March 22nd: Getting out of the barrel
In which the barrel gets emptied but thirst for accuracy remains.
Well, regular readers, especially those curious about the lens distortion, might have noticed that I posted nothing last Sunday. Sorry to leave everyone in the lurch but at the time, Laura and I were walking around the polders of South Flanders with my friend and former postdoc Gerrit Beemster and his wife Magreet. We stayed them for three days and before that I attended a two-day symposium in Ghent, so there was precious little lab work to relate. And while I was away, I could not plant seeds, and so there was alas no experiment last week either. Well, that is not strictly true – I had snuck some arabidopsis plates into a growth chamber on the Monday before I left and so last week I measured root growth rate over time and made a long movie, but nothing to report about all that, yet. I spent most of the week on the case of the distorted lens (read about it here).
Happily, I found a sheet of graph paper for testing, part of a cache carefully stored in the front office, perhaps awaiting Elijah? The old cache reminds me of the drawer in my own lab full of Letterset. I imaged the graph paper in my rig (exactly as if it were segments) and the barrel distortion was depressingly obvious. The first thing I tried was comparing the images with iris wide open and cranked shut. To my surprise, this made zero difference (by eye) to the barrel. This meant computation to the rescue. I called upon the friendly neighborhood image analyst, Mike Pound, for help. And he helped. The figure shows the raw image of the graph paper and the corrected one. Appropriately enough, the software used to correct the images is called ImageMagic, a sort of command line Photoshop, but free and open source. By assuming that the graph paper in reality has straight lines, the raw image tells us how far each point got moved by the lens and so that tells us how far to move the points back for the corrected image. This process is hugely aided in practice because the lens is radially symmetric and distortion fixed (for a given focal distance).
I un-distorted the images for the previous two experiments and here is the first experiment:
Feb 25th All data are rates in % per hour
… Water KPO Sucrose Calcium KCl
DL Raw 4.8 4.8 2.5 4.7 5.7
DL Cor 5.7 4.7 2.6 4.7 5.8
DW Raw 0.3 0.5 0.8 0.1 0.9
DW Cor 0.7 0.3 0.3 0.4 0.6
Well, hardly upside down. Most of the corrected values are close to the raw ones, with the notable exception of the water control. This is not surprising because some segments move from the center to the edges while others move the other way, so the errors tend to balance. But in the water treatment, most of the segments moved one way, causing a net distortion. It is interesting that for expansion in width the corrected data appear a bit more regular than the raw data, but that could be wishful thinking. These are small changes and measurement error sure to be large. Here is the next experiment:
March 5th All data are rates in % per hour
.. Water 10 mM KCl 20 mM KCl 40 mM KCl 80 mM KCl
DL Raw 6.1 4.2 4.7 4.0 5.0
DL Cor 6.3 4.1 4.6 4.5 4.9
DW Raw 1.0 -0.5 -0.2 0.2 0.1
DW Cor -0.3 1.1 0.1 0.4 0.1
Here nothing changes substantially. And the reproducibility problem remains. On Feb 26th the water and 10 mM KCl treatment were the same but on March 5th, the water treatment was better. This is not the lens. Good to have the lens correction, but the search continues. Next week I will try acid and cutting segments in a way that I hope will make more regular ends. We’ll see about that.