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Micro
Spherometer
For very
small lenses.
This describes modifications so a
standard microscope will measure
the radius of curvature of extremely
small lenses to a high precision.
Copyright – P. J.
Smith
But permission is given to distribute this material in unaltered form as
long as it is not sold for profit.
Background
I have more and more felt the need to measure
and test extremely small lens surfaces.
These are mostly destined for eyepieces.
The radius of
curvature may be as small as 2 mm.
Here is a typical example. .
A steel ball was used as a lap although this
lap is for a slightly smaller lens than the one pictured . The lens is bonded to an aluminium disk
Clearly these small lenses cannot be measured
successfully with normal spherometers.
This brought to mind the devices described in
ATM 3 (a chapter by Gardner) and in Optics and Optical Instruments by B. K.
Johnson which always intrigued me but were previously relegated to ‘someday
projects’.
Recently, I made a simplified version in the
form of an attachment for a standard microscope. It has so successful that I am thrilled with its
performance.
General Description
This photograph shows a microscope and
attachments. No modifications have been
made to the microscope which cannot be undone.
This unit simply lifts out of the eyepiece tube.
While this microscope has a trinocular
head, it is not necessary. During use, the binocular eyepieces are not
used. More important is the optical and
mechanical quality allowing positive and convenient movements.
1/ The surface under test can be seen in
this photograph. It is a miniature concave
piece of F4 glass bonded to a small Aluminium disk for the lens polishing
machine. It is visible on the
stage. The stage has fine X and Y
movements. This makes operation a
pleasure.
In fact, I would go so far as to say the XY stage allows much
better centring and consequently improves accuracy. It certainly reduces profanity during use.
2/ A dial indicator and gauge blocks are visible on the
right. This measures rise and fall of
the stage.
It has been used very effectively in this and various
other optical measurements involving refractive index and focal length with
this microscope.
The indicator is attached to
an aluminium block. This itself clamps around the microscope frame so it may be
removed easily.
If extended measuring range or higher
precision is needed, gauge blocks are
necessary.
One possible error with this setup is cosine error. The plunger should be parallel to the stage
movement, which hopefully is exactly
perpendicular to the stage surface. Of
course all dial indicators have errors, which should be investigated. One usual scheme is for manufacturers to
guarantee repeatability to 0.2 of one division but over the range (excluding
the very far extremes) only guarantee an accuracy of 1 division.
The Attachment
The attachment is constructed from
readily available plumbing fittings, aluminium tube, an eyepiece, a cheap laser
pointer, and a small half silvered mirror (from Surplusshack).
Because a Laser diode is used, the eyepiece
does not have to be colour corrected.
And because a microscope works at a high F:NO an old fashioned Ramsden
or Huygens eyepiece works just as well as a more expensive alternative. I used a Symmetrical eyepiece because it was
available. The eyepiece does not need a
separate focusing mechanism..
The instrument as described in the original
articles used cross hairs illuminated by a half silvered mirror. But as I used a small laser to adjust the
mirror orientation it occurred to me to try the laser diode as a ‘point
source’. The small collimating lens on
the laser was simply unscrewed and removed.
This has worked very well and I have no
inclination to change the system. There
is a double image but this is no problem.
In fact, there are some advantages.
While some speckle and diffraction rings are
very evident, focus is repeatable to a few tenths of a thousandth of an inch
with a 4 X objective and even less with a 10 X objective. The diffraction pattern – especially when
slightly defocused, is very sensitive to centring of the surface under
test. Simply move the test surface
until the image shows no signs of coma or astigmatism as evidenced by a round
out of focus diffraction pattern.
It is worth baffling and a good black
paint/sawdust treatment in the laser tube as the uncollimated light from the
laser diode bounces everywhere unless checked.
The half silvered mirror is a unit from
Surplusshack. It is mounted in a small
square tube. I have a quality beam
splitter but consider this cheap half silvered mirror perfectly adequate for
this use. The cross piece is bored so
the mirror unit is a firm push fit. It
can then be pushed and twisted into position and a cover screwed in place.
The cross piece is a rough brass fitting from
my junk box and the other screw on fittings are made from brass plumbing
fittings. These are a cheap way to
purchase brass.
