Archive for category math
We were looking at various microscope objectives – those lenses on the turrets that aim toward the slides. Or, if you’re like me, the expensive silver thing that just went ‘crunch’ on the slide while I was trying to focus the image.
Pete noted that there seemed to be a parabolic curve fit – better NA, numerical aperture, better light collection, and the more expensive the objective lens gets. Here’s the curve, and the supporting data.
Here’s a curious article by Steve Smith, author of The Scientist and Engineer’s Guide to Digital Signal Processing, where he shows that 1/f noise is its own Fourier transform!
I find it much easier to remember complicated ideas when there’s a clear graph. Smith shows a range of graphs, showing that “there is an inverse relationship; if the time domain decays faster, then the frequency domain decays slower, and vice-versa. This means that there must be a certain decay rate that is unique, where both domains are equal.”
Read the article – the mystery of 1/f noise continues. Perhaps the observation of this mathematical property will point toward learning the physical underpinnings that cause 1/f noise.
We notice the assertion that A/D converter quantization noise is equal to ADU/SQRT(12), where ADU is the quantization unit or LSB. We saw this in Hobbs’ excellent book Building Electro-Optical Systems, Making It All Work.
So, we decided to derive this. Took us a while to get the ‘trick’, and to remember how to perform calculus, to get that pesky root-mean-squared function.
Think of the quatization error as a sawtooth function that repeats. Then work out the RMS noise of that sawtooth wave (it happens to be the same as a triangle wave). And, yes, it does work out to that value.
Now the next part is Hobbs’ assertion that this quantization noise is not a Gaussian distribution. Get to work.
This tech note was motivated by the question – how does the response of our eyes
differ from the response of a CCD camera sensor.
Using the data of a particular Hammamatsu CCD camera as an example,
we compared how silicon ‘sees’ to the photopic eye response
and compared both to a Planck black-body curve of a light at a particular
We don’t know what those lumps are in that CCD response curve – maybe some
strange reflection interference??
If you know – tell us!
Color temperature is based upon the idea of a Planck black-body radiator.
Here’s a Tech Note that shows how our eyes respond to the Planck Black-Body radiator.
For a lamp filament at a certain ‘color temperature’ there’s a curve of how our eyes
respond to the lamp. Pete put this into a MathCAD model, and there’s a pdf here
that shows off a few nice graphs.
Ok, we have a book problem.
Both of us waay like good engineering books. A good explanation, or a great
graph that sums up why that camera ‘sees’ differently than my eyes, etc.
Since we’re always stumbling on more good books, this list will grow.
Drop by later see what’s new.
Here’s some of the books we like, as a pdf file here,
and here’s some more books we like:
- the Feynman Lectures on Physics, a 3 volume set. Here’s a guy who can explain anything well. Like how sine, cosine and the magic number e all relate to the imaginary number i (square root of -1). He also has a great description of how a ’50 Ohm’ transmission line acts like ’50 Ohms’ no matter how long it is. For a really great puzzle – read his description of how charging a capacitor really involves magnetic fields outside the cap’s plates.