Coaxial Light Alone Does Not Settle Fine Scratches on Polished Metal

LIGHTING

Switching on coaxial light seems to settle polished metal, yet collimated light brightens only 32% of this field, and with diffuse light the angle at which a scratch turns dark changes from place to place.

With one setup that views 24.6 mm across through a 75 mm lens, I calculated the light a half mirror leaves, the tilt tolerance, and the scratch sensitivity that shifts with position in the field.

About 14 min read

Put a mirror-polished aluminum cover on the inspection stage and switch on a ring light, and the image shows the ceiling lights and the grains of the LEDs before it shows any scratch. A mirror-like surface with high reflectance throws incoming light back in almost one direction only, so the camera sees what the surface reflects more than the surface itself. A hairline scratch about 20 μm wide disappears among the edges of those reflections.

Read the edges of reflections as defects and one more person joins the re-inspection line; loosen the threshold to stop that and a few hairlines leave in the box. On mirror-finished parts, where appearance is the value of the product, a single scratch can turn into a customer complaint and a full re-sort. As long as only the threshold is adjusted and the lighting stays the same, these two costs keep taking turns.

That is why, on mirror-like surfaces, coaxial illumination¹, which lays the light and the camera’s line of sight on one axis, comes to mind first. Switching it on does not finish the design, though. Whether the light is close to collimated or diffuse, and whether the lens is a telecentric lens², changes how much of the image lights up and at what tilt a scratch turns dark. I fixed one setup, a 75 mm lens viewing 24.6 mm across, and calculated the difference in angles.

The tilt of a scratch wall decides its brightness

Switch on coaxial light and look at the image, and the first thing you notice is the background. When a half mirror³ sends light down along the optical axis, a flat mirror-like surface returns it to the lens along the same path by specular reflection⁴, creating a white, even background. The walls of a scratch are tilted, so light that hits a wall bends by twice the tilt and escapes outside the lens. That spot sinks into a dark line. What makes the split is the tilt of the surface, more than the strength of the light.

Here is the setup behind the numbers. A 4,096 × 3,000 px sensor with 3.45 μm pixels carries a 75 mm F/5.6 lens and views 24.6 mm across and 18.0 mm down. Each pixel covers 6.0 μm of the surface, so a 20 μm wide scratch images 3.3 px wide and a 40 μm dent 6.7 px across. The sensor, the lens and the field of view are all assumptions for the calculation, and at a magnification of 0.574 the thin-lens object distance comes to 205.6 mm. The tilt at which the surface turns dark is set by the size of the lens opening. The entrance pupil⁵ of a 75 mm F/5.6 lens is 75 ÷ 5.6 = 13.4 mm across, and seen from a point on the surface 205.6 mm away, it opens to a half-angle α of 1.87°. If the light comes down parallel to the optical axis as collimated light, the reflection leaves that half-angle once it bends by 2θ, so at the center of the image the tilt tolerance⁶ for the surface to stay bright is half of α, 0.93°. It works like catching a ceiling lamp in your eye with a hand mirror: turn the wrist just slightly and the lamp is gone.

Scratch walls are usually far steeper than this, so they drop to dark. The trouble is the gentle waviness that polishing leaves behind. Assuming that waviness runs around 1°, every spot past 0.93° puts a dark blotch in the background, and the blotch gets over-detected as a signal on the same side as a scratch. By my standard, this tolerance belongs on the defect criteria sheet before it goes on the lighting spec sheet.

Collimated coaxial light covers only the lens opening

0.93° is the value at the very center of the image. The edges differ. An ordinary lens that is not telecentric views points at the edge of the field at a slant. From the end of the horizontal field, the direction toward the lens tilts 3.4° from the optical axis, and from a corner, 4.2°. Collimated light reflects straight up from a flat mirror-like surface, so for that light to enter the lens opening, the point on the surface has to sit within 6.7 mm of the axis, the radius of the entrance pupil.

Work it out and the only place a flat mirror-like surface lights up is a single circle 13.4 mm across, 31.8% of the 24.6 × 18.0 mm field. The rest stays dark even without a scratch. Tilt the part by 1° and the reflection bends by 2°, pushing the center of the bright circle 205.6 × tan 2° = 7.2 mm to the side, and since the circle has a 6.7 mm radius, even the very center of the image falls on the dark side. If the seating tolerance of the jig is around 1°, this configuration first shows you one side of the image going dark as a whole.

