Volltext Seite (XML)
September 18, 1891.] THE PHOTOGRAPHIC NEWS. 657 SPHERICAL ABERRATION. BY T. R. DALLMEYER. It is surprising that this simple subject, confronting one at the very outset of the study of theoretical optics, should still be put forward as a matter of such uncertainty as to necessitate further discussion. When Mr. Burton says (in italics), “ It would be very easy to prove anything I wanted to prove,” argument with him becomes an impossibility, for from his standpoint he must be always right or never wrong. I have looked up Mr. Burton’s former letter (and my reply thereto) and compared it with the present one, and am glad to find that he now understands the corres pondence of distances before or behind the plane of average focus in their true bearing, viz., the reverse of his previous statement. As to the drawing, it looks pretty, but is worthless in its bearing on the subject. That the areas of circles are dependent on the squares of their radii is familiar to a novice in geometry, but what does it matter in a drawing if the boundary lines of equal or unequal areas are represented, so long as they cross the axis at the proper positions in the locus of longitudinal aberration ? The longitudinal aberration increases or diminishes as the square of the diameter of aperture. Mr. Burton misses the mark when he loses sight of this fact, and that, practicatly speaking, there is a definite measurable area of the lens near the axis exhibiting no measurable aberration at all, light from the whole of this area being concentrated at the apex of the axial cone—the area of the base of this cone being determined by the amount of positive spherical aberration in the entire system or lens—in a single point. When this aperture is ex ceeded and aberration is traceable, every measurable area, however small, has a focus nearer and nearer the lens, the further the zone is removed from the base of the axial cone, until the extreme zone of full aperture is reached. The focus of this zone determines the limit of the locus towards the lens, the distance between this and the axial cone determining the locus of longitudinal aberration. In short, when spherical aberration is present, there is a definite measurable aperture free from practically measur able aberration, which we will call the aplanatic cone of rays ; and when this is passed, and the spherical aberration becomes measurable or visible, every infinitely small area of increase of aperture has a focus of its own along the locus of longitudinal aberration. The apex, then, of the axial aplanatic cone is the posi tion of greatest concentration theoretically and practically, and is the best focus, unmistakable to a practised eye, either on contrasted subjects of light on dark grounds, or vice versa. The remaining zones, however small, have no collective focus on the axis, but each a separate one that forms out-of-focus zones around the concentrated focus of the axial aplanatic cone. I hope Mr. Burton will now see the absurdity of placing his focus midway in the locus of longitudinal aberration as ‘ ‘ fair. ” The first of all tests (known to every astronomer) is the observance of a point of light, or a flame, when focussed for; if the structure is still maintained outside the focus with the halo around it, positive spherical aberration is present; and if the reverse, negative. It is the main tenance of structure that is the real test, and this is best visible at the apex of the axial cone corresponding to a central portion only of the lens if aberration is present. Now, a word as to the conclusions to be drawn from Mr. Burton’s observations, that he invites readers to draw for themselves. In the best visual images formed by an accurate observer, there is no difference, theoretically or practically, between the two classes, viz., a dark object on a bright ground, or a bright object on a dark ground. There is one and only one position of focus to show the structure in the best possible degree. What Mr. Burton describes as “personal equation ” in focussing, I should term want of practice in accurate observations. There are two reasons why the practical results are not absolutely identical with the visual, one general, the other particular in their application. The general reason I have already explained in the paper contributed on this subject to the Camera Club Conference. In photography a dark object on a light ground, particu larly in the case noted by Mr. Burton, of “ fairly ample exposures,” the printed results in this case (hastily prepared in collotype) were in certain instancesnot in keeping with the original visual impression; the negative obtained, however, showed the structure, by careful examination, sufficiently clearly to be conclusive as to the best definition. The effect of spherical aberration in the visual appear ance of a dark object—say a disc—on a bright ground is that of a disc dark in the centre, and gradually becoming lighter towards its edges, but still maintaining its structure ; and the effect round the edge in cases of fairly ample exposure might, as it were, be eaten into by the halation effect produced, so as to cause the definiteness of the outline to soften off, appearing, to a casual observer, out of focus. Now, if this disc be removed nearer to or further from the lens, what happens? In the former case the black disc becomes a dark ring with a definite edge in the negative, with a lighter centre 1 In the latter case, a dark centre with the halation asserting itself more and more as it approaches the edge ! It is evident the structure is maintained best at and beyond the best focus. The appearance of the bright point of light on a dark ground is identical, in the true sense of maintenance of structure, under the same conditions. As before stated, this is the optical test used by astronomers. (I notice Mr. Burton has succeeded in proving this latter test for structure to himself.) The second reason for the difference between visual and chemical results I have not mentioned before for obvious reasons. It applies to personal manufacture, and I have not had any encouragement to reply to any previous superficial utterances and letters, except upon premises taken up upon those occasions. Mr. Burton mentions that his experiments were conducted with a lens recently manufactured on the principle of the invention of my late father to produce spherical aberration at will. Has it never struck Mr. Burton that if the lens were actinic when the back combination was in its normal position, free from aberration, that it would not be perfectly so when the back flint was removed from the crown by the process of unscrewing ? It not only introduces posi tive spherical aberration purposely, but also a slight amount of positive chromatic aberration. In the con struction as it stands, and for the amount of positive spherical aberration introduced, this alteration will be hardly noticeable, and very difficult to trace, but the tendency is to favour the definition of objects slightly in front of the plane focussed for. For planes behind this, the inward concentration of rays already referred to continues, tending to maintain structure, but softening off