as well as for different numerical apertures and aperture shapes. Special detectors are only sensitive to one component of the electric energy density, e.g. the longitudinal component. For certain parameters this has advantages concerning the resolution when comparing to polarization insensitive detectors. It is also shown that in the latter case zeros of the MTF may appear which are purely due to polarization effects and which depend on the aperture angle. Finally some ideas are presented how to use these results for improving the resolution in lithography.

Analysis of the disturbing diffraction orders of computer-generated holograms used for testing optical aspherics

Aspheric surfaces are increasingly used in the design of high-quality optical imaging systems. Therefore accurate testing methods for aspherics are also necessary. One possibility is to use a computer-generated hologram (CGH) as a part of a null lens in an interferometric testing device. However, CGHs normally have more than one diffraction order, thus causing disturbing areas in the interferogram. Here a simple approximative analytical expression is given for the spatial frequencies of the disturbing light in the interferogram coming from the different diffraction orders of the CGH. This expression also enables one to calculate the size and the shape of the disturbing areas in the interferogram. Some design examples for CGHs are given in an application of the expression.

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).

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.

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.

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.

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.

Axicon-type test interferometer for cylindrical surfaces: systematic error assessment

The principle and the alignment aberration functions are described for an axicon-type test interferometer for measuring cylindrical mantle surfaces. Additionally, we show that the derived systematic alignment functions fulfill for reasonably small misalignments the requirements for measurements in the range of approximately 1/100 of a fringe. We verify this with optical path-length calculations, using ray tracing.