Image formation by a lens (new and improved version, July 19, 2011) -- Image formation by the eye
Snell's law
Total internal reflection - this shows light going from glass to water, as in a microscope. The two cases of the electric field perpendicular to the plane of incidence and parallel to the plane of incidence are shown (the intensities were calculated using the Fresnel equations). Total internal reflection is at angles greater than 63. Note also the Brewster angle at 42, where the reflected light is all perpendicular. Reflection and transmission intensities for air to glass - air to water
Dispersion (not that great, it only shows red and blue because more colors overlap too much) --
wave fronts and refraction - how to explain Snell's law
wavelets and refraction - another way to explain Snell's law, using Huygens wavelets
The Principle of Least Time (first attempt) - running vs swimming

Constructive / destructive interference
Phase delay
Transmission through a polarizer
Elliptical polarization
Differential interference contrast (DIC) - move the specimen and change the bias.
Differential interference contrast (DIC) - make a linescan image

arrow keys don't work: Light scattering - light passes through a material of variable thickness and scattering properties. In this animation, 100 photons begin at the left and are scattered as they pass through a scattering material. The brown dots in the lower part are a graph of the number of unscattered photons. Color dependence of scattering - this attempts to show that shorter wavelengths are scattered more than longer wavelengths. 100 each of red, green and blue photons start out and are scattered approximately according to the fourth power of the wavelength.

Confocal microscope - blue photons cause green photons as they travel through the specimen. The photons generated at the focal region are bright green, and the ones that go back through the lens become focused at the pinhole. Other out of focus photons are generally rejected by the pinhole, but some definitely get through.
Two-photon excitation - red photons cause no fluorescence / photons except at the focal region, where they cause two photon excitation. The green photons captured by the lens are focused at the pinhole. This animation does not take into account scattering of light in the specimen (see next animation).
Effect of scattering - a cohort of green photons are generated at the focus. There is scattering in the tissue; the scattered photons are changed to dark green. The lens collects unscattered photons and directs them towards the pinhole. In the case of two photon microscopy, where the only photons generated are at the focus, it is desirable to collect the scattered photons - this is achieved by getting rid of the pinhole.

An attempt at numerical aperture of different lenses - data from D.B. Murphy "Fundamentals of light microscopy & electronic imaging"

Fourier synthesis of a square wave

"Point spread function" - A sharp object is imaged by a lens. The point spread function is approximated here by a gaussian distribution instead of an airy disk. The width of the object and of the p.s.f. can be varied. (the image is made by convolution of the object with the gaussian)

Black body radiation

Kon, Koff, and FRAP - same with running, normalizeable trace - smaller number of binding sites (for fluctuations), co-varying kon koff
diffusion & FRAP - diffusion & photoactivation

Noisy image - simulation of a CCD image under low light conditions 1 - 2

A simulation of PALM

Laser -- This is meant to show "light amplification" by "stimulated emission". In this simulation, you press "play" to start the excitation. The lifetimes of the 4 states can be changed. The mirrors are added in order to make light amplification possible. It takes 10-20 seconds or more to get going. In order to get light amplification, there must be a population inversion, which is caused by "state 2" having a longer lifetime than "state 3". Once the laser is "going", you can turn it off by changing the lifetimes of state 2 and 3 to 10 and 1000 psec respectively.

Fluorescence lifetime imaging - How fluorescence lifetime is measured.The lifetime depends on the molecule and can also be affected by the molecule's environment or by the presence of FRET. The laser pulse of a Ti-sapphire laser (which lasts about 100 femtoseconds) brings molecules into the excited state. The molecule decays from the excited state and emits a photon with a characteristic "fluorescence lifetime". In practice, the laser power is attenuated so that either 0 or 1 excitation occurs per pulse. This is done in order to make the lifetime measurement feasible. The Ti Sapphire produces 80 million pulses per second, so it is possible to generate enough measurements within a reasonable amount of time. This animation is not realistic because it shows around a hundred excitations per laser pulse - the animation would take too long otherwise!

Fluorescence correlation spectroscopy - animation 1 shows an "experiment" with modifiable diffusion coefficient. animation 2 shows how the auto-correlation is calculated. The goal is to determine the diffusion coefficient. The "best" way to do this would be make a movie at microsecond time resolution of the molecule (fluorescently labeled). But this is not possible with present technology. Instead, FCS provides a somewhat indirect way to do this. The laser beam is stationary so that it illuminates a small region. A photodetector determines whether 0, 1, 2, 3, etc particles are present in the region with microsecond time resolution. If the particle has a high diffusion coefficient, it will not spend much time on average in the region, because it will diffuse out of the region. If a particle has a low diffusion coefficient, it will spend relatively more time in the region. Since the particles are not imaged (their presence is only detected), a math method is used to determine how long on average a particle stays in the region. This method is called "auto-correlation". If a particle is present at one time point, the question is whether it is present at the next time point, at the following time point, etc.
In the first animation, an "experiment" is done with a large enough number of data points to make a meaningful estimation (the animation does not show every time point). The actual diffusion coefficient can be changed, in order to see how the data changes. In the second animation, a small number of data points is analyzed in order to show how the auto-correlation function is determined. In both of these animations, the area illuminated by the laser is approximated by a square - in a real experiment, this would be an airy disk / gaussian distribution.

Fluorescence intensity decrease in thick specimens - Based on Terasaki, Biology of the Cell 98:245 (2006) - The specimen here is an egg. The fluorescence intensity decreases exponentially as the focal plane advances into the egg, due primarily to scattering. The "optical section" in this animation is an idealized sharp slab rather than a gaussian. Blue dots show what a microscope with 1 µm optical section would see. The default values are for a starfish oocyte, which has diameter 180 µm, and whose fluorescence decreases by half every 30 µm. The default optical section of 30 µm corresponds approximately to a 20x 0.5 N.A. lens with half open confocal pinhole. Variation #1 - In a real confocal z series, as focal level goes deeper, the center of the oocyte image is darker than the edges. The oocyte is a sphere, and light from the central part of the image passes through more cytoplasm than light from the periphery. This animation simulates this effect, though it is for an ideal slab optical section with thickness 1 µm.

A curious effect of scattering in a multiphoton microscope - the signal is greater in shallow focus on brain tissue than in aqueous solution. Download swf file -- source files