Jestersix

What SG to Calibrate Refractometers to

jccaclimber

Supporting Member
This came up in another thread, so I figured I would write this up.

What we want when taking measurements is something that is both sufficiently accurate and sufficiently precise for our needs. I'm not going to go into accuracy vs. precision right now, but let's assume that our refractometers are sufficiently precise. In the chart below the X axis is the salinity (as specific gravity) of the water. Not what our device tells us, what it actually is. The Y axis is the value our instrument is telling us, which may or may not be correct.

The blue line is what we get if our instrument is perfect. At any point on the line the reported value perfectly matches the actual value. We tend to pretend this is how the world works, even if it is rarely the case.

Next we have the red line. The linearity, slope in this case, is correct, but it is incorrectly calibrated by a 0.002 offset. As a result when we test 1.025 SG water it reads 1.027 and when we test 1.026 SG water it reads 1.028. This device could be better, if only it was calibrated correctly. Because the slope is correct, it doesn't matter where we calibrate it.

After this we have the gray line. The gray line has a 1% error in its slope. It was calibrated with RODI water (or tap, it's close enough). It reads perfectly at 1.000 where we calibrated it, but with 1.025 water it reads 1.0275 and at 1.026 it reads 1.0286.

Finally we have the yellow line. It also has the 1% slope error, but we calibrated it at 1.025. As a result, while it is incorrect reading RODI water at 0.9975, it is spot on at 1.025. By 1.026 it is still very close, reading 1.0261.

2020-09-30 20_00_49-Book1 - Excel.png


You might next ask "How do I get my refractometer to read correctly at 1.000 and 1.025 SG?" The answer is either you get it dialed in at one of those two points and it's already correct at the other, or there is nothing practical you can do. Our refractometers only have one adjustment on them, which is the offset. The slope is what it is, and you then have to move that line up and down until it's somewhere you are comfortable with.

Better than this would be a 2 point calibration. In that you are able to set both ends of the line, and thus get good accuracy at all of the points in between. This is why pH probes are calibrated with 2 references. That process lets you get things correct across a range, not just at one point. In the real world this gets a bit more complicated because the error in the instrument isn't often a straight line like I drew above. It's probably curved, maybe not in an obvious way, and likely changes with time, temperature, and other factors as well. No matter what though, you will still get the best results when you calibrate as close to your measurement value as practical.

The other big assumption this is making is that our calibration fluid is correct. I've found this to not always be the case. A couple years ago I bought 3 bottles of calibration fluid from a well known supplier. One for me, and two for friends. I found an almost 0.002 SG difference between the three bottles, which arrived together. One of these days I'll make my own solution, or find a way to verify some. Until then I actually use tap or RODI water because I know it to be consistent. In the case of my specific refractometer, when I calibrated it at 1.000 with RODI water it read between the three bottles of calibration solution at 1.025. I am assuming, although without actually knowing, that the slope does not change over time. I would not assume this to be true of other refractometers, so while tap water is likely just fine for many of us, there are probably a few members out there where it produces more error than we would like at 1.025 SG, or wherever you choose to run your system.

What, you use tap water not RODI? If I have RODI nearby I'll use RODI. If I'm in front of a sink I'll use tap. Periodically I'll calibrate with one, then immediately check with the other. I've yet to find a difference between the two.
 
You can correct for the idiosyncrasies of your refractometer if you want to do the math, AND you can trust you calibration fluid.

Start by calibrating to zero with RO/DI water (or let steam condense on your refractometer in the shower...)
Use the calibration fluid, which you trust is exactly 35ppt (or exactly 1.025). You sort of have to make a leap of faith here.

Now you have two points, let's say Y = absolute salinity because we're trusting it. X = refractometer reading.

A line is Y = mX + B

We've say Y = real number, X = reading and B = offset = zero because we set 0 reading = 0 salinity (ppt)

M = (Y2-Y1)/(X2-X1)

Where Y2 = 1.025 (or 35 ppt depending on the units you want), X2 = The reading on your refractometerr you get using the calibration fluid
Y2 = 0, X2 = 0 (because we set X2 to be zero, when using RO/DI, which we are saying is 0 salinity)
So really,m = 1.025 divided by your reading with the calibration fluid

So;
Salinity of water sample = (1.025/reading using calibration fluid) times(reading with your water sample)


But who wants to do this? If you're lucky you get a refractometer that is spot on at zero and 1.025. The old refractometer I have with a broken lense cover is good, the one I just bought is off by .002 or so. I'm returning it because. Because I want one that doesn't have as much error as this one.
I mean, it's easier to just calibrate at 1.025 and call it done, but if I'm paying for something, I want one that works better than this. ie; mine has too much variance in "slope" than I want.

V

PS. Yeah, maybe my math is wrong, but I don't think it is.
 
I didn't check the math, but yes, if you're willing to do some then you can get a good reading. You don't even need to fix the zero offset if you're going to do that.
That's what I did with a car I used to drive where the rear diff had been changed (different ratio as well), but the vehicle speed sensor gear had not been corrected. You get pretty quick at doing it in your head, and I kept a lookup table on the dash for common speeds until I got used to it.
No disagreement that it makes sense to buy a better instrument if you can. 0.002 SG at 1.025 is quite a bit, and I appreciate having one with a good enough slope that I can still obtain an accurate calibration without calibration fluid.
The post above wasn't so much pointed at your specific situation as the fact that this is a question I need to answer at least a couple times per year. Now I can just point people (not always forum members) to this post.
 
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