H. AMAMOU ET AL. 727

0

244:0.1:248 nm,246 nm,

0.3 nm,0.3 nm

DL

thus the parameter .

0.8326a

Our formula is also a very interesting method for easy

calculation of the Voigt function. For the calculation of

the integrals of Equation (2) the trapezoidal rule method

and the adaptive Simpson’s method give very good re-

sults.

Table A1 (Appendix 2) gives the values of the Voigt

function calculated with the Formula (2) for the very

small values of the parameter a where the calculation is

notoriously difficult [12]. This table gives also the com-

putation time(s) for the values of each column of the

table. This calculation time depends obviously on the

performances of the computer. The computer that we

have used has a processor Intel pentium 2.3 GHz and a

memory (RAM) 4 GHz. This table gives the reference

values of the Voigt function calculated from Equation

(2).

Table 1 gives a comparison between our results of

calculation of Voigt function in the in the region of very

small values of the parameter a with those of the various

algorithms of other authors.

3. Conclusion

The new representation integral for Voigt function that

we have demonstrated and used to adjustment “fitting”

of lines spectral in a precedent article is used in this work

for calculation of Voigt function. Thus, this function is

easily calculable. We also made a comparison between

the results obtained by our formula and those obtained by

the various algorithms of other authors in the region of

Table 1. Comparison between our results and the results of

various algorithms of other authors (D is here for 10).

Calculation of Voigt in the region

of very small values of the parameter a

Author u = 5.4 a = 10−10 u = 5.5a = 10−14

Amstrong et al. [13] 12

2.260842D 14

7.307387Da

Humliek [14] 12

2.260842D 16

1.966215Da

Humliek [15] 12

2.260845D 14

7.307387Da

Hui [16] 8

2.667847

9

9.238980Da

Lether and Wenston [17] 12

2.260845D 14

7.307386Da

Mclean et al. [18] 5

4.89872D

5

4.24886Da

Poppe and Wiyers [19] 12

2.260850D 14

7.307805Da

Shippony and Read [1] 12

2.260845D 14

14

7.287724Da

Zaghloul [8] 12

2.260844D 7.287724Da

This Works 12

2.260844D 14

7.307387Da

very small values of the parameter a where the calcula-

tion is notoriously difficult.

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