A Posteriori determination of PSF (continued)

Similarly it can be shown that the Fourier Transformation of the image of a line oriented at an angle to x-axis furnishes in the u -plane the values of along a line of orientation. +90 ° . Therefore if a scene that has been photographed contains lines at various angles , ..., , then from the photograph of such a scene we can derive the values of along radial lines passing through the origin at slopes + 90 °, + 90 °..... + 90 °

If PSF is known to be circularly symmetric then , is also circularly symmetric, so that it needs only to be known along one radial line for it to be known everywhere . If no such a-prior knowledge is available would in general have to be known along many closely spaced radial lines. Once is known, is obtained by Fourier inversion.

The problem of determining PSF from the images of lines at various orientations is identical to the problem of reconstructing objects from their projections. Other techniques also exist but this is only one of the many available.

Usually the original scene or picture will not contain any sharp line or points. It is quite likely however that it will contain sharp edges. We will show that the derivative of the image of an edge is equal to image of a line source (LSF) parallel to the edge.

Let us consider an ideal edge along x- axis.

Such an edge is mathematically represented by where

	=

	=

Let be the image (ESF) of this edge

(continued in the next slide)