Zoom Lens Total Magnification & FOV Calculator: Worked Examples (2X–50X)

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① The three-factor total magnification formula

Optical magnification is the ratio of the image size on the sensor to the real object size. In a modular zoom system it splits into three multipliers that you simply multiply together:

Total magnification = zoom-body magnification × TV tube (camera adapter) magnification × APO objective magnification

The zoom body sets the variable ratio — a 6.5X body spans 0.7×–4.5×, while a 12.5X telecentric body spans 0.58×–7.5×. The TV tube matches the image circle (the usable circular field the optics project) to your sensor format. The APO (apochromatic) objective raises the whole range: the MPO series runs 2×, 5×, 10×, 20× and 50×, with numerical aperture (NA) rising from 0.055 to 0.42.

TV tube multipliers are documented inconsistently — one catalogue page lists 0.65×, another lists 0.67× — so this article assumes a 1× tube everywhere and labels that assumption on each result. Replace it with your actual tube value before quoting.

② Field of view = sensor size ÷ total magnification

Once you have total magnification, field of view (FOV) is a single division:

FOV = sensor dimension ÷ total magnification

Sensor dimensions are fixed by the camera: a 2/3" sensor is 8.8×6.6 mm. At 9× total magnification the FOV is 8.8 ÷ 9 = 0.98 mm wide and 6.6 ÷ 9 = 0.73 mm tall. The same rule works upward: at 45×, FOV = 0.20×0.15 mm; at 75×, 0.12×0.09 mm. This is a pure geometric result, independent of lighting or NA. For the objective's own field, the MPO series quotes a nominal Φ12 mm at 2× falling to Φ0.48 mm at 50×, following Φ = FN24 ÷ magnification.

③ Three worked examples (6.5X and 12.5X bodies + APO)

All three examples below use a 1× tube (assumed) and a 2/3" 8.8×6.6 mm sensor. Each is computed by multiplication, not yet verified for this combination.

Example 1 — 6.5X body (0.7×–4.5×) + 2× APO. At the low end, 0.7 × 1 × 2 = 1.4×; at the high end, 4.5 × 1 × 2 = 9×. The range is 1.4×–9×, and FOV spans 6.3×4.7 mm down to 0.98×0.73 mm.

Example 2 — 6.5X body + 5× APO. The objective multiplies the body range by five: 0.7 × 5 = 3.5× at the low end and 4.5 × 5 = 22.5× at the high end. FOV at 22.5× is 8.8 ÷ 22.5 = 0.39×0.29 mm. Note that the 5× objective has the longest working distance in the series at 45 mm — longer than the 2× objective's 34.6 mm.

Example 3 — 12.5X body (0.58×–7.5×) + 10× APO. With a 1× tube the range is 5.8×–75×, so FOV runs from 1.52×1.14 mm down to 0.12×0.09 mm. The 10× objective uses NA 0.28 and a 34 mm working distance.

④ The display magnification trap

A frequent quoting error is confusing optical magnification with what a customer sees on screen. Display magnification = optical magnification × (screen size ÷ sensor size). Swap a 24-inch monitor for a 27-inch one and the picture grows; the optical magnification — the number that defines resolution, FOV and price — does not change. Always quote optical magnification. Vignetting (darkening at the image corners) is a second trap: it is an image-circle and sensor-format issue, not a magnification error. In an internal test on a 2/3"-class camera (2448×2048), the illuminated field measured Ø1774 px at the low zoom end — 72.5% of sensor width and 78.6% of the diagonal — with corners at zero brightness. Because those raw images carry no magnification or combination label, that figure describes only the tested combination. See the full guide to zoom lens + APO magnification and vignetting for how image-circle limits interact with these multipliers.

⑤ Given-input → output calculation table

The table below fixes four inputs — body, tube and objective magnification, plus sensor — and shows the two outputs you quote. Tube is held at 1× (assumed). Every row is computed by multiplication, not yet verified for this combination.

⑥ Pixel-limited cross-check

Magnification matters only if the camera can sample the detail it produces. Project one pixel back to the object: object-space sampling = pixel pitch ÷ total magnification. A camera with a 3.45 μm pixel at 9× resolves to 3.45 ÷ 9 = 0.38 μm on the object — finer than the 5 μm optical resolution quoted for the 2× objective. In other words, at 9× the pixel is not the bottleneck; the objective's diffraction limit (resolution ≈ 0.61λ/NA, λ ≈ 0.55 μm) is. Where the two cross over, the coarser (larger) value governs the smallest feature you can actually detect. For lens selection guidance across the stack, see the motorized zoom lens complete guide.

⑦ What these numbers do not cover

Two limits are worth stating plainly. First, no official zoom + APO combination table exists, so no zoom + APO combination has an official FOV or vignetting figure — everything combined here is computed by multiplication, not yet verified for this combination. Second, sensor-format boundaries are documented separately: on the 4K series, a 1" sensor needs at least a 1× tube, 4/3" needs at least 1.5×, and a Φ32 mm sensor needs a 2× tube; combinations marked "----" are not supported. Parfocality (staying in focus through the zoom) is likewise not specified for zoom + APO stacks. For a matched body, the LZ-650104 6.5X motorized continuous zoom lens is the 0.7×–4.5× platform these examples are built on. To size a specific stack against your camera, contact us with the sensor, tube and objective you intend to use.