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• 2.     Because of the cyclic nature of the individual terms (proportional to , , etc.), it is possible, by tilting  N elements (mirrors or lenses having curved surfaces), and each tilted through the correct angle and having its tilt-axis oriented in the proper direction, to make  N-1  of the terms cancel out completely.
  
  
• 3.     By applying a properly designed warping harness to one of the mirrors of the system, acceptable control or cancellation of the residual astigmatism ( terms) can be affected.
  
  
• 4.     If the radii of curvature of the two mirrors are made great enough in comparison with the aperture of the instrument, only the first two terms in the infinite series indicated by Eq. (1) will be large enough to require cancellation.

     The first term in the series (the term) is coma and the second, astigmatism. In the Yolo designs the tilt angles are adjusted to make the coma term of the secondary mirror just cancel the coma of the primary, and the astigmatism terms from the two mirrors are taken care of by some additional stratagem. If a third tilted element, such as a lens of long focal length and which itself may introduce a small coma term, is employed, the tilts of the two mirrors may be altered slightly so as to cancel this small additional amount of coma.

     With small apertures and relatively long radii of curvature, the residual uncompensated tilt-aberrations (mainly astigmatism, in this case) may be so small as to be tolerable. In this case no additional optical or mechanical device is necessary. With slightly larger apertures and higher standards of optical excellence, the addition of a small cylindrical lens or a tilted spherical lens of relatively long focal length, located in the light path a

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