Phase contrast microscopy generates contrast from a sample by the wave interference between background (reference beam) and sample light.
The microscope contains two optical devices: The Phase Annulus in the condenser and the Phase Plate in the objective.

A Phase Plate (i, below) is placed in the back focal plane of the objective. The plate is an optically clear piece of glass with a circular mask that retards light exactly 1/4 wavelength (of green light). Optically, the diameter of the phase-retarding mask is the same diameter as the annulus in the condenser.

The Phase Annulus ( ii, below) acts somewhat like a DF annulus, except the light-passing circle (annulus) falls within the collecting angle of the objective. With the annulus in place, the sample plane is illuminated by a cone of light.

With no sample present, the illuminating light continues as an undiffracted plane wave (the "Surround wave" or "S-wave") that is focused on the phasing mask (Phase Plate), and uniformly spreads over (illuminates) the image plane. The light is retarded in phase by 1/4 wavelength (green).

With a phasing sample present (phasing is due to a difference in refractive index between sample and background), refraction (and diffraction) of light produces a spherical wavefront (Diffracted wave or "D-wave") that shifts the sample image rays away from the phasing mask on the phase plate. The D-wave (sample light) is focused on the image plane, while the S-wave fills the image plane. Optical path differences in the sample (vs. background) results in sample light being retarded in phase a variable amount up to 1/4 wavelength. When combined at the sample plane, background light (exactly -1/4 wavelength) constructively interferes with sample light (<-1/4) increasing the amplitude of the wave through constructive interference. This results in bright sample image on a darker background. This type of phase contrast (bright sample on a darker background) is known as Negative Phase Contrast.

Positive Phase Contrast has the inverse phase relationships between the background (S-wave) phase and sample (D-wave), producing a dark sample image on a uniform gray background. Zernike's original discovery/invention was Positive Phase Contrast.

Frits Zernike (1888–1966).
Nobel Prize in Physics 1953 for Phase Contrast Microscopy