Geodesic
Fresnel Tomography: A Novel Approach to Wave-Function Reconstruction Based on the Fresnel Representation of Tomograms
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 384-393

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We introduce a new type of tomographic probability distribution containing complete information about the density matrix (wave function) related to the Fresnel transform of the complex wave function. We elucidate the relation to the symplectic tomographic probability distribution. We present a multimode generalization of the Fresnel tomography and give examples of applications of the present approach.
Keywords: tomographic map, phase space, Wigner function, Bose–Einstein condensate, Fresnel tomogram. 
@article{TMF_2005_144_2_a15,
     author = {S. De Nicola and R. Fedele and M. A. Man'ko and V. I. Man'ko},
     title = {Fresnel {Tomography:} {A} {Novel} {Approach} to {Wave-Function} {Reconstruction} {Based} on the {Fresnel} {Representation} of {Tomograms}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {384--393},
     publisher = {mathdoc},
     volume = {144},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a15/}
}
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S. De Nicola; R. Fedele; M. A. Man'ko; V. I. Man'ko. Fresnel Tomography: A Novel Approach to Wave-Function Reconstruction Based on the Fresnel Representation of Tomograms. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 384-393. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a15/