The 15 to 40 µm Boundary the Human Eye Misses in PCB and Semiconductor Surface Inspection

ALGORITHM

The human eye separates detail down to 73 μm at 250 mm, and catching 15 to 40 μm defects by machine takes 8 μm pixel coverage and a narrow aperture window between f/4 and f/5.6.

For PCB and semiconductor package surfaces seen by a 4,096 px camera, I calculated the pixel coverage, diffraction and depth of field, the number of fields to cover a 300 mm board, and the inspection parameters in turn.

About 10 min read

PCB and semiconductor package lines still keep steps where a person inspects with a magnifier. The problem is the size of the defects to find. Fine scratches, solder bridges and particles of 15 to 40 μm sit below what the naked eye can separate, so the verdict on the same board changes from inspector to inspector and whenever the lighting changes. Defects that slip through come back as field failures and rework after assembly. Moving to a machine is not just a camera swap either; it means working backward from the defect size through pixel coverage, lens and inspection parameters.

The surface comes first. Green solder mask is close to matte and scatters light evenly, and scratches and particles on it stand out through shadows and scatter under low-angle light. Metal surfaces such as solder balls, gold-plated pads and leads, on the other hand, have strong specular reflection¹, so the result flips under the same lighting. Results on plated surfaces change with a few degrees of lighting angle and cannot be guaranteed before a sample test, and the calculation below assumes the solder-mask surface.

Human vision tops out near 73 μm

20/20 vision² means an eye that can separate two points one minute of arc, a sixtieth of a degree, apart. On a board 250 mm from the eye, one minute of arc is 250 mm × tan(1/60°) = 72.7 μm. Defects of 15 to 40 μm are a fifth to a half of that spacing, so their shape cannot be resolved by the naked eye and they show up, barely, as dots only when the brightness difference is large. A magnifier makes them visible, but from then on the verdict leans on the magnification in hand, the inspector’s fatigue and the lighting at the moment.

This is where the case for a machine comes from. A camera has fixed pixel coverage and fixed lighting, so it records the same defect as the same number. By my rule, the first line of a spec sheet that turns visual inspection into machine inspection is the sentence stating the defect size and how many pixels it should cover, and every other line follows from that sentence by calculation.

Seeing 25 μm over 3 pixels takes 8 μm per pixel

In my view, a defect needs to cover at least 3 pixels in the image to be caught reliably. A dot of one or two pixels is hard to tell from noise, and when a defect straddles a pixel boundary its brightness splits across two pixels and fades. Seeing 25 μm, from the 15 to 40 μm range, over 3 pixels requires 8.3 μm per pixel or less, so 8 μm is chosen. At that coverage 25 μm spans 3.1 pixels and 40 μm spans 5, but 15 μm only 1.9.

With a camera of 4,096 px across and 3.45 μm pixels, 8 μm per pixel gives a field 32.8 mm wide and a magnification³ of 3.45 ÷ 8 = 0.43. Matching this magnification with a 50 mm lens puts the WD⁴ from the lens principal plane to the board at about 166 mm. On package lines the board-handling equipment and the lights share the space in front of the lens, so the height for a low-angle light is checked inside this distance first.

The aperture is boxed in by diffraction and depth of field

Choosing 8 μm per pixel does not guarantee that the lens draws 8 μm. Light spreads as it passes the lens opening, and the diameter of the circle a point spreads into is 2.44 × wavelength × f-number. This diffraction⁵ spread grows as the aperture closes, and at a magnification of 0.43 the working f-number⁶ grows 1.43 times, so f/8 behaves like f/11.5. Calculated for 520 nm light, the spread diameter on the sensor is 7.3 μm at f/4, 10.2 μm at f/5.6 and 14.5 μm at f/8, which on the board becomes 16.8 μm, 23.6 μm and 33.7 μm.

At f/8 the spread circle is larger than the 25 μm defect, and the contrast of the defect dissolves into the background. Open the aperture, though, and depth of field⁷ shrinks: with a circle of confusion of two pixels it is 0.85 mm at f/8, 0.59 mm at f/5.6 and 0.42 mm at f/4.

If board warpage or component height varies by more than 0.42 mm within one field, f/4 blurs the edges. My choice for this setup lies between f/4 and f/5.6: I measure the height variation within the field and use f/4 if it stays within 0.42 mm, or f/5.6 if within 0.59 mm.

