About collimation in Czerny-Turner spectrometers

[Rigelleo]

Goodmorning,
I'm designing an unfolded Czerny-Turner spectrometer like the one in picture

I'm trying to use toroidal mirrors to decrease off axis astigmatism.
In my first try i made an optimal off-axis collimator (Mirror 1), a mirror that has a good collimation in both the planes: the plane of the layout that you can see in the picture and the plane perpendicolar to this layout. This solution decreases astigmatism in both the grating and the detector but since there are few degrees of freedom avaiable by using only two mirrors (even if they are toroidal) to archieve two goals i still have some astigmatism on the detector.

After that i am wondering if it is really necessary to collimate in the second plane, if it is really necessary to compensate astigmatism on the grating.
In the simulations with Zemax I noticed that by changing more the transverse radius of curvature of the toroidal collimating mirror I can reduce astigmatism more efficiently, but this happens by sacrificing collimation on this plane, in this plane (the one perpendicular to the plane of the layout) the rays they come out of the collimator slightly convergent.
I was wondering if this could be a problem, my first impression is that it shouldn't be a problem because in grating equation the angle of incidence is the component on the plane of the layout.

Is this reasoning correct? Am I missing something?

Best regards

 

[Gleb1964]

In Czerny-Turner spectrometer one wavelength in a middle of spectral range can be balanced for coma aberration. Coma would change the sign at balanced wavelength passing zero value. I would not struggle with astigmatism, just adding a defocus it is possible to get one of astigmatism focies making the best sharpness across the slit. Sharpness along slit is not important.