31 March 1999 
Glasses, glasses everywhere but not a drop to drink. 
So of the 16 people sitting in Harmonic Analysis this morning, only 4 were 
not wearing glasses.  One of those 4 I know to wear contacts.  My 
observation is not necessarily that mathematicians have worse eyesight 
than the general public, but that we like to wear glasses more often than 
the general public.  I find that few people have perfect eyesight, but 
most people prefer to wear contacts. 
I don't know, perhaps we like to look "intellectual".  Now that pocket 
protectors & slide rules are no more, we have to have a new way to stamp 
ourselves as geeks when we're away from computers and our other 
accoutrements.  We don't have those little corporate badges that our IT 
brethren wear.  So I guess glasses it must be. 
On to other matters, my mother visited last weekend, huzzah.  I do not 
recognize my apartment.  All my stuff is pushed away in plastic boxes. 
There is not a piece of furniture in my apartment without something tucked 
away underneath or inside it.   
Alas, I mourn the sucking of the NCAA final.  Actually, it was a great 
game.  Blergh.  They had more shots of cheerleaders this year, so it was 
good according to my book. 
Go Carey GO! 
So here's the deal with two-photon imaging: 
First, let's consider the idea of fluorescence.  Actually, let's consider 
light.  First of all, light has energy based on its frequency - so blue 
light, which is of higher frequency than red light, has more energy than 
red light, photon for photon.  Photons are particles of light (but isn't 
light a wave? I hear someone in the distance calling.  I say to that 
person: shut up.)  and to get total energy of a bunch of photons, just add 
up their individual energies.  Okay, that's light. 
Next, let's consider electrons - specifically electrons hanging around an 
atom or some chemical or something.  Electrons live in energy levels. 
They can move to another energy level as long as they take care of the 
difference in energy.  So, say I'm an electron sitting in my little niche 
at 3 eV (eV is a unit of energy -- how much energy it takes to move an 
electron through one volt), and I drop to a 1 eV level.  I've got to get 
rid of 2 eV, and I do it by spitting out a photon that has 2 eV of energy. 
Likewise, say I'm sitting at 1 eV and want to get back to my old home of 3 
eV.  I have to wait until a photon with exactly (well, close enough) 2 eV 
comes close enough that I can absorb it and go to a higher energy level. 
So far, so good. 
Well, there's something called fluorescence which involves 3 energy 
levels:  (I'll put in numbers just as an example) 
	------------ 3 eV			 -------e------- 3 eV	 
			   here comes a photon:         ^	 
       ------------- 2 eV   ~~~2 eV~~~>		 -------|------- 2 eV 
	------e----- 1 eV  			 -------|------- 1 eV 
So a photon with 2 eV is absorbed, and the electron is kicked up to the 3 
eV energy level.  But because of the ways electrons are, it prefers to 
lose energy by going down one energy level at a time (obviously, it's more 
complicated than this, but I'm just getting to the marrow, you see.)  Each 
time the electron drops down to a lower level, it gives off a photon with 
the appropriate energy (energy must be conserved! woo!) 
(dammit peak != pique!  and toe != tow.  my lord!) 
Okay, back to my long explanation.  So the electron gets nervous about 
having som much energy, seeing how there's that cozy 1 eV to go home to 
(noone write emails to me about anthropomorphizing electrons.  I feel like 
it, dammit).  So it falls down to 1 eV, but doesn't go there directly - it 
preferes to take the short hop from 3 to 2 then 2 to 1.  Each time the 
electron loses energy, it lets out a photon with the appropriate energy. 
	-----|------ 3 eV             		----------------- 3 eV 
 <~1 eV~~~~~~|						 
	-----e------ 2 eV			---------|------- 2 eV 
					   <~~~~~~1 eV~~~| 
	------------ 1 eV			---------e------- 1 eV 
So we're back where we started.  To recap, one photon came in, wait a bit, 
and then two photons with lower energy came out.  That's fluorescence. 
For example, if you put something under a black light, which is 
ultraviolet radiation and invisible to humans, and you see it glow -- 
you're seeing the lower energy visible light after this 2-photons-for-one 
exchange has been made. 
Say you want to use this technique for imaging purposes: you inject a 
fluorescent dye into a neuron, for example, and it just so happens this 
dye likes to follow calcium ions around.  You're thinking of taking 
advantage of its fluorescence by shining a laser in the small area you 
want to look at and capturing the fluorescing photons.  The problem, 
though, is that living tissue has so much =stuff= in it that likes to 
interact with light - the laser will get scattered coming in, so you can't 
focus your laser on a little area - and the fluorescent photons coming out 
will also get scattered, so you might lose some of the light coming out. 
Behold: the two-photon process.  It's really fluorescence in reverse: two 
lower energy photons will come in and one higher energy photon will come 
out.  The idea is this: suppose there's a 1 eV level, and a 3 eV level, 
but no intermediate level.  But all you've got is a laser that will shoot 
out 1 eV photons.  For the electron to change energy levels, it's got to 
absorb two photons at the same time.  If only one 1 eV photon comes by, 
the electron can't do anything with it, because there's no 2 eV energy 
	------e------ 3 eV		-------|-------- 3 eV 
	      ^				       | 
	      |				       | 
  ~~~1eV~~~~> |				       | 
  	      | 			       |~~~~~~~~~2eV~~~~~~>	 
  ~~~1eV~~~~> |				       |	 
	      |				       v 
	------|------ 1 eV		-------e-------- 1 eV 
		above: two photons come in: success! 
	------------- 3 eV		---------------- 3 eV 
  ~~~1eV~~~~>					~~~~1eV~~~~~~> 
	------e------- 1 eV		--------e------- 1 eV 
		above: an electron watches a lonely photon go by 
Now why will this make all the difference?  If you've got your laser 
trained on a small area, the light will still scatter; however, the 
likelihood that you'll get =two= scattered photons getting close enough to 
be absorbed by the same electron at the same time is very, very small.  So 
you won't get these unwanted areas glowing.  That also solves the problem 
of lost light.  Since almost all of the 2 eV light coming out (using my 
example from above) is coming from the area you're focussing on, all you 
have to do is collect all the 2 eV light coming out -- surrounding the 
specimen with photoelectric tubes in every direction, say. 
Anyway, some guys have done this and have used it to look at synaptic 
events.  Synapses are really small.  They're little nubs (kinda) on 
tendrils that are on neurons.  That's tiny. 
That's all I have to say about the two-photon imaging process.  Don't ask 
me about it if you want to know more. 
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