Ten fields for one 300 mm board

Setting the pixel coverage also sets how many shots one board takes. Covering a 300 mm wide board at 8 μm per pixel needs 37,500 px across, so a 4,096 px area camera has to split it into 10 fields of 32.8 mm even with no overlap. Even a 16,384 px line-scan camera⁸ covers 131 mm at a time and needs 3 lanes. A request to capture the whole board in one field amounts to a request to enlarge the pixel coverage.

For a line-scan camera, the board speed and the row spacing set the line rate. Assuming the board passes at 150 mm per second, a row has to be captured every 8 μm, which makes 18,750 rows per second, 18.75 kHz. The control of the mechanism that moves the board needs a separate review, but this line rate sets the camera and lighting specs. The calculation of making up the shortened row exposure with light is covered in the line-scan TDI article.

What changes when the limit drops to 15 μm

The table puts a 25 μm limit, a 15 μm limit and a line-scan configuration side by side on the same 4,096 px camera. The defect shrinks by only 1.7 times, yet the number of fields and the depth of field move together. All distances in the table are from the principal plane of the 50 mm lens.

Setup	① Minimum defect size	② Optical setup · WD	③ Algorithm parameters
Area 4,096 px, 8 μm/px	25 μm = 3.1 px (15 μm = 1.9 px)	50 mm lens, magnification 0.43, WD about 166 mm, f/4 (diffraction 16.8 μm, depth of field 0.42 mm), low-angle dark field	blobs of 3 px or more, relative contrast starting at 15 to 20 %, 10 fields across 300 mm
Area 4,096 px, 5 μm/px	15 μm = 3 px	50 mm lens, magnification 0.69, WD about 122 mm, f/4 (diffraction 12.4 μm, depth of field 0.20 mm)	blobs of 3 px or more, 15 fields across 300 mm, consider height following per field
Line scan 16,384 px, 8 μm/px	25 μm = 3.1 px	magnification 0.43, WD about 166 mm, 3 lanes, 18.75 kHz at a board speed of 150 mm/s	blobs of 3 px or more, remove duplicate verdicts in lane overlaps

Comparing the three rows shows that the single lower end of the spec, 15 μm, moves the number of fields from 10 to 15 and the depth of field from 0.42 mm to 0.20 mm. In my judgment, of the 15 to 40 μm in the spec sheet, it is the lower end that actually sets the cost. The opposite approach has its conditions too: if 15 μm defects occur only in specific areas, viewing just those areas with a separate high-magnification camera uses fewer fields than viewing the whole board at 5 μm, and if board height varies widely, adding height following to the line scan comes first.

Inspection parameters follow from the pixel count

Inspection parameters follow directly from the pixel count. With the blob⁹ size filter at 3 pixels or more, every dot smaller than 24 μm is filtered out at 8 μm per pixel, so a spec that promises 15 μm defects and a 3-pixel filter cannot both hold. The contrast threshold starts at 15 to 20 % of the background brightness and is tuned on samples, and it is worth checking that normal pixels near the threshold do not cross into defects when the lighting drifts a few percent from lot to lot. How much that drift changes verdicts is covered in the calculation for a light that dims by 5 %.

The people who move visual inspection to machines are vision engineers, and for a beginner a good start is placing a single hair on white paper and looking at it from 250 mm to feel where the naked eye stops telling thin from thinner. From the investment side, fine-defect inspection grows camera count and inspection time together each time the lower end of the spec drops, so where that lower end sits decides the size of the equipment. This article explains technology and is not investment advice. See our Disclaimer.

Field Note

If I move this step to a machine, I first measure the warpage of one board at intervals of 32.8 mm, the field size, to see whether the height variation within one field stays within 0.42 mm. If it does, I stay at f/4; if not, I stop down to f/5.6 and compare on the same spot how much the contrast of a 25 μm specimen drops. I also check the defect history for where 15 μm defects actually occur, to decide whether to view the whole board at 5 μm or only those areas separately.

Field Checkpoints

To move the numbers derived from the defect size into spec-sheet sentences, answer the questions below.

