150 wave

1
1/50 wave
Report of 6 inch f12 to ideal sphere
RMS 1/110 wave surface
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007

• From the website below two sample mirrors were
  evaluated
• by calculus for wavefront profile RMS.
• raised center, 20, 1/8 wave surface error
• raised edge, 80 span out (20), 1/8 wave surface
  error

http//home.earthlink.net/burrjaw/atm_math.lwp/at
m_math.htm by James Burrows
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Raised center
Raised edge
Step function or gradual roll off unknown
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Wavefront RMS for high center mirror calculates to
1/20
1/20.4
Wavefront RMS for high edge mirror calculates to
1/8
1/8.3
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Mathematical principles published show that RMS
has the potential to improve mirror
characterization by taking into account the size
of the deviated area of the optic surface (or
wavefront). But, no RMS standard has been
established or universally accepted.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
It can be shown by mathematical calculus that a
mirror that is smooth but under or over corrected
by ¼ wave at the wavefront calculates to an RMS
value of
1/14 wave
14 is 4 3.5
Rigerous calculation yeilds 1/13.856
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
This is an important conclusion. If you get an
RMS value for your mirror where the denominator
is 3.5 times the P-V denominator you may not have
any new information aboutyour mirror. Chances
are that if you get a mirror or run your Foucault
data through some available program you will find
that this ratio holds.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
What to watch out for regarding RMS
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
RMS is arithmetic. You can perform RMS arithmetic
on any quantity where the difference between the
quantity and an ideal is known. What makes RMS
meaningful is the choice of dataset.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
RMS is a statistical method to find the standard
deviation from an ideal surface. Dataset should
include a statistically significant number of
points which usually means many. Dataset should
be a mapping of the surface. Dataset should be
surface deviation (or wavefront
deviation) Foucault knife edge readings are the
wrong stuff and too few.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Foucault knife edge readings would need to be
converted to wavefront errors or surface errors
then integrated (somehow) into 3D by rotating
about axis. Not an easy job. More common is RMS
of surface profile (2D). This does not account
for local defects only zonal defects. Still, the
zones should be small, like 1mm.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
OK. Lets look at some knife edge data
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Autocollimation test Mirror figured
to autocollimation null
Mirror, test and image by R. Parker June 2006
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Mirror, test and image by R. Parker June 2006
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Mirror, test and image by R. Parker June 2006
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Mirror, test and image by R. Parker June 2006
19
Central obstruction
Mirror, test and chart by R. Parker
Mirror, test and chart by R. Parker June 2006
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Central obstruction
Mirror, test and chart by R. Parker
Mirror, test and chart by R. Parker June 2006
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(No Transcript)
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Conclusions about RMS RMS has the potential of
capturing an improved characterization provided
the optimum dataset is used. If RMS denominator
is 3.5 times the P-V denominator the RMS my not
give you new information about your mirror. If
less than 3.5 times then the deviated area may be
large enough to affect the image. Be very
suspicious of meaningful RMS from Foucault
knife edge readings.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Strehl ratio definition Ratio of intensity of
the peak of the diffraction pattern of an
aberrated image compared to the intensity at the
peak of an unaberrated image. Strehl ratio
ranges from 0 to 1. 1 being perfect mirror.
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Strehl ratio Basis on wave theory. SR(2/r )
int sinf(y)y dy) (int cosf(y)y
dy).. Where f(y) 4pdx(y)/l
r 0
2
r 0
2
2
2
http//home.earthlink.net/burrjaw/atm_math.lwp/at
m_math.htm by James Burrows
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Strehl ratio Although RMS and Strehl ratio are
different, when RMS is small, they are related by
the approximation SR 1 4p RMS Common
criteria RMS lt 1/14 and SR gt 0.8
2
2
http//astro.isi.edu/notes/strehl.html
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
Equivalencies for use as a guideline P-V.
RMS RMS
Strehl fraction fraction
decimal ratio 1/4
1/14 .071
0.82 1/8
1/28 .036
0.95 1/10 1/35
.028 0.97
expanded table on www.rfroyce.com/standards.htm
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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007

• Conclusions
• A peak valley wave rating within the Rayleigh
  criteria is
• adequate to define a mirror PROVIDED that it
  is understood
• that correction for spherical aberration is
  being defined and
• that there are no other surface issues. (e.g.
  turned edge, hole)
• RMS has the potential to capture in its rating
  number the relative
• size of defects PROVIDED the mirror surface is
  completely
• mapped. BUT there is no accepted standard.
• Strehl ratio provides an easy to comprehend
  scale, relative to a
• perfect mirror, BUT is probably only as good as
  the RMS
• measure

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Mirror Quality Part II2nd Amateur Astronomy
Symposium, 2007
End of presentation