L12 - Optical and Photoacoustic Imaging

Snell’s Law

$$\begin{array}{rl}{n}_1\sin {\theta }_1& =n_2\sin {\theta }_2\\ \frac{\sin {\theta }_1}{\sin {\theta }_2}& =\frac{v_1}{v_2}\end{array}$$

Brigthfield Microscopy

Why is it not so simple?

• Lenses for cascading effect of magnifications
• Sharper images compared to magnifying glass

Lens

• Objective Lens $\to$ change field of view and resolution ($\text{Field of view}\propto \frac{1}{\text{Resolution}}$
• Condenser Lens $\to$ illuminate sample
• Ocular Lens $\to$ Collect light from sample
• Lamp light $\to$ collimated on sample plane

Phase Contrast Microscopy

Differentiate between light propagating through cells and light unaffected by sample

$$\Delta \varphi =\frac{2\pi }{\lambda }(n_{cell}-n_{water})d$$

$\Delta \varphi$	Phase difference
$d$	Diameter of cell

Phase Plate

1. Causes unscattered and scattered light to be $\pi$ out of phase
2. Destructive interference
3. More contrast

Histological and Fluorescent Stains

Increase contrast of specific object by chemical approach, reduce background via reflection geometry and spectral filtering.

• Histological stains
  • Golgi for neurons
  • Hematoxylin for cancer
  • Eosin (H&E) for cancer
• Fluorescent stains
  • Autofluorescence for bacteria
  • Exogenous “fluorochromes” for cells

Emission filter should never allow the excitation light to pass through

Confocal Microscopy

Emission pinhole that only allow specific layer of light to pass through

• In vivo imaging
• Eliminate the need for thin specimens
• Optical sectioning replacing physical tissue sectioning

Photoacoustic Tomography

1. Light absorption
2. Temperature rise
3. Thermoelastic expansion
4. Acoustic emission

Photoacoustic effect

$$\begin{array}{rl}& p_0\propto {\mu }_a\\ & p_0\propto {\eta }_{th}\end{array}$$

$p_0$	Initial photoacoustic pressure
${\mu }_a$	Optical absorption coefficient (wavelength dependent)
${\eta }_{th}$	Fraction of absorbed optical energy converted to heat (efficiency)

Thermal Relaxation Time

$${\tau }_{th}=\frac{d_c^2}{{\alpha }_{th}}$$

${\alpha }_{th}$	Thermal diffusivity ($\mathrm{m}{\mathrm{m}}^2/s$)
$d_c$	Characteristic length ($\mu \mathrm{m}$)

Stress Relaxation Time

$${\tau }_s=\frac{d_c}{v_s}$$

$v_s$	Speed of sound ($\mu m/ms$)
$d_c$	Characteristic length ($\mu \mathrm{m}$)

The laser pulse width ${\tau }_l<{\tau }_s\ll {\tau }_{th}$, then the excitation is in stress and thermal confinements.

Resolution and Penetration

$$\begin{array}{rl}\text{Spatial resolution}& \propto \frac{1}{\text{Acoustic bandwidth}}\\ \text{Penetration limit}& \propto \frac{1}{\text{Acoustic bandwidth}}\\ & \\ \frac{\text{Penetration limit}}{\text{Spatial resolution}}& =\text{constant}\end{array}$$

Image Properties

$\text{Absorption coefficient}\propto \text{Photoacoustic signals}\propto \text{Image brightness}$

The absorption property of light is used for imaging, which is different from our eyes that used reflection property.