?????s? ?pt???? F?t????? Se ??????????? St?????

1
?????s? ?pt???? F?t????? Se ??????????? St?????

• Te?d???? ??a???st?p?????
• S.?.?.F.?. ?.?.?.
• ?pe?????? ?a????t?? ?.?.?a???p?????

2
? ep?d?as? t?? a?t???ß???a? se ß?????????? ?st???
?a? ? e???t?s? t?? ap? t? µ???? ??µat?? t??
f?t?????

• ?ta? ??a f?t???? p??s????e? se ??a ?????,
  µp????? ?a s?µß??? ??µ???? a??a???, t? µ??e???
  ?a? t? e?d?? t?? ?p???? e?a?t?ta? ap? t??
  e????e?a t?? f?t????? (ep?µ???? ap? t? µ????
  ??µat?? ), ?a? t? e?d?? t?? ??????. ???d????
  µp????µe ?a d?a??????µe t? ??e?t??µa???t???
  f?sµa se t?e?? pe?????? .

3

1. F?t???a pe?????? t?? ??e?t??µa???t???? f?sµat??
   µe ????? e?e??e?a?? pe??e??µe??,?p?? ??sµ????
   a?t??e?, a?t??e?-?, a?t??e?-x, s?????? p???a????
   ??t??e? ??µ???? a??a??? sta µ???a-st?????.
2. St? a?t??et? ???? t?? ??e?t??µa???t???? f?sµat??,
   t? e?e??e?a?? pe??e??µe?? t?? a?t???ß?????(?p?????
   ?, ?ad????µata) e??a? p??? ????te?? d?ast???,
   ?at? s???pe?a f?t???a t?? pe?????? a?t?? µp?????
   ?a p???a??s??? pe?????sµ??e? a??a???, ?p??
   pa?µ???? ?/ ?a? pe??st??f???? µetapt?se?? t??
   µ?????-st????.
3. ?eta?? t?? d?? a?t?? pe?????? t??
   ??e?t??µa???t???? f?sµat??, ?p???e? ??a µ????
   tµ?µa, ? ?e??µe?? ??at? pe????? t?? µ a?t?? p??
   ???µ????µe f??. ? e????e?a t?? f?t????? t??
   ??at?? pe?????? t?? f?sµat?? epa??e? ??a ?a
   p???a??se? d???e?s? µ?????

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?st????? ??ad??µ?

• Einstein-Smoluchowski ?e????sa? t? µe??t? t??
  ????s?? Brown ?a? t?? d????s?? ??a? a???a p???
  ???? t?? p??ß??µ?t?? st? stat?st??? µ??a????.
• ?? p??te? ?e???e? d????s?? ?ta? ep??e?t??µ??e?
  st?? ????s? µ????? p?? e??a? d?a??µ??a se ??a
  ????.

6

• ????t?? ??a t? µe??t? p????? efa?µ???? t??
  ?pt???? te???????a? e??a? ?t? ? ??tas? t?? f?t??
  p?? ???s?µ?p??e?ta? ??a d?a???st????? ?????? de?
  e??a? ?a?????????? se a?t??es? µe e?e??e? t??
  µ??f?? ape?????s?? t?? ßas?sµ??e? st?? ???????sa
  a?t???ß???a.
• ??a pe?a?t??? ????t?? ??a t? ???s? ?pt????
  te?????? ßas?sµ???? se f?t???a p?? e?p?µp??ta?
  st? ???t??? ?p??????, e??a? ?t? a?t? e??a?
  e?a?s??ta st?? p????f???e? p?? ????? s??s? µe
  µetaß?????? d?ad??as?e? ?a? t? ??? t?? a?µat??.
• ???t? ???s? ?pt???? te?????? ????e ap? t??
  Cutler t? 1926 st? µast???af?a, ?µ?? ?ta? ???e?
  ?? p????f???e? p?? p??e ??at? de? ?p???e ?
  apa?a?t?t? te????? ?p?d?µ? e?e??? t?? ep???.

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???t??a ?????s?? ?s?t??p??? M?sa

• ?? µet??se?? d????s?? ???????ta? se 3 ?at?????e?
  
• 1)?????-pe?????sµ??e? µet??se??
• 2)µet??se?? s??e??? ??µ?t?? (continuous -
  wave measurements)
• 3) µet??se?? ped??? s????t?ta?

