Hi Ying,

It’s going to come down to a matter of definition. Image space NA is the index of image space times the sine of the angle between the paraxial on-axis chief ray and the paraxial on-axis +y marginal ray calculated at the defined conjugates for the primary wavelength. As such, adding a grating won’t affect the angle difference between the two rays. 

You’d probably be better off defining NA with real rays in this case. That’s why OpticStudio has so many different definitions, f/#, working f/#, NA, cone angle and so on. 

I think Working f/# would be better for you as it uses real rays.  In non-axial systems like your grating system, working F/# is determined by the average of the square of the numerical aperture between the axis ray and four marginal rays, at the top, bottom, left, and right side of the vignetted pupil. The average of the square of the numerical aperture of the four rays is converted back to equivalent F/#.

However, you may have a better definition for your application, in which case writing a macro to trace the rays and extract the data you need is a simple way to get what you want.

• Mark