I've refigured a number of Schmidt Cass optics over the years and all the ones I've worked on had aspherical secondaries when they were tested agianst a concave test plate. By the way aspheric is any conic from an ellipse to a hyberbola. In the Schmidts that I have worked on the primaries are also not perfect spheres but close but what is important is that they are optically smooth. The same goes for the corrector plate. In the book "Optics Cooke Book" by Frank Cooke who wrote a monthly article in Applied Optics there is chapter on figuring commerical Schmidt optics that quotes Tom Johnson founder of Celestron and explains what they were doing at Celestron.
There are couple of reason why you aspherize the secondary. When your making mass produced optics, they all will have some level of error in them so to tune out these errors you select one surface and figure it so the system nulls. The secondary was selected because it requires the least amount of glass removal and Johnson stated this in his article. The other reason for aspherizing the secondary is that it allows for better correction of coma. If you don't what to aspherize the secondary to remove coma but leave it spherical, you can move the corrector plate forward ie away from the primary and place it at the radius of curvature of the primary. The reason why this is not done is that it make for a longer tube and reduces the portablity of the telescope. The other method is to add additional optics and that is what is being done now, with a two element corrector placed in the main buffle. The corrector in theory corrects for coma and also spherical aberration of the spherical secondary but reality, you still need to touch up a surface to get the system to null out, so again the secondary is figured to do this.
Edited by DAVIDG, 18 August 2014 - 09:21 AM.