In image-forming optical systems the image of a three-dimensional object consists of a superposition of focused and defocused object layers. For a quantitative evaluation of the object it is necessary to decompose the superposition image into different images corresponding to single object layers. For this purpose the object radiation is measured with different optical transfer functions of the imaging system, for example by simply changing the focus plane. Each image contains focused and defocused parts of the object and can be described as a linear equation of the object layers, assuming linear space-invariant imaging properties. From these images the real object distribution can be calculated by the evaluation of the resulting linear system of equations in the Fourier domain. Due to noise in the detected images it is only possible to get an estimate of the true object distribution. In our case this estimate is based on an integral minimal mean square error in the reconstructed object. The algorithm is presented and demonstrated by simulation experiments and reconstructions of real human cell images in optical microscopy.
G. A. Laub,
W. H. Bloss,
"Three-Dimensional Object Representation In Microscopic Imaging Systems", Proc. SPIE 0593, Medical Image Processing, (5 May 1986); doi: 10.1117/12.952146; https://doi.org/10.1117/12.952146