Chromatic Aberration Calculator

• Thin lens dispersion scaling: lens power is proportional to (n − 1). Therefore f(λ) = f_d · (n_d − 1)/(n(λ) − 1).
• Longitudinal chromatic aberration (LCA): LCA = |f_F − f_C|.
• Abbe approximation: using V_d = (n_d − 1)/(n_F − n_C), a common estimate is LCA ≈ f_d / V_d.
• Defocus blur diameter: for f-number N, d ≈ LCA/N.
• Lateral chromatic aberration: at image height y, Δy ≈ y · (LCA/f_d).

1. Enter your reference focal length f_d in millimeters.
2. Either provide n_d, n_F, n_C or provide V_d.
3. Optional: add f-number to estimate chromatic defocus blur.
4. Optional: add image height to estimate lateral color shift.
5. Optional: add pixel pitch to convert mm into pixels.
6. Press Submit to view results above the form and export.

Chromatic aberration in measurable terms

Chromatic aberration is the change in focus and magnification with wavelength. It is commonly split into longitudinal color (axial focus shift) and lateral color (field scale change). Reference wavelengths are the F-line 486.1 nm, d-line 587.6 nm, and C-line 656.3 nm.

Longitudinal focus spread from dispersion

For a thin lens with fixed curvatures, optical power scales with (n−1), so focal length scales as 1/(n−1). With indices n_d, n_F, and n_C, the calculator estimates f_F and f_C, then reports LCA = |f_F−f_C| in millimeters. It also derives V_d = (n_d−1)/(n_F−n_C) to cross-check dispersion. If only V_d is available, it uses LCA ≈ f_d/V_d as a quick estimate.

Lateral color at the sensor plane

Lateral chromatic aberration is estimated at image height y using Δy ≈ y·(LCA/f_d). This ties edge fringing to field position: doubling y doubles the predicted shift, making corners the most sensitive region for wide fields.

Blur diameter, aperture, and pixel impact

When the system is focused at the reference wavelength, out-of-focus wavelengths produce defocus blur. The calculator uses d ≈ LCA/N, where N is the f-number, and reports blur in millimeters and micrometers. Enter pixel pitch to convert blur and lateral shift into pixels. Values above 1–2 px often appear as colored softness on edges.

Reading the Plotly wavelength curve

When indices are provided, the graph fits a smooth dispersion curve through n_C, n_d, and n_F, then plots focal length versus wavelength and focus shift relative to f_d. Markers highlight the three reference wavelengths, and the curve helps visualize which spectral regions drive the focus error. Steeper variation across 420–700 nm generally indicates stronger broadband fringing.

Worked example and practical mitigation

With f_d=50 mm and V_d=64.17, the estimate gives LCA ≈ 0.779 mm. At N=4, predicted defocus blur is about 0.195 mm (195 µm). With 3.45 µm pixels, that is roughly 56 px. At y=10 mm, lateral color is about 0.156 mm. Higher V_d glass, achromatic pairs, stopping down, and software correction reduce artifacts.

1) What is the difference between longitudinal and lateral chromatic aberration?

Longitudinal color shifts the best focus with wavelength, so different colors blur differently at the same sensor position. Lateral color changes magnification with wavelength, creating colored outlines that grow toward the image edges.

2) Should I enter refractive indices or only the Abbe number?

Use indices when you have n_d, n_F, and n_C from a datasheet; the calculator can estimate f_F and f_C directly and plot a wavelength curve. Use V_d when you only need a quick LCA estimate.

3) Does stopping down reduce chromatic aberration?

Stopping down mainly reduces the visible blur from longitudinal color because defocus blur scales roughly as LCA/N. Lateral color is largely geometric and does not shrink as strongly with aperture, though reduced blur can make it less noticeable.

4) How do I interpret results in pixels?

Enter your pixel pitch to convert millimeters to pixels. If predicted blur or lateral shift is below about one pixel, fringing may be hard to see. Several pixels usually means visible color edges and reduced micro-contrast.

5) Why are the F, d, and C wavelengths used?

They are traditional reference spectral lines that bracket visible light. Using the blue F-line, yellow d-line, and red C-line gives a compact, standardized way to describe dispersion and compare optical materials.

6) Will an achromatic doublet always eliminate chromatic aberration?

An achromat typically brings two wavelengths to a common focus, greatly reducing longitudinal color. Residual secondary spectrum and lateral color can remain, especially off-axis. Use the calculator to estimate whether the remaining error is acceptable.