How to read lens performance curves for vision inspection

A lens can look strong on one performance plot and still fail your inspection. High central contrast does not guarantee readable corner features, uniform brightness or stable measurements as part height changes. For inspection designers comparing machine vision lenses, the useful question is which curve predicts the failure you cannot tolerate.

Start with your smallest feature, sensor dimensions, field of view and height variation. Then compare curves under matching conditions. The method below connects each plot to an inspection requirement, with a worked example and checks before ordering.

Match each curve to an inspection requirement

Performance curves answer different questions. Treat them as separate gates rather than combining everything into a single lens quality score.

MTF is not a brightness specification. Relative illumination is not a resolution specification. Low distortion does not establish measurement accuracy by itself.

For the underlying contrast concepts, use lens contrast and resolution. Here, the emphasis is connecting several curve types to one selection decision.

Check the conditions before comparing plots

A curve describes a lens under stated conditions, not every possible installation. Record these conditions beside each candidate:

• Working distance or magnification.
• Aperture setting.
• Wavelength or spectral band.
• Image-space or object-space frequency units.
• Field positions and active sensor coverage.
• Focus criterion and whether every field shares one focus setting.
• Whether the data are calculated, nominal or measured.

A plot at a different working distance can be useful background, but it is not direct evidence for your application. Likewise, monochromatic data do not establish broadband performance.

Read every legend independently. Solid and dashed lines have no universal meaning across documentation. They might distinguish orientations, field positions or different conditions.

Field height usually means radial distance from the optical axis in the image plane. For a centered rectangular sensor, the corner radius follows:

In this example, a curve ending at a field height of 4 mm does not describe the sensor corners. Do not substitute a nominal sensor-format label for actual active dimensions. The lens selection guide explains the broader coverage and mounting checks.

Convert your feature size into a curve frequency

MTF commonly uses image-space spatial frequency in line pairs per millimeter. Translate the inspection requirement into those units before reading a contrast value.

For an equal-width dark-and-light pattern, one line pair contains one dark bar and one light bar. The following relationship is a sizing estimate, not a complete model of an isolated scratch or edge:

Consider a hypothetical inspection with an 8 mm sensor width covering an 80 mm object field. The narrowest repeated bars are 0.10 mm wide.

You should therefore examine lens performance near 50 lp/mm, at the field positions where those bars can appear.

Now check sampling. Assume a pixel pitch of 4 micrometers, equivalent to 0.004 mm:

Being below Nyquist is necessary for unaliased sinusoidal sampling, but does not guarantee reliable detection. Pixel integration, feature alignment, noise and image processing still matter. Use the object-space pixel size calculation to connect magnification and sampling.

Read MTF at the frequency and field you need

An MTF-versus-frequency plot shows how contrast transfer changes as details become finer. Another common format plots MTF against field height, with separate traces for selected frequencies. Check the axes before interpreting either format.

For a sinusoidal target in a linear, unsaturated imaging system:

An MTF of 0.40 means that 40% of the input sinusoidal modulation remains at that frequency under the stated conditions. It does not mean that an arbitrary defect will have 40% image contrast. Binary bars contain additional spatial frequencies, while isolated defects have different frequency content.

Read the center, intermediate field and required corner positions. If the inspection accepts parts anywhere in the image, use the weakest required position rather than the best central trace.

Off-axis plots may separate sagittal and tangential orientations. These describe different orientations relative to the field direction. A substantial separation means detail orientation can affect performance. If scratches may run in any direction, evaluate both traces.

There is no universal MTF threshold that guarantees inspection success. Establish a task-specific contrast requirement using representative good parts, defects and expected noise. The small-pixel camera selection guide explains why finer sampling alone cannot restore lost optical contrast.

Separate edge brightness from geometric accuracy

Relative illumination predicts brightness roll-off

Relative illumination normally expresses off-axis brightness relative to a reference, often the image center. Confirm the normalization in the documentation.

Suppose a hypothetical curve gives 60% relative illumination at the corner. If the center produces 10,000 photoelectrons under uniform scene conditions, the corner would produce approximately:

Multiplying corner values by 1.67 can equalize average brightness, but it does not recover missing photons. Under shot-noise-limited conditions, the corner signal-to-noise ratio relative to the center is approximately:

Stopping down may improve relative illumination while reducing absolute light throughput. Compare the curve with the exposure budget, not independently of it. Actual image shading also includes illumination geometry, sensor response and mechanical obstruction.

Distortion predicts mapping error

Distortion plots describe departures from an ideal geometric mapping. Definitions and axis directions vary, so check whether the document reports radial distortion, another geometric definition or a television-style metric.