For collimated coaxial light to light the whole field, the lens has to view every point parallel to the optical axis, and such a lens is an object-side telecentric lens. The Edmund Optics note on in-line illumination also states that with telecentric lenses, in-line lighting is the only way to get reflected brightfield across the entire field. In exchange, the front aperture of the lens must be larger than the 30.5 mm diagonal of the field, and with a lens of NA 0.02 the tolerance narrows further to 0.57°. I would choose collimated coaxial light only when pairing a flat part such as a wafer with a telecentric lens, and for a polished cover I would look at the diffuser option first.

Add a diffuser and the tolerance changes by position

A diffuse coaxial light with a diffuser sends light from many directions to each point at once. Assuming the diffuser gives every point light spread evenly over ±10°, an incoming direction that returns to the lens remains even when the surface tilts by θ, and the tolerance widens to (α + β) ÷ 2 = (1.87 + 10) ÷ 2 = 5.93°. Polishing waviness of around 1° falls inside this, the background brightens evenly, and the image no longer collapses when the jig tilts 1°. The graph below draws the tolerance of the two lights side by side.

The two curves in the graph are values calculated at the center of the image, and toward the edges things change. Where the direction to the lens tilts by ψ, the tolerance for a surface tilted away from the axis shrinks to (α + β − ψ) ÷ 2, while for a surface tilted toward the axis it grows to (α + β + ψ) ÷ 2. At the end of the horizontal field that gives 4.22° and 7.65°, and at a corner 3.81° and 8.05°. So the 5.93° measured at the center cannot be carried over to the corners of the field as it is.

Picture a shallow hairline scratch with 5° walls and the difference becomes clear. At the center of the image both walls sit inside 5.93°, stay bright, and the scratch does not show. Lay the same scratch at a corner so that it runs around the optical axis, and the wall tilted away from the axis passes 3.81°, so it appears as a thin dark line on one side only. Same part, same light. Only the position changed, and the judgment splits. Flat-field correction⁷ only evens out brightness levels, so it cannot erase this threshold difference born from angles.

There are two ways to shrink this difference. An object-side telecentric lens makes ψ zero at every point, so the tolerance becomes the same across the field; a NA 0.02 lens with the same diffuser evens it out at (1.15 + 10) ÷ 2 = 5.57°. If the ordinary lens stays, a reference scratch sample of known wall slope goes at the center and at each of the four corners in turn, to check that the judgment comes out the same. I trust a detection-limit number that has not been through this check only at the center of the image.

Two passes through the half mirror leave a quarter

Coaxial light also charges a price in light. Light passing a 50:50 half mirror keeps half by reflection on the way down and half again by transmission on the way back up from the surface, so at most 0.5 × 0.5 = 25% of the source output returns toward the sensor. The background ends up a quarter as bright or less compared with the same source shining on the part directly, so a setup that needs short exposures has to calculate strobe drive to raise the instantaneous output as well.

The missing 75% does not vanish; it becomes stray light⁸ inside the light housing. The half that first passes through the half mirror strikes the far wall of the housing, and of the returning light, the reflected half heads back toward the source. When this light bounces off an inner wall or the back of the half mirror and enters the lens, a faint veil covers the background and cuts the contrast. Edmund Optics also explains that a beamsplitter brings in several sources of stray light that keep dark regions from looking truly black.

That is why I would put the half mirror type and the inner-wall treatment on a coaxial light spec together. A thick plate half mirror tilted at 45° in the imaging path can cause astigmatism and a double image from its back-surface reflection, so pairing a thin pellicle-type or cube half mirror with a non-reflective black interior is the safer choice. The static part of the veil, the share that always lies in the same place at the same strength, is removed by flat-field correction with an image of a scratch-free mirror reference plate. The part that changes with the reflection of each part lands on the same pixels as the defect signal, so image processing alone cannot erase it all.

