A 210° figure on a fisheye data sheet tells you nothing on its own about what lands on your sensor. Whether the lens works on an M12 board camera comes down to three numbers: image circle against the sensor's diagonal, back focal length against the holder's focus travel, and the projection that maps the rated angle onto the circle. This guide gives you the arithmetic for a 1/2.3-inch board sensor — active area about 6.2 × 4.65 mm, diagonal 7.75 mm — so you can size a true circular-frame fisheye, predict where black corners appear, and order a lens that reaches focus on the first try. It is aimed at engineers building compact embedded cameras: mobile robots, ceiling-mounted awareness and tight enclosures.
What three numbers decide whether a fisheye works on your M12 board camera?
Three numbers decide it: the image circle must span your sensor's diagonal — 7.75 mm on a 1/2.3-inch part — the back focal length must land inside the holder's focus travel, and the projection must map the rated angle onto that circle. A 210° rating alone guarantees none of this.
The checks are independent, and failing any one sinks the design. Image circle decides coverage: too small and you get a circular image, planned or not. Back focal length decides focus: mismatched, and the lens never sharpens at your working distance. Projection decides what the degrees mean: the same 210° through different mappings lands on circles from 4.6 to 7.6 mm across at a 1.45 mm focal length. A data sheet that prints the angle but not the circle, the projection and the BFL cannot be judged on paper, so those missing numbers are the first questions you ask. The checks apply to every M12 holder in the board-level cameras range, and the M12 lens selection guide covers format matching and IR-cut for ordinary rectilinear lenses; a fisheye adds the projection step on top.
Which projection type gives the field of view you need?
Most M12 fisheyes use the equidistant projection, where image radius grows in direct proportion to angle, r = f·θ; fisheye angles usually run 100° to 180°, and 210° designs exist as specialty circular-frame parts rather than mainstream board-lens options.
Equidistant is the mapping behind most security and machine-vision fisheyes, and it is the only one that makes the arithmetic in this guide exact. The other mappings compress the outer angles differently, which changes the circle the same lens produces.
The figure shows the geometry every projection maps onto: sensor extent, focal length and angle. A rectilinear lens records r = f·tan θ, which blows up at 90°; a fisheye swaps tan for a bounded function, so angles beyond 90° can be recorded at all.
| Projection | r(θ) | 210° circle at f = 1.45 mm | Where you meet it |
|---|---|---|---|
| Equidistant | f·θ | 5.31 mm | Most M12 and CCTV fisheyes |
| Equisolid | 2f·sin(θ/2) | 4.60 mm | Classic photographic fisheyes |
| Stereographic | 2f·tan(θ/2) | 7.56 mm | Wide-angle photo and AR optics |
| Orthographic | f·sin(θ) | capped at 180° | Door-eye and barrel viewers |
Each circle in the table is D = 2·r(Θ/2) at Θ = 3.665 rad; this article assumes equidistant from here on. The 100° to 180° typical range and the projection families are standard references (Fisheye lens).
How large does the image circle have to be?
Match the image circle to the diagonal first: a 1/2.3-inch sensor's active area is about 6.2 × 4.65 mm, so its diagonal is √(6.2² + 4.65²) = 7.75 mm, and a fisheye drawing at least 7.75 mm covers the frame edge to edge.
Catalog listings group lenses into image-circle buckets, and the buckets cap the circle. The up-to-8-mm bucket is the territory of 1/2.3-inch sensors, whose 7.75 mm diagonal just fits; the 8-11 mm bucket is where 1/1.8 inch lives, with its 8.9 mm diagonal. Pick the bucket from the diagonal, then use the projection to know whether the circle fills the frame or draws a disc inside it. A circle smaller than the diagonal is not automatically a defect: on a circular fisheye it is the intended look, so decide which look you are ordering before comparing models.
For a 1/2.3-inch board camera, the stocked fisheye starting point is:
- Sensor format
- 1/2.3"
- Mount
- M12
- Resolution
- 6-10 MP
- Image circle
- Up to 8 mm
Its listing prints a 1.45 mm focal length, a 1/2.3-inch sensor format, 10 MP resolution and image circle up to 8 mm. The arithmetic below shows what a 1.45 mm equidistant design produces at 180° and at 210°.
What focal length gives a 210° circular frame on a 1/2.3-inch sensor?
For an equidistant fisheye the circle diameter is D = f·Θ with Θ the full angle in radians, so a 210° circle that just fills a 7.75 mm diagonal needs f = 7.75 / 3.665 = 2.11 mm.
Read the three cases as decisions. Case (b) is what a 1.45 mm equidistant fisheye delivers on 1/2.3 inch: a genuine circular frame, 210° left to right, about 184° up and down. Case (a) buys edge-to-edge coverage and pays in per-axis angle. Case (c) is the pure disc look. For the rectilinear version of this same calculation — focal length from field of view and sensor — use the calculator below; a fisheye swaps its tan for f·θ.
The rectilinear walk-through, with the same working-distance logic, is in how to choose a machine vision lens focal length.
Will the lens reach focus on your holder?
A fisheye reaches infinity only when its printed back focal length matches your holder's seat within the thread's travel — 0.5 mm per full turn on the common M12 × 0.5 thread — so get the BFL in writing and measure the seat before ordering.
The seat is the lens-to-sensor distance your holder forces once the lens is screwed in; sensor cover glass and IR filter add thickness. If the BFL is shorter than the seat, the image distance can never get short enough, and the lens focuses only close — the diagnosis and the extension-tube confusion around it are in lens focuses only at close distance. If the BFL is longer than seat plus travel, infinity is out of reach from the other side. Both are ordering mistakes, not bench-tuning problems.
