Using optical properties to simplify the electron microscope

1. Applying Laser
Physics to Electron
Microscopy
Andrew and Kevin

2. Theory
● An optical cavity is used to trap and intensify
light
● We used two supermirrors with 99.99%
reflectivity

3. How light affects electrons
● intensified resonating light utilizes the
compton effect

4. Ponderomotive Force
● Compton effect on the large scale

5. How an electron microscope works
● Zernike phase plate shifts electrons to
increase phase contrast

6. Our Professor’s theory
● The effect the Zernike phase plate creates
can be replicated by an optical cavity
● Gets rid of durability issues

7. Implementation: Laser Power
The necessary laser power can be calculated using the following equation:
where delta is the deflection of the electrons, gamma =1/(1-(v^2c^2)), v is the velocity of the electrons, P is the
power required, and N = 0.030(Numerical Aperature)/1-r, where r is the reflectivity of our mirrors.

8. Basically, because we want our phase shift (ẟ) to be pi/2,
we, want the right part of the equation to be equal to 1. This
means that, after plugging in numbers, we wanted to make
an optical cavity where we maximized our numerical
aperture and finesse on our cavity.
Numerical aperture can be thought of as the range at which
an optical tool can accept light, and finesse can be thought
of as how effective the cavity is at trapping light.
So we want a cavity that accepts light over a wide range
and has high reflectivity

9. Approach 1: Parabolic Cavity
The first way that was attempted was to use a
parabolic shaped optical cavity to focus light at
the parabola focus.

10. Advantages of this were that
1. The parabolic mirror was actually easier to
manufacture than the next method we will
describe
2. It is easier to reduce loss with this system,
resulting in a greater finesse

11. However, a disadvantage was that a lot of light
spilled over the edge of the parabola, resulting
in a low Numerical Aperture (acceptance
angle). In addition, a lot of efficiency was lost
because the light wasn’t radially polarized.

12. Radially Polarizing the Light
● waveplates work because they are
birefringent! (polarization affects refractive
index)

13. Segmented Waveplate
80k euros :(

14. Approach 2: Spherical Cavity
We get a pair of mirrors that make parts of a
sphere, and place them so that they are
concentric: as in the diagram below:
L
RM = 2(f)
R(L/2)

15. Advantages of this were a higher Numerical
Aperture, while keeping a pretty high finesse.
This is the design that we worked on

16. This was our schematic
It looks scary but
much of it was for
shaping and
directing the laser
beam so that it
suited our needs

17. This is what our lab table looked like
LASER SOURCECAVITY

18. Close-up of Cavity Setup
MIRROR 2
MIRROR 1
MEASURING
EQUIPMENT

19. Determining Numerical Aperature
We used a camera to
capture the light that left
the cavity
The bright spot in the
middle shows the size of
the light leaving the cavity
(should be same as the
light entering the cavity),
giving us our Numerical
Aperture

20. Determining Finesse
We scanned the
frequency of the cavity,
and plotted the light
brightness vs.
frequency on an
oscilloscope. The
brightness of the light
spikes at the resonant
frequency of the cavity.

21. The thinner and taller the spike was, the higher
the finesse of our cavity turned out to be. Thus,
you can see we had a fairly thin and tall spike,
indicating a decently high finesse.
The high NA and finesse fit our power
requirements as calculated before, and so we
proved that the theory of using lasers to create
phase contrast is viable.

22. Keeping the Cavity Locked
One issue we had was that the resonance of
the cavity kept drifting away due to
uncontrollable factors (room temperature,
shaking, frequency drift, etc). We decided to
implement a negative feedback loop to correct
the cavity

23. Pound-Drever-Hall Lock
Commonly used technique in
laser optics, basically
implemented a feedback loop
to correct the cavity of any
errors.
By taking data using a photodetector, we could
generate an error signal to show how much the
frequency was off by, and autocorrect the laser.