Instructions for Using CaliBall

Using the CaliBall

Using the CaliBallTM to calibrate interferometer transmission or reference spheres using the random ball test is almost fool proof.

However, observing a few simple precautions will improve the results of the calibration. These precautions are listed below in approximately the order they should be followed.

Because interferometers come in many configurations it is impossible to have a set procedure for every situation.

Remember the calibration is a measurement over a finite area of typically several hundred thousand points where the heights of concern are no more than a few nanometers.

Virtually every possible noise source will affect the results of the calibration to some small degree.

Also there are systematic errors associated with the test that these instructions show ways of avoiding or minimizing.

1) Secure the CaliBall

Secure the CaliBallTM kinematic mount to a rigid x-y-z stage with the flat edge of the mount parallel to the flange of the transmission sphere.

Nothing on the stage should project beyond the flat edge of the kinematic mount as this may prevent getting the ball to the focus of the transmission sphere particularly for the fast (f/1 or faster) spheres.

A right angle adapter plate affixed to one of the x-y-z lens/mirror mounts that are supplied with commercial interferometers is an ideal way to mount the CaliBallTM.

Lack of repeatability from CaliBallTM placement test to test during the averaging due to lack of mount stability will lead to a poor calibration.

2) Thoroughly Clean

Thoroughly clean the CaliBall and the tops of the three balls in the mount with acetone or methanol.

Handle the ball itself with lint free cotton gloves. Finger prints and other contamination have substantial thickness compared with the roundness of the ball and will seriously degrade the calibration.

This is probably the most important single precaution to observe. Keep the ball clean. 

Contamination is a random but systematic error that will affect how many samples must be in the average that becomes the calibration.

3) Set the ball

Set the ball on the kinematic mount and adjust the x-y-z stage to position the center of the ball at the focus of the transmission sphere to be calibrated.

Mark the top of the transmission sphere and always orient it with the top up when the transmission sphere is used subsequently. 

At the nanometer level this orientation is important and is a systematic error if the transmission sphere is installed oriented 1800 to how it was calibrated.

An even better method is to calibrate the transmission sphere every time it is installed on the interferometer.

Even slight errors in the alignment of the alignment dots when the transmission sphere is installed will affect the interferometer wavefront to some degree.

4) With the ball aligned

With the ball aligned so its center is at the focus of the transmission sphere, set the interferometer to give fringes and continue the alignment laterally and in focus until a single fringe is fluffed out over the aperture.

(Prior to this, while there are a few fringes over the aperture check that the intensity has been properly set on the interferometer. This is difficult to do when one fringe has been fluffed out.) 

This is also an important step as the existence of tilt fringes may introduce a small amount of coma in the calibration and defocus will introduce a small amount of spherical aberration.

These are systematic errors that are small but will show up directly in the calibration.

 (For non-believers, do the experiment.)

5) Establish the Repeatability

Establish the repeatability of measurements with the interferometer and transmission sphere in this test setup and environmental conditions by taking 10 interferograms of the same location on the ball, and remove piston, tilt and focus from each result.

Average the 10 wavefronts to find the rms of the average. 

Using the rms of the 10 individual wavefronts, find the standard deviation of the rms of the average. 

The standard deviation of the rms of the average is a measure of the repeatability of the measurement.

It says that if another measurement of ten interferograms were done without changing anything there is a 67% likelihood that the rms of the average in the second set will be the same as the rms of the average of the first within the standard deviation.

Speaking of environmental conditions, it is suggested that the air conditioning be turned off during the actual taking of the interferograms.

Also, it may be necessary to occasionally realign the ball for a fluffed out fringe as environmental conditions cause the ball center to drift slightly.

(Do not leave the air conditioning off for long periods of time as the air in the laboratory will stratify and make it look like the transmission sphere has a small amount of astigmatism aligned with gravity.)

6) Perform the Random Ball Test

Perform the random ball test1,2 by taking a first interferogram without touching the ball from the previous test.

Then pick the ball up with a gloved hand and rotate it arbitrarily and set it back on the kinematic mount.

The same fluffed out fringe should appear on the monitor as in the previous interferogram.