For a definition based on radial displacement, a hypothetical magnitude of 1% at an ideal image radius of 4 mm implies:

That calculation does not establish dimensional measurement error across an arbitrary feature. Local scale variation and calibration residuals also matter. Use camera calibration for length measurement when converting image coordinates into dimensions.

Software correction also remaps image boundaries. Allow coverage margin using the guidance on black borders after undistortion.

Read depth of field as a thresholded focus range

A through-focus plot shows contrast transfer as object distance or image-plane focus changes. Unlike an MTF-versus-frequency plot, it usually holds spatial frequency fixed while sweeping focus or distance.

First identify the horizontal axis. An object-distance shift and an image-plane defocus displacement are not interchangeable. Then confirm the plotted frequency, aperture, field positions and whether focus remains fixed throughout the sweep.

Select a task-qualified contrast threshold. The usable interval is the distance range where every required field and orientation stays above that threshold. The center trace alone can substantially overstate usable focus tolerance.

For example, suppose all required traces exceed a hypothetical threshold of 0.30 between object-distance offsets of −0.8 mm and +1.1 mm. The common interval is:

A required offset range of −0.5 mm to +0.7 mm fits inside that interval. A range of −1.0 mm to +0.5 mm does not, despite having a smaller total span. The location of the interval matters as much as its width.

Stopping down can improve defocus tolerance, but eventually diffraction reduces fine-detail contrast. Compare several apertures rather than assuming the smallest opening wins. The depth-of-field simulation guide explains why a sharp-looking preview is not sufficient evidence.

Work through a selection using all the curves

Continue the hypothetical 50 lp/mm inspection. Assume preliminary application testing establishes a design target of 0.30 MTF at that frequency. Required object-distance variation is −0.5 mm to +0.5 mm around nominal focus.

The following values are invented teaching examples for anonymous optical designs. They are not specifications for any catalog product.

Design A has stronger central contrast and a larger aperture opening. However, its common focus interval does not cover the required height variation. Design B is the stronger optical candidate for this particular task, subject to exposure and application validation.

Do not stop at that recommendation. At equal transmission and ignoring aperture-dependent vignetting, image irradiance approximately follows the inverse square of the f-number:

If the larger aperture permitted a 100 microsecond exposure, the smaller opening would require approximately 196 microseconds for equal central signal under these assumptions. Moving parts might not tolerate that increase.

The decision therefore becomes explicit: provide more illumination, change motion timing, reduce height variation, or evaluate another optical candidate. Better corner curves do not remove the exposure constraint.

Use catalog specifications to shortlist, not invent curves

First filter machine vision lenses by coverage, mount, focal length or magnification, working distance and mechanical compatibility. The lens finder helps narrow that list. Then request performance data matching your operating conditions.

For example, LS-FFL-0679 is identified in the catalog as a 35 mm, 2/3", 6 MP, C-mount machine vision lens. That description establishes useful screening information, but does not establish its MTF at your required frequency or working distance.

Another catalog candidate is LS-FFL-0567. Its listing identifies a 16 mm, 1.1", 20 MP, C-mount machine vision lens. It is not a drop-in optical equivalent to the preceding candidate; framing must be evaluated separately.

Neither product description supplies the complete set of performance curves discussed here. Do not infer those curves from a megapixel label, sensor-format designation or focal length. Use the lens configurator after defining the actual field and distance requirements.

Verify the decision and know when curves are insufficient

Use this checklist before approving the optical configuration:

• Match the plotted conditions. Record distance, aperture, wavelength, field positions and frequency units.
• Check complete sensor coverage. Include the actual corner radius, not just horizontal edges.
• Test the weakest detail. Include low-contrast defects, not only a high-contrast resolution target.
• Sweep the height range. Keep focus fixed and check both ends of the production tolerance.
• Check orientation sensitivity. Rotate representative features or use targets with multiple orientations.
• Separate shading from lighting variation. Evaluate both the optical roll-off and the installed illumination.
• Validate calibrated geometry. Measure residual errors across the usable field after correction.
• Repeat with the production exposure. Longer laboratory exposures can conceal motion and noise limits.

Conventional curves may be insufficient when magnification must remain stable with changing part height. Consider the decision criteria in when you need a telecentric lens for gauging. Thermal drift, severe vibration or broadband imaging may also require additional application-specific data and testing.

A nominal curve supports a shortlist; it is not a guarantee of every assembled system. For a practical test sequence, follow the lens and lighting selection test plan.

Next, send your sensor dimensions, field of view, working distance, smallest feature, exposure limit and height tolerance through applications support. Request matching curve conditions before committing to a lens, then validate the selected configuration against measurable inspection acceptance criteria.