Computational
Microscopy

Brightfield microscopy is the simplest and most widely used optical microscopy technique. Light passes through the specimen, and contrast arises from absorption and scattering. The image intensity is determined by the specimen's transmittance: I = |t(x,y)|².

The Fourier view shows the incoherent Optical Transfer Function (OTF), which determines the spatial frequency bandwidth of the system. The cutoff frequency is 2 NA / λ, and the Rayleigh resolution limit is 0.61 λ / NA.

Limitation: Phase objects (like unstained cells) are nearly invisible because brightfield only detects amplitude changes.

Invented by Frits Zernike in the 1930s (Nobel Prize 1953), phase contrast microscopy converts phase shifts in the specimen into visible intensity changes. A phase ring in the back focal plane advances or retards the undiffracted (surround) light by π/2 relative to the diffracted light.

The resulting image intensity follows the thin-object approximation: I ≈ A² + 2A·a·sin(φring)·φ(x,y), where a is the ring attenuation and φ_ring is the phase shift. The characteristic "halo" artifact appears at sharp phase boundaries.

Key insight: The Fourier view shows the phase ring annulus in the pupil plane — the critical optical element that makes phase visible.

FPM uses an LED array to illuminate the specimen from many angles. Each LED shifts the specimen's spectrum in Fourier space, allowing different frequency bands to pass through the objective's pupil. By capturing images under each LED and computationally stitching them in Fourier space, the effective NA (and resolution) far exceeds the physical objective.

The synthetic NA is NAsyn = NAobj + sin(θmax), where θ_max is the maximum illumination angle from the LED array. This can turn a 4x objective into a 40x-equivalent without any mechanical changes.

Watch the Fourier view: Each LED adds a pupil-sized circle to the synthesized aperture, progressively building up resolution.

DHM records the interference pattern (hologram) between the specimen wave and a tilted reference beam. The hologram encodes both amplitude and phase of the specimen field. The recorded intensity is I = |Eobj + Eref|², which expands to DC, +1 and -1 diffraction orders in Fourier space.

By digitally filtering the +1 order and applying the angular spectrum propagation method, we can reconstruct the full complex field at any distance from the focal plane. Switch between Hologram, Amplitude, and Phase display modes to see each stage.

In the Fourier view: The DC term (white), +1 order (green, selected for reconstruction), and -1 order (red) are clearly separated by the carrier frequency.

Flow cytometry passes particles single-file through a detection zone, measuring forward scatter (FSC) and side scatter (SSC) for each event. FSC correlates with particle size (∼r&sup4; for Rayleigh), while SSC relates to internal complexity. The scatter plot reveals populations and subgroups.

Dynamic Light Scattering (DLS) is integrated as the autocorrelation view: g2(τ) = 1 + β·exp(-2Γτ), where Γ = Dq² and the diffusion coefficient D = kBT / (6πηr) gives the hydrodynamic radius via the Stokes-Einstein equation.

The Fourier view shows the angular Mie/Airy scattering pattern, with the characteristic concentric ring structure determined by the size parameter.