Motivation for Dioptrice

After the invention of the telescope in 1608, early telescopic observations provided tantalizing glimpses of the Sun, Moon, and planets. The Sun turned out to have spots, whose origins were often explained in terms analogous to terrestrial features. Likewise, lunar features were named as mountains and seas. For many astronomers, lunar and planetary markings evoked images of distant earth-like worlds.

For these early observers, the quest to observe more details was closely linked to improving the optical performance of their telescopes. Careful analysis of the light-gathering objective and of the magnifying powers of the eyepiece yielded numerous papers, discussions, and telescopic designs.

Two technical issues in particular proved a challenge. Lens-makers were able to make lenses only in a spherical shape, which cannot focus rays at a single focal point; this yields images with fuzziness or extraneous colors. Just as problematic was a law of physics; rays of different colors do not get bent equally. In practice, these two problems can be difficult to distinguish.

These problems are described in most standard physics and astronomy texts, as are their solutions. One of the best-known strategies involved making an objective with a long focal length, minimizing the distortions of the image. Another solution involved using a mirror rather than a lens to gather the light. The more complete solution to the lens problem was solved in the 1750s with the development of the achromatic lens, which involved two (or three) lens components made of different types of glass whose "defects" compensated for each other when lenses were shaped accordingly.

So the standard story proceeds, correct both in outline and in essential details. Our project here is to investigate it more closely by examining pre-achromatic and early achromatic telescopes to test their actual optical performance. Our strategy is to develop an efficient, portable, and relatively inexpensive testing technique that allows us to make a quantitative measure of the optical quality of a refracting telescope and to create images that convey such information. Our eventual goal is to gather optical information on as many pre-achromatic and early achromatic telescopes as possible, enabling a better understanding of the evolution of techniques for crafting telescopes across makers and across the career of individual makers.

Our solution involves determining the color curve of each objective, and obtaining an informative Ronchigram and Focogram. Simply put, the greater the separation between the focal points of different colors, the more spread out the image, the fuzzier the image, the poorer quality of the image. Conversely, the narrower the separation, the better the image, the more detail observable.

The color curve of a telescope objective lens can found by careful measurement of the focal point of specified wavelengths. This is obtained in conjunction with the Foucault knife-edge test, which is typically used to test the quality of telescope mirrors. By moving the knife-edge into the beam of light focused by a lens, say from the right side, one can find the focal length by noting the point at which the image appears to dim from the one side rather than the other. That transition point, sometimes difficult to determine in practice, marks the focal point of the wavelength of light used. With a careful selection of filters to provide a range of wavelengths, a useful color curve can be produced and an evaluation of the optical performance determined. Comparison of curves for different lenses can yield valuable results about their comparative quality, the evolution of the skill of a lens-maker over the course of his career, of different lens-makers across regions and time, and the actual merits of different telescope designs.

Whereas a color curve tells us about chromatic aberration, a Ronchigram provides insights into spherical aberration. A grating with about 20 lines per centimeter is placed between the test lens and the viewer. Simply put, the more distorted the lines appear, the more problematic the curvature of a lens. The Ronchi test provides a quick look at the shape of a lens, and the Ronchigram, a photograph of this test, can even reveal different zones of a lens that can provide clear or distorted images.

The Foucault test with white light also reveals zones of the lens that have different curvatures, revealing these areas as mountains and valleys illuminated in different colors. This set-up can be used also to produce a shadowgram of the lens, revealing bubbles, striations, and other variations in the glass quality itself. This photograph, aside from its illustration of the technical aspects of a lens, also yields a strikingly beautiful image of the lens.