Fig. 166.—Foucault Test of Parabolic Mirror.
One may thus explore the surface piecemeal and detect not only zones but slight variations in the same zone with great precision. In case of a parabolic mirror as in Fig. 166 the test is made at the focus by aid of the auxiliary plane mirror, and a diagonal as shown, the pinhole and knife edge being arranged quite as before. A very good description of the practical use of the knife edge test may be found in the papers of Dr. Draper and Mr. Ritchey already cited.
It is also applied to refractors, in which case monochromatic light had better be used, and enables the experimenter to detect even the almost infinitesimal markings sometimes left by the polishing tool, to say nothing of slight variations in local figure which are continually lost in the general illumination about the field when one uses the star test in the ordinary manner.
The set-up for the knife edge experiments should be very steady and smooth working to secure precise results, and it therefore is not generally used save in the technique of figuring mirrors, where it is invaluable. With micrometer motions on the knife edge, crosswise and longitudinally, one can make a very exact diagnosis of errors of figure or flexure.
A still more delicate method of examining the perfection of figuring is found in the Hartmann test. (Zeit. fur Instk., 1904, 1909). This is essentially a photographic test, comparing the effect of the individual zones of the objective inside and outside of focus. Not only are the effects of the zones compared but also the effects of different parts of the same zone, so that any lack of symmetry in performance can be at once found and measured.
The Hartmann test is shown diagrammatically in Fig. 167. The objective is set up for observing a natural or artificial star. Just in front of it is placed an opaque screen perforated with holes, as shown in section by Fig. 167, where A is the perforated screen. The diameters of the holes are about 1/20 the diameter of the objective as the test is generally applied, and there are usually four holes 90° apart for each zone. And such holes are not all in one line, but are distributed symmetrically about the screen, care being taken that each zone shall be represented by holes separated radially and also tangentially, corresponding to the pairs of elements in the two astigmatic image surfaces, an arrangement which enables the astigmatism as well as figure to be investigated.
Fig. 167.—The Principle of the Hartmann Test.
The arrangement of holes actually found useful is shown in Hartmann’s original papers, and also in a very important paper by Plaskett (Ap. J. 25 195) which contains the best account in English of Hartmann’s methods and their application. Now each hole in the screen transmits a pencil of light through the objective at the corresponding point, and each pencil comes to a focus and then diverges, the foci being distributed somewhere in the vicinity of what one may regard as the principal focus, B. For instance in Fig. 167 are shown five pairs of apertures a, a′, b, b′, etc., in five different zones. Now if a photographic plate be exposed a few inches inside focus as at C each pencil from an aperture in the screen will be represented by a dot on the photograph, at such distance from the axis and from the corresponding dot on the other side of the axis as the respective inclinations of the pencils of light may determine.
Similarly a plate exposed at approximately equal distance on the other side of the general focus, as at D, will show a pattern of dots due to the distribution of the several rays at a point beyond focus. Now if all the pencils from the several apertures met at a common focus in B, the two patterns on the plates C and D would be exactly alike and for equal distance away from focus of exactly the same size. In general the patterns will not exactly correspond, and the differences measured with the micrometer show just how much any ray in question has departed from meeting at an exact common focus with its fellows.