Copyright – P. J. Smith

But permission is given to distribute this material in unaltered form as long as it is not sold for profit.




To cement the above material in ones mind, it is suggested users attempt to fully evaluate the following before looking at the answers.


The consequences of misinterpretation and subsequent misfiguring are frustrating, painful, and time consuming.  It is worth putting some time into assuring your interpretation is accurate.


It is highly suggested you use this in conjunction with my downloadable program “RonchiZ”.  With this you can choose a defective mirror and view Ronchigrams (also Foucault and Wire test images) simulated at any position of the grating and with different PV errors.





Reflective surface Outside COC.


(a)      How do we check that the grating is actually outside COC ?

(b)      Aiming for a sphere,  what needs to be done to the centre ?

(c)      Does this represent a small or large departure from spherical ?

(d)      What would this look like inside COC ?

(e)      Why are the bands unevenly spaced ?





Reflective surface Inside COC.


(a)    Does this represent a depressed or Raised centre with respect to a Sphere ?

(b)    Would we call the edge a Turned Down or a Turned Up edge ?

(c)    Where is the greatest slope (with respect to a reference sphere) ?

(d)    Where does the slope change the fastest ?





Reflective Surface OUTSIDE COC


(a)      Is the edge turned up or down ?

(b)      What shape is the inner 90 % of the surface ?

(c)      Draw what this surface would look like inside COC.







Reflective surface INSIDE COC


(a)    Is the edge turned up or down ?

(b)    If the edge is masked off, is the centre raised or lowered with respect to a sphere ?

(c)    Is this general shape similar or opposite to a parabola ?

(d)    Is the centre of the returning wavefront advanced or retarded during the test?






(a)     If this is a reflective surface, is the centre raised or lowered with respect to a sphere ?

(b)     Is the test wavefront advanced or retarded by the centre ?

(c)     If this is a refractive surface tested by transmission, is the centre raised or lowered ?

(d)     Explain the previous answer.






(a)    If this is a reflective surface, is the surface defect produced by local heating or cooling ?

(b)    If this is a refractive surface, is the surface defect produced by local heating or cooling ?

(c)    Can you think of a use for this when figuring a complex set of surfaces ?

(d)    If this is a glass defect instead of a surface defect, is the local glass of higher or lower refractive index ?




Reflective surface INSIDE COC


(a)    Which zone has its Centre of Curvature closest to the grating ?

(b)    Draw a ray diagram showing the grating and convergence of rays from the inner and outer zones.

(c)    Which zone has more curvature ?

(d)    Draw the surface with respect to an overall sphere.

(e)    Draw a Ronchi pattern seen when the grating is Outside COC.




(a)    Assuming these all have the grating inside the COC, draw each surface with respect to a sphere.  If possible, choose the reference sphere which corresponds best with the majority of the surface area.

(b)    Now draw what the Ronchi pattern would look like in each case if the grating is moved outside the COC.




Use the program RonchiZ (see under software for download instructions) to generate Ronchigrams with a turned down edge of 0.5 wave and impress this on a 200 mm mirror.


Try it with both a sphere (conic const = 0 ) and parabola (conic const = -1.0).


Now vary the Radius of curvature of the mirror from F:12 to F:2.


What are your conclusions about detecting turned down edge in typical situations ?




Both these use a grating OUTSIDE COC


(a)    Draw a profile of the first with respect to a sensible reference sphere.

(b)    Draw a profile of the second with respect to the same reference sphere as used in (a).

(c)    In which position does the maximum slope occur ?  This should be referred to the spherical reference sphere.