Mathematical Question

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Mathematical Question

Post by augusthouse »

I've been reading a couple of older posts and have a question.

A picture tells a thousand words - so here's the picture:


References: ... 000695.php ... .php?t=879

When I look at David Scharf's images I can immediately comprehend (somewhat) the actual size of the object I am looking at; unless I am reading it incorrectly. I originally found the link to David Scharf's website in the post by Charlie above. (I realise that it is an SEM and there are no optical lenses involved. That 'Color Synthesizer' is...well..extraordinary).

What is the formula...for someone who is not a mathematician.

For example; what is the correct information that should accompany the image I posted here: ... php?t=5541

To use a classic quote from 'Antz' - "I almost know exactly what I'm doing!"

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Post by rjlittlefield »

What is the formula...for someone who is not a mathematician.
Forget formulas (said the mathematician :wink: ). The intuition is that in making the print, you have to magnify the sensor by 169/15.5.

So the overall magnification becomes 20*(169/15.5) = 218.

20x @ 23.7 x 15.5 mm


218x @ 254 x 169 mm.

(And you'll have to crop 4 mm from the end of the larger image, since 23.7 x 15.5 actually scales to 258 x 169 mm, not 254 x 169 mm.)
For example; what is the correct information that should accompany the image I posted
There are lots of different kinds of "correct" information that might be provided. Magnification at specified image size is one; field width is another; scale bar is a third.

The key rule is just never specify magnification by itself.

In the image that you posted, you specified magnification at the sensor and the sensor size, so you covered the bases correctly.

Whether that's the best approach is another question.

I think it works well here in the forum, where so many of us are used to thinking in terms of sensors and lenses.

For use outside the forum, I suspect it would be better to follow Scharf's approach: specify magnification in terms of an 8"x10" print -- something you'd ordinarily view at reading distance. That number is also close to the power of microscope that you would need to see the same field. In your example, we calculate 218X; looking through a 200X scope would show a similar view.

The earlier thread you referenced makes a case for embedding a scale bar in the image. The main advantage of that approach is that the scale information never gets lost. However, scale bars do require some education and practice on the part of the viewer. So, they're often not the best approach for communicating with the general public. And of course if the main point of an image is its beauty, then scale bars are very much out of place.


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