Laser Measurement Repeatability on Various Surfaces

Main Question or Discussion Point

Hello Everyone,

Here is my situation: I am using a laser to take distance (height) measurements on a variety of surface types (e.g. mirror, machined surface, plastic, etc.) and I would like to quantify the repeatability of the laser measurements on each surface type. Please note that I care only about the repeatability of the laser and NOT the overall measurement system.

Setup:
The surface samples are mounted to a baseplate which is attached to a linear actuator and the laser is fixed overhanging the baseplate pointing in the negative z-axis direction. I move to a position centered in each surface sample (e.g. surface 1 --> actuator position = 10.50 mm), record the laser distance measurement and the actuator position at time of measurement (may not be exactly 10.50, could be 10.52), and repeat “x” number of times (call this a “batch” of measurements).

Question:
What is the appropriate way to quantify the repeatability of the laser measurements for each surface type?

My Initial Thoughts:
It seems like no matter what I do I will be reporting the repeatability of the entire system, not just the laser.

For example, the standard deviation of each surface in a “batch” would provide some information about the repeatability of the laser on a given surface but it also includes the actuator position variance (and error) at the time of measurement.

Similarly, the standard deviation of several surface-batch-means will provide some information about the reproducibility of the laser on a given surface but it also includes the actuator variance.

Is there any way to extract just the laser repeatability from this data?

Someone else suggested using a Gauge R&R (gauge repeatability and reproducibility) for this purpose but doesn’t that have the same issue (i.e. repeatability and reproducibility of the entire system, not just the laser)? Also, there is only one sample plate (I think there must be at least 10 for a “proper” gauge R&R) and the process is completely automated so there should be no operator variance.

My statistics is a bit rusty so I appreciate any help or feedback.

Thanks!

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Stephen Tashi
The following things aren't clear to me from your description:

1. By "laser", are you referring to a laser rangefinder device? Or is the "laser" a simpler component that is indeed a laser, such as a chip containing a solid state laser?

2. Is the variation you get in repeating a measurement at the same distance just in the last digit of the distance readout? That was true in the example you gave ( 10.50 vs 10.52) ?

3. Assuming "laser" means a laser rangefinder, surely you (or someone) cares about more than "repeatability". For rexample, if the readout was stuck on the same number all the time, it would certainly be repeatable.

4. Do you have other instruments to measure the distance besides the laser being tested?

chiro
Hey n00bcake22 and welcome to the forums.

I'm a little confused about repeatability, but from your post it seems you have n surface types, with b numbers of measurements (i.e. your batch) for each surface type. All your measurements use the same sample plate (what exactly is this used for?) and everything is completely automated.

What are you trying to do? What is the end game? Are you trying to find what surface has the highest measurement? Are you trying to determine if there are any statistically significant differences? Are you trying to test properties of the actuator with respect to all of the measurements for specific surface types?

It will be easier to tell us what you are ultimately trying to find out, so that we can relate particular statistical methodology back to the particular goals you have at hand.

Thanks for your replies. Here are the answers to your questions. Also, I have attached a horrible paint drawing of my setup; let me know if you have any other questions. Thanks.

1. By "laser", are you referring to a laser rangefinder device? Or is the "laser" a simpler component that is indeed a laser, such as a chip containing a solid state laser?
Yes, the laser is a rangefinder device.

2. Is the variation you get in repeating a measurement at the same distance just in the last digit of the distance readout? That was true in the example you gave ( 10.50 vs 10.52) ?
Yes. If the laser is fixed over a surface sample the measurement usually varies at the micrometer level (I am reading the height in xx.xxx mm). It can be more, however, on some surfaces (e.g. machined metal surface has less fluctuation than plastic surface). I observe this by using the rangefinder's attached display.

The 10.50 mm and 10.52 mm values were the actuator's desired and actual position, respectively, at the time of the height measurement. For example, surface sample 1 actuator position = 10.50 mm, surface sample 2 = 30.00 mm, etc.

3. Assuming "laser" means a laser rangefinder, surely you (or someone) cares about more than "repeatability". For rexample, if the readout was stuck on the same number all the time, it would certainly be repeatable.
Well, yes but my primary focus is the repeatability of the rangefinder on various surface types and how I should properly quantify this. For example, the rangefinder's display fluctuation on a machined surface is much, much lower than it is on the plastic surface.

Eventually, this rangefinder will be used on a metrology system to measure the height at various points on a completed product. These points will be of varying materials and, therefore, surfaces.

4. Do you have other instruments to measure the distance besides the laser being tested?
Not really. I have other laser rangefinders but I will run into this exact same problem.

I'm a little confused about repeatability, but from your post it seems you have n surface types, with b numbers of measurements (i.e. your batch) for each surface type. All your measurements use the same sample plate (what exactly is this used for?) and everything is completely automated.
Exactly. Basically, the sample plate is what all the various surface samples are attached to and it is then attached to the linear actuator. I tell the actuator to go to surface sample 1 (i.e. 10.50 mm actuator distance), wait for the "move complete" signal, take measurement (i.e. read actual linear actuator distance (may get move complete signal when actuator is at 10.52), read laser height measurement), go to surface sample 2..., repeat "b" times.

What are you trying to do? What is the end game? Are you trying to find what surface has the highest measurement? Are you trying to determine if there are any statistically significant differences? Are you trying to test properties of the actuator with respect to all of the measurements for specific surface types?
In the end, this laser rangefinder will be used on a metrology system to measure various points (of various materials) on a finished product. I am attempting to confirm that this laser will be capable of doing so repeatability. For example if the laser is very "repeatable" on machined surfaces but less so on plastic surfaces I need to know.

My questions are:

1. How do I quantify "capability of repeatability" of the laser on each surface type (mirror surface, machined surface, plastic surface, etc.). Simple standard deviation calculation of each surface for "b = 150, 200, ?" samples? Is it more involved?

2. The actuator isn't perfect and the laser point is very fine (120 um diameter). Perhaps the slight variance (and error) of the actuator's position is adding to the height measurement variance. Is it possible to obtain JUST the laser's surface repeatability from the data (i.e. can I "filter out" the actuator variation/error)?

Thanks again for the assistance.

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Stephen Tashi
In my opinion, you can't separate the variability of the laser from the variability of the complete measuring system just by applying statistics. You must either do more physics (employ more devices) or make enough assumptions to create a stochastic model of the situation. As far as the purely mathematical aspects of the problem go, if you can only get variation in the last digit of the readout, this creates a complication in doing the usual sort of parametric statistics since the truncation loses information. (I'm sure there are many papers written about what to do in such a situation, so it isn't hopeless.)

I'll just imagine your apparatus and say what comes to mind.

If you leave the instrument in the same position and take repeated measurements at various times, I'd think that the main variable causing variation would be temperature. (temperature of the room and also of the laser rangefinder itself, and any other equipment that uses power.) You can measure the temperatures and see if they correlate with the readings.

Mechanical systems with gears have "gear lash". There are devices used by machinsts to measure distances. You might be able to use one to check the repeatability of the positioning system. You could test this at close distances without worrying about what the laser says. There are also ways to measure distances by magnifying small differences. For example if the position head pushed against a spring loaded mirror and tilted it, a laser pointer aimed at the mirror would cast a reflection on a distant wall. The movment in the reflection woudl magnify the effect of any variation in the positioning.

You haven't completely answered chiro's question about what you are trying to do because you need to explain the significance of quantifying the variability of the laser. Is it merely a number you need to put in a report? What decisions or computations will be based on the number you provide? Will other laser rangefinders eventually be tested? Will the number be used to compare their performance?

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