# How repeatably can the Point Source Microscope find best focus at a center of curvature?

Recently, a client asked how well can you focus if you really had to do better? I did not know but it was easy to do an experiment with our centering station that has a motorized stage and the ability to log data as the stage moves.
It is easily demonstrated that the PSM lateral sensitivity to centroiding on a return reflection from a center of curvature is better than 1 μm with a 10x objective. In the usual case the sensitivity is better than 0.2 μm. However, the sensitivity axially, or in the direction of focus is less sensitive, typically ± 2-3 μm judging by the size and shape of the image on the video screen.

### Was I surprised by the results!

Using our centering station I got repeatability of better than 0.1 μm using the center of a 1/8” steel ball as my mirror and a 10x objective with a NA of 0.25 on the PSM. Classically, the depth of focus is λ/2*NA or about 0.635/.5 = 1.27 μm in this case.

To do the experiment to find focus you have to adjust the shutter speed on the PSM so there are about 10-15 pixels above threshold at what appears from the video screen to be best focus. The area designation on the PSM control panel is a count of the number of pixels above threshold so the illumination is easy to set to get the right number of pixels. Then you scan through where you expect best focus while logging the number of pixels above threshold as you scan. These data are saved to a file that is then copied to Excel. When the data of number of pixels versus scan position are plotted as in the graph below you can fit a second order polynomial as shown in the equation on the chart.

Remembering that we can find the maximum of the curve by taking the derivative and setting it to zero, we get -2*81691*x -707493 = 0, or x = 4.3303 mm. When this scan was repeated another 4 times I got 4.3303, 4.3302, 4.3303 and 4.3301 mm as the scan position at maximum pixels above threshold. This represents repeatability of less than 0.1 μm even though the data are rather noisy due to the small number of pixels used in the data.

This experiment points out the advantage of using a digital camera on the PSM. Without the ability to digitize the intensity at each pixel it would be impossible for this process to work.

The exact set of parameters used in this experiment may not be optimized, but this data shows the remarkable sort of focus repeatability that can be achieved with the PSM. It may be possible to do even better.

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#### Robert Parks

Robert Parks received a BA and MA in physics from Ohio Wesleyan University and Williams College, respectively. His career started at Eastman Kodak Company as an optical engineer and then went on to Itek Corp. as an optical test engineer.

He learned about optical fabrication during a 4 year stay at Frank Cooke, Inc. This experience led to a position as manager of the optics shop at the College of Optical Sciences at the Univ. of Arizona and where he worked for 12 years and had a title of Assistant Research Professor. During that time he had the opportunity to write about the projects in the shop and the optical fabrication and testing techniques used there including papers about absolute testing and the installation and used of a 5 m swing precision optical generator.

Mr. Parks left the University in 1989 to start a consulting business specializing in optical fabrication and testing. Among the consulting projects was one working for the Allen Board of Investigation for the Hubble Telescope where he stayed in residence at HDOS for the duration of the investigation. In 1992 he formed Optical Perspectives Group, LLC as a partnership with Bill Kuhn, then a PhD student at Optical Sciences.

The consulting and experience with Optical Perspectives provided many more opportunities to publish work on optical test methods and applications. While still at Optical Sciences, Mr. Parks became involved in standards work and for twenty years was one of the US representatives to the ISO Technical Committee 172 on Optics and Optical Instruments. For two years he was the Chairman of the ISO Subcommittee 1 for Fundamental Optical standards. Recently Mr. Parks temporarily rejoined Optical Sciences part time helping support optical fabrication projects and teaching as part of the Opto-Mechanics program.

Bob is a member of the Optical Society of America, a Fellow and past Board member of SPIE and a member and past President of the American Society for Precision Engineering. He is author or co-author of well over 100 papers and articles about optical fabrication and testing, and co-inventor on 6 US patents. He remains active in development of new methods of optical testing and alignment.

### Case Studies & Testimonials

• Sometimes good news goes unnoticed for the longest time. We just stumbled on this unattributed, but complimentary note about the PSM.

Notice the PSM in the top center of Fig. 9.  Optical Perspectives Group would like to express "thank you, IDEX".

• ### "We are enjoying our Point Source Microscope and finding it invaluable in alignment and diagnostic tasks."

Dr. John Mitchell
Senior Optical Metrologist
Glyndwr Innovations Ltd., St. Asaph, Wales, UK

• ### "Just wanted to share a recent success aligning an adaptive optics test bed with the PSM. We used to use a traditional alignment telescope in the past, but the PSM made the whole process really easy and fast. The main requirements were to quickly determine the quality of beam collimation and pupil conjugates since there are several beam expanders and compressors with multiple pupil and focal planes."

Suresh Sivanandam
Dunlap Institute for Astronomy and Astrophysics
University of Toronto

• ### "You are always responsive and give us lots of useful information!!"

Dr. Shaojie Chen
Dunlap Institute for Astronomy and Astrophysics
University of Toronto

• ### "As always we are very much loving the instrument, I personally love the camera upgrade from what I'm used to!"

Weslin Pullen
Hart Scientific Consulting International, LLC
Tucson, Arizona

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