Fixed focus code reader field of view: match focal length to sensor

A fixed focus code reader hands you a spec sheet with a focal length, a sensor format and a shutter, and your bracket fixes the working distance. From those numbers you can predict the field of view before the reader is mounted, and decide whether the narrowest bar of your label will still cover enough pixels to decode. This page gives the formula, two worked examples with the arithmetic shown, the pixels-per-module rule, and a table that sets the catalog's focal lengths, sensors and shutters side by side. It is written for anyone mounting fixed code readers over a conveyor, an indexing fixture or a pick-and-place cell who wants the number first and the part second.

How do you calculate a fixed focus code reader's field of view?

Multiply sensor width by working distance and divide by focal length: a 4.80 mm wide sensor behind an 8.0 mm lens at 200 mm working distance frames 4.80 × 200 ÷ 8.0 = 120 mm across. Both dimensions follow the same ratio, so compute width and height separately:

Every term is in millimetres: WD is the distance from the lens front to the label, w and h are the sensor's active width and height, f the focal length. The ratio WD ÷ f is the magnification of the geometry, and the ratio form treats it as exact. It lands within a few percent once the working distance reaches ten focal lengths; below that, use the thin-lens correction:

At 100 mm working distance with a 12 mm lens the two answers differ usefully. The ratio form gives 4.80 × 100 ÷ 12 = 40.0 mm. The exact form gives 4.80 × (100 - 12) ÷ 12 = 35.2 mm — 12% tighter, which moves your margin brackets if you ignore it. Rule: ratio form at WD ≥ 10 × f, exact form below that. The same optics, drawn out:

The physics is the one behind lens field of view: why sensor size and focal length set it and how camera field of view changes with working distance, both written around interchangeable lenses. A fixed focus reader is the same geometry sealed into one housing: focal length and sensor ship together, so the spec sheet plus one tape-measured distance is the whole input set.

What does an 8 mm lens frame on a 1/3-inch sensor at 200 mm?

An 8.0 mm lens on a 4.80 x 3.60 mm sensor frames 120 x 90 mm at 200 mm working distance, because every sensor millimetre maps to 200 ÷ 8.0 = 25 object millimetres. Example inputs, not a product spec: 4.80 x 3.60 mm is the standard 1/3-inch active area, and 1280 x 960 pixels over it give a 3.75 µm pitch.

• Magnification ratio: 200 mm ÷ 8.0 mm = 25
• Width: 4.80 mm × 25 = 120 mm
• Height: 3.60 mm × 25 = 90 mm
• Exact form: (200 - 8) mm ÷ 8.0 mm = 24, so 115 x 86 mm — 4% tighter

Cross-check the scale two independent ways. By field: 120 mm ÷ 1280 px = 0.0938 mm per pixel. By pixel pitch: 3.75 µm × 25 = 93.8 µm. The routes agree, as they must. Keep 93.8 µm per pixel — the module rule in the next section consumes it, and the exposure budget later reuses it.

How small a barcode module can a given field of view resolve?

Make the narrowest bar or module span at least 3 pixels for 1D codes and 4 pixels for 2D codes; at 93.8 µm per pixel that floors the module size at 0.28 mm and 0.38 mm. The reasoning: a decoder rebuilds each module from several pixel samples. Below about two pixels per module the bar pattern aliases and reads turn intermittent; three pixels is the dependable 1D floor, and 2D codes want four because finder and timing patterns must resolve too.

Worked on the 120 x 90 mm view: 120 mm ÷ 1280 px = 93.8 µm per pixel, so the floors are 3 × 93.8 µm = 281 µm and 4 × 93.8 µm = 375 µm. A Code 128 with 0.25 mm modules spans 0.25 ÷ 0.0938 = 2.7 pixels — under the floor. Shorten the bracket from 200 mm to 150 mm: the field drops to 4.80 × 150 ÷ 8.0 = 90 mm, the scale to 90 mm ÷ 1280 px = 70.3 µm per pixel, and the same module now spans 0.25 ÷ 0.0703 = 3.6 pixels.

Distance, focal length and module size are one trade, and Code 128 module size, reading angle and reader distance walks it symbol by symbol. Keep the label within about 15° of perpendicular as well: tilt stretches a module's apparent size along the tilt axis and eats your pixel margin.

Which focal length fits the mounting distance you have?

Turn the formula around: focal length = working distance × sensor width ÷ field of view. To frame a 100 mm wide field at 250 mm on a 4.80 mm sensor you need 4.80 × 250 ÷ 100 = 12.0 mm, which is why 12 mm is the common compact-reader focal length. Pick the bracket distance first — guard clearance, service access, vibration — then solve, because focal length is the variable the catalog sells in steps:

Height check on the same solve: 3.60 × 250 ÷ 12.0 = 75 mm, so an 80 x 60 mm label fits with margin on every side. Scale: 100 mm ÷ 1280 px = 78.1 µm per pixel, and a 0.25 mm module spans 0.25 ÷ 0.0781 = 3.2 pixels — passes with room.

The calculator below solves the same pair of equations; its button opens the lens finder filtered to the focal length it returns. The same solve for interchangeable glass is machine vision lens selection: focal length calculation.

Twelve millimetres shows up twice in the catalog: the MV-ID3013PM-12M-WBN combines a 12 mm focal length with a 1.3 MP global-shutter sensor on an M12 mount over Fast Ethernet, and the LS-CRD-0052 is a 1.2 MP reader with a 12 mm focal length on Ethernet.

Close brackets pull the focal length under 5 mm. The MV-IDB005EXI-05NRP is a fully isolated polarized reader with a 4.63 mm focal length and a 70 mm focus distance on Fast Ethernet and an M5.8 mount; the LS-CRD-0047 reads at 60-120 mm over USB 2.0. The rated focus distance is the bracket number these short solves land on — set the bracket there, not wherever the gantry happens to stop.

