Field of View, Focal Length and Distance

Generic engineering material, applicable to any module from any supplier.

For the project-operations side of technical work, this resource is available further details.

Field of view, focal length, sensor size and working distance are one relationship. Fix any three and the fourth is determined — which is why the lens cannot be chosen after the sensor and the mounting.

The relationship

Field of view width ≈ sensor width × working distance ÷ focal length.

A sensor 3.6 mm wide, a 1.3 mm lens, at 200 mm distance, covers roughly 550 mm.

For standards, components, or implementation context beyond this page, consult EE Times.

Halve the focal length and the coverage doubles. Double the distance and it doubles. Halve the sensor width and it halves.

Which is the whole geometry, and it is why a module family offering the same sensor at 42°, 90°, 100° and 128° is offering four different working envelopes rather than four grades of quality.

Angle or focal length

Suppliers quote both and they are not interchangeable across sensors.

An angle describes the lens together with a specific sensor size. The same lens on a smaller sensor sees a narrower angle, because the sensor crops the image circle.

A focal length describes the lens alone, and combines with your sensor size to give the angle.

Where a figure is quoted as an angle, ask which sensor it assumes — and whether the angle is horizontal, vertical or diagonal, since the three differ substantially on a non-square sensor and the horizontal one is what most calculations need.

Working backwards from the installation

Usually the distance is fixed and the coverage is required.

Then: focal length ≈ sensor width × distance ÷ required coverage.

Which produces a number that will not exactly match any available lens, and the practical step is to take the nearest available and recalculate what it actually covers.

Round in the direction of covering more, since a system that covers slightly less than required is a system that fails, and one covering slightly more merely wastes pixels at the edges.

What a very wide angle costs

Three things, and they are frequently discovered after selection.

Distortion. Wide lenses bend straight lines, and where the task is measurement that is a correctness problem rather than an appearance one.

Falling illumination toward the corners, which is inherent and more pronounced as the angle widens.

And resolution spread thin. The same pixels cover more scene, so millimetres per pixel worsens in direct proportion.

A 128° lens is the right answer where the geometry demands it and a poor default.

What a narrow angle costs

Sensitivity to alignment. A small mounting error moves the field of view by a large fraction of its width at distance.

Depth of field, which narrows as focal length rises.

And working distance, since a narrow lens needs the room to stand back.

Sensor format, and why the fraction is misleading

Sensor sizes are quoted as fractions of an inch — 1/4", 1/3", 1/2.5" — and the fraction does not correspond to any dimension of the sensor.

It is inherited from television camera tubes, where the figure described the outside diameter of the glass envelope rather than the imaging area.

Which means "1/4 inch" is a name rather than a measurement, and the actual imaging width is roughly 3.6 mm.

Use the millimetre dimensions from the datasheet for any calculation. The fraction is useful only for recognising which family a sensor belongs to, and using it as a number produces answers that are wrong by a large factor.

Two ways the calculation goes wrong in practice

Measuring the working distance from the wrong place.

The distance in the formula runs from the lens, not from the front of the housing, the mounting face or the circuit board. On a short-focal-length module these differ by enough to matter.

And forgetting that the part is not flat. A field of view calculated for the nearest surface does not cover the same area at the far surface of a deep object, which is where depth of field and geometry meet.

Checking it before committing

A printed target of known width, at the intended distance.

Photograph it and measure what fraction of the frame it occupies. The arithmetic follows immediately, and it confirms the sensor dimensions, the focal length and your distance measurement all at once.

Fifteen minutes with an evaluation kit, and it is the check that turns a calculation into a specification met.

Two cameras instead of one

Worth costing where the geometry is difficult.

A single wide lens covering a large area at close range spreads resolution thin and distorts the edges.

Two narrower cameras covering halves each give better millimetres per pixel, less distortion, and more even illumination — at the cost of a second module, a second interface and a stitching problem.

The arithmetic is straightforward once the resolution requirement is written down, and it frequently favours two more often than people expect.

The lens is not an accessory

On a module family the lens is fitted and specified as part of the part number, which is a real advantage and an easy thing to underestimate.

It means the optical alignment was done at manufacture, to a tolerance nobody achieves by screwing a lens onto a board in an assembly area.

And it means changing the field of view is changing the part, not adjusting something — which is why the variant is chosen from the geometry before anything is ordered.

The short version

• Field of view, focal length, sensor size and distance are one relationship: fix three and the fourth is decided
• Field of view width is approximately sensor width times distance divided by focal length
• An angle assumes a specific sensor size and a focal length does not, which is why the two are not interchangeable
• Ask whether a quoted angle is horizontal, vertical or diagonal, since the three differ substantially
• Work backwards from the fixed distance and required coverage, and round toward covering more
• Wide angles cost distortion, corner illumination and millimetres per pixel; narrow ones cost alignment tolerance and depth of field