Lens Optics and Resolution: A Practical Guide

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How a lens resolves detail

A camera records detail in two stages. First, the lens forms an image on the sensor. Second, the sensor samples that image into pixels. The final sharpness depends on both stages. A lens that forms a very sharp image can be wasted on a sensor with large pixels, and a fine sensor cannot improve an image the lens has blurred.

This guide explains the physics behind each stage and how they interact. It starts with light as a wave, moves through diffraction and lens design, and ends with the sensor.

The main limits

Two limits set the sharpness of an image. The diffraction limit comes from the wavelength of light and the size of the aperture. It is a physical limit that every lens faces. Aberrations, such as spherical and chromatic aberration, add further blur and depend on the lens design. The sensor adds a third limit, set by pixel pitch through the Nyquist frequency.

Each limit can be calculated or measured. Knowing which one is dominant tells you where improvement will come from.

Where to start

Start with the Airy disk calculation, because it gives the diffraction limit in concrete numbers. Then read about aperture softening to understand why the best aperture is rarely the widest or the smallest. Next, read the aberrations article and the MTF chart article to see how lens design and measurement fit together. Finish with the sensor article to connect the optics to the pixels.

Glossary

Airy disk: the bright central spot of a diffraction pattern from a circular aperture, surrounded by fainter rings.

f-number (N): focal length divided by the entrance pupil diameter.

Diffraction limit: the smallest detail a diffraction-limited lens can resolve at a given wavelength and f-number.

Aberration: a departure from ideal focusing, such as spherical or chromatic aberration.

MTF: modulation transfer function, the contrast a lens or system retains at each spatial frequency.

Nyquist frequency: the highest spatial frequency a sensor can record without aliasing, equal to 1 divided by twice the pixel pitch.

Common questions

Is a sharper lens always better? Only up to the limit of the sensor. Beyond that, extra lens sharpness adds no detail the sensor can record.

Why is my image softer when I stop down? Diffraction increases as the aperture gets smaller. The Airy disk grows, and fine detail blends together.

Do more megapixels always help? Only if the lens can resolve the extra detail at the aperture you use.

A worked chain from lens to sensor

Consider a 50 millimetre lens at f/8 recording light at 550 nanometres onto a sensor with 4 micrometre pixels. The Airy disk is about 10.7 micrometres across, so it covers roughly two and a half pixels. The lens therefore limits the detail to about the same level the pixels could sample, and the image is sharp to the extent that the Nyquist limit of 125 line pairs per millimetre allows. At f/16 the Airy disk doubles, and the diffraction limit becomes the main constraint.

How to decide what to improve

If the image is soft at the widest aperture, the first suspect is aberration, and the remedy lies in the lens choice or in stopping down. If it is soft at the smallest aperture, diffraction is the likely cause, and opening up will help unless depth of field is the priority. If fine detail shows colour fringes or moire, the sensor sampling and the lens chromatic correction are the places to look. A test target at several apertures, read against the calculations in this guide, separates these causes.

Measurement sources

Manufacturer MTF charts describe a lens under stated conditions. ISO 12233 describes methods for measuring a whole camera with standard test charts. Independent laboratory tests, when available, use these methods and give comparable results. Compare like with like: the same aperture, the same frequency range and the same measurement method.

Working through a complete example

Consider a photographer who wants to know whether a new lens will sharpen images from a 24 megapixel full-frame camera with 6 micrometre pixels. The Nyquist frequency is 1 divided by 0.012 millimetres, about 83 line pairs per millimetre. At f/8, the diffraction cutoff for 550 nanometre light is about 227 line pairs per millimetre, which is well above the Nyquist frequency. At f/16 it falls to about 114, which is still above the Nyquist frequency. The lens is therefore not the limit at these apertures, and the sensor is. A sharper lens would show little gain, but a lens with poor contrast at 40 to 80 line pairs per millimetre would be visibly softer.

Reading the limits as a decision tool

The three limits in this guide give a simple way to judge upgrades. If the lens limit is above the sensor limit at the aperture you use, a better lens is unlikely to help. If the sensor limit is above the lens limit, a better lens will help. If the aperture needed for depth of field pushes the diffraction limit below the sensor limit, the trade-off must be accepted or the scene arranged differently. The articles explain each step, and the calculator checks the arithmetic.

Terms used across the site

Terms such as Airy disk, f-number, MTF, Nyquist frequency and aberration are defined in the glossary above. Where an article uses a term in a particular sense, the article says so. The guide uses SI units throughout, and it gives wavelengths in nanometres and sensor dimensions in micrometres or millimetres.

Full-frame and crop-sensor comparison

A lens that covers a full-frame sensor can be used on a crop sensor, which records a smaller area of the same image circle. The crop sensor records the central part of the image, where the lens is usually sharpest. The pixel pitch of the crop sensor may be finer or coarser than the full-frame sensor, and the Nyquist comparison must be made for the sensor in use. Crop sensors also magnify the image less than a full-frame camera at the same distance, which changes which lens focal length is needed.

Diffraction at different sensor sizes

The Airy disk depends only on wavelength and f-number, so it is the same on any sensor. What differs is the number of pixels it covers. A small sensor with fine pixels can show diffraction softening at an aperture that looks harmless on a larger sensor with coarser pixels, and the reverse can also be true. Always compare the Airy diameter with the pixel pitch of the sensor in use.

Keeping the guide up to date

The formulas in this guide are stable, but sensor pixel sizes, lens designs and measurement standards change over time. Readers should check the current sensor specifications and the current version of any standard before relying on a specific figure. The review date at the foot of each page shows when the content was last checked.

How to use this guide with your own equipment

Start by writing down the lens, the sensor and the aperture range you use most. Look up the sensor pixel pitch and calculate the Nyquist frequency. Calculate the Airy diameter at your main apertures and compare it with the pixel pitch. These three numbers give a first picture of which limit applies to your setup, before any testing.

Then test the setup with a standard target at a few apertures, and compare the results with the calculations. Where the test disagrees with the calculation, the difference points to a real lens error, a focus error or a measurement problem, and the articles explain how to tell them apart.

What this guide does not cover

This guide does not cover the design of new lenses, the detailed chemistry of glass, the electronics of image sensors, or the software used to process raw files. Those topics are large, and each has its own specialist literature. The guide covers the physical limits that every lens and sensor combination faces.

Reading the three limits together

No single limit tells the whole story. A lens can be diffraction-limited at one aperture and aberration-limited at another, and a sensor can be the limit for some subjects and not others. The most useful habit is to ask, for each image, which limit is closest to the result you see. The answer tells you what to change: the aperture, the lens, the sensor, or the subject distance.

Over time, a clear picture of your own equipment develops. You learn which apertures are sharpest, where the lens falls off, and whether the sensor is sampling finer than the lens can resolve. That knowledge is worth more than any single specification.

Sources

Eugene Hecht, Optics, Pearson (any current edition).
Max Born and Emil Wolf, Principles of Optics, Cambridge University Press (any current edition).
ISO 12233: Photography, Electronic still picture imaging, Resolution and spatial frequency responses.

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General information only. This page explains optical principles and does not replace lens design work, lens testing or advice from a qualified optical engineer.