Re: Updated Wiki Page: Diverger lens Residual Spherical aberration #wiki-notice

Bruce Griffiths

With an equibiconvex lens the fact that the test surface brings the collimated reference beam to a focus one test surface focal length in front of the test surface whereas the test beam from the laser is collimated results in a small mismatch in SA between the test and reference beams. As long as the test surface focal length is much greater than that of the diverger then this SA mismatch is typically negligibly small.

If a PCX lens is used it contributes an SA mismatch between test and reference beams.

The formula allows this SA mismatch to be estimated.

If the refractive index is unknown using a value of 1.5 allows a ballpark estimate of the SA mismatch so one can see if the resultant SA mismatch can be neglected when testing  a particular test surface when using a PCX diverger lens (a PCX lens may be all that's immediately available). If the resultant SA mismatch is significant it can be easily measured if the diverger lens can be reversed allowing measurements to be taken with both orientations of the diverger lens.

If for example, one were testing a slow test surface a long efl diverger lens that better matches (allows sorter exposures by using more of the laser beam) the test beam to the test surface may only be available as a PCX lens. In which case an estimate of the resultant SA mismatch can be very useful.


On 13 May 2021 at 02:24 "George Roberts (Boston)" <bb@...> wrote:

Lol.  Basically in a Bath, there if you use a biconvex lens there is a tiny contribution of that lens to the spherical aberration term.  Typically it may add less than 1/1000 of a wave of error to the DFTFringe result.  No big deal.  It depends on things like how big and fast your mirror is and what type of glass is in the thin lens and so on.  Bruce has an equation that lets you calculate the error.  I might make a web page calculator where you enter the terms but the error is so small it's probably not worth the trouble except...

If you use a PCX lens instead of a BCX lens (PCX - plano convex lens - that means one side of the diverger lens is flat) then this spherical aberration grows.  It's still typically less than 1/50th of a wave but it could be significant if you have an unusual mirror.  I have a calculator here to see how much PCX will affect your mirror here - just plug in your mirror parameters:

However Bruce improved the equation to include the index of refraction of your PCX lens which most people probably won't know.  So maybe best to use the older version which just assumes 1.5 which is hopefully close enough.

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