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• St?? p??t? ap? a?t?? ??a? pa?µ?? f?t?? p??
  pa???eta? ap? µ?a a?t??a
• ????e? µpa??e? st?? ?st? ?a? ?? µet??se??
  t?? ??tas?? f?t?? ???? t??
• f?t????? p?? epa?e?p?µp??ta? st?? ep?f??e?a
  ?st?? s???????ta? s??a?t?se?
• t?? ??????.
• St?? µet??se?? s??e??? ??µ?t?? (cw) µ?a
  s??e??? a?t??a f?t?? p??s????e?
• st?? ep?f??e?a ?st?? ?a? ? ??tas? t??
  a?a???µe??? f?t????? µet??ta? ?at?
• µ???? t?? e??te????? ep?f??e?a? p?? ?????e?
  t?? ?st? ap? t? pe??ß?????.
• ??t?? ?? µet??se?? ?????ta? s??a?t?se? t??
  ap?st?se?? µeta?? t?? p???? ?a?
• t?? a????e?t???? d??ta???.
• ?????, st?? µet??se?? ped??? s????t?ta? µ?a
  pe???d??? d?aµ??f?µ??? a?t??a
• e?s??eta? st?? ?st? ?a? ta st???e?a
  ap?te????ta? ap? t?? µet??se?? t??
• µetat?p?s?? e????? ?a? f?s?? s??a?t?se? t??
  s????t?ta?.

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???t??a ?????s?????s?t??pa ??sa

• ? t?p?p???µ??? d?at?p?s? t?? ?e???a? d????s??
  ??e? epe?ta?e? p??sfata ??a ?a ??ße? ?p??? ?st???
  t?? ?p???? ?? ?pt???? pa??µet??? e??a?
  a??s?t??pe?.
• ? a????s? e??a? ?d?a µe ta ?s?t??p??? µ?sa ?µ??
  apa?te?ta? ???s? µetas??µat?sµ?? µe t? ß???e?a
  p?????? ???? t?? a??s?t??p???? ?a?a?t??a t?? µ?s??

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11
???s?s? d????s??
?p??????e? t? p??a??t?ta ?a ß?e?e? ??a f?t???? se
s???e???µ??? ??s? r t? ??????? st??µ? t.
P(r,tro)
12
? ???s?s? t?? ???e??af?t? (The telegraphers
equation)
? ???s?s? t??e??af?t? e??a? µ?a ???? µ??f? t??
e??s?s?? d????s?? p?? µa? ß????e? ?a ?ata??ß??µe
ta fa???µe?a s??das?? se a??s?t??p??? µ?sa
13
S??µat??? a?apa??stas? p??s?µ???s?? Monte Carlo.
Oscattering center WTIphoton weight at i-th
scattering center DIabsorbed dose during i-th
scattering.
14

• ?et??se?? ?pt???? ?d??t?t?? p??s?µ???s?

?ata??µ? f?t?? (a) ?ta? ep???ate? ? ap????f?s?,
(b) ?ta? ep???ate? ? s??das?, (c) ?ta? ?
ap????f?s? e??a? pe??p?? ?s? µe t? s??das?. ?a
t??a a?t?st?????? st?? s??das? ?a? ?? ?aµp??e?
st?? ap????f?s?.
15
????st??µat???? ?st??
????? t??a ????µe ?e???se? ????? t??? ?st??? µe
?µ????e?e?? ?pt???? ?d??t?te? ?µ?? ?p?????? ?st??
p?? e??a? ßa?µ???? se st??se?? ?a? a?t? e??a?
??t? p?? p??pe? ?a t? ??ß??µe ?p??? . ??t????
?st?? e??a? ?? ??ste?, ? ??s?f???? , t? ??te??,
t? d??µa ?a? t? st?µ???. ????? ???e? p????
pe???µata ??a ?a de????? p?? ? st??µat?p???s?
ep??e??e? t?? µet??se?? t?? ?pt???? ?d??t?t?? t??
ß????????? ?st??. ??a pa??de??µa µe??t??
p???st??µat???? ?st?? e??a? ? µe??t? t??
???????s?? t?? e??ef????.
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???a? a??et? ap?? ?a pa???e?? ap? t?? e??s?se??
d????s?? t? s??te?est? a????as?? ??a ?p???d?p?te
a???µ? st??µ?t??, p??? s???? ?????ta? µe
s??d?asµ? µetas??µat?sµ?? Fourier ?a? Laplace,
a??? µp????? ?a a?t?st?af??? µ??? a???µ?t???.
??t? e??a? ??a s?st?µa 2 st??µ?t?? ?a???a ap? ta
?p??a ta ?e????µe ?s?t??p???.
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??a p??? p??se?t??? ?a? ?ept?µe??? ??e??a ??a
??a p???st??µat??? p??t?p? t?? d????s?? f?t?????
st? d??µa ????e ap? t?? Schmitt. ???s?µ?p???se
??a µ??t??? d????s?? t? ?p??? ??µßa?e ?p??? t??
pepe?asµ??e? (????????) d?ast?se?? t?? p???? ?a?
t?? a????e?t?. ?p?te??sµata t?? a????s??
e???????a? pe??aµat??? ?a? ap?de?????a? ?a e??a?
se p??? ?a?? s?µf???a µe t?? ?e???t????
p??ß???e??. ?p?s?? d?ap?st?sa? p?? de? e??a?
d?s???? ?a ß?e?e? ? a???µ?? t?? st??µ?t??(n
layer problem) a? ?p?????ste? ? s??te?est??
d????s?? e??a? ?µ?? ?????ß??a ?a? ?p?????st???
d?s???? ? a?t?st??f? ??s? t?? p??ß??µat??. ?e
a?t? t? µ???d? p??s?µ???s?? ? ?p??a efa?µ?st??e
??a 2 st??µata µp??esa? ?a ?p?????s??? t?
s??te?est? s??das?? ?a? t? p??t?? t?? a??te???
st??µat??.
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???ß??µata st??? ?p?????sµ???