If it doesn't there may be a particle of dirt on one of the balls or the x-y-z stage is not stiff enough (or the ball has not been set down delicately enough).

Every time the ball is picked up, rotated and set back down again the same fringe pattern should repeat on the monitor.

 If it doesn't there is something wrong with the set up. (See step 1.)

Also check the monitor for evidence of contamination on the surface of the ball like a piece of lint.

This can be removed by lightly wiping a finger of the glove over the place on the ball illuminated by the interferometer.

Take a second interferogram, store it, pick the ball up again and rotate it to another position.

Take another interferogram and repeat this until ten interferograms are stored.

7) Average the Ten Interferograms

Average the ten interferograms from the random ball test, find the average rms and its standard deviation.

If the standard deviation is close to or less than the standard deviation found doing the repeatability test in step 5, the calibration is complete and the wavefront map of the average of the random ball test is the error introduced into a test by the interferometer and transmission sphere.

If the standard deviation is larger than the standard deviation of the repeatability test, continue taking interferograms of different randomly located patches on the ball.

Another 10 might be an appropriate number. 

Average these with the first ten and calculate the standard deviation of the rms for the 20 and compare it with that of the repeatability test.

Continue adding samples to the average until the standard deviation is the same or less than the repeatability test.

If more than 20 random ball interferograms are necessary, it is an indication that either something is wrong with the experimental technique and the whole process should be repeated from the beginning, or that the errors in the interferometer and transmission sphere are very small and the test environment very good, in which case, continue taking random ball measurements.

There are a couple of other somewhat related matters to be aware of when doing the random ball calibration; when using a slow transmission sphere such as f/10 or slower, the light rays going back into the interferometer will not retrace the exact path as they exited and this can cause errors of around 15% of the calibration error.

Using f/3.3 spheres and faster there is virtually no retrace error effect.

This means for testing slow optics it may be better to calibrate a faster transmission sphere and only use the part of the calibration that maps to the slower part under test. 

This will reduce the spatial resolution of the test but will not affect the optical path being measured.

A related comment is that when doing the random ball test, the extent of the solid angle cone of light is limited by the transmission sphere.

 When performing a test on an actual optical component the cone of light will be limited by the optic under test. 

The best way to assure that the reference wavefront is correctly subtracted from the optic under test is not to change the interferometer magnification by zooming once the calibration is done.

Then when the reference or calibrated wavefront is subtracted from the component under test there will be a pixel to pixel match of the wavefronts being subtracted.

If the zoom is used this one-to-one match is destroyed and a sheared reference will be subtracted giving erroneous results.

The other way of using the calibration so perfect matching is not a problem is to simply say that the errors in the transmission sphere are no more than the value found during the calibration. 

These calibration errors can be legitimately reduced as a function of the f/number of the cone of light being used to perform the optical component test.

While these instructions appear complex, the test is actually very simple to perform and once one is used to doing the calibration, it need take no more than ten minutes.

Because it is so quick to perform it can be done in the presence of, or by, the customer or vendor. This is invaluable in settling questions of quality.

Papers referred to above are available on this website in the Technical Library.

There is also a paper called "A Practical Implementation of the Random Ball Test" that shows a set of typical data and a sample calculation of finding the repeatability of the calibration.

Read more


Both CaliBall models are available directly from Optical Perspectives Group.



"Calibration of Interferometer Transmission Spheres" R. E. Parks, C. J. Evans and L. Shao, OSA OF&T Workshop, Hawaii1998.

"A Simple Ball Averager for Reference Sphere Calibrations" U. Griesman, Proc. SPIE, 5869, 2005.


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Case Studies & Testimonials

Why is proper alignment so important?

Here is a case of a very happy customer due to better optics.

A few days ago an astronomer friend of mine commented that he had gotten the optics of his telescope improved and the improvement reduced the time it took to get data by a factor of 3. For an astronomer this is a dramatic improvement since observing time on large telescopes can cost thousands of dollars an hour.

My friend did not say how the optics had been improved, but the important point is that better optics, whether due to figure errors, mounting or alignment mean more productive optics. I generally think of better optics as a better product leaving the manufacturing facility without thinking about how much the better optics mean to the productivity of the customer.