From minimum width to lighting, three lines of a spec

Moved onto the first page of a spec, the calculation so far becomes three lines: the size of the scratch to catch, the lighting and lens that put that size onto pixels, and the algorithm that reads those pixels. The WD (working distance)⁹, the distance from the front of the lens to the part, has to make room for the height of the coaxial housing, so it goes on the optics line as well.

Item	Reference value	Condition and basis	In plain words
① Minimum defect size · scratch	20 μm wide or more, 300 μm long or more	3.3 px wide and 50 px long at 6.0 μm/px. Design assumption	A width that barely clears three pixels
① Minimum defect size · dent	40 μm across or more	6.7 px. Design assumption	A dot about seven pixels wide
② Optical setup · lighting	Diffuse coaxial, ±10° spread assumed, 50:50 half mirror (pellicle or cube)	Tolerance 5.93° at the center, 3.81° outward at the corners. At most 25% of the light reaches the sensor	The threshold for a scratch to show drops toward the edges
② Optical setup · lens and sensor	75 mm F/5.6, 4,096 × 3,000 px, 6.0 μm/px	Entrance pupil 13.4 mm, acceptance half-angle 1.87°. Design assumption	The lens opening sets the tolerance
② Optical setup · WD	WD of 180 mm or more secured (design assumption)	Thin-lens object distance 205.6 mm. Confirm with the lens spec and a measurement, housing height included	Secure the height for the housing and lens first
③ Algorithm parameters · background	Flat-field correction with a scratch-free mirror reference plate	Removes illumination unevenness and the static part of the stray-light veil	Subtract the same old blotches in advance
③ Algorithm parameters · detection	Black-hat10 kernel 11 px, candidate if 30% or more darker than the local background, linear 50 px or more or area 9 px or more	Kernel larger than the largest target (6.7 px). The 30% is an assumption to re-estimate from 30 good parts	Keep only narrow dark lines and dots
③ Algorithm parameters · position check	Place a reference scratch sample at the center and four corners and confirm matching judgments	Reflects the 3.81° outward tolerance at the corners	See whether every spot gives the same answer

The first thing to read from the table is that the margin of this setup lies in angles more than in pixels. A 20 μm scratch at 3.3 px barely clears my rule of 3 px, and a scratch with gentle walls shows or hides according to an angle threshold of 5.93° at the center and 3.81° at the corners, however wide it is. Only with pixel resolution, tilt tolerance and position in the field on one table can a detection limit be stated.

Coaxial light is not always the answer. On parts with large curvature, or with tilt variation several times the tolerance, the bright coaxial background does not hold, and a dome light that gives light from wide angles does better. On brushed finishes, where the machining lines carry their own slope, the coaxial background fills with stripes, so a low light across the lines at a right angle, or dark-field lighting, gives a cleaner image. On a bead-blasted surface that scatters light in every direction, no bright coaxial background forms and only the 25% light loss remains. Reflection changes widely with polishing conditions and oxide films, so which of coaxial light and the other methods wins cannot be guaranteed before a sample test.

Calculating tilt tolerance from the lens opening and position in the field is the sum you end up doing most often once you take on inspection optics, and since it needs nothing more than an atan and two divisions, it is easy to try by hand on your own setup. For the person signing the purchase order, whether the same reference scratch gets the same judgment at the center and the corners of the field says more about real detection power than a line that reads coaxial lighting applied. This article explains technology and is not investment advice. See our Disclaimer.

Field Note

To look at a polished metal cover under coaxial light, I would measure how far the part actually tilts on the jig before choosing the light. With collimated coaxial light a 1° tilt alone pushes the bright circle 7.2 mm aside, and even with diffuse coaxial light the outward tolerance at the corners is 3.81°, about 2° narrower than at the center. Next comes one reference scratch sample of known wall slope, placed at the center and the four corners, to see whether the black-hat kernel and threshold give the same judgment at all five spots. When the material or the polishing conditions change, these five images get taken again.

Field Checkpoints

Once the jig tilt and the five-spot sample have tested the angle assumptions, I run the whole setup past the questions below once more.

