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Optics & resolution

How I compare optics

Comparing optics by magnification alone is one of the most common early-career mistakes.

One of the biggest mistakes I made early in my career was comparing optics by magnification alone.

How depth of field shrinks at high magnification
Depth of field is one of the criteria that magnification alone tells you nothing about.

What actually matters

  • Resolution
  • Working distance
  • Depth of field
  • Illumination compatibility
  • Throughput
  • Mechanical constraints

The math that replaces "magnification"

Two numbers tell you more than magnification ever will: sampling and numerical aperture.

Sampling - how big is one pixel on the object?

pixel on object = sensor pixel size / magnification

example: 3.45 um pixels at 2x  ->  1.7 um per pixel
a 5 um defect spans ~3 pixels  ->  detectable, barely measurable

My rule of thumb: 3 pixels across a feature to detect it, 10 to measure it with confidence.

Numerical aperture - can the lens physically resolve the feature, and what does that cost in depth of field?

resolution limit ~ 0.61 * wavelength / NA
depth of field   ~ wavelength / NA^2

NA 0.14:  resolution ~2.4 um,  DOF ~28 um
NA 0.28:  resolution ~1.2 um,  DOF ~7 um
NA 0.42:  resolution ~0.8 um,  DOF ~3 um

This table is the whole tragedy of high-resolution imaging in two columns: every step toward finer resolution costs you a square step in depth of field. A lens that resolves your defect but has less depth of field than your part warpage has not solved your problem.

My evaluation process

  1. Determine the smallest feature that must be resolved.
  2. Determine the required field of view.
  3. Determine the cycle time.
  4. Check the candidates on paper first: sampling, NA, depth of field versus part height variation, working distance versus mechanical reality.
  5. Test the survivors against real parts.
  6. Validate with production-representative samples, not just the nice ones.

Step 4 eliminates most candidates for free. I keep a one-page calc sheet per application and fill it in before requesting a single demo lens.

Things datasheets do not tell you

  • Edge-of-field performance. Many lenses are quoted at center; corners can be 2x worse. Test with a grid target across the full field.
  • Performance at your working distance, not the designed one.
  • How the lens behaves with your lighting - telecentric lenses and coaxial illumination interact in ways the datasheet never mentions.
  • Thermal drift of focus. A lens that holds focus from a 20 degree morning to a 35 degree afternoon is worth real money.

The lesson

The best optic is not the most expensive optic. It is the optic that solves the problem while satisfying all the constraints.