Handbook of Biomedical Optics

424 Handbook of Biomedical Optics

transformation, which is discussed in (Xu and Wang 2006, Patch

and Scherzer 2007, Anastasio et al. 2007). Analytical exact recon-

struction algorithms have been developed for specic detection

geometries, including spherical surfaces (Xu and Wang 2002,

Finch et al. 2004, Kunyansky 2007a), cylindrical surfaces (Xu

et al. 2002b), and planar surfaces (Xu et al. 2002a). A universal

reconstruction formulation for these three geometries was also

provided by Xu and Wang (2005, 2007), whose time-domain for-

mulation is expressed as

p p t t

p t

t

t v

0

0

1

2 2( ) ( , )

( , )

,

/

r r

r

= −

∂

∂

⎡

⎣

⎢

⎤

⎦

⎥

∫

= −

Ω

Ωd

s

d

d

r r

d s

(21.12)

where d