We derive an approach for imaging attenuative sample parameters with a confocal scanning system. The technique employs computational processing to form the estimate in a pixel-by-pixel manner from measurements at the Fourier plane, rather than detecting a focused point at a pinhole. While conventional imaging system analysis and design assumes an independent scatterer at each point in the sample, attenuation must be treated with a tomographic approach. We show that a simple estimator may be derived that requires minimal computation and compare it to the conventional pinhole estimate.
The method can potentially be used to image attenuation parameters and occlusion with incoherent detection, as well as refractive index variation with coherent detection, and could potentially allow for video rate imaging due to its computational simplicity. We further consider the application to the problem of an unknown gain or phase value, such as in the measurement of phase with a gradient sensor. And we propose a technique to mitigate the effect by computationally imaging off-focus planes. The principles are demonstrated with numerical simulations in two dimensions.
K. Dillon and Y. Fainman, “Depth sectioning of attenuation,” J. Opt. Soc. Am. A, vol. 27, no. 6, pp. 1347–1354, Jun. 2010. (pdf)