• Is a WD of 180 mm or more secured by measurement, including the coaxial housing height and the clearance between the lens front and the top of the part? (whether there is height for the housing and lens)
• Have the surface material and reflectance of the part been confirmed first? (mirror, hairline finish, or a finish that scatters light)
• Has the spec sheet confirmed whether the coaxial light is close to collimated or diffuse, and its spread angle? (how widely the light spreads)
• With an ordinary lens, has the tolerance at the corners of the field (3.81° outward in this setup) been calculated? (whether the threshold drops at the edges)
• Does the tilt of the part on the jig fall inside the tolerance? (with collimated light even 1° darkens one side of the image)
• Has the stray-light veil been reduced with the half mirror type and a black interior? (whether the background turns hazy)
• Does the pixel resolution give the minimum scratch width 3 px or more? (20 μm is the floor at 6.0 μm/px)

Frequently Asked Questions

How do a dome light and diffuse coaxial light differ?

Diffuse coaxial light gives light from a narrow range around the optical axis, while a dome gives light from the whole inside of a hemisphere. So diffuse coaxial light lifts shallow scratches on a flat mirror-like surface more strongly, and a dome covers curved surfaces whose tilt changes by tens of degrees more evenly. A dome has a weak spot: the camera hole at its apex reflects in the part and leaves a dark spot in the middle, so for flat parts the coaxial image tends to be cleaner.

How much longer should the exposure be after switching to coaxial light?

With at most 25% returning after the round trip through the half mirror, start from the view that the same source at the same distance needs four times the light or more compared with direct lighting. In practice the transmission of the diffuser and the housing design make it darker still, so recalculate with the illuminance value on the light source spec sheet. For imaging on the move, where exposure cannot be lengthened, consider strobe drive to raise the instantaneous output as well.

Glossary

• [1] Coaxial illumination in-line illumination
  Lighting that sends light down on the same axis as the optical axis of the camera by way of a half mirror. Flat mirror-like areas image bright and tilted spots image dark. ↩
• [2] Telecentric lens telecentric lens
  A lens that views every point in the field from a direction parallel to the optical axis. Its front aperture has to be larger than the field, so the lens is large and heavy. ↩
• [3] Half mirror beamsplitter
  A mirror that reflects half the light and lets half pass. In coaxial lighting it both sends light down and passes the returning light on to the lens. ↩
• [4] Specular reflection specular reflection
  Reflection from a smooth surface that bounces light off in one direction only, at the same angle it arrived. It is why a lamp in a mirror shows from only one spot. ↩
• [5] Entrance pupil entrance pupil
  The opening for light as seen from the front of the lens. Its diameter is estimated as focal length divided by the f-number. ↩
• [6] Tilt tolerance tilt tolerance, θmax
  The limit up to which a tilted surface still looks bright. Tilt beyond this value becomes a dark signal. ↩
• [7] Flat-field correction flat-field correction
  A correction that divides out brightness unevenness using a defect-free reference image. It fixes brightness levels only and leaves angle thresholds as they are. ↩
• [8] Stray light stray light
  Light that is not part of the image, wanders inside the housing and leaks into the lens. It lifts areas that should be dark into a haze. ↩
• [9] WD working distance
  The distance from the front of the lens to the surface being inspected. The light housing and the part have to fit in between. ↩
• [10] Black-hat black-hat transform
  A morphology operation that subtracts the original from its closing, leaving only dark features narrower than the kernel. It is used to lift thin scratches off a bright background. ↩

References

• Edmund Optics Knowledge Center, In-line Illumination (why in-line lighting suits specular and semi-specular inspection, the stray light a beamsplitter brings in, and how to get reflected brightfield across the whole field with telecentric lenses)
• Formulas: pixel resolution = field of view ÷ pixel count, magnification m = sensor width ÷ field of view, thin-lens object distance u = f × (1 + 1/m), entrance pupil D = f ÷ f-number, acceptance half-angle α = atan(D/2 ÷ u), tolerance θmax = (α + β) ÷ 2, direction angle at field position ψ = atan(h ÷ u), tolerance by position = (α + β ∓ ψ) ÷ 2, collimated bright radius = D/2, bright circle shift with tilt = u × tan 2θ, half mirror round trip = 0.5 × 0.5

Related reading — For Scratches on Highly Reflective Metal, Choose the Lighting First · A Dark-Field Ring Light Tolerates Far More Tilt Than Coaxial Light · On Thick Parts, Silhouette Measurement Error Comes from the Backlight’s Angle