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Technical Objectives
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- General Aspects
- Measurement of the topography of flat and slightly unflat surfaces
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General Aspects
The problem of topometric absolute measurement of surfaces is not satisfactorily solved. Techniques such as interferometry, wavefront sensorics or triangulation measure relative to a "known" reference surface. These methods of measurement are thus limited by the accuracy of the reference. The quality of complex optical systems decisively depends on the agreement between the individual optical surfaces and the desired shape. While spherical surfaces today can be fabricated and measured with accuracies of up to a few nanometres, the fabrication of other surfaces is limited by the measuring technology available. Here, interferometry up to now has furnished only relative but no absolute results. Precise surface manufacturing requires precise measuring techniques. This means deviations of artefacts from the desired shape in orders of nanometres. The test piece dimensions may cover diameters of up to a few hundred millimetres, and the surfaces may have the shape of flat and slightly unflat surfaces. The geometry of the test pieces, their mechanical holder, the influence of gravitation, and temperature influences may have an effect on the surface shape. It must be guaranteed that a sufficiently high reproducibility allows the required measurement uncertainty to be achieved and that subsequent use of the test pieces with the required specification will be possible at all. The answer to the question to which reference the measurement is traced back is decisive for the measurement accuracy which the method can claim to achieve. Examples are solid references, mathematically ideal virtual references, scanning techniques, and, in particular, procedures without reference, such as difference methods.Measurement of the topography of flat and slightly unflat surfaces
The measurement of flat and slightly unflat surfaces with an uncertainty of some nanometres for the topography poses considerable problems. In the following measuring procedures are discussed which are counted among those eligible for such a measuring technology. Table 1 shows the measurands to be measured and, furthermore, the base quantities for the traceability as well as problems and advantages are stated. In interferometry high measurement range can be mastered only with a reference, i.e. a suitable prototype. This prototype is also the reference required for interferometry, probably a plane. For coordinate measuring machines, several plane references are needed for the measurement of which measuring means with the necessary accuracy are not available either. Further decisive errors are the Abbe error for the scanning of the test specimen and support on the reference, and particularly a whole-body movement of the test specimen with respect to the measuring facility or by deformation of the measuring facility itself, for example due to temperature influences. Whole-body movement and the deformation of the measuring facility are other decisive influences for high-accuracy measurements.| Measuring | Method | Reduction of measurement range by: | Traced back to | Problems | Advantages |
| Topography | Interferometer | matched reference | Length | Reference available, mathematical permutation possible | 2 D, fast |
| Topography | CMM, length measurement | not necessary | Length | References, Abbe error, whole body movement | Nearly unlimited measurement range |
| Slope | ACT, angle measurement | first derivative | Angle | Strong curvature, whole body movement | Very high reproducibility |
| Curvature | Various | matched adjustment and second derivative | Various | Scaling factor | High reproducibility |
| Slope difference | ACT, angle measurement | matched adjustment and matched shears and first derivative | Angle, length | Very strong curvature | Very high reproducibility |
Methods for measuring flat and slightly unflat surfaces.
For angle measuring procedures, a very high reproducibility and a reduction of the measurement range by the first derivation can be observed. For procedures of direct curvature measurement, different possibilities of measuring the local curvature are imaginable. The measurement range is reduced by the second derivation of the topography but it is also decisively lessened by the possibility of placing the surface element whose curvature is to be measured vertical to the measuring facility in any location of the test specimen. This is possible for the measurement of curvature because curvature of the test specimen is a quantity which is independent of the local and angular position of the test specimen. A further procedure will be discussed, namely the measurement of angles (slopes) and of angle (slope) differences with large shears. In the latter case the measurement range is decisively reduced by the possibility of placing test specimen and measuring facility vertical to each other because the local and the angular positions of the test specimen are not of importance in the measurement of angle differences. At the same time, the selection of the shear allows the measured angle differences to be adapted to the necessary measurement range so that large measuring signals are obtained compared with the small measuring signals in direct curvature measurements. These procedures have the advantage not only of large measuring signals but also of very high reproducibilities. Furthermore, whole-body movements and deformations of the facility have no influence unless they occur during the very short time the difference measurement takes. Moreover, the difference measurement and thus the error separation can serve to eliminate the residual first and second-order error influences of the facility. In summary it may be said that this technique combines the following properties: very high reproducibility, adapted reduction of the measurement range, no influence of whole-body movements of the test specimen, no influence of deformations of the facility, elimination of errors of the facility by error separation. In conclusion, techniques for measuring slopes and slope differences are most favourable and will be discussed, proposed and followed in this project.