Telecentric Lens Numerical Aperture: Light, Resolution and Depth of Field

Numerical aperture is the one telecentric specification that sets three things at once, and they pull in opposite directions. Raise NA and the lens collects more light, resolves finer detail, and loses depth of field. Lower it and the part stays sharp through a larger axial range, but the smallest resolvable feature grows. Reading NA correctly is mostly a matter of knowing which consequence binds on your station.

The other reason NA is worth reading carefully is that it is not published for every telecentric model. Several POMEAS pages carry the NA field with no value beside it, and that cannot be filled in from the magnification — the relationship runs through the f-number, which is itself published only on some models.

Why NA is not the same question as resolution

Resolution is what the lens can separate; NA is how wide a cone of light it accepts. They are linked by diffraction but not interchangeable: two lenses can publish the same resolution and differ in NA, and a higher-NA lens can be the worse choice on a station where depth of field is already marginal.

The six things numerical aperture sets and decides

1. What NA measures

Numerical aperture is defined as:

NA = n × sin θ

where θ is the half-angle of the cone of light the lens accepts and n is the refractive index of the medium. In air, n = 1. On a telecentric lens the relevant figure is object-side NA, because that is where the resolvable feature size is defined.

POMEAS publishes object-side NA on a subset of the line, from 0.005259 (PMS-LTCM0063-416-G, 0.063×, 416 mm) to 0.3 (PMS-LGX8-95, 8.0×, 9.5 mm) — a spread of roughly a factor of fifty-seven.

2. NA from magnification and f-number

Where a model publishes both the f-number and the magnification, NA follows directly:

NA = m / (2 × F)

The agreement is exact for the first two and within the rounding of the published F for the third. This is the practical use of the relation: on a model publishing NA but not F, or F but not NA, the missing one can be computed rather than guessed — provided the other two terms are genuinely published.

3. The diffraction limit, and what it is not

The smallest separation a diffraction-limited lens can resolve is commonly estimated as:

resolution ≈ 0.61 × λ / NA

This is the optical limit of the lens at wavelength λ, not the measurement accuracy of a station, and the two must never be quoted as the same number.

Taking λ = 550 nm as the assumed wavelength — a test assumption, not a published value — against published NA figures:

Every row agrees with the published figure to the precision at which it is published. That tells you the published resolution is a diffraction-limited figure computed from the published NA, not an independently measured contrast-transfer result — worth knowing before comparing resolution figures across suppliers.

4. Light collection and contrast

A higher NA delivers a brighter image and, at the same f-number, more contrast at high spatial frequencies. POMEAS publishes centre MTF at stated spatial frequencies for several models:

- PMS-LTCM2-65-S — centre MTF > 50% at 100 lp/mm, NA 0.152 - PMS-LTCM0061-398 — centre MTF > 50 at 70 lp/mm - PMS-LTCM016-189 — centre MTF > 60 at 70 lp/mm - PMS-LTCM0088-120 — centre MTF > 75% at 70 lp/mm - PMS-LTCM0088-398-G — centre MTF > 60% at 70 lp/mm - PMS-LTFM017-416 — centre MTF > 65% at 50 lp/mm - PMS-LTFM1-127 — centre MTF > 40% at 50 lp/mm

These are per-model values at the stated frequency; a 50 lp/mm figure cannot be compared with a 100 lp/mm figure.

5. The depth of field consequence

This is where NA usually decides the selection. Published POMEAS pairs:

The ordering is monotone and the range is large: 0.017 mm at NA 0.3 against 7.25 mm at NA 0.024. If the part's Z position is uncertain by more than a fraction of a millimetre the highest-NA options are unusable however fine their resolution; if the feature is smaller than the resolution figure the lowest-NA options are unusable however generous their depth of field.

No formula is offered for deriving one column from the other, because POMEAS publishes depth of field per model rather than as a computed value, and the figures do not follow a single constant across the line.

6. Which side the NA is quoted on, and whether it is quoted at all

Object-side NA governs resolvable feature size on the part; image-side NA governs the cone arriving at the sensor and matters for sensors with microlens arrays. A datasheet saying only "NA" without qualifying the side should be queried.

Equally important: many POMEAS telecentric models publish no NA value at all — PMS-LTCM016-189, PMS-LTCM12-110, PMS-LTC2-110, PMS-LTC2-110C, PMS-LTC1-110C, PMS-LTC1-65 and PMS-LTFM1-127 all carry the field without a value. For those the reading is "not published".

