Coaxial lighting for measurement through transparent substrates

Glass wafers, display substrates, cover lenses and bonded packages hide the features you have to measure: through-glass vias, sintered marks, buried metal pads, adhesive fillets. An ordinary ring light glares off the top surface, and refraction bends every depth under the glass by about a third, so an uncorrected setup both fails to see and fails to size. This guide is for vision and process engineers building a 2D measurement station on a flat transparent substrate. It explains why a coaxial light on the optical axis of a telecentric lens is the geometry that works, puts numbers on the exposure and contrast budget, and works the depth correction end to end: a 700 µm through-glass via reads 461 µm until the refractive index goes back into the formula.

Why does ordinary bright field fail on a transparent substrate?

About 4% of the light bounces off each uncoated air-glass boundary — R = ((n − 1)/(n + 1))², which for soda-lime glass is ((1.52 − 1)/(1.52 + 1))² = 4.3% — and the rays that leave a ring or bar light at the specular angle come straight back into the lens, blooming those pixels to white.

The two surfaces of a plain substrate reflect about 8.6% between them, more than most features you are chasing, and the reflection lands wherever the geometry puts it: a bright band, a hot spot, the outline of the LED. Below that glare the buried features are light-starved. Diffusers soften the hot spot on the top surface but cannot feed light to features under an optically smooth sheet, because the sheet is still the best mirror in the scene and it wins the exposure. Coaxial lighting changes the geometry instead of fighting the reflection; the illumination geometry guide places it among the other families.

How does coaxial lighting see under the glass?

A beamsplitter at 45° injects the LED light into the imaging path, so illumination and camera share one optical axis; light leaves and returns normal to the flat surfaces, and no shadow, holder or off-axis highlight can cross the field.

Half the light goes down the axis. The top surface returns its 4.3% evenly across the whole field, so the substrate becomes a uniform dark-grey background instead of a hot spot. Anything in the stack that faces the axis and reflects — a via bottom, a buried pad, a laser mark — comes back bright along the same path, while steep via walls return nothing and stay dark, which is exactly what separates a diameter from a wall position. Because light and image share one path, part edges and clamps cast no shadow; the same property makes this geometry the fix for recessed connector contacts. The parts live in the coaxial lights and telecentric lenses categories.

Which telecentric lens and magnification do you need?

Magnification is sensor width divided by field width — a 25 mm field on a 12.8 mm wide 1-inch sensor needs 0.5x — and for through-glass work pick a lens with a built-in coaxial port so the beamsplitter alignment is fixed at the factory.

Fixed magnification also means a part that sits a little higher does not change the measurement, which matters twice under glass because the focus plane sits below the top surface. The telecentric gauging guide gives the full crossover logic, and the telecentric lens finder filters by magnification and coaxial port. Three catalog lenses carry that port across the common die-scale magnifications:

All 3 share: Mount C-mount. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Object-space pixel size is camera pixel divided by magnification: a 3.45 µm sensor resolves 2.3 µm at 1.5x, 2.5 µm at 1.36x and 6.9 µm at 0.5x. The object space pixel size guide runs the same division for any camera and lens pair you are considering. The worked example below uses the LS-TCL-2194, the 0.5x, 110 mm working distance, 1-inch, C-mount lens whose port takes an external light.

Fields wider than one shot use a bi-telecentric lens with an external beamsplitter and a wide collimated beam:

How much light survives, and is the contrast enough?

Count on a quarter of a ring light's signal — the beamsplitter keeps half on the way down and half of the return — but the contrast decides the exposure: an 80% reflective metal pad under the glass returns about 17 times more light than the 4.3% top-surface reflection.

The budget for soda-lime, step by step:

• One crossing transmits T = 1 − 0.043 = 0.957 of the light.
• A round trip under the glass keeps 0.957 × 0.957 = 0.916, so 92% of a feature's own return survives.
• Metal pad at 80% reflectance: 0.5 × 0.957 × 0.80 × 0.957 × 0.5 = 0.183, so 18% of the LED output reaches the sensor.
• Top surface: 0.5 × 0.043 × 0.5 = 0.011, about 1%.
• Ratio 0.183 / 0.011 ≈ 17. Expose the pad to about 90% of full scale; the background lands near 5%, a clean threshold in 8 bits.

Use red at 630-660 nm or infrared at 850-940 nm through plain soda-lime, and confirm your camera still responds there; float glass absorbs ultraviolet steeply below about 400 nm. The LED colour guide covers the sensor side of that choice.

Feed the port one of two ways:

Values as printed in each product's data sheet; open a part for its drawing and full specifications.