Some listings print the number directly: the CS-mount pinhole LS-MBL-0176 specifies a BFL of 12.53 mm. Compare that value against your measured seat. The focal-length side of the relationship is in lens focal length vs back focus in board cameras, the travel mechanics in M12 lens thread travel, and the focusing procedure with corner checks in M12 lens focusing.
When is a fisheye the wrong lens for the task?
A fisheye is the wrong lens whenever straight lines or dimensions matter: its projection bends every off-axis line, while rectilinear designs keep lines straight but saturate near 120° diagonal, so gauging and template matching belong on low-distortion or telecentric glass.
Measure nothing through an uncorrected fisheye. The remap is a fixed pixel table once the projection is known: fisheye undistortion shows how the mapping works, and building a lens distortion profile without an LCP file gets you there from a checkerboard when no model ships with the lens.
Where fisheyes win: one camera watching a whole room, ceiling-mounted overflow detection, mobile-robot awareness in tight aisles — anywhere the 210° horizontal span beats the distortion cost. Where they lose: gauging, OCR near the frame edge, any job the telecentric lens guide exists for. Staying rectilinear, the low-distortion end of M12 board lenses keeps lines straight to roughly 120° diagonal; the lens finder filters by format, focal length and distortion class.
The catalog spans that trade-off in three lenses:
| Specification | LS-MBL-0041 | LS-MBL-0018 | LS-MBL-0159 |
|---|---|---|---|
| Resolution | 10 MP | 8 MP | 16 Megapixel |
| Focal length | 1.45 mm | 2.8 mm | 3.3 mm |
| Sensor format | 1/2.3" | 1/2.5" | – |
| Aperture | F2 | F2.8 | F2.8 Fixed Iris |
| Distortion | – | 3.00 % | <1% |
| Price | $88.00 | $50.00 | $109.00 |
All 3 share: Mount M12. Values as printed in each product's data sheet; open a part for its drawing and full specifications.
Read the table as: the fisheye for circular coverage, the 2.8 mm rectilinear for wide-but-straight, the low-distortion part for measurement-grade edges.
What do you check before ordering a fisheye?
Before you order, check five things: image circle against sensor diagonal, projection type and rated angle, printed back focal length against holder seat and travel, barrel length against holder depth and any front cut-out, and the lens resolution class against your sensor's pixel pitch.
- Image circle vs diagonal. 7.75 mm on 1/2.3 inch; an 8 mm circle covers it, a 5.3 mm disc circles it. Decide which look you are ordering.
- Projection and angle. Convert degrees to a circle with D = f·Θ; at f = 1.45 mm the same 210° rating moves the circle by 7.56 − 4.60 = 2.96 mm between stereographic and equisolid.
- BFL vs seat and travel. M12 × 0.5 gives 0.5 mm per turn; measure the seat with the lens out, then match the printed BFL to it.
- Barrel and front element. Fisheye front elements sit proud of the thread; check holder depth and any enclosure window so the element does not foul the panel.
- Resolution class and IR. A 10 MP-class lens matters only against pixel pitch — 10 MP on 1/2.3 inch runs about 1.5 µm pixels — and the matching test is in Nyquist limit and camera resolution. For colour work, plan an IR-cut filter from the lens accessories range; the wavelength side is in color camera near-infrared imaging.
The decision, per case. For a true 210° circular frame on a 1/2.3-inch board camera, order an equidistant fisheye near 1.45 mm and plan for black corners with about 184° of vertical coverage, or near 2.1 mm for full-frame coverage at 168° × 126° per axis. For measurement, stay rectilinear at the low-distortion end. For anything between, size the circle with D = f·Θ against your own diagonal, then confirm the BFL against the holder. Filter the catalog in the lens finder or start at the lens configurator; free expert support comes with every order, and we will check a candidate lens's numbers against your holder before you commit.
Questions
Why does my fisheye image have black corners?
Black corners mean the image circle is smaller than the sensor diagonal, which is the intended geometry of a circular fisheye, not a defect. An equidistant 1.45 mm lens at 210° draws a 5.31 mm circle on a 7.75 mm diagonal, so the corners receive no light at all. Compare the printed circle with your sensor diagonal before blaming the holder or the sensor.
Can I measure parts through a fisheye lens?
Yes, but only after undistortion. Fit the projection model, remap the image so straight edges become straight, then measure on the corrected frame. Accuracy falls toward the edge, where the projection compresses the most, so keep gauging features near the middle of the circle and confirm the scale against a calibration target before trusting a dimension.
Which sensor size suits a 1.45 mm fisheye best?
At 210° equidistant the lens draws a 5.31 mm circle. On 1/2.3 inch (7.75 mm diagonal) that is 69% of the diagonal, a clear circular frame; on 1/3 inch (6.0 mm diagonal, about 4.8 × 3.6 mm) it is 89%, nearly filling the frame, with the vertical axis clipped to about 142°. Smaller sensors make the same lens look fuller, so choose by whether you want the disc or the coverage.
Does a 10 MP rating on a fisheye lens guarantee sharp edges?
No. A resolution rating says the lens resolves enough for that pixel count across its image circle under the maker's test conditions; a fisheye's contrast falls fastest at the rim, where the projection squeezes the outer angles together. Expect the centre half of the circle to look best, and when rim sharpness matters, read the MTF curve rather than the megapixel figure.