One of the interesting tests for aspheric surfaces that
has been figured out is the Mosby Null Test. This test is a variation of
the Ronchi Grating Test in that a grating is made that compensates for
the curvature of the Ronchi lines on the mirror image that are caused by
the aspheric surface under test. The calculations are to bend the lines
of the grating so that when the test is done, you see the lines as straight
if the aspheric curvature of the mirror is correct. The only restriction
for the test is that the test is specific for a particular focal length
and size of mirror. If you are interested in doing several mirrors of the
same focal length, this is a nice test for you as it is an easy test to
run on the mirror and is accurate in determining if the mirror is good
or not. If you make the grating large enough and you apply circles of differing
radius, you can test differing diameters, one for each size you have put
on the grating.

**An Introduction to the test.**

The article by A D. Malaraca and Cornejo in Applied Optics Vol 13-8 is the source for this article.

The Ronchi test has been popular for many years for testing spherical surfaces as the test produces nice straight lines which are easy to understand. This method has also been used for testing aspherical surfaces but, as the fringes thus produced at the detector are not straight, thier shapes must be calculated to get the correct surface shape. However, this procedure does not give accurate results mainly because of the following reasons:

The technician figuring the
surfaces has no easy way to match a curved fringe to a theoretical curve
line. I would be a lot simpler to match a straight fringe to a straight
line.

Since the fringes are curved, the diffraction effects tend
to diffuse the fringes, making the measuring procedure very uncertain and
inaccurate.**The Theory.**

The ruling is computed using the following procedure:

- The transverse abberation

**Fig.1**
**General layout of the test.**

**Fig. 2**

5 points on the shape of the surface.

A system of five linear simultaneous equations then has to be solved in order to determine the coefficients of the following aberration polynomial:

The value obtained for the
coefficient *a*_{1} depends on the position of the ruling
and not on the asphericity of the mirror. Therefore, changing the value
*a*_{1}
is the equivalent to changing the position of the ruling. Since the exact
desired position for the ruling still to be determined, the coefficient
*a*_{1}
may be considered to be unknown.

The shape of a curved line on the ruling required for a given
straight fringe on the surface is now computed using the following relation
obtained from Fig. 2:
Next *TA(r)* is calculated from Eq. 1 and X_{R}
and Y_{R} from Eqs. (3) and (4). The values assigned to *X _{s}*
are on both edges of the desired fringe in order to obtain both edges of
the curved line on the ruling.

The ruling must be positioned very precisely when the test is made because the aspericity compensation depends very critically on that position. This is easily done if a circle is drawn on the ruling so that it's projection on the mirror surface conincides with the outer edge of that surface. The diameter of this circle can easily be computed.

Fig. 3 Fig. 4 Fring indication Where the lines are measured

**Fig. 5**
**Computed grating.**

Fig. 6

Photo of a normal Ronchi Grating Test.

Fig. 7

Photo of Mosby Test on a mirror.

**Conclusions to ponder**

The theoretical sensitivity of this test is the same as that of the basic Ronchi Test but in practice the sensitivity is greater because of the greater simplicity in the matching process and the reduced diffusion of the fringe patterns.

This test has, however, the restriction that it must be performed with a monochromatic point source. A small gas laser is ideal for this purpose. The pictures shown in Figs. 4 and 5 were made with a He-Ne gas laser.

**Further notes**

The original article was, as noted above, originally in
Applied Optics by Malaraca and Cornejo and Eliezr Jarn did the photos and
drawings. I'd also like to thank Richard Schwartz and Micheal Lindner for
putting up the GIF version so that I could do this article. The text is
pretty much verbatim from the article.

I would also note that apparently a guy named Mosby was
the original thinker on the test and thus, it carries his name. I have
some software from Stillman and Diaz and that code is here.