The diffuse source images: marks, via presence, contamination, anything where uniformity beats edge position. A collimated source from the collimated lights range gauges: telecentric illumination holds an edge's apparent position while part or glass height drifts, which is what a dimensional result needs and what the 10:1 metrology rule puts in tolerance terms. Pick by the output: a picture, or a number.

How far does glass shift a depth measurement?

Every in-glass depth reads short by (n−1)/n of itself — 34.2% in soda-lime at n = 1.52 — so a 700 µm through-glass via displays as 461 µm unless you correct it.

This is the apparent-depth result for normal viewing through a flat plate, and it holds to about 1% at the numerical apertures a telecentric gauge runs. Typical substrates:

Worked example — a through-glass via to a metal pad in 700 µm soda-lime, measured from the top surface:

1. True depth: 700 µm.
2. Apparent depth: 700 µm / 1.52 = 460.5 µm.
3. Uncorrected error: 700 − 460.5 = 239.5 µm, 34.2% short — hopeless against a ±10 µm tolerance.
4. Corrected: 460.5 µm × 1.52 = 700 µm.
5. Focus sits at 700 × 0.342 = 239 µm closer than the top surface, about 0.24 mm.

Depth is not the only thing glass bends. Chief rays that arrive at an angle θ shift features laterally by about t × θ × (n−1)/n: at a 5° field-edge angle on 700 µm glass, 700 µm × 0.087 × 0.342 = 21 µm. A telecentric lens sends chief rays normal to the substrate, so its lateral shift is effectively zero — one more reason the entocentric vs telecentric decision matters more under glass than in air.

How do you calibrate the refraction out?

Multiply every in-glass apparent depth by the refractive index — 460.5 µm × 1.52 = 700 µm — and refocus 0.34 × t closer; both steps belong in the setup, not in post-processing after a scrapped lot.

Correct in the measurement formula rather than by re-training on a golden part: the factor moves with the substrate recipe, not with the camera. Then prove it on your own stack with a calibrated step standard under the same glass; the corrected reading should land within about 1%.

Refocus is the second half. The via's virtual image sits 0.24 mm closer than the real one in the worked example, so set the standoff with the glass in place and focus on the pad, not on the top surface. Thickness tolerance moves that focus: at ±50 µm of glass, the shift is 0.342 × 50 = ±17 µm. That is small next to a typical telecentric depth of field, but check it for your magnification and f-number with the depth of field calculator below, and see the telecentric depth of field guide for turning the margin into a measurement claim. For the residual microns — temperature, mounting drift, telecentricity — the measurement drift guide lists what actually moves.

When is coaxial the wrong tool for a transparent part?

Coaxial measures what returns light normal to the axis; if your feature transmits instead of reflecting — cracks, inclusions, liquid levels — go to backlight, and if you need a 3D profile, go to a profilometer instead of forcing a 2D setup.

Three common detours:

• Defects inside the glass volume need light to pass through and break on the flaw. A collimated backlight turns them into shadows, and the screen projection method does the same for fine defects with a displayed pattern.
• Wavy or curved top surfaces scatter the axial return into haze. A dome light restores uniformity on formed parts, where the flat-plate correction also stops applying.
• Deep, steep-walled vias need wall profiles, not just the bottom diameter. A 2D coaxial image returns one focal plane; a laser profilometer or line confocal sensor is the purpose-built class for 3D through transparent materials.

What do you check on the bench before ordering?

An hour on the bench beats a month of rework: get n from the glass datasheet, budget four times a ring light's exposure, refocus 0.34 × t closer, prove the correction inside 1% with a step standard, and mount the beamsplitter so it cannot creep.

Optics

• Magnification: sensor width ÷ field width, then the next lower standard magnification for margin.
• Built-in coaxial port, or a beamsplitter cube mounted so it cannot shift.

Light and exposure

• A wavelength the substrate passes and the camera responds to — red or near-IR for soda-lime.
• Exposure about four times the ring-light estimate; background about 5% when the feature sits at 90%.

Calibration

• n and t as recipe fields; correction factor (n − 1)/n.
• Refocus 0.34 × t closer; standoff margin for thickness tolerance, ±17 µm at ±50 µm of glass.
• Step standard under the same glass, corrected reading within about 1%.

Stability

• Rigid beamsplitter and light mounts; no cable strain in the axis.
• Top-surface flatness good enough that the background stays uniform.

When the numbers hold, size the hardware in the lens configurator or work backwards from the working distance in the light finder; the lighting topic page collects the companion geometry guides. If you want a second pair of eyes on a specific stack — thickness, index, tolerance, wavelength — send it through the contact page.