Geodesic
On identification of optical parameters of a~plane slab
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 4, pp. 309-316.

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A new method for the identification of the phase function and optical thickness of a homogeneous plane slab by using the data of measurement of angular distribution of the intensity of transmitted radiation is proposed. The equation of radiation transport is regarded as an evolution equation that specifies a semigroup of the operator. The generating operator of this semigroup is restored by using the transmission operator obtained from measurements. This operator contains the entire information about the optical parameters of the slab. The desired optical parameters can be found by calculating the generating operator. 
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V. S. Antyufeev. On identification of optical parameters of a~plane slab. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 4, pp. 309-316. http://geodesic.mathdoc.fr/item/SJVM_2001_4_4_a1/

[1] Glushko V. N., Ivanov A. I., Livshits G. Sh., Fedulin I. A., Rasseyanie infrakrasnogo izlucheniya v bezoblachnoi atmosfere, Nauka, Alma-Ata, 1974

[2] Antyufeev B. C., Ivanov A. I., Livshits G. Sh., Mikhailov G. A., “Opredelenie aerozolnykh indikatris rasseyaniya bezoblachnoi atmosfery v spektralnoi oblasti 0,55–2,4 mkm”, Izv. AN SSSR. Ser. FAO, 16:2 (1980), 146–155

[3] Antyufeev B. C., “Determination of a phase function in a radiative transport equation by the Monte Carlo method”, Russ. J. Numer. Anal. and Math. Modelling, 14:3 (1999), 193–204 | DOI | MR | Zbl

[4] Antyufeev B. C., “Opredelenie fazovoi funktsii uravneniya perenosa izlucheniya s pomoschyu metoda Monte Karlo”, Dokl. RAN, 369:5 (1999), 583–585 | MR | Zbl

[5] Kozlov V. L., Malkevich S. M., Turchin V. F., “Ispolzovanie metodov matematicheskoi statistiki dlya resheniya nekorrektnykh zadach”, UFN, 3:2 (1970), 82–95

[6] Turchin V. F., Nozik V. Z., “Statisticheskaya regulyarizatsiya resheniya nekorrektnykh zadach”, Izv. AN SSSR. Ser. FAO, 5:1 (1969), 121–135

[7] Spanier J., Gelbard E. M., Monte Carlo principles and Neutron Transport, Addison-Wesley, Reading, Massachusetts, 1969 | MR | Zbl

[8] Springer-Verlag, Berlin, 1980 | Zbl | Zbl

[9] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, Izd-vo Inostrannaya literatura, M., 1962 | MR

[10] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR

[11] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[12] Lavrentev M. M., Savelev L. Ya., Teoriya operatorov i nekorrektnye zadachi, Izd-vo instituta matematiki SO RAN, Novosibirsk, 1999 | MR

[13] Ershov Yu. I., Shikhov S. B., Matematicheskie osnovy teorii perenosa, Nauka, M., 1985 | MR

[14] Ershov Yu. I., Shikhov S. B., Metody resheniya kraevykh zadach teorii perenosa, Nauka, M., 1977 | MR

[15] Vladimirov B. C., Uravneniya matematicheskoi fiziki, Nauka, M., 1981 | MR

[16] Maslennikov M. V., “Problema Milna s anizotropnym rasseyaniem”, Tr. mat. in-ta AN SSSR, 97, 1968, 3–134 pp. | MR

[17] Antyufeev B. C., “Granichnaya zadacha perenosa izlucheniya cherez ploskii sloi”, Teoriya i prilozheniya statisticheskogo modelirovaniya, Sb. nauch. trudov, AN SSSR. Sib. otd-nie. VTs, Novosibirsk, 1990, 157–169