---
title: "Lens Aberration Clinic Interactive Lab | Sandbox Physics"
description: "How do you identify a lens aberration from its blur and fix it without creating another? Start from the shape of the blur."
canonical_url: "https://sandboxphysics.com/labs/lens-aberration-clinic/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/lens-aberration-clinic/"
last_modified: "2026-10-27"
---

Optics 027 · Imaging, instruments, and visual systems

# Lens Aberration Clinic

**How do you identify a lens aberration from its blur and fix it without creating another?** Start from the shape of the blur. Spherical aberration leaves a round halo, coma a comet-shaped tail, and astigmatism a line-like smear. Each shape comes from its own term in the wavefront error, and the matching correction cancels that term. Judge the fix across the whole lens opening, not by one spot size, so the error is not simply moved into another aberration.

A 2D optical diagnostics bench turns Seidel wavefront terms into analytic transverse ray fans, spot diagrams at physical scale, a signed exit-pupil map and a treatment sweep for spherical aberration, coma, astigmatism, field curvature and primary chromatic correction.

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

The reference lens is a normalized 50 mm f/2.8 teaching system with a circular pupil. Its coefficients are not the prescription of a commercial lens. The diffraction PSF, MTF, distortion, vignetting, tolerances, coating loss, polarization and higher-order aberrations are not included.

Physics tutorial

## Audit the physics of Lens Aberration Clinic

**Background** First-order optics predicts a single Gaussian image point, but a real wavefront can depart from the ideal reference sphere. This Clinic describes that departure with the normalized third-order expansion $W=W_{040}\rho^4+W_{131}H\rho^3\cos\phi+W_{222}H^2\rho^2\cos^2\phi+W_{220}H^2\rho^2$. Each term has its own symmetry across the pupil and leaves a recognizable pattern in the ray fans and the spot diagram, so you can identify it from that pattern instead of guessing from a round blur.

**Why it matters** How do you identify a lens aberration from its blur and fix it without creating another?

Start with the essentials

- **Focus question**: How do you identify a lens aberration from its blur and fix it without creating another?
- **One-sentence intuition**: Where a ray lands in the spot diagram is set by the local slope of that same wavefront, scaled by the reference focal length and pupil radius: $\Delta\mathbf r=f\frac{\lambda}{R_p}\nabla_{\!p}W$. The pupil map, the two ray fans, the spot cloud, the RMS radius and the treatment sweep all come from one wavefront, so any disagreement between them would point to a computing error.

### Core mathematical model

#### Third-order wavefront

$$
W(\rho,\phi)=W_{040}\rho^4+W_{131}H\rho^3\cos\phi+W_{222}H^2\rho^2\cos^2\phi+W_{220}H^2\rho^2
$$

Spherical aberration is rotationally symmetric. Coma is odd along the field direction. Astigmatism focuses the tangential and sagittal fans at different places. Field curvature acts on a flat sensor as defocus that changes with field position.

#### Wavefront slope to ray error

$$
\Delta\mathbf r=f\frac{\lambda}{R_p}\left(\frac{\partial W}{\partial x_p},\frac{\partial W}{\partial y_p}\right)
$$

The Lab differentiates the polynomial analytically at every sampled pupil point. Before any point is drawn, a finite-difference check confirms that gradient independently.

#### Small-error Strehl estimate

$$
\widehat S_M=\exp\!\left[-\left(2\pi\sigma_W\right)^2\right]
$$

Piston and tilt are removed before the RMS wavefront error over the pupil is calculated. The result is a Maréchal estimate, and the Lab marks where that approximation stops holding. It is not a computed diffraction PSF.

#### Primary achromat condition

$$
\Phi_1/V_1+\Phi_2/V_2=0
$$

Two elements of opposite power, made from glasses with different Abbe numbers, can bring the F-line and C-line foci back together. The d line can still be left with secondary spectrum, which stays visible in the last treatment scene.

### Common difficulties

#### Calling every small spot diffraction limited

**Typical misconception** If the geometric spot fits inside the Airy reference circle, the displayed point cloud is already a diffraction point-spread function.

**Better mental model** A spot diagram shows where rays hit; an Airy pattern shows coherent diffraction intensity. This Lab draws only the radius of the first dark ring, as a scale reference, and reports the Maréchal estimate separately.

### Run the experiment

1. 01

   #### Scene 1: Spherical and coma diagnosis

   Open spherical and coma diagnosis. Increase the aberration magnitude and compare the radial spherical fan with the lopsided coma tail. Then raise treatment and watch the same points draw in while the plot scale stays fixed.

   **What to observe:** Pure spherical aberration stays centered and rotationally symmetric. Coma sends different parts of the pupil to different places and leaves a comet-shaped cloud, even after the centroid is removed.

2. 02

   #### Scene 2: Astigmatism and field curvature

   Switch to astigmatism and field curvature. Compare the solid tangential fan with the dashed sagittal fan and verify that the field-flattener prescription reduces their separation at the fixed image plane.

   **What to observe:** Astigmatism can make one ray fan look corrected while the perpendicular fan stays broad. A single RMS number cannot reveal that direction-dependent error on its own.

3. 03

   #### Scene 3: Achromat and asphere treatment

   Select achromat and asphere treatment. Sweep treatment from singlet toward doublet and verify that the blue F and red C spot families reunite while a smaller green d-line residual remains visible.

   **What to observe:** Primary achromatization can match two selected wavelengths without eliminating every wavelength-dependent focus shift. More elements or anomalous dispersion are required to control the residual spectrum further.

Physical conclusion

To diagnose an aberration, check that its pupil symmetry, wavefront slope, tangential and sagittal fans, spot size and response to treatment all point to the same cause, and remember where geometric optics gives way to diffraction.

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)