Lens aberrations astigmatism

So far, only defocus and spherical aberration have been considered as aberrations affecting the image contrast. Both depend only on the magnitude of the spatial frequency g[ but not on the diffraction direction, thus resulting in rotationally symmetric phase shifts (Equation 11). However, the objective lens may exhibit further aberrations resulting in additional phase shifts, which are not necessarily rotational symmetric. The most important of these additional aberrations are astigmatism and coma. 

Astigmatism is due to asymmetry of the magnetic field about the axis of the lens. Fortunately, this aberration can be corrected by means of Astig-mator, which superimposes an additional magnetic field (whose strength and direction can be controlled by the microscopist) across the gap in the pole piece of the lens. 

The absolute size of the aberrations inereases with the size of the lens and its f number. Moreover, oblique beams experienee eoma and astigmatism, i.e. the spot where the rays are eombined is no longer eireular. Moreover, the surfaee of best focus is curved. 

We have also received and ultrasonically examined 21 silicon nitride tensile specimens. These samples are cylindrical and have a diameter of 6.4 mm in the gage section, which was the only region inspected. The evaluation was conducted using a 75-MHz. spherically focused transducer. As we have mentioned in previous reports, the sharply curved entry surface of small-diameter cylindrical specimens introduces both severe astigmatism and spherical aberration in the ultrasonic beam distribution inside the solid and limits the depth at which critical flaw sizes can be detected to a few hundred microns. Our work has indicated that this limitation could be greatly reduced by aspherical shaping of the transducer lens, but the cost of such a transducer has thus far proved prohibitive. No indications were observed in any of the specimens although we could not perform a 100% inspection on any of the rods because of equipment limitations. 

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