By Akira Ishimaru

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**Example text**

These two steps can be separated. We can first perform the continuous convolution and then the sampling. In this way we can generalize the image formation process and separate it from the sampling process. 6) in a single convolution process. Therefore 46 2 Image Formation and Digitization Space Domain ---0 * ••• ~ ____ . _ . , , , ,, • .. 1_ ................. . ill • Weighting Function hex) = const. , Bandlimited Spectrum Infinitely extended smoothed Image ·· ... • ... •••. ~. 16: Derivation of the sampling theorem I: schematic illustration of the imaging and sampling process in the x and k spaces.

2. We can then distinguish three separate steps: imaging, sampling, and the limitation of a finite image matrix. Image Formation Digitization cannot be treated without the image formation process. The optical system, including the sensor, influences the image signal so that we should include the effect in this process. Digitization means that we sample the image at certain points of a discrete grid, zm,n. 36) Generally, we do not collect the illumination intensity exactly at these points, but in a certain area around them.

The PSF blurs the points and lines, but they can still be distinguished if they are not too close to each other. Points or lines are extended objects in Fourier space, i. , a constant or a plane. Such extended objects partly coincide with the non-zero parts of the OTF and thus will not vanish entirely. 2 Image formation corresponds to the opening angle of the lens, are not eliminated by the OTF. Intuitively, we can say that we are able to recognize all 3-D structures in which we actually can look into.