HETEROCHROMATIC PHOTOMETRY WITHOUT BEAM SPLITTING

In relative photometric measurements, as a rule, the intensities of two light beams are compared, either entering two parallel optical systems (fields, comparison, differential schemes), or successively replacing one another in one and the same measuring apparatus. In heterochromatic photometry, however, the problem often arises of relative photometric measurements for two different spectral regions of one and the same radiation. Usually it is solved by artificially splitting the light beam into two parts, isolating in each of them the corresponding spectral region, and then photometrically comparing these prepared beams. The authors of the note under review*) describe another method, which makes it possible to dispense with splitting the light beam, something that in a number of cases is very significant.

Although this method was developed and tested only for measuring the relative intensity of two spectral lines (sodium and lithium) in flame radiation, the principle on which it is based may be of broader interest. The essence of the method is as follows. The light beam under investigation is first subjected to filtration—

) E. G. Walsh and H. S. Wolff, Nature 167*, 683 (1951).

tion, the purpose of which is to isolate the two spectral regions of interest (in the present case, the regions near 5900 and 6700 Å). It then passes through a colored photometric wedge (a wedge-shaped cuvette with an aqueous solution of chromium alum) and a rotating light filter. The latter is a circular disk made up of two semicircles of gelatin light filters with different transmission spectra, making 9 revolutions per second. Behind the rotating light filter there is a photocell, the current of which, after amplification at the corresponding frequency, is fed to the measuring device.

By shifting the colored wedge, the amplified photocurrent can be made to go to zero. This occurs when the mutual change of the two light filters forming the rotating filter leaves the total actinic effect of both radiation components unchanged.

Denoting by \(I_i\) the intensity of the radiation of wavelength \(\lambda_i\) (after preliminary filtration), by \(T_i\) the transmittance of the colored wedge, by \(a_i\) and \(b_i\) the transmittances of the two halves of the rotating light filter, and by \(p_i\) the sensitivity of the photocell, we obtain the condition for constancy of the total actinic effect of the radiation in the form:

\[ \sum_{i=1,2} I_i T_i a_i p_i = \sum_{i=1,2} I_i T_i b_i p_i, \]

whence

\[ \frac{I_1}{I_2} = \frac{T_2}{T_1}\frac{p_2}{p_1}\frac{b_2-a_2}{a_1-b_1} = \frac{T_2}{T_1}q, \]

where

\[ q=\frac{p_2}{p_1}\frac{b_2-a_2}{a_1-b_1} \]

is a constant for the given apparatus and the given values of \(\lambda_1\) and \(\lambda_2\).

Introducing the optical density of the wedge \(D_i=\lg \frac{1}{T_i}\) and taking into account that \(D_i\) is a linear function of the wedge thickness (and hence of its displacement \(R\)), while the ratio \(\frac{D_1}{D_2}\) depends only on the material from which the colored wedge is made, we finally obtain

\[ \lg \frac{I_1}{I_2}=sR+t, \]

where \(s\) and \(t\) are instrumental constants whose determination presents no difficulty.

Thus, the measurement of relative intensity is reduced to finding the position of the wedge at which the amplified photocurrent goes to zero. Owing to this, the method described possesses all the advantages of a null method—independence from the characteristics of the amplifier and fluctuations in them, the possibility of measurement at low intensities (with high amplification), etc. In addition, there is no need for light filters that isolate only the radiation of a given wavelength and completely eliminate radiation of another wavelength—the latter, as is known, is far from always feasible and is usually associated with very large losses of light. Finally, the fact that one and the same wedge and one and the same rotating light filter can be used for heterochromatic photometry over a wide range of wavelengths is also essential. It is also very significant that the measurement is carried out for both components simultaneously with the aid of one and the same photocathode.

G. R.