Machine Vision Optics Calculators and Formulas

POMEAS optical applications team · Reviewed by Tiger Xie · Published 2026-10-16

These pages are meant to be used with numbers rather than read once. Each one either computes a value from others or publishes a table you can look up while specifying: field of view and pixel size from sensor and magnification, magnification and field of view for telecentric and zoom lenses, cycle time and station count from a throughput target, and the control data needed to command a motorised lens.

Every calculated figure on these pages is labelled as a calculation with its inputs, so you can reproduce it and substitute your own values.

1. The guides in this index

A. Field of view, magnification and pixel size

• FOV Calculator: Field of View and Pixel Size from Sensor and Magnification — Interactive FOV and pixel-size calculator from sensor size, magnification and resolution, plus a working-distance mode, the three formulas behind it and worked examples.
• Zoom Lens Total Magnification & FOV Calculator: Worked Examples (2X–50X) — Calculate total magnification and FOV for zoom lens APO objective setups, including the 0.55x APO adapter coupling factor.
• Telecentric Lens FOV, WD & Magnification Formula (0.3x-2.0x) — Calculate telecentric lens magnification, FOV, working distance and resolution from sensor size.

B. Selection arithmetic and common errors

• Industrial Lens Selection: Calculations and Errors FAQ — Work backwards from tolerance to magnification, check image circle, mount and working distance, and avoid the five mistakes that show up during commissioning instead of on...

C. Throughput and station count

• Inline Measurement Cycle Time: How Many Stations Do You Need? — How to calculate inline measurement cycle time and station count: takt time vs cycle time, the per-part time budget, availability, worked examples for 2,000 parts per...

D. Control data and reference tables

• Motorized Zoom Lens RS-232 Protocol: 5 Commands Explained — RS-232 command reference for POMEAS motorized zoom lenses: five ASCII commands, both position formulas, the 0x55 stop byte, and why the link pauses while the motor moves.
• Zoom Lens Pulse Position: Magnification Mapping Explained — How POMEAS motorized zoom lenses map optical magnification to absolute pulse position, with two complete factory pulse tables and the reading trap in summary tables.

2. How to use this index

Work through in the order the numbers depend on each other: pixel size and field of view first, then the selection arithmetic, then throughput if the station count is still open. The control tables are lookup data and can be used at any point.

3. Frequently asked questions

What is the formula for field of view?

Field of view equals sensor dimension divided by magnification, measured on the object side. Working from pixel size instead, object-side pixel size equals pixel pitch divided by magnification, and field of view equals object-side pixel size multiplied by the number of pixels in that axis. Both routes give the same answer, so the useful check is that they agree.

How do I calculate the pixel size on the object?

Divide the sensor pixel pitch by the magnification. A 3.45 micrometre pixel behind 2x magnification gives 1.725 micrometres on the object. Compare that with the smallest defect or tolerance you must resolve; a common working rule is at least two to three pixels across the feature you need to judge.

How many stations do I need to reach a throughput target?

Station count equals target throughput multiplied by time per part, divided by the availability you actually achieve, normalised to the same time unit. Availability belongs in the denominator: dropping from 0.95 to 0.85 increases the required station count by roughly twelve percent for the same target.

What is the difference between takt time and cycle time?

Takt time is the pace the process must meet, derived from demand. Cycle time is what the equipment actually takes per part. They are compared rather than equated: a station whose cycle time exceeds takt time cannot keep up, however the target was set.

Where do I find the pulse values for a magnification position?

In the pulse-to-magnification mapping table for the lens in question, which pairs a command value with the resulting magnification. Treat it as calibration data for one lens and re-check the mapping on the actual unit after installation, because the relationship is mechanical and can differ slightly between units.

Can I use these formulas with any manufacturer lens?

The geometric relationships hold for any lens, which is why they are worth learning. The values you substitute must come from the lens you intend to use, taken from its published data. Where a value is not published, measure it rather than assuming a typical figure.

4. Related POMEAS resources

• Machine Vision Optics Selection Guides: Complete Index
• Machine Vision Inspection Application Cases: Complete Index
• Machine Vision Optics Technical Guides: Complete Index
• Machine Vision Optics Comparisons: Complete Index
• Machine Vision Optics Troubleshooting: Symptom Index
• All POMEAS machine vision knowledge articles
• POMEAS zoom lenses
• POMEAS telecentric lenses
• POMEAS FA lenses
• POMEAS machine vision lighting
• POMEAS Technical Reference Series — full-length notes on optical imaging performance testing and measurement method

Talk to a POMEAS Engineer About Selection Calculations

If you have the inputs but want the arithmetic checked, send the sensor pixel pitch, the magnification, the field of view and the throughput target. We can go through the calculation with you and point out where an assumption is doing more work than it should.

Email: [email protected] | WhatsApp: +86 185 9810 2007

Reviewed by Tiger Xie.