Abstract

The work described in the foregoing paper made the development of a quantitative method of surveying surfaces necessary, that could be used for local measurements and on nonsymmetric surfaces. The theory of the method and the experimental technique are described. The accuracy of the survey is better than 1/20 wave-length with visual subjective observation and could be carried up to 1/100 wave-length with objective photographic measurements. The errors of the Foucault knife-edge test, especially the one produced by parallax, are discussed. Ways of reducing or eliminating them are described.

© 1936 Optical Society of America

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Figures (7)

F. 1
F. 1

(a). Scheme of knife-edge arrangement. (b) Steepness diagram. (c) Contour curve.

F. 2
F. 2

Contour curves of the same mirror measured independently with the knife-edge moving in opposite directions.

F. 3
F. 3

Underdone parabolic mirror measured at the center of curvature and at the parabolic focus. The difference between the two curves should be equal to the theoretical contour observed at the center of curvature.

F. 4
F. 4

Theoretical curves of a parabolic mirror measured at the center of curvature.

F. 5
F. 5

Parallax when testing with a flat mirror.

F. 6
F. 6

Two focographs of the same mirror taken with and (nearly) without parallax, (a) Knife-edge displaced parallel to the parallax vector, (b) Knife-edge displaced perpendicular to the parallax vector. Notice that in the first case the surface appears more asymmetric and smoother than in the second.

F. 7
F. 7

Measuring a parabolic mirror at the focus with the help of a perforated flat without parallax. P, half-transparent thin glass plate at 45° with the optical axis. D, drum for measuring the transversal displacements of knife-edge and source of light. S, scale in contact with the surface to be surveyed. (Sketch by Russel W. Porter.)

Equations (3)

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d ( Δ X ) / d Y = Y ( Y 0 2 2 Y 2 ) / 4 R 3 .
δ X = Y 2 2 R · δ R R = Q Y 2
d ( Δ X ) / d Y = Y ( Y 0 2 2 Y 2 ) / 4 R 3 + Q Y