X-Message-Number: 13568
Date: Sun, 16 Apr 2000 07:44:09 EDT
Subject: Brain reading with X-ray QND

The problem with molecular level X ray pictures is the mere radiation
quantity absorbed by the sample to be imaged. Even if that is done 
on an extended period of time, so that the object is not simply roasted,
radiation dammages are enormous. This is not an option if the "sample"
is in fact the brain of a person on cryostasis. So we must find a way to
"see in darkness" and get the picture without submitting the brain to an
X-ray flood. This can be done by the so called Quantum NonDemolition
(QND) process.

There are many potential QND configurations, the simplest seen here
is the Michelson interferometer. I must first recall what is such an

Assume you have a ligth path forming a cross, such that: +.
The radiation beam (light, X-ray,..) enter by the bottom branch,
the up and left harms end with a mirror, the exit is at right.
At the junction of the horizontal and vertical line, a semi silvered
in that position: \ splits each photon wave in two: One goes
unperturbed to the up branch mirror, the other is diverted on the
left side and impiges on the left mirror. Back to the half silvered
mirror, each half wave splits anew in two, one transmitted and
one reflected componment. If the paths along the up and left
branches are equal or differ by a whole number of wavelengths,
there will be a destructive interference on the exit path and a
constructive one on the bottom entry channel. The beam will
return to its origin and nothing get out on the exit branch. On
the contrairy, if there is a difference length of half a wavelength
in the travel along the up and left branch, nothing get back and
the full beam get to the exit way.

Now I go to the QND version: Assume the radiation is linearly
polarized, that is it oscillates in a single plane, for example the
vertical one. First, the wave travels in a polarizing rotator so that
its plane is tilted by some small value. There in now a big wave
componment in the vertical plane and a small one in the horizontal
direction. In the Michelson interferometer, the half silvered mirror
is now a polarization sensitive device: It is transparent to vertical
polarization (who goes to the up branch of the interferometer) and
reflective to the horizontally polarized wave (who goes to the left

The up and left branch paths are adjusted so that after recombining
the wave goes along the bottom branch. Here, after the polarization
rotator it encounter a mirror sending it back in the interferometer.
After many travels, each tilting the polarization plane by a small
amount, the wave gets fully horizontally polarized. The path on the
left or up branch is then adjusted so that the beam goes to the
exit way. Here it encounter a filter blocking vertical polarization
and finally a detector. Because the wave is in horizontal polarization,
the filter has no effect and we get a "click" in the detector.

Now we put a sample in the left branch of the interferometer, this
object absorbs the wave traveling here. because this one is the
horizontal componment, it is wipped out and each travel in the
interferometer let only the vertical polarization. At the end of the
process, the beam is turned to the exit path as before. There is
two possibilities for each photon: or it has been absorbed in the
left branch of the interferometer by the sample or it is in a state
of vertical polarization and is absorbed by the horizontal filter.
In any case there is no "click" in the detector and we know there
is a sample in the interferometer.

Now, the miracle: Assume ten travels in the interferometer must
be accomplished so that the wave is turned from vertical to
horizontal polarization. Each time the amplitude of the horizontal
wave is near 0.1 and the photon probability of presence is the
square of that amplitude or 0.01. If the photon is indeed present
here, it will be absorbed by the sample. After ten travels, there is
0.01 x 10 = 0.1 absorption probability in the sample. We have 100
percent detection with 10 percent radiation absorption. If there was
one million travels in the interferometer, the detection probability
would be always 100 percent, on the other hand, absorption by the
sample would falls to 0.0001 percent. We see an object put in near
total darkness!

If the sample is a brain, there is no more radiation problems. We have
a nondestructive tridimensionnal scanner working at molecular level.
Next time I'll look at the technical challenges of X-ray QND interferometers
and how to overcome them.

Yvan Bozzonetti.

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