Which focal lengths and sensors do the catalog readers pair?

The catalog prints focal length, resolution, sensor format, shutter and frame rate together, so every reader's field of view is computable from the spec sheet before you order anything. The table gathers the fixed-focus models side by side:

A dash means the sheet does not print that value. Where the sensor format is missing, find camera sensor size and focal length with no datasheet shows how to project a ruled target and measure the format yourself.

One worked read of the table. The LS-CRD-0028 pairs an 8 mm lens with a 2560 x 2048 global-shutter sensor on a 1/1.7-inch format, reading at 30 fps and up to 60 codes/s. A 1/1.7-inch active area is about 7.4 x 5.6 mm, so at 200 mm working distance the field is 7.4 × 200 ÷ 8.0 = 185 mm by 5.6 × 25 = 140 mm. Scale: 185 mm ÷ 2560 px = 72 µm per pixel, for module floors of 0.22 mm (1D) and 0.29 mm (2D) — the finest module reach in the table at that distance.

When does a smaller pixel beat a longer focal length?

Pixel size never changes the field of view — sensor format and focal length set that — it changes how finely the field is sampled: 2560 pixels across 185 mm give 72 µm per pixel where 1280 pixels across the same view give 145 µm. On that field the module floors are 0.22 mm against 0.44 mm. The catch is optics, not geometry:

At 550 nm the disk is 3.8 µm across at f/2.8, 5.4 µm at f/4 and 10.7 µm at f/8. The 5 MP reader's 7.4 mm ÷ 2560 px = 2.9 µm pixel pitch is already finer than the f/2.8 disk, so the lens passes less detail than the pixel records. Airy disk size and the diffraction limit: match pixel to feature works that match in full, and sensor resolution in lp/mm: match lens MTF to pixel pitch covers the lens side. Depth of field pulls the other way: stopping down past f/4 to gain focus range softens fine modules, as aperture, f-number and depth of field in machine vision quantifies.

Decision by module size. Modules of 0.3 mm and larger: a standard-pixel reader resolves them with room to spare, so spend nothing extra. Modules of 0.15-0.25 mm at an unchanged field: take the higher pixel count, keep the aperture no slower than f/4, and accept the tighter focus range. Pixel pitch below what the optics pass buys nothing but noise.

How fast can the label move before blur kills the read?

Keep motion blur under one pixel of object scale: at 93.8 µm per pixel, a label moving at 300 mm/s must be exposed for 0.0938 mm ÷ 300 mm/s ≈ 0.31 ms, and a 2D code wants half that. Blur is speed × exposure, so the budget is:

Numbers on the 200 mm / 8.0 mm example: 1 pixel of blur allows 0.0938 ÷ 300 s = 0.31 ms; 0.5 pixels for a 2D code allows 0.16 ms. A global shutter exposes the whole frame at once, so a short exposure freezes the label completely. A rolling shutter reads lines over a few milliseconds: at 300 mm/s a 3 ms readout shifts the frame's bottom 3 × 0.3 = 0.9 mm against its top, and on a 0.25 mm module code that is 3.6 modules of shear. The decode dies even though every individual line is sharp.

Throughput is the milder limit. At 30 fps and 300 mm/s the belt advances 300 ÷ 30 = 10 mm between frames, so parts spaced 100 mm apart arrive every 0.33 s and take 10 frames each. Frame rate rarely binds at line speeds under 500 mm/s; exposure does. The focus half of moving-target blur — set the lens at the real working distance, never at infinity — is global shutter camera blurry image: focus the lens at working distance.

For the stop-and-read station the motion constraint disappears and resolution becomes the spend: the MV-ID5120RM-08M-RBN is a 12 MP rolling-shutter reader on GigE with an M12 mount.

What do you check before ordering a fixed focus reader?

Four numbers decide the order: field of view at your true bracket distance, micrometres per pixel across it, the pixel span of the narrowest module, and the exposure budget at line speed — every one computable from the spec sheet and your bracket drawing. Run them once on paper, then confirm on a sample label:

• Working distance — from the bracket drawing, minus guard and label height; it sets every other number.
• Field of view — sensor width × WD ÷ focal length, exact form when WD < 10 × f; check against label plus margin.
• Module pixels — field ÷ pixel count is the scale; narrowest module ÷ scale must clear 3 pixels for 1D, 4 for 2D.
• Exposure — scale ÷ belt speed, halved for 2D codes; the reader must offer a shutter mode that reaches it.
• Focus — the bracket sits at the rated focus distance, with part height variation inside the depth of field.
• Shutter — moving belt: global; indexed stop: rolling buys resolution.
• Label finish — glossy film glares; a polarized front cuts the specular highlight.

The decisions, case by case. Bracket under 100 mm: solve to a 4.6-5 mm focal length — the 70 mm focus distance and 60-120 mm reading distance readers above. Bracket at 200-250 mm for a 60-80 mm label: 8-12 mm, and 12 mm at 250 mm lands exactly 100 x 75 mm. Modules under 0.3 mm at an unchanged field: the 5 MP, 1/1.7-inch pairing. Belt at 200 mm/s or faster: global shutter with the exposure budget computed above. Stop-and-read station: the highest pixel count the distance allows.

Then filter hardware: the code reader finder sorts by interface, resolution and shutter, the machine vision lenses route covers stations you build from a separate camera and lens, and the configurator walks a full station — camera, light, trigger, mount — in order. For the wiring afterwards, bottle label barcode verification: fixed reader and PLC serial link shows the same reader class talking to a PLC. More worked reads live on the code-reading topic page.