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The next terms of the series expansion are in y2x and y3 and correspond to Coma 3. One derives from these coefficients that if

this aberration is zeroed. Then, the projection of P and P', on the symmetry plane normal to the lines, belongs to the Rowland circle. This circle of radius Rs/2 is tangent to the grating vertex.

• Saddle deformed concave gratings: If the grating shape is an outer cut of a toroidal surface, Haber [7] pointed out that exact stigmatism can be obtained for two images in the spectrum located symmetrically from the grating normal. Let us move P and P' onto the Rowland circle, hence form (3.80), r = Rscos a and r' = Rs cos a'. From (3.78), the correction of astigmatism is achieved if

and after substitution of r and r' and for a given value a ' = a '0, the condition

provides stigmatic points at diffraction angles ±a0.

Let us generate an elastic deformation in r2 cos 29 (saddle) which is co-added to an axi-symmetric grating of curvature 1/R. We set the latter as the mean of sagittal and tangential curvatures, hence

2-1 + 1 R Rs Rt and solving this equation set,

0 0

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