A New Photometer for Measuring Weak Light Sources.

C. Gehlhoff u. H. Schering, Über ein neues Photometer sehr hoher Empfindlichkeit und einige Anwendungen. Zeitschrift für technische Physik, I, 247, 1920.

All existing visual photometers designed for precise measurements (to 1%) are necessarily associated with obtaining two uniformly illuminated surfaces, to be compared, of more or less considerable area. This is achieved by placing diffusely scattering white surfaces, or ground and milk glass, in the path of the rays from the source. This method, however, is accompanied by a strong weakening of the light perceived by the eye. The lower limit of still measurable illumination is approximately equal to 0.01 lux (one lux is the illumination obtained on 1 sq. cm from a Hefner candle at a distance of 1 meter). In stellar photometers the measurement is reduced to comparing the brightness of two luminous points, and thereby the accuracy of measurement is reduced to 8–10%.

The photometer proposed by Gehlhoff and Schering and now being manufactured by the firm Goerz is based on the following simple principle, which makes it possible to avoid the chief shortcoming of existing instruments mentioned above. If, when viewing a luminous point through a lens, the image of the point is formed in the crystalline lens of the eye, then on the retina there will be produced an image of the lens uniformly illuminated over its whole area. In this way it becomes possible to transform a luminous point into a uniformly illuminated surface without the aid of ground glass or gypsum plates.

This simple observation was used by the authors in their photometer. A possible scheme of such a photometer is shown in the drawing: \(L_1\) is the source whose brightness is being measured, \(L_2\) is a normal light source whose brightness may, as desired, be weakened either by a rotating sector or by means of a pair of nicols, \(W\) is Lummer’s cube, \(O_1\) and \(O_2\) are two auxiliary lenses. The eye \(A\) is placed directly against the diaphragm \(P\), on which the image of both luminous points is obtained. Owing to the presence of Lummer’s cube, the usual picture of two concentric fields, immediately adjoining one another, is obtained on the retina; their brightness can be equalized by changing the brightness of the light falling from the source \(L_2\).

Denoting by \(J\) the intensity of the source \(L_1\), by \(e\) the distance \(O_1L_1\), by \(f\) the focal length of the lens \(O_1\), by \(S\) the focal length of the crystalline lens accommodated on the cube, and by \(k\) the transmittance of the optical parts of the system, it is easy to prove that the illumination \(b\) in the plane of the retina is equal to:

\[ b = k \cdot \frac{J}{(e - f)^2} \cdot \frac{f^2}{S^2} \]

i.e., \(b\) increases very strongly with an increase in the focal length of the lens. In the photometer constructed by the authors, \(f = 30\) cm, and the distance of the diaphragm \(P\) from the cube \(W\) is 25 cm, i.e. equal to the distance of best vision. In the details of construction there are no substantial innovations.

The threshold of visual stimulation at a visual angle greater than \(1^\circ\) is approximately \(1.10^{-5}\) lux. Dividing this value by \(\frac{f^2}{S^2}\), which in the authors’ photometer is equal to 100, we obtain the limiting sensitivity of the instrument, i.e., \(1.10^{-7}\) lux (the brightness corresponding to a star of the sixth magnitude). By increasing the focal distance to 1 meter, one can reach \(4.10^{-9}\) lux (a star of the tenth magnitude).

With the aid of their instrument, the authors measured the absorption of light by air in the lower layers of the atmosphere, and found that in the layers adjacent to the earth, red light is absorbed more strongly than blue light.

The photometer was successfully used to measure the brightness of stars down to the 8th magnitude inclusive. The accuracy of the measurements in all cases proved to be about 1%.

The instrument is very convenient for measuring weak luminescence in various cases.

S. Vavilov.