Where POMEAS telecentric lenses land on those six

Reading the table against the six checks:

- PMS-LGX8-95 is the extreme high-NA option: NA 0.3, resolution 1.1 µm, depth of field 0.017 mm at 9.5 mm, M12 mount, maximum 1/3-inch sensor. It buys resolution with almost no axial tolerance. - PMS-LTCM2-65-S at NA 0.152 and 2.2 µm is the high-NA option at a usable working distance (65 mm). It publishes no depth of field and no distortion. - PMS-LTCM03-110 and PMS-LTCM05-110 sit close in NA (0.03 and 0.027) and differ more in depth of field (4.4 mm against 2.96 mm) than in resolution (11.18 µm against 12.43 µm). Where the part has real height variation, that depth-of-field difference decides. - PMS-LTC08-90 at NA 0.0375 and 8.947 µm on a maximum 1/2-inch sensor is the compact mid-NA option at 90.5 mm, with a four-step field-of-view table. - PMS-LTCM1-110 at NA 0.045 and 7.46 µm with 0.89 mm depth of field is the 1:1 option here, supporting 1/4" through 2/3".

Every figure is the published value for that model; a blank is a gap in published data.

What those numbers mean on the line

Scenario 1 — A micro-feature station that cannot hold Z

The station needs to resolve a feature near 2 µm and the part is presented by a fixture with sub-millimetre repeatability. PMS-LTCM2-65-S publishes NA 0.152 and 2.2 µm resolution, which meets the feature requirement; the constraint to verify before ordering is the depth of field, which is not published for this model.

Scenario 2 — Micro-hole or slot gauging at 8×

PMS-LGX8-95 publishes NA 0.3, resolution 1.1 µm, depth of field 0.017 mm and a working distance of 9.5 mm. The mechanical envelope is tight and the axial tolerance is measured in tens of micrometres: this works on a rigid station with a precision stage, and poorly anywhere else.

Scenario 3 — Multi-height parts on a conveyor at 0.3×

PMS-LTCM03-110 publishes NA 0.03, resolution 11.18 µm, depth of field 4.4 mm and F 4.99, with a field of 29.3 mm × 22.0 mm on a 2/3-inch sensor. The 4.4 mm depth of field makes it a conveyor option; the 11.18 µm resolution is the price.

Scenario 4 — Choosing between two lenses at nearly the same NA

PMS-LTCM03-110 (NA 0.03, 11.18 µm, 4.4 mm) and PMS-LTCM05-110 (NA 0.027, 12.43 µm, 2.96 mm) differ by about a tenth in NA and eleven percent in resolution, but by nearly fifty percent in depth of field. On NA alone they look equivalent; on a station with height variation they are not.

What this article does not tell you

This is a technical reference, not a diagnosis of your station. No claim is made about which numerical aperture your application requires, and none should be inferred. That depends on the feature size, the part's Z repeatability, the illumination and the algorithm.

Optical resolution is not measurement accuracy. The figures here are diffraction limits and published optical specifications; measurement accuracy additionally depends on pixel sampling, contrast, edge definition, illumination stability, and the algorithm.

Every figure here is the published value for the specific POMEAS model named beside it, not measured under a single common condition. The 550 nm wavelength is an assumed test wavelength, not a POMEAS published value, and the results of that calculation are calculations rather than specifications. Where a field is absent — depth of field for PMS-LTCM2-65-S, NA for PMS-LTCM016-189 and others — read it as "not published".

The telecentric content already on this site covers the four-number selection procedure, per-magnification model families and sensor matching as separate pages. This article is about NA specifically.

FAQ

What does numerical aperture actually set on a telecentric lens?

Three things at once: how much light the lens collects, the diffraction-limited resolvable feature size, and — inversely — the depth of field. Raising NA improves the first two and costs the third.

How do I get NA if the datasheet only gives magnification and f-number?

Use NA = m / (2 × F). On PMS-LTCM05-110 that is 0.5 / (2 × 9.26) = 0.027, which matches the published value exactly.

Is 0.61 × λ / NA the accuracy I will measure to?

No. It is the diffraction-limited optical resolution of the lens at a given wavelength. Measurement accuracy additionally depends on pixel sampling, contrast, edge definition, illumination stability and the algorithm.

Why do the published POMEAS resolution figures match the diffraction formula exactly?

Because they are computed from the published NA at a stated test wavelength. On PMS-LTCM03-110, 0.61 × 550 nm / 0.03 gives 11.18 µm, which is the published figure.

Does a higher NA always mean a better lens?

No. PMS-LGX8-95 has the highest NA in the line at 0.3 and a depth of field of 0.017 mm. On a station with any axial variation, that is the wrong choice no matter how fine the resolution is.

What if NA is not published for the model I am considering?

Then it is not published, and neither the diffraction limit nor the f-number can be derived from the page. Ask for the value rather than substituting the figure from a similar model.

Next Step

If you are specifying a replacement and need measured values for your own conditions — your sensor size, your working distance, your feature size — send us those four numbers and we will run them against the current catalogue and tell you what actually fits, including when nothing does.