[ATM] RMS error vs Strehl Ratio

["Richard F.L.R. Snashall" <rflrs@rcn.com>]

When I first started learning design, I quickly accepted that
RMS wavefront error and Strehl Ratio were correlated, and even
that an equation approximated the relationship between the two.

However, I have come across something that makes me start to
question what is going on.  I have come up with what I think is
a reasonably well corrected achromat (100 mm f/14):

    http://users.rcn.com/rflrs/d03-31.len
    http://users.rcn.com/rflrs/d03-31.zmx

I'm only listing the OSLO and ZEMAX files this time for a reason.
I've also added an additional surface near the focal surface.  I
used the GSUM tool to generate this design, but optimized the
focal surface using ZEMAX with a 5 ring, 12 arm RMS wavefront
error Default Merit Function.  I then manually put in a correction
of -0.092 mm.

For both ZEMAX and OSLO, if you allow them to re-optimize the
focal surface:

    ZEMAX -- generate an RMS wavefront error Default Merit Function
             and optimize
    OSLO  -- < evaluate >
             < autofocus >
             < minimum on-axis RMS OPD(polychromatic) >

both will pretty much effectively remove that -0.092 mm.

However, calculation of the Strehl Ratio (use at least 256x256
pupil sampling in ZEMAX) gave some results were a bit surprising
to me.  In the form I have presented the design, the photopic
Strehl ratio is about 0.833.  When the system is re-optimized as
suggested above, the photopic Strehl ratio drops to 0.805!

In his design article, Roger Ceragioli suggests that, for an
achromat with its characteristic parabolic color curve, the
best focus would be selected quite close to the minimum
focus.  The minimum focus here is -0.224 mm from the best
RMS OPD point; or still -0.132 mm from the best Strehl
Ratio point.  I tried the combination N-ZK7/SF2 that (with nulled
longitudinal aberration and OSC at both the 70% and 100% zones
at 555 nm) yields a minimum focus wavelength closer to the Photopic
peak (552.98 nm vs. 544.09 nm for the N-BK7/F5 combination) under
the assumption that what I was seeing was some sort of pickup
of "photopic" in photopic Strehl ratio.  Although the motion was
larger (-.107 mm or so), the separation between the minimum
wavefront error point and the minimum focus had also increased,
even more, to -0.259 mm.
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