He then took a nice sine wave, (actually a cosine wave which differs from a
sine wave by a phase of 90o) and called whatever was waving, Y:
Y(x,t) = A cos(kx-wt) = Real part of Aei(kx-wt).
He noted that both k and w were in the exponent, and could be obta
A far sighted person can see things clearly if they are far away, but has
trouble focusing on things close.
When things are close, the eye has to bend the light a lot in order to focus,
and the far sighted persons eyes have trouble with that. When things
How do we make light?
Heat and Light: Incandescent Lighting
(5-10% efficient)
Atoms and Light: Fluorescent Lighting & LEDs
(20-40% efficient)
Well review Heat and Light first. Later in this part we will consider Atoms
and Light.
Heat loss by radiation was
1/fobj = 1/s1+ 1/(27.5 cm)
1/(2.778 cm) = 1/(2.5 cm) + 1/(-25cm)
30 cm = 27.5 cm + 2.5 cm ,
and
-100 = (27.5 cm/s1)*(-25 cm/2.5 cm).
Although the first equation has two unknowns, the fourth equation only has
one, so we can solve for s1:
-100 = (27.5 cm/s1
What DOES happen?
Look at a very bright laser beam
going through a vertical slit.
(A laser has one frequency
unlike white light.)
We will consider this situation
but only after we consider another:
the DOUBLE SLIT experiment:
Note that along the solid gre
At this point, lets fill in the knowns into the four equations:
1/fobj = 1/s1 + 1/s1,
1/feye = 1/s2 + 1/s2, or 1/feye = 1/s2 + 1/(-25cm)
L = s1 + s2 ,
and
M = (s1/s1)*(s2/s2), or -100 = (s1/s1)*(-25 cm/s2).
There are many ways to choose two unknowns. We c
For other types of light (based on the technology used to make the light):
radio:f is 1MHz for AM, 100 MHz for FM
so l is
1 km to 10 cm
microwaves/radar:
infrared:
visible
ultraviolet
x-ray & g ray
10 cm to 1 mm
1 mm to 700 nm
700 nm to 400 nm
400 nm to 1
So far, the wave theory has explained things very well:
speed of light
different colors
reflection
refraction (dispersion, thin lenses)
To look at the next property, shadows, we need to review the wave idea a
little bit.
Sine waves are nice.
Other types o
1.22 n l = D sin(qn) where q1 = qlimit ,
so 1.22 l = D sin(qlimit) ; also sin(qlimit) tan(qlimit) = h/s. Therefore, 1.22 l
D*h/s, or h 1.22 l*s/D where h is the smallest size that is resolvable.
This means that h l .
microscopes: smallest size = l = 500
Consider the (ideal) resolving ability of the eye
Estimate D, the diameter of the pupil
Use l = 550 nm (middle of visible spectrum)
Now calculate the minimum angle the eye can resolve.
Now calculate how far apart two points of light can be if they are 5
When a wave on a string encounters a free end, the reflected wave does
NOT have to destructively interfere with the incoming wave. There is NO
phase shift on this reflection.
When light is incident on a SLOWER medium (one of index of
refraction higher tha
We can solve this differential equation for N(t): dN/dt = -lN , or dN/N = -l
dt , or log (N/No) = -l t , or N(t) = No e-lt .
Further, if we define activity, A, as
A = -dN/dt then A = lN = lNoe-lt = Aoe-lt ;
which means that the activity decreases exponent
However, from the Heisenberg Uncertainty Principle (i.e., from
wave/particle duality), we are not really sure which electron is electron
number #1 and which is number #2. This means that the wavefunction
must also reflect this uncertainty.
There are two w
example: 6C14
N14 + -1b0 + 0u0
7
(a neutron turned into a proton by emitting an electron; however, one
particle [the neutron] turned into two [the proton and the electron].
Charge and mass numbers are conserved, but since all three (neutron,
proton, and e
In the same way, the square of the wavefunction is related to the probability
of finding the electron!
Since the wavefunction is a function of both x and t, the probability of
finding the electron is also a function of x and t!
Prob(x,t) = Y(x,t)2
Differe
size of atoms:
take water (H2O)
density = 1 gm/cc,
atomic weight = 18 gm/mole, (alternately, get mass of one molecule
from mass spectrograph)
Avagadros number = 6 x 1023/mole
(1 cm3/gm)*(18 gm/mole) / (6x1023molecules/mole)
= 3 x 10-23 cm3/molecule, so
da
But if an electron acts as a wave when it is moving, WHAT IS WAVING?
When light acts as a wave when it is moving, we have identified the
ELECTROMAGNETIC FIELD
as waving.
But try to recall: what is the electric field? Can we directly measure it?
Recall tha
1) For the following wavelengths (in vacuum), give the type of light (microwave, xray, IR, etc; IF VISIBLE, give the color, i.e., green, red, etc). Also give the frequency
for each of the wavelengths:
Wavelength
Type (color)
Frequency
9.0 x 10-1 m
Radio/M
FERMIONS. Electrons, protons and neutrons are fermions. These particles can NOT be in
the same location with the same energy state at the same time.
This means that two electrons going around the same nucleus can NOT both be in the
exact same state at the
Similar question: The energy of the electron in the hydrogen atom is -13.6
eV. Where did the 13.6 eV (amount from zero) go to in the hydrogen atom?
Answer: In the hydrogen atom, this energy (called the binding energy) was
emitted when the electron fell do
Factors influencing image spatial resolution
1. Gamma camera system spatial resolution (distance and depth dependent)
Collimator geometric spatial resolution depends on collimator design and subject-to-collimator
distance + organ depth (more important on
Limitations to Planar projection imaging
Planar imaging = imaging of radioactivtity distribution by 2-d gamma camera detector
Ambiguities in depth localization
Image contrast lower than T:NT in effects of activity in overlying and underlying tissue
Ima
99m
Tc leukocytes
Advantage
Disadvantage
99mTc more readily available vs In111oxine
Imaging characteristics better w/
99mTc and allow higher admin A and
improve hands/feet visualization
Lower rad exp to pts (peds)
Faster uptake of 99mTc
Poor labeling
2.3PlanarImagingofhumansubjects
Imaging human subjects
Distribution of different tissue types in 3d coordinate system (x,y,z)
Plane perpendicular to long axis of body = transverse slice plane (y-z)
Sagittal (y-z), coronal (z-x)
Aconc based on tissue t
Unit 3.1 Gamma Camera Design
4 stages of imaging process:
1. Image formation (collimation) on detector
Produces image on detector
Formed by absorbing that should not contribute to image using pinhole/multihole Pb collimator
Parallel-hole coll passes on
OTHER FOCUSING COLLIMATORS converging collimator
Allow angled gamma rays through one hole (pinhole) or many holes (multi-hole) to be
detector
Use of angled gamma rays can magnify or minify an image
Magnification, efficiency + FOV of focusing collimator
Unit 3.6 Collimator Types & Performance
PARALLEL-HOLE COLLIMATORS
Allows only parallel gamma rays to be detected
Use of parallel gamma rays give image same size as object = no magnification
FOV does not change with obj-to-coll distance
Collimators diff
Process of labelling 111In:
1. Collect 40cc blood in syringe w/ heparin and/or ACD (ACD reduces tendency to adhere to
plastic)
2. Sep white cells from red cells + platelets (In-oxine labels WBCs more readily than RBCs)
3. Wash WBCs with saline to remove p