Phase object
Retards part of the beam without bending it — invisible on its own, and the thing an interferometer exists to reveal.
Open in the canvas →In the real world
Most of what a microscope is pointed at does not absorb light. A living cell in culture medium, a gas flow, a flame, a fibre being drawn, a layer of transparent polymer — all of them are close to perfectly clear. Shine light through and almost exactly as much comes out the other side, so a detector that measures intensity sees nothing at all. Such an object is called a phase object: it is invisible not because it fails to affect the light, but because everything it does happens in a quantity ordinary detection throws away.
What it does affect is the arrival time. Light slows in a medium of refractive index n, so a thickness t of material with an index different from its surroundings advances or retards the wave that crosses it relative to the wave beside it. The accumulated optical path difference is
The numbers involved are small and stubbornly invisible. A typical cell is perhaps 5 µm thick with an index around 1.37 in medium of index 1.33, giving an OPD near 0.2 µm — well under half a wavelength of green light. No amount of contrast stretching recovers it from an intensity image, because the intensity image genuinely does not contain it.
Every technique for seeing such an object works the same way underneath: interfere the light that passed through it with a reference that did not, so the phase difference becomes a difference in brightness. Two beams of intensity I₁ and I₂ meeting with a phase difference Δφ give
Frits Zernike built the first practical instrument on exactly this idea. His phase-contrast microscope splits the light a specimen scatters from the light that passes it undisturbed, retards one against the other by a quarter wave in a ring etched into a glass plate at the back focal plane, and lets them recombine — turning a phase object into a bright-and-dark image without staining or killing it. It won the 1953 Nobel Prize in Physics and remains the reason live-cell microscopy is possible at all[1].
The same principle scales far beyond a microscope. Differential interference contrast interferes each point of the specimen with a slightly sheared copy of itself, so the image reports the phase gradient. Quantitative phase imaging recovers the OPD map as a calibrated number per pixel, which for a cell of known index is essentially a dry-mass measurement. And a Mach–Zehnder interferometer with a wind tunnel in one arm turns the density field of a shock wave into countable fringes[2] — the technique that made compressible flow visible long before computational fluid dynamics.
The practical rule in every one of these is the same. A phase object shifted by a whole wavelength is indistinguishable from no object at all, because the wave recombines exactly as it started. Contrast is maximised near half a wave, where the recombination is fully destructive, and that is the condition instruments are designed around.
In OpticalSetup
The Phase object writes optical path across the beam without bending it. It has no index and no thickness to configure; it is specified directly by the quantity that matters, the peak path difference it adds, and by how that path is distributed across its clear aperture. Four profiles are available:
- Central bar — the middle third of the aperture retarded, the rest untouched. A phase-contrast test object, and the default.
- Wedge — path rising linearly from one edge to the other, the classic tilted-plate fringe generator.
- Step — half the aperture retarded, half clear.
- Curved — quadratic, thickest at the centre and falling to zero at both edges, like a lenslet or a droplet.
Each ray crossing the plate picks up the path its own crossing point calls for, so the phase written across the beam is a real spatial pattern rather than a single number. Recombine that arm against a reference and the pattern becomes intensity — which is the whole reason the element exists. The default is a central bar of 0.27 µm, half a wave at 532 nm: the phase-contrast condition.
Two behaviours surprise people, and both are real optics rather than simplifications.
The profile spans the clear aperture, not the beam. A narrow beam through a wide wedge samples only a short section of the ramp and picks up an almost uniform delay — a piston, not a tilt, and pistons produce no fringes. Match the aperture to the beam and the full profile is written. The inspector's “Fringes across the beam” readout uses the span the trace actually lit, so it reports what the light picks up rather than what the plate could write.
Some settings move a port total and some cannot, and the difference is not about strength. Averaging the two-beam formula across the beam leaves the port at half the light plus a term that swings with the reference arm, and the size of that swing is the length of the mean phasor of the written phase — |⟨eiΔφ(u)⟩| over the illuminated aperture. When the phases written across the beam cancel as a phasor, the total is pinned at half the light however the reference is set, and the fringes merely slide sideways underneath an unchanging number.
That happens at particular settings rather than for particular profiles. A wedge spanning exactly one whole fringe cancels, and so does one spanning two, or twenty; but the same wedge at half a fringe swings harder than anything else here, between 0.19 and 0.81 of the input. A half-aperture step cancels when its step is exactly half a wave, and swings once it is not. The central bar is asymmetric — a third of the beam against two thirds — so it swings by a third, between 0.67 and 0.33, which is why it makes the most legible default. When the current setting genuinely cannot move the total, the readout says total stays put, read the profile rather than leaving the element looking inert.
The added path is genuine, not a bookkeeping phase: a pulse crossing the plate arrives later by OPD/c, which a photodetector or autocorrelator downstream will report. And on its own the element is exactly as invisible as its physical counterpart — put a detector straight after it at any setting and the reading is unchanged. It takes a reference arm to reveal it.
This is a pure phase screen. It has no absorption and, more significantly, no refraction: a real transparent object with an index step both delays light and bends it, and a strong phase gradient deflects a ray by an angle this element does not apply. The rays leave exactly parallel to how they arrived, carrying only the added path.
The profile is one-dimensional across the aperture, matching the tracer's 2D meridional plane — there is no second transverse axis, so a true 2D phase map such as a real cell presents cannot be authored. The four shapes are fixed; arbitrary OPD maps, measured phase data, and the Zernike quarter-wave ring at a back focal plane are not available, so the phase-contrast microscope cannot be reproduced as an instrument even though the physics it exploits is here.
The path difference is specified in micrometres and held fixed across wavelength, which correctly makes the resulting phase scale as 1/λ but means the element carries no material dispersion of its own: a real object's index varies with wavelength and its OPD varies with it. Nothing scatters, and there is no partially coherent imaging theory — the fringes come from the tracer's coherent recombination, so the contrast a real instrument loses to finite condenser aperture and source extent is not modelled.
Related components
References
- F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955) — the Nobel lecture account of the method
- W. Merzkirch, “Flow Visualization,” 2nd ed., Academic Press (1987) — interferometric density measurement in compressible flow