Simultaneous distance, slope, curvature, and shape measurement with a multipurpose interferometer

Abstract

The use of interferometers is usually divided into two areas. One of them is that of single-dimensional length measurement where the distance along an optical axis is measured, often with more than one wavelength for absolute distance determination. Here one "beam" is considered. The other area is interferometric surface or wavefront measurement where the laterally varying phase distribution of a largely extended wavefront is the property of interest. In this presentation a combination of the two types of use which opens up quite new and challenging applications will be presented.One of the applications which requires simultaneous measurement of distance, slope and curvature is high-accuracy form measurement of aspheres and free form surfaces by the Large Area Curvature Scanning (LACS) method. For a high-accuracy LACS set-up it is most important to measure (and control) the absolute distance between the interferometer and the surface under test (including the multiples of the half wavelength), as well as the slope of the wavefront. In the present set-up, a commercial general purpose interferometer is used.The simultaneous measurement of distance, slope, curvature and shape with this instrument is presented. Special emphasis is laid on the specific fringe evaluation method adapted to the determination of these quantities. It uses a model of the real interferogram image and the superimposed disturbing effects. A suitable global optimization method allows the desired quantities to be determined rapidly and reliably.For the future use of LACS, a new, specifically designed multi-purpose interferometer is introduced which can be used in LACS systems with nanometer form measurement accuracy.

Uncertainty of topography determination based on slope difference or curvature measuring systems in laboratory and industrial environments

“…To measure the distance, a multiple wavelength absolute distance measurement is performed for the center of the interferogram. For details, see [11][12][13][14][15][16][17][18]. The uncertainty analysis [13] yields a value in the range of 1 nm.…”

“…steep aspheres, measurable. For detailed information on the measuring method, see [11][12][13][14][15][16][17][18]. Using a small interferometer as curvature sensor has a very important advantage: the principle of transparent measurement [11] can be realized.…”

“…The uncertainty analysis [13] yields a value in the range of 1 nm. The measurement time is long due to the time consuming control loops for tilt and distance, the interferogram evaluation [ 14,18] and the averaging-out of the measurement noise. The topographies of several scans are typically averaged, leading to measurement times of hours for one surface section.…”

“…The measurement of the angle difference between two surface points [1][2][3][4][5][6][7][8][9][10] or the curvature of the surface at a surface point [11][12][13][14][15][16][17][18] generates a signal which is independent of such error influences. These two methods are analyzed in the following with respect to their limits under laboratory conditions.…”

“…In the last few years, two methods of topography determination have been developed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] whose focus is on the measurement of the form of a surface with a very low uncertainty. They are based on the measurement of intrinsic properties of the surface to make long measurement times possible.…”