# Precision Lapping

Some thoughts on what it takes – Ian Anderson

When I entered the precision optics industry, I promised myself I would not
rant about wave front errors, Strehl ratios or Raleigh limits, so I am loathed
to be writing this.

The heat sink industry, however, uses “optically flat”
even more loosely than the “Christmas trash” telescope business and frankly,
even using the manufacturer stated accuracy, they have a laughable amount of
error for an optical surface.

Technically, a (well used) pizza pan is an
optical flat. They have been used as make-shift flats (for research no less)
in micro-wave and radio telescopes. The generally accepted definition of an
optical surface is “1/4 wave front surface accuracy”. Lets break this
statement down, shall we:

• “generally accepted” – this means most people in the optics industry will agree this is technically correct
• “optical surface” implies it is used to reflect or refract light
• “1/4 wave” (here is the fun part) “1/4” means one fourth or 25%
• “wave front” is the length of the electromagnetic wave used to test the optic, this could be anywhere from 100 nanometers for ultra violet to 21 centimeters for radio waves (there is a much larger range but this the range I deal with); therefore, 1/4 wave front can be anywhere from .05 m to .000000025 m
• “surface accuracy” – this is a statistical analysis of surface error

With proper analysis, a segment of the Keck primary mirror could be replaced with a chicken and still fall under the ¼ wave requirement. For more information on this topic, go
HERE and
HERE.

So why ¼ wave then? It’s just convention; at this level of accuracy, the error
is less than what is caused by film grain, and the errors are not readily
apparent to the eye. For the purposes of this article and the upcoming ones,
“optical surface” will be considered peak to valley error of 150nm and RMS
error of 100 nm or less. This satisfies the ¼ wave criterion for the entire
visual spectrum and is about as good as you can do by hand.

Most often, surface error takes three forms:

• Pits
• Roughness
• Mechanical

{mospagebreak}

Pits (can also be streaks) are the remnants of a poor pre-polishing
process or incomplete polishing. If a surface has pits, this means the
manufacturer did not complete one or more grit size steps, usually between
the last two stages. This is indicative of a cheap manufacturing process.

Pitting can be seen with a magnifying glass or microscope. A good way to
visualize it over the surface is with a laser (on a perfect surface you will
not be able to see where the laser hits it). At a glancing angle, pits will
show up like dust; these are the difference between shiny and dull. This has
varying effect depending on how much pitting there is.

Roughness, or zonal
error,
is what happens when one (or more) part of a surface is not the same
height as desired.

It is possible to have a perfectly flat surface with a
great deal of roughness if the average is below the margin for error. This
is often caused by differential heating from friction during polishing, or
polishing using a rotary buffer. A surface can be exceedingly shiny and
still be rough enough to have noticeable effect.
To avoid this, the cooling
system should be on during polishing and you should use a pitch lap.

Mechanical error is a type of roughness introduced in the manufacturing
process if the polish is not completed by hand. Any error in a machine will
translate itself into surface error and build every cycle the machine goes
through.

For most people, it is difficult to believe they can polish a
surface better than a machine using their hands, but the randomness of the
human hand creates a perfect sphere.

A machine can perform the same action
over and over again, but it can not do it perfectly – because of this, it will
not create a sphere.

There is no easy way to test roughness and mechanical
error on a flat. The best way to do this is with an interference test, where
you place a reference flat on the surface being tested. It uses the
principle of interference.
When the distance between the two surfaces is
equal to one wavelength (of the colour light you are using), the reflection
off the bottom surface will come back in step with the reflection on top and
build to create a bright fringe. When the distance is one half wavelength,
the bottom reflection will return out of step and create a dark fringe.

You can read the image you see like a topographic map where each bright fringe
represents a height difference of one wavelength. You can see examples of
this test being used by Bill Adams HERE (the green image on the
last page of his reviews).

In the case of the PolarFLO SF, it is quite easy to see the error in the
surface.

