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OPTICAL IMAGING AND SPECTROSCOPY Phần 10

Tham khảo tài liệu 'optical imaging and spectroscopy phần 10', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 460 COMPUTATIONAL IMAGING field per unit solid angle and wavelength. The radiance is well-defined for quasi-homogeneous fields as the Fourier transform of the cross-spectral density B x s n W Dx x n e 2pin cs Dxd Dx 10.49 Under this approximation measurement of the radiance on a surface is equivalent to measuring W. Of course we observe in Eqn. 6.52 that if W Dx Dy X ỹ n is invariant with respect to X ỹ over the aperture of a lens then the power spectral density in the focal plane is 4n2 S x y n C2F2 W Dx Dy X y n H nDx nDy 2CF 2CF . .__4 ._.xDx D i J A. J A. X exp 2ipn--- ---- d Dxd Dy cF J 10.50 where we set z F H u v is the optical transfer function and X ỹ can be taken as the transverse position of the optical axis. Neglecting the OTF for a moment we find therefore that the power spectral density at the focus of a lens illuminated by quasi-homogeneous source approximates the radiance specifically b x Sx x Sy n S x y n FF 10.51 The radiance emitted by a translucent 3D object is effectively the x-ray projection described for example by Eqn. 10.12 . We have encountered such projections in diverse contexts throughout the text. One may ray-trace the radiance to propagate the field from one plane to the next to construct perspective views from diverse vantage points or apply computed tomography to radiance data to reconstruct 3D objects. As mentioned in our discussion of tomographic reconstruction in Section 2.6 the 4D radiance over a surface containing a 3D object overconstraints the tomographic inverse problem. Reconstruction may be achieved over a 3D projection space satisfying Tuy s condition. Computed tomography from focal images 74 168 from RSI EDOF images 170 and from cubic phase EDOF images 72 are discussed by Marks et al. More recently optical projection tomography has been widely applied in the analysis of translucent biological samples 220 221 . Optical projection microscopy commonly applies full solid angle sampling to obtain diffraction limited 3D .