The optical paths to eyepiece and laser diode
should be equal so the position of the
laser diode should be adjustable. More
on this later.
Unfortunately, when it was constructed, the
unit was a quick prototype. Some
shortcuts were taken. Since it works so well, I now regret not taking more care
with the unit, although it would not work any better.
One change I would make is to reduce somewhat
the length of the eyepiece tube. This
would also mean a corresponding reduction in the length of the laser tube. I made the laser mounting tube first without
enough thought as to its length.
WARNING.
It would be possible with inappropriate choice of a laser diode and
inappropriate use of this instrument to cause irreversible eye damage.
Crucial considerations are
:-
1/ The laser diode should NOT be extremely
close to infrared wavelengths. Laser
diodes beyond about 660 nm appear very faint to the eye – yet still send as
much energy in concentrated form to the retina. Thus one of the eyes’ safety mechanisms is overridden. Newer laser diodes from laser pointers are
closer to 650 nm and under 5 mw. Only
these should be used in such a way that the beam is greatly attenuated. Even one of these used inappropriately is
potentially hazardous.
2/ The laser diode is used UNCOLLIMATED. That is, the COLLIMATING LENS IS
REMOVED. Unlike gas lasers, a laser
diodes produces a diverging cone of rays which is inherently safer unless
collimated. In this application, only a
small fraction ever reach the microscope objective for return to the eye. Substituting a narrow beam or collimated
laser diode could be dangerous. If in
doubt, another type of source should be considered. Do NOT consider a gas laser
for this project.
3/ The surfaces under test should not be
silvered or aluminised. Thus the
returned beam is reduced further by another 1/20th.
Total attenuation in this
instrument, even with a perfect beamsplitter, is well under 1000.
This has been achieved by
both a rejection of rays (uncollimated) and inefficient reflections (glass/air
surfaces). An unsilvered glass surface
used as a beamsplitter would reduce this much further if desired.
If in doubt, do your own
research on laser safety or substitute a different source.
There is excellent
material on the web relating to Laser safety.
Theory
and Use
For any surface, whether concave or convex,
there are two positions of the microscope objective for which the rays
are exactly returned. These correspond
to the positions where the microscope forms a clear image of the laser diode.
One position is when the focal plane of the
microscope is on the surface. The other
is when the focal plane is at the centre of curvature.
Thus, the difference gives the radius of
curvature.
If the optical paths from laser diode and
eyepiece are equal, this relationship is exact.
As pointed out in the article by Gardner (ATM
3), there is a correction to be applied if the optical path lengths are
different.
But it
is easy to ensure these path lengths are equal by :-
1/
Place a flat glass surface under the microscope
2/ Focus on some fine scratches or dust on the surface using
normal microscope illumination.
3/ Without changing the position of the microscope, adjust the
position of the laser diode so the image reflected from the flat surface is
sharp.
Now the difference of height of the microscope
gives radius of curvature directly.
Note that the microscope objective is always
further from a concave surface. This
means that longer focal length objectives must be used for convex surfaces.
One potential pitfall is ghost reflections from
different surfaces. Johnson warns that
it is better to coat unwanted surfaces with vaselene to stop unwanted
reflections and I tend to agree. It is
easy to focus on the wrong image.
Also beware of testing a lens on a microscope
with the substage condenser in place.
This will return many reflections which are confusing. The stage can be easily removed or an opaque
object placed in such a way as to stop the laser rays entering the condenser..
Performance.
It is easy to attain 1 % accuracy and with
attention to detail I would expect 0.1 % is possible. This is estimated from
two methods and the repeatability of settings.
Both a steel ball lap and some small test
plates which have been originated from ball lenses of known diameter were used.
Certainly, the instrument will be accurate
enough for my purposes.
If higher accuracy is needed then :-
1. Higher power, or more particularly higher NA objectives on the
microscope may be used to better define the focus.
2. More care in equalising the optical paths - or applying the correction may
be needed.
3. A guaranteed accurate dial indicator perfectly aligned perpendicular to
the direction of travel should be used.
It is possible that an accuracy of 1/10000 inch is achievable with these very
small lenses. This I find stunning.
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