• Sta p??ß??µata µ???? t??a t?? ???a??? s?????e?
  t?? ????µe p??e? ?µa??? p???µa t? ?p??? de?
  ?s??e? ?ta? ?p???e? ep??????? ?st??.
• ?e? µp????µe ?a ????µe a???ße?? µet??se?? ??a
  p??? s??t?µa ??????? d?ast?µata.
• ??? µp????saµe ?a p????µe µet??se?? se µ????
  ??????? d?ast?µata ?a e??aµe ?a?? a???ße?a ??at?
  ? t????? t?? f?t????? de ?a e??e ep??easte? ap?
  ta ?e????ta s??das??.

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???t??a t??a??? pe??p?t?? p???µat?? (Lattice
random walk models)

• ? ???s?µ?t?ta t?? pe??p?t?? p???µat?? e??a? ?t?
  p??? s???? µp????? ?a ?????? µe t? ???s?
  pa?a????? s??a?t?se?? pa?? ?a ??s??µe t??
  p???p???? s????t?s? d????s??.
• ????? ????? e?as????s?? µe a?t? ta µ??t??a e??a?
  ???? t?? p??ß??µat?? e?t?µ?s?? t?? pe?????? p??
  ß??s?eta? t? f?t???? ?at? t? d????e?a t?? ?pt????
  µet??se??.

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S?s??t?s? ?e???a? d????s?? ?a? ?e???a? p?e?µ?t??

• ?? ?d??t?te? t?? ?e???a? p?e?µ?t?? s?s?et????ta?
  µe e?e??e? t?? ?e???a? d????s??. ?.?. ? ??s? t??
  e??s?s?? d????s?? e??a? a?????? µe t? ??s? t??
  p??ß??µat?? t??a??? pe??p?t?? se d??t??t? p???µa.
  ??a? t??a??? pe??pat?? e??a? ap?? ??a p?s? ap?
  t??a?e? µetaß??t?? ???e µ?a ap? t?? ?p??e?
  a?t?p??s?pe?e? t? µ??e??? ?a? t?? ?ate????s? e???
  e??a??? ß?µat?? t? ?p??? µa? ???e? p????
  p??ß??µata µeta??ste?s?? f?t?????.

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???s????s? t??a??? pe??p?t?? d??t??t?? p???µat??.
22
?et??se?? st? de?µat??? ?st? µe t? µ???d? t??
d????t?? a?a??ast???? fasµat?s??p?a?

• ? fasµat?s??p?a d????t?? a????as?? st?? pe?????
  t?? ??at?? ?a? ???t???? ?p??????? f?sµat??
  p??sf??eta? ?? µ???d?? st? d?e?e???s? ???t??
  ?st??, ?p?? e??a? ? de?µat????, ??a t?? s??????
  p?e?st?? p????f????? p?? s?et????ta? µe t??
  f?s??????a ?a? ?e?t?????a t??.

