The specimen shifts the phase but barely dims the light
A thin transparent object mostly delays the light: it shifts the phase and passes almost the same amplitude. For such a weak phase object, an in-focus intensity image shows little first-order contrast. Staining adds contrast by absorption, but it changes how the specimen is prepared and may limit what can still be observed alive.
Zernike’s 1953 lecture starts with flaws in diffraction gratings and the faint spectral ghosts they produce. Comparing the ghosts with a coherent reference revealed their relative phase. The microscope method grew out of controlling that phase relation.
Separate the two waves in the pupil, recombine them in the image
Near its back focal plane, the objective forms an image of the light source. The direct light passes through that small image, and light diffracted by the specimen spreads around it. A phase strip or ring placed there shifts the relative phase of the two and often dims the direct light. The two overlap again in the image plane.
The direct light acts as the reference: the small change made by the specimen interferes with it. A coloured overlay painted on the final image cannot do this.
Sources: [1]
In a real objective, the back focal plane sits among the glass
Zernike put his strip where a plane wave comes to a focus. In the lecture that focus lies ‘closely above the objective (in its back focal plane)’, and his first microscope trial had the strip ‘placed closely above a low-power objective’. A modern objective is a stack of thick lenses, and the plane where it focuses parallel light often falls inside the stack. Nikon’s MicroscopyU guide notes that this plane usually lies near an internal lens element, so some phase objectives carry the ring etched into a lens surface.
A single thick lens already shows why the plane is not where the glass ends. Its focal length is measured from the place where it acts as if it bent the light once, which opticians call the rear principal plane, and in a thick lens that place can lie well inside the glass. A plano-convex lens 11.7 mm thick, with a focal length of 25.4 mm, focuses parallel light only 17.6 mm behind its flat face, because the plane is 7.7 mm inside the glass. Rock such a lens in a parallel beam and the focused spot stays still only when the turning axis passes through that plane; the thick-lens Lab lets you find it.
A small-phase calculation shows where the contrast comes from
Take the incident field to have a real amplitude of one and let the weak specimen phase vary relative to a uniform background. The direct, undiffracted component supplies the reference; the spatially varying first-order field is a quarter cycle out of step with it, so it adds no first-order intensity contrast in focus. Shift the direct component alone by a positive quarter cycle, and the ideal image gains the linear phase term below. A phase common to the entire field gives no contrast.
The sign below comes from choosing that positive shift; reverse the relative phase and the contrast reverses. The calculation ignores absorption, the finite numerical aperture and the size of the phase ring. It shows how contrast arises; it is not a method for recovering phase quantitatively.
Sources: [1]
Halos keep brightness from reading as thickness
Real phase-contrast microscopes have finite apertures, and the phase element also shifts some of the diffracted light at low angles. Halos and shade-off can appear as a result. Without a calibrated transfer model, brightness cannot be read as thickness, refractive index or dry mass.
Optical Zernike phase contrast and electron phase-contrast imaging both rely on interference, but their illumination, interaction potentials and transfer functions differ. Sharing the word phase does not let one explanation vouch for both instruments.
Sources: [1]
Find the reference wave before reading the image
In the lecture, read the grating experiment and the phase-strip construction before the biological application. In the linked model, compare an amplitude specimen and a phase specimen at the same aperture, then change what happens in the pupil plane. The prediction worth checking is how the image changes when the relative phase changes.
Sources: [1]