The Ronchi test for checking the 'profile' of a spherical or parabolised mirror uses a precisely ruled 'grating.' The grating which is usually a film with 'ruled' parallel lines and spaces of equal width, generally about 2 to 5 lines per millimeter. This is interposed between the mirror, (which is illuminated by a narrow slit light source,) and the reflected wavefront from the mirror. It is placed close to and a short distance inside the focus of the reflected beam near the center of curvature.
In theory - the lines will have, for a paraboloid, a moderate outward curvature each side of center see image at left. The shorter the desired focal length, the deeper the curve in the mirror, and the more the ronchi lines curve outward from each side of center. If the grating is too close to the focus point the lines will be fewer and more curved so you should have at least five or six lines showing across the face of the mirror during this test. The curved lines should be smoothly curved, any pronounced defects in the 'figure' of the mirror will show as variations in the smoothness of the curvature in these lines. See the image at the left below"
For a spherical mirror the lines should be perfectly sraight, again variations in the straightness of the lines, or bends at the top and bottom of the lines will show a 'turned up' or a ' turned down' edge for example. See image at right below:
In order to do this test you need a simple 'tester' - a light source with a narrow vertical slit. This could be made as a basic 'light-box' similar to the tester shown on my "testing" page, click here but just simply containing the 'light-box part.
Some suppliers can send you (for a parabolic mirror) a special 'grating' which has the lines curved the opposite way (according to the measurements of your mirror) and then you have to try to figure the contour of the mirror to make the lines appear straight when this grating is placed at a measured point close to the center of curvature. When this is accomplished the mirror should be correctly 'figured' to a parabolic profile.
So to a degree it can be a 'quantitative' measurement..although accurate figuring then depends on the tester's ability to decide when the lines at the center of curvature are really straight. It also depends on the accuracy in positioning the grating at exactly the right place inside the focus of the reflected rays at this point. So in my humble opinion - it could be a fairly accurate test, or it could be somewhat 'rough and ready' depending on the experience of the person using this test. At least, if you are not happy with using all the mathematics involved with the Foucault, or other more complicated tests with care and experience you can produce a satisfactory mirror.
Even though I don't use the Ronchi grating as a quantitative test for the shape of mirrors. I do use it frequently as a qualitative check on the shape of the mirror during figuring. The lines can show if there are noticable irregularities in the overall surface of the mirror, and if there are any major high and low areas, as the gentle curve of the lines are consequently affected.
The test method of my choice is the Foucault knife-edge test using a narrow slit source with Couder screens, as described in the "Testing" section of my web-page. Also I check the shadows seen without a mask in place, to check the smoothness of transition between the various radii of the mirror. Still, along with these observations I rely mostly on the quantitative measurements taken in the Foucault test for the final evaluation of a mirror.