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Hi Dave,
I usually understand your posts but this one is a puzzle, so I'm sure I'm missing something.
There are two conventions for expressing magnification of a brain slice or section on the published page, originally made down a microscope or with other some kind of imaging system. Both involve the linear dimension (mm, µm, nm), not area. The first convention involves drawing a short line on the Figure that represents the original length of that line in the tissue, and next to it writing '1 mm', '10 µm' or whatever that length was (or it gets written in the figure legend as 'scale bar : 10µm'). In optical microscopes, this is based on photographing a calibrated mini-ruler at the same microscope magnification. The second convention that used to be required by some publications involved stating in the figure legend something like 'magnification: 40x', meaning that the linear dimension had been scaled up 40 times, so that 100 µm on the original section was now 4000 µm (4 mm) on the submitted figure, which usually used to be a photographic print. This was/is a dangerous method, because if the printer decided to reduce the size by (say) half to publish it, as often happened, the mag factor was then wrong (then should be 20x instead of 40x). In the field, telescopes and binocs are classified this way as 10x or whatever, but this represents the magnification at the eye, not in a subsequent image, which would still have to be calibrated. Nowadays it's mostly digital images from microscopes so only convention 1 is safe.
You can of course make subsidiary statements about area, a usefully imaginative one from undergraduate textbooks being that the human neocortex when fully flattened out is 'about the area of a large pizza' (linear dimension usually not given).
The now very common pictures of brain scans expressed in 2-D with false colour squares in them are usually calibrated in voxels (3-D cubic elements, basically mm^3), but these appear as squares on the page because the page is 2-D. These are very low resolution images (usually limited to 2 mm best resolution of the imager, often worsened by the need to average several voxels to reduce noise). This is a factor of ~10,000-100,000 worse than would be needed if you wanted to visualize by such methods parts of the individual nerve cells that do the heavy lifting in the brain.
Steve (Hfx)
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of David & Alison Webster [dwebster@glinx.com]
Sent: Friday, January 31, 2014 8:28 PM
To: NatureNS@chebucto.ns.ca
Subject: [NatureNS] magnification/reduction
Dear All, Jan 31, 2014
The Feb. issue of National Geographic has an article on the brain which
nicely illustrates a common convention for expressing magnification in terms
of area as opposed to length (foldout after page 43; magnification by 100
decreases length to 1/10).
But when something is represented at say 1/3 natural size the linear
dimensions are decreased to 1/3 of natural.
Does anyone know the background of the convention for expressing
magnification in terms of area ? Does this convention apply only to objects
viewed through some optical instrument; mike, telescope, binoc.?
Is it perhaps because, for equal image brightness, light
intensity/capture/sensitivity must be increased to the same extent as does
magnification expressed on an area basis ?
Yt, Dave Webster, Kentville
.
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