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????t?µe? p????f???e? s?et??? µe t?? f?s??????a,
µ??f?????a ?a? s???es? t?? d??µat?? µp????? ?a
pa????? µe ??a? µ? epeµßat??? t??p? ?a? se
p?a?µat??? ?????, µe t?? ???s? µ?a? ?pt????
µe??d?? a????s??. S?µa?t???? e?e???t????
p??sp??e?e? e?e??ss??ta? se ?st??? p?? ap????????
t?? f?s????????? ?st?? (µe?a??µata, sp????,
e??a?µata ??p) µe st??? ?a a?apt???e? ??a s?st?µa
a???p?st?? ?a? e??a???? d?a???st???? e?????? ??a
?at????/??????? ???s?. ? p?s?t??? a????s? t??
fasµ?t?? a????as?? e??a? p???p????, ß?s? t??
?e????t?? ?t? t? d??µa ??e? µ?a p??? s???et? ?a?
µ? ?µ??e?? d?µ? µe ??a ?????? µetaßa???µe??
de??t? d????as??, p?? ?a?????eta? ap? t??
pa???s?a µe?a????? . St?? pe??ss?te?e? ap? t??
???????? efa?µ???? ?p?? e??a? ???st? ta f?sµata
a????as??, e??a? a?a??a?? ?a e?a?????µe t??
s???e?t??se?? p??????? e??st?te ???µ?f????, ??a
ta ?p??a e?d?afe??µaste. ??t?? ?? d?ad??as?e?
e?a?t??ta? ap? t? ???µat?sµ? t?? d??µat?? skin
pigmentation, t?? s???es? t?? e??st?te ?st??,
t?? a?µ?t?s? t??, ?a? t?? d?µ??? f?s? t?? ????
????a?????, ? ?p??a ?a?????e? t?? ?????? ?ata??µ?
t?? f?t????? µ?sa st??? a?t???ß??????te? ?st???.

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25
? ßa?µ???µ?s? ???s?µ? d?ad??as?a, ßas??? ??a t??
ep?te??? s?st?? ap?te?esµ?t?? ap?te?e? ?
ßa?µ???µ?s? t?? fasµat?µet??? ?a? ?? p??? t??
??????t?? ????a, t?? µ???? ??µat?? sta f?sµata,
a??? ?a? ?? p??? t?? ?ata????f? ????a t???, ?
?p???? s?et??eta? µe t?? s?et???? ?a? ap???te?
e?t?se?? a?a???µe??? f?t??.
F?t???af?a ap? t?? a????as? f?t?? st?? ep?f??e?a
t?? st??ta?t Spectralon p?? ???s?µ?p??e?ta? ??a
t? ßa?µ???µ?s? t?? f?sµat?? a????as??.
26
?? d??µa e??a? ??a p???st??µat??? ?a?
a??µ????e??? ???a??. ?a ß???????? ?a?a?t???st???
t?? ?????? s?stat???? ?a? ep?µ????? st??µ?t??, ta
?p??a ep??e????? t?? µet?d?s? ?a? ap????f?s? t??
f?t?? e??a? ta a??????a ?p?? fa????ta? pa?a??t?.
27
??ß?????af?a

• Photon diffusion in biological tissues - Olga K.
  Dudko and George H. Weiss
• A. Yodh and B. Chance, Phys. Today, 48, 34
  (1995).
• G.H. Weiss, Aspects and Applications of the
  Random Walk
• ?et??se?? st? de?µat??? ?st? µe t? µ???d? t??
  d????t?? a?a??ast???? fasµat?s??p?a? µ?a p??t?
  p???ata?t??? p??s????s? - ??????? ?.
  S?a???d??1, ????? ??a????2, ??????? ?a?a??3
• ????? t?? Lasers O.Svelto
• ??t???ß???a ?a? ?????p?? ??a?t??? e??as???
  s??ed???? ???s?? e?????? f?s????.
• ?at???? Lasers ?p?st?µ? ?a? ??????? efa?µ???
  J.A.S.CARRUTH A.L.Mc KENZIE ???
• G.F. Odland, Structure of the skin, in L.A.
  Goldsmith (Ed.), Physiology, Biochemestry and
  Molecular Biology of the Skin, vol. I, Oxford
  University Press, Oxford, 1991, pp.3-62.
• S??est?a?? µ????s??p?a ?a? f????sµ??- ?.G?????
  ?.G???????
• http//omlc.ogi.edu/spectra/
• Anisotropic Solute and Solvent Diffusion - Ruslan
  Archipov a,1, Aleksandar Cvetkovic b,2, Frank
  Stallmach a and Adrie J.J. Straathof
• Medical Engineering Physics 26 ,Optical
  characterization of mammalian tissues by laser
  reflectometry and Monte Carlo simulation,D.
  Kumar, R. Srinivasan, Megha Singh