From the pictures I’ve seen, it is likely it could be hand polished to
about five times the surface quality they claim in ten to twenty minutes. In
fact, most well lapped waterblock surfaces are perfect, except they are 1000nm
convex over the contact area. Polishing this by hand using an undersized lap
will quickly flatten it out.

The convex surface is likely due to heat build
up from friction during polishing. It only takes a few degrees to change the
size of a piece of metal a noticeable amount.

HOW-TO CONTINUED page 3…

Theory

Making a perfect surface is impossible. Accept it (but you can come close),
even ion beam figuring will have errors. What many of you believe, at this
point, can be summed up in the opinion of a person who, for privacy sake, I
will refer to as Yoda:

Ian, surely utter nonsense, take the ball bearing for example, is this not perfectly (or near as dam it) spherical? Let the hand try and make bearings and see how long they provide a good mechanical interface without friction.

As for perfection in hand lapping, that’s not my experience, usually the
edges are significantly
more lapped i.e. lower than the rest of the surface, hands tend to
“rock” the object, and
whilst in the realms of heatsinks this would have an imperceptible
difference in the
performance of the heatsink, you are not in fact correct.

I’m a mechanical engineer by trade, and I will take machines everyday,
providing someone
with skill and experience sets them up and runs them, there are way too
many variables
from the human hand I’m afraid.

Yes, with sand paper glued to glass, you are correct. Not when you are
talking about a pitch lap; if you can make machine perform better than hand,
the optics industry will beat a path to your door.

A flat is effectively a
sphere of infinite radius. Making one well is a function of geometry. When
you grind two objects against one another in random directions, the only
shape they can take on is a sphere. When it comes to polishing spheres, the
more random the better. If a surface is polished in one direction for too
long, it will begin to develop an astigmatism (the sphere will begin to
become a torus [donut]). It is difficult to avoid this with a machine, and
it is difficult to cause this by hand. With a simple back and forth motion,
it is next to impossible to make anything but a sphere.

When creating precision surfaces, there are a few extra factors to consider
as appose to sanding:

Oxidation: This has slight, but noticeable, effect on
performance. It can also impact on your ability to test the surface – I
recommend using latex gloves when handling surfaces made of copper or silver
and, if possible, coating or immersing them in an inert fluid (i.e. generic
thermal paste or Vaseline).

A bigger problem is heat build up during
polishing. If you look at the fringe tests on Bill Adams water block tests
(HERE) you will notice an
even, convex curve over the mating surface of about 1 micrometer – this is
caused by the heat generated during polishing. Using a pitch lap, this will
be much more severe because there is more friction. Fortunately, you are not
doing it all in 15 seconds, so take your time. Towards the end, use slow,
relatively light strokes. If possible, I would also recommend attaching and
starting your cooling system during the final twenty minutes or so of
polishing.

This is a pointless exercise unless you have already done all you can to
improve your cooling system. First, switch to water-cooling and get a copper
block; if you are doing it yourself, use silver. If you are using a radiator
fan combo, switch to evaporative cooling
(See Here), use a chiller, and throw on one
or two TECs, then put the evaporative cooler outdoors.

There are two reasons to polish a mating surface to within 100nm:

• You are testing a new design and need to discount poor contact, or
• You want bragging rights for having polished a 100nm surface yourself.

PROCEDURE continued on page 4…

Procedure

Basic thermodynamics states when a water block heats up, the base will become
slightly convex due to the temperature gradient. So when you are polishing
the mating surfaces, you will want to err on the side of concave so long as
it is not intentional.

For more information, I recommend looking into amateur telescope making
literature – there are likely plenty of good books at your library (How to
Make a Telescope by Jean Texereau is a must read if you want to do this
properly). Or on the internet, I would recommend starting at
Stellafane.com, they have many good links to precision hand made optics.

