It doesn't matter that your drawing has a curve in it.
Draw the perpendicular at the top of the curve, and that is the maximum
amount of tilt the 2D chip will have to tip.
The software reads the columns in threes.
For each pixel in the middle column, it looks for minimums in the adjacent pixels
in the two columns on either side. When it finds the minimum, that pixel is where
that color of light is perfectly focused.
The green light will be perfectly focused on one of the top rows.
The far red and far violet will be perfectly focused on some row lower down.
In between, there will still be pixels where that color of light will be perfectly
focused.
You don't have to do any fancy math, no spherical trigonometry, just look for
the minimas. Even the cheapest, slowest chips can do it.
The next bit of math comes in when the software self-calibrates from the mercury vapor
line spectra from the fluorescent light. The sensor chip will not be perfectly aligned,
(if it were then no extra math would be needed). The error in alignment becomes obvious
when the software notices that the distance between the red and green line gives a
different pixel/nanometer ratio than the distance between the green and blue lines do.
You then simply multiply by the ratios so that the software makes the numbers look
like the detector was aligned perfectly. This is how I adjust for the user aiming the camera
at the spectrum differently each time and zooming differently. But in your design, it will
simply adjust for small placement errors when the kit is put together.
Your two slit trick is just a bad way of trying to simulate a point source at infinity.
Instead, use a simple lens to collimate the light. Don't waste money on a lens
corrected for chromatic aberration -- the light is going into a diffraction grating. :-)
So, I hope it is now clear that your spherical aberration focus problem is simple to
fix by using a 2D sensor. And the result will be guaranteed to be perfect focus,
without having to carefully adjust the focal length of the optics (which will always
be focused at infinity). So there is nothing to go wrong during assembly, and nothing
to get out of adjustment in shipping or use. The software auto-calibrates both in the
frequency domain and in the amplitude domain (using the trick of the sample only
blocking half the slit).
-----
Get a free science project every week! "http://scitoys.com/newsletter.html"On Mon, Nov 21, 2011 at 12:40 PM, John Griessen <john@industromatic.com> wrote:
On 11/21/2011 01:19 PM, Simon Quellen Field wrote:
Here is where the value of using a two dimensional imager comes into play.
Tilt the imager, so the top row of pixels is where the green lines focus, and
the bottom row of pixels is where the far red and far violet focus.
The problem of path lengths is not linear though... see my
non-reflective spectrometer sketch:
http://ecosensory.com/diybio/spectrometer_focus_problem-1.gif
You find curvy reflective hologram diffraction "gratings" for sale
for 2D imager chips.
It just hit me that they are to correct the setup you describe above.
I'm still wondering if a hologram lens in a transmissive film setup
could simplify, and where you find makers of such, and what are trade offs
of superimposing them.
Meanwhile Nathan is on a quest for flow cytometry, " with the right grating/optic
configuration you can disperse a spectrum with sub-nanometer per pixel resolution.",
"The double slit will reduce aberration, but it will also reduce the
signal a lot too." I'm sorry if I caused you any grief Nathan, but it took
so long to get your specs stated. If I'd known these before, I would not
have critiqued your ideas so much. You might get something working well,
and I wish you luck selling the high performance. Model a new kickstarter
after this one: http://www.kickstarter.com/projects/printrbot/1239090607
and you'll get a kick out of it. Notice how they offered the smallest,
easiest to assemble or modify, and got more preorders than donation premiums.
They got 115 backers at $500 for a full kit, unassembled. Only 8 bought stripped
down incomplete kits. 10 bought assembled systems for $250 extra
I've found a beagle-bone
compatible collaborator and will be evolving one of those for cheap --
mostly because Nathan jogged my thinking about them as I compared to Raspberry-Pi
modules for $35. The layout and schematics were done with proprietary
software, but the results show a working way to add decoupling caps
and route wires away from the dense package for its processor so
it's something to consider. There is an ecosystem of hardware and
linux bring up developers to get help from, that seems better established
than for R-Pi.
I can't see aiming for a performance spectrometer at this time, so I'm just collecting
notes for a "el cheapo robusto" miniature spectrophotometer selling some day
for $199 (and less the week between Xmas and new year's). maybe 2013.
John
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