• Do the low-angle light and the board-handling equipment both fit inside the roughly 166 mm WD (from the principal plane) of the 50 mm lens? (the lens front is closer)
• Is the number of pixels the minimum defect should cover written as a number in the spec sheet? (25 μm spans 3.1 px at 8 μm/px, 15 μm only 1.9 px)
• Does the board height variation within one field stay inside the 0.42 mm depth of field at f/4? (otherwise use the 0.59 mm of f/5.6)
• Do the number of fields or lanes covering the 300 mm width, and their capture time, fit inside the inspection time? (10 fields or 3 lanes at 8 μm/px)
• Do the blob filter and the lower end of the spec agree? (a 3-pixel filter discards anything under 24 μm at 8 μm/px)
• For strongly reflective areas such as solder balls or gold-plated pads, have you checked the results for each lighting angle on samples? (the calculation assumes solder mask)

Frequently Asked Questions

Couldn’t a higher-resolution camera cut the number of fields?

More pixels widen the field at the same 8 μm per pixel, so the number of fields drops. With smaller pixels, though, the diffraction spread covers more pixels at the same coverage, narrowing the aperture window further, and the lens also has to resolve those pixels. The problem of the lens setting the ceiling on resolution is covered in the 8K line-scan and lens article.

With a deep learning model, can defects smaller than 3 pixels be caught?

A model learns the brightness differences contained in the image. If a defect spread over one or two pixels has faded to noise level against the background, the model cannot learn that difference either, and forcing it raises overdetection, calling the noise of good boards defects. It is more stable to secure the pixel count and contrast on the optical side first and use the model on top of that to sort defect types.

Glossary

• [1] Specular reflection specular reflection
  Reflection in which light bounces off a smooth surface in one direction only, at the same angle it came in. It is strong on solder balls and gold-plated pads. ↩
• [2] 20/20 vision visual acuity 20/20
  The acuity that separates two points one minute of arc, a sixtieth of a degree, apart. It is written as 1.0 in decimal notation. ↩
• [3] Magnification magnification
  The size of the image on the sensor divided by the size of the object. When a 3.45 μm pixel covers 8 μm on the board, the magnification is 0.43. ↩
• [4] WD working distance
  The distance from the lens to the surface being inspected. The values here use a thin-lens approximation from the lens principal plane; the distance from the lens front comes from the lens drawing. ↩
• [5] Diffraction diffraction
  The spreading of light as it passes through a narrow opening. The diameter of the circle a point spreads into, up to the first dark ring, is roughly 2.44 × wavelength × f-number. ↩
• [6] F-number f-number
  The focal length divided by the diameter of the lens opening. For close objects, light and diffraction are calculated with the working f-number, multiplied by (1 + magnification). ↩
• [7] Depth of field depth of field, DOF
  The depth range in front of and behind the focus distance that still looks sharp. The values here assume a circle of confusion of two pixels (6.9 μm). ↩
• [8] Line-scan camera line-scan camera
  A camera with a single-row sensor that builds an image by stitching rows together as the board passes. The board speed and the row spacing set the line rate. ↩
• [9] Blob blob
  A cluster of connected pixels that crossed the threshold. Keeping only clusters above a certain pixel count filters out noise. ↩

References

• Wikipedia, Visual acuity (6/6 or 20/20 vision defined as resolving two points one minute of arc apart)
• Edmund Optics, Limitations on Resolution and Contrast: The Airy Disk (Airy disk diameter ≈ 2.44 × wavelength × f-number)
• Formulas: spacing the eye separates = distance × tan(1/60°), pixel coverage = defect size ÷ pixel count, magnification m = pixel ÷ pixel coverage, object distance = f × (1 + 1/m), working f-number = N × (1 + m), diffraction diameter (on the board) = 2.44 × wavelength × N × (1 + m) ÷ m, depth of field ≈ 2 × N × c × (m + 1) ÷ m², number of fields = board width ÷ (pixel count × pixel coverage), line-scan line rate = board speed ÷ pixel coverage
• Assumptions: 4,096 px area camera (3.45 μm pixels) and 16,384 px line-scan camera, 50 mm lens, wavelength 520 nm, circle of confusion 6.9 μm, board width 300 mm, board speed 150 mm per second, viewing distance 250 mm

Related reading — In PCB Inspection, the Lens Comes Before the AI · When You Add Cameras to a Semiconductor or PCB Line, the Interface Rewrites the Optics · In the Age of 8K Line-Scan Cameras, the Lens Still Sets the Ceiling on Inspection