It is surprisingly easy to polish a surface to between 50 and 100 nm if
you have the patience to do it. Fortunately, you are not making a telescope
mirror – you will be trying to make a perfect mating surface, which means you
can have all the curvature you want as long as it is complimentary on both
surfaces. It goes without saying you will void any and all applicable
warranties, any damage done to your system is your own fault.

Step 1: Sand and finish the surfaces as you normally would up to 1000 grit. Once you have it nice and shiny, make sure you have removed all the pits and streaks left by the 220 grit stage. At this stage, perfect flatness is not
necessary so long as the pits are gone. You should do the IHS as well if you
use Intel (DO NOT grind a die).

Step 2: Follow the Directions on Stellafane.com for fine grinding (they go into much more detail than I want to). Start with 12 micron and use the IHS as
the “tool”; this will mate the surfaces and provide the concave surface you
are looking for (this step can be skipped if the surface is already within
1000nm).

Step 3: Make a pitch lap (Texeareau and Stellafane for more information). I recommend a small (smaller than your water block) ceramic tile as your base. Melting tar can be dangerous and you should follow the precautions described

Step 4: Polish the surface spherical as described by Stellafane.

Step 5: Once the surface is polished, you should smooth it by taking very slow (1/second) and light (finger pressure) strokes to reduce roughness.

If done properly, the surfaces will be mated within 100nm using this process.
Proper testing is not necessary for the purposes of overclocking. At this
level of accuracy, when the two surfaces come into contact, it may become
difficult to separate them due to air pressure (when dry, the processor will
stick to the waterblock).

If you plan to get involved enough to want to test your work, you should
read Texereau for information on tester theory, construction, and use.
Interference tests were invented by Isaac Newton – they work!
{mospagebreak}

After the first two articles, I received many questions and comments from
[email protected] with tips for consolidating my debt, [email protected]
who has a natural supplement to increase my bust size, to Scott who had no
comment or question but really felt I needed to know his credentials and
privacy policy. Or my personal favorite: A VP who felt I didn’t know what I
was talking about and I should change my article to be an advertisement for
their product.

Sorry, I have my own products to sell (note to equipment
manufacturers: when trying to argue how much better your process is than one
that has stood since before Galileo, be more specific than “it’s
different”). Hopefully in this next section I will be able to address these
and other concerns.

WARNING: Any damage to your equipment is your own responsibility.

The term lapping is a misnomer for the process described in the last
article.

When you are using grit, it is grinding; when you are using polish,
it is polishing, and when you are correcting error, it is called figuring.
Polishing is not simply grinding using fine grit; it is a function of the
interaction between surface, polish and pitch. What you are doing is
shearing off the tops of the peaks left from grinding. Technically it
should be called flat surface figuring.

Polishes

Aluminum Oxide

By far the most common polish, found in automotive and lapidary polishes
and kits. I would only recommend this if you can’t find anything else. It
works slowly and leaves a poor finish.

Diamond

Works faster than aluminum oxide but leaves the same surface; also
expensive.

Cerium Oxide

Works faster than aluminum oxide but leaves a much better surface

Zirconium Oxide

Slower than Cerium similar surface. Use this if you don’t want to
overshoot your target

Red and Black Jewelers Rouge

Works extremely slow but leaves (although there is some debate over this)
the best possible surface. Provides the most control when polishing. Use
this if you plan to build testing equipment as well.

Ion Beam Figuring

A CNC ion beam polishes the surface. Far and away the best surface and
virtually no cost or work involved once you have the equipment. Enormous
overhead cost. Overkill.

The Pitch Lap

For the purposes of lapping a 2” square copper surface, concrete and plaster
are somewhat impractical. I would recommend a piece of ceramic tile or piece
of glass between 1” and 2” square (or any other shape so long as the widest
part is less than 2”).

Choosing Pitch

A decent substitute to optical pitch is roofing tar (you can buy 50
lbs for less than \$10). Choose the hardest (highest melting point) type you can
find. This will help prevent turned edges.

The total cost of equipment is about \$20 and you can do about 1000
waterblocks.

The total time is less than 2 hours (each).

You may want to look into a four step rock polishing kit which includes the
polish and grit needed to do this (this also helps if you use the double
pass method described below.

{mospagebreak}

The Case of “Tips 458”

Yes, this is good advice if you do not build a testing device. If you are at
all worried about the quality of job you do and want to use thermal grease,
you may have better results by stopping between 7 and 12 micron aluminum
oxide. You should remember the author did not do a quantitative test and did
not know the true cause of this phenomenon.

I am a little skeptical because
optical quality quartz is not copper or silicon. I never place metal in
contact with an optical component in any situation where there will be a
temperature change of more than 1 degree Celsius, otherwise there is a risk
of the metal cracking the component from thermal expansion. Quartz has
several orders of magnitude lower thermal expansion than aluminum, so if at
one temperature they are in perfect contact, then at another they wont be. At
temperatures where quartz could be damaged the setup described in the text
would be ideal.

Whether Or Not To Use Thermal Paste

“Tips 458” brings up a good point: particles in thermal paste have a diameter.

If the diameter of the particles exceeds the size of the surface error, there
will be nowhere for the particles to go. When this happens, the source of
greatest thermal resistance becomes the thermal paste itself. You may think
I need to have my head examined for saying this, but if the error of the
joint is smaller than the size of the particles, you may have better
performance with a thin layer of oil.

I should warn you if you do this
directly to the die, there is a risk of damaging the chip if they are
separated improperly (slide the two apart rather than pull). If you intend
to use thermal grease, stopping at 7 micron grit may be a good idea.

Hand Polishing is only effective on mirrors under 1000mm. Larger and it
becomes exponentially expensive and time consuming (think decades). Ever
since the Hubble COSTAR incident, almost all professional optics are finished
using ion beam figuring after computer controlled small tool polishing. One
of my favorite quotes on this subject was from the operator of the Altair
system for the Gemini telescopes: “The adaptive optics are so good, now we
can see the errors in the telescope.”

Testing Tips

If you will be using the interference test, a laser with a diffuser (piece
of white paper) on the end makes a good, low cost monochrome light source.
The prism from an old pair of binoculars will make a good flat because you
only need to test the contact area.

How To Know It Is Done Without a Tester

If, when dry, the processor will stick to the waterblock by air pressure and
there are no pits, it is unlikely you will be able to do better unless you
have tested the surface to know where the errors are. Doing more will likely
have no noticeable effect on performance.

If you cannot find a reference surface, you can do a double pass Foucault
test:

Step 1: Make a Foucault/Ronchi tester

Step 2: Make a concave spherical telescope mirror as a reference surface.

It is possible to test this surface directly using the Foucault/Ronchi
tester without a reference surface or calculus. The size of this need only
be larger than the surface being tested, so you can build it out of the
bottom of a drinking glass or canning jar.

Step 3: Set up the test system so the light must be reflected off the flat,
then the mirror, then back on the flat, then back to the tester i.e., bend the
light path ninety degrees using the flat. What you are doing is testing
the reference mirror in the reflection from the flat. Any error in the flat
will appear as an imperfection in the reference mirror. This is a double
pass test, so the size of any error appears doubled.

Notes About Hate Mail

You disagree, great – I would like to hear why. But before you send off your
white hot flaming E-mail, there are a few things you may wish to consider:

1. Make sure you have a complete grasp of the English language.
2. Make sure you understand what I have written in the document.
3. Do not insult my intelligence because you do not understand my article.
4. When claiming I need more evidence, make sure you have evidence to back your statement.

5. When you provide said evidence, make sure it supports your argument; i.e.,
200 > 100 is true, 100 > 200 is not.

6. Do not use quotes unless you are quoting something.

7. Finally, using multiple exclamation marks, especially in the
middle of a sentence, does not make you appear more intelligent.