特集 第7回光源の科学と技術に関する国際会議



専務取締役主席研究員 平本立躬



Tatsumi Hiramoto
Ushio Inc.,1194 Sazuchi,Bessho-cho Himeji city,Japan


Discharge Lamps have recently been used as a light source in an optical instrument in the wavelength region of UV-B, -C and VUV.It is required that the half-width of a spectral line used is extremely narrow, because of difficulty in designing fully achromatic optical system in this range of wavelength.However, its intensity is required to keep a short exposure time or a large exposure area.

In this report,physical properties of such high-radiance lamps are deduced and some lamps are shown as an example.

2.Physical properties of high-radiance lamps.

From the equation of radiative transfer in LTE, the spectral radiance Lλ and radiance LT on the surface of a lamp in the normal direction are respectively expressed as Eqs.(1)and(2),

wher λ, R, r, Bλ, Kλ denote wavelength, the lamp radius, the distance from the lamp axis,Planck function and the absorption coefficient being expressed as,

where λ0, f, nι are the unshifted center wavelength of the line, the oscillator strength and the density of absorbing species respectively. The normalized line profile function is denoted as P(Δλ).

The physical image of Eq.(1)can be describted as follows:radiation emitted at r reaches the lamp surface with absorption of the factor of exp(-∫RrKλdr’) on the way.Physical properties of high-radiance lamps are deduced as follows: in general, the spectral line used shoul have a large f, and should be very high in the arc and steeply decreases with reduction in the temperature in the periphery.High-arc temperatures are required. Moreover, it is better that a buffer gas has a large polarizability and a low ionization energy.

In the case of a line with a limited half-width, or kλ0 should be kept to be an optimum value,and a steep-temperature distribution is required.For the buffer gas a small polarizability and a high ionization energy are required.

3.Examples of high-radiance lamps

  • (1)Lamps emitting a line with a large probability of the transition of which lower level is highly excited.E.g., high-pressure or super high-pressure mercury lamps emitting the 436,365nm lines
  • (2)High-current Lamps.filled with species of high vapor pressure and low ionization energy,which emit resonance lines of ions1).E.g., Cd+ lamps operated with high currents,which emit the 214.4nm line.
  • (3)Lamps emitting strong atomic lines within the arc and almost all the atoms are in the form of an allotropic molecular gas in the periphery of the arc.E.g., lamps containing S emitting the 181nm line

In the above three types of lamps, self-controled distributions of the density of absorbing species are established inside the lamps.

4.Numerical example

Calculated spectral radiances of the resonance line of Cd+ (214.4nm)from a short-arc lamp as well as from long-arc lamps are shown in Fig.1.Both of a parabolic distribution and a constant distribution were assumed for the temperature inside the lamps.The distribution measured by H.Burck et al.2)was used for a short-arc lamp.This calculation has been done using the quasi-static approximation of line broadening.The ratio of LT of the long-arc lamp with the parabolic distribution to that of the lamp with the constant temperature is 0.258.which is as large as twice compared with that of NaD lines of HPS lamps filled with Xe gas.The high ratio due to less self-absorption is shown.According to the reference1) the resonance radiation at 228.8nm of Cd atom in the short-arc lamp is not observed except in the far wing.This is a piece of evidence of high radience of ionic resonance lines from the lamps.


It is concluded that even if the spectral width is limited to be very narrow, the spectral line with a large oscillator strength can be of high radiance under the following condition: the lamp is operated at high electrical power densities and one chooses the absorbing Species of which density varies with strongly depending upon the temperature.

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