As shown in Figure 1927a, the caustic curve in TEM appears elliptical when the astigmatism of the objective lens (OL) exists. Therefore, by rounding the caustic curve the OL astigmatism can be corrected. The advantages of this method are: A) Applicable to any materials including magnetic/crystalline/thick materials, and B) Coma-free alignment can be performed at the same time.
Figure 1927a. Caustic image taken from an amorphous carbon (C) film under
an illumination condition with objective lens astigmatism. Adapted from 
There are mainly two steps to correct the astigmatisms in TEMs:
i) Correct the astigmatisms of the diffraction (inter-mediate, IL) and condenser (CL) lenses. Before the astigmatism correction for objective lens (OL) , the IL and CL astigmatisms should be corrected. The CL astigmatism must especially be corrected (without objective aperture) to ensure the proper correction of the OL astigmatism. In caustic image in TEM, as shown in Figure 1927b the presence of the CL astigmatism result in an elliptical beam (the bright strip) on the specimen, causing an elliptical shape of the caustic curve even though there is no OL astigmatism.
ii) Correct the OL astigmatism.
Figure 1927b. Caustic image taken from an amorphous carbon (C) film under
an illumination condition with condenser lens astigmatism. Adapted from 
 Q. Xing, T. A. Lograsso, A rapid method to correct objective lens astigmatism in a TEM, Ultramicroscopy 109 (2009) 287–290.