---
title: "Phase Microscopy Lab Interactive Lab | Sandbox Physics"
description: "Can a transparent cell be seen without staining, and is the relief it seems to have real? It can."
canonical_url: "https://sandboxphysics.com/labs/phase-microscopy-lab/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/phase-microscopy-lab/"
last_modified: "2026-10-29"
---

Optics 065 · Diffraction, Fourier optics, and computational imaging

# Phase Microscopy Lab

**Can a transparent cell be seen without staining, and is the relief it seems to have real?** It can. Zernike phase contrast, darkfield and DIC all turn the delay the cell gives the light into brightness differences, with no stain. The relief is not real height, though. DIC shading depends on direction, so the cell looks lit from one side, and phase contrast adds halos around edges.

Use a phase microscope with four imaging modes to make transparent patterns visible. See where halos and false relief appear, and follow the same complex specimen field all the way to the sensor.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The specimen is synthetic, thin and purely phase, treated in the scalar paraxial approximation with periodic sampling and sixteen incoherent sources on a ring. DIC is modeled as ideal coherent lateral shear, not as a full commercial polarizing microscope. The unit-magnification inverting relay is drawn unfolded, and apparatus parts use unequal scales. Absorption, multiple scattering, camera noise and phase recovery are not included.

Physics tutorial

## Audit the physics of Phase Microscopy Lab

**Background** A thin transparent specimen changes the phase of the light passing through it but not its local intensity: $\phi=2\pi\,\mathrm{OPD}/\lambda,\qquad t=e^{i\phi}$. The specimen is a known, programmed map of optical path difference (OPD), not a photograph. The same specimen is sent through four different optical setups.

**Why it matters** Can a transparent cell be seen without staining, and is the relief it seems to have real?

Start with the essentials

- **Focus question**: Can a transparent cell be seen without staining, and is the relief it seems to have real?
- **One-sentence intuition**: Light from mutually incoherent illumination directions adds in intensity, not in amplitude: $I=\sum_j w_j|U_j|^2$. Brightfield and Zernike phase contrast share the same ring of sixteen source points. Darkfield moves the direct illumination outside the angles the objective accepts. DIC uses an ideal polarized pair of fields on the axis instead, so its illumination is not the same partially coherent source.

### Core mathematical model

#### The annular phase filter in the pupil

$$
\begin{aligned}P(\boldsymbol\nu)&=\mathbf1_{|\boldsymbol\nu|\le\nu_c}\\&\quad\cdot\left[1+\left(\sqrt{T}e^{i\delta}-1\right)\mathbf1_{\rm ring}\right]\\\nu_c&=\mathrm{NA}/\lambda\end{aligned}
$$

The ring is centred at sixty-five percent of the coherent pupil radius and has a full width of fifteen percent. The transmission is an intensity transmission, so the amplitude uses its square root. The ring phase is set for the chosen wavelength; it is not a fixed manufactured coating.

#### Ideal DIC: two shifted fields interfere

$$
\begin{aligned}U&=\mathcal F^{-1}\{P_{\rm clear}\mathcal F[t]\}\\I_{\rm DIC}&=\frac14\left|e^{i\beta/2}U(\mathbf r+\mathbf s/2)\right.\\&\quad\left.-e^{-i\beta/2}U(\mathbf r-\mathbf s/2)\right|^2\end{aligned}
$$

An equal split and an ideal crossed analyzer give the factor of one quarter relative to the total incident intensity. The shear direction is measured clockwise from the right of the image. The fields are shifted with Fourier phase ramps, not by rounding to whole pixels. The pupil filter acts before the two fields interfere.

#### Why the shadow is directional

$$
\begin{aligned}I_{\rm DIC}/I_0&=\sin^2\!\left(\frac{\beta+\Delta\phi}{2}\right)\\\Delta\phi&\approx\mathbf s\cdot\nabla\phi\\I_{\rm empty}/I_0&=\sin^2(\beta/2)\end{aligned}
$$

This pure-phase limit assumes the objective passes the field that matters. The gradient approximation needs a shear that is small compared with the features. The full model keeps the exponential specimen field even when the phase is not weak, and at larger OPD the contrast follows no general linear law.

#### Darkfield blocks the direct light; gain only changes the display

$$
\begin{aligned}|\boldsymbol\nu_{\rm DF}|&\approx1.2\nu_c>\nu_c\\B&=\min(1,G I/I_0)\\|t|^2&=1\end{aligned}
$$

A discrete outer ring of illumination lights the same pure-phase object. The objective accepts no direct light, so an empty specimen gives zero intensity. The display gain scales all four images equally; it does not represent exposure physics, camera noise, automatic normalization or a phase reconstruction. The finite periodic cell and the sixteen source directions can cause discretization artifacts.

### Common difficulties

#### Visible contrast is not a map of specimen height

**Typical misconception** Every phase microscope shows true thickness; a brighter halo means more material.

**Better mental model** Zernike halos and shade-off appear because some diffracted light also passes through the phase ring. DIC responds to how the OPD changes along the shear direction, so rotating the shear changes the apparent shading. A uniform phase offset is invisible in every mode. No single intensity image is presented as a recovered phase.

### Run the experiment

1. 01

   #### Scene 1: Nearly invisible brightfield

   Start with brightfield, then switch to phase contrast without changing the specimen. Reverse the ring phase and compare the same raw centre cut.

   **What to observe:** The annular condenser aperture and the phase plate in the back focal plane sit in conjugate pupil planes, not in planes conjugate to the specimen image. Raising the NA changes the physical stop and its matching ring.

2. 02

   #### Scene 2: Phase ring: contrast and halo

   Use the wide phase disk to see the halo and shade-off. Then make the ring fully transmitting with zero delay, and the phase-contrast image turns back into brightfield.

   **What to observe:** Darkfield records only light scattered into the objective. With no specimen, the direct illumination stops on an opaque region of the pupil and never passes through the absorbing detector.

3. 03

   #### Scene 3: DIC: direction is not height

   Choose DIC and rotate the shear by a quarter turn. Then select darkfield and press the labeled exposure button. It changes only the display gain, not the raw intensity.

   **What to observe:** All recorded images share one fixed linear gain and clipping level. The OPD colour map has a fixed range of positive and negative values. Neither shows a measured biological specimen.

Physical conclusion

Follow the phase through the pupil filter and the field interference. The contrast you see is an optical measurement, not automatically a picture of height.

## Related experiments and articles

Probes and measurement · Reading path

### Diffraction, phase and surface structure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Zernike: a reference wave makes transparent structure visible**](https://sandboxphysics.com/stories/probe-evidence/zernike-phase-reference/)
2. [Lab **Thick Lens Designer** Find where a thick lens measures its focal length from](https://sandboxphysics.com/labs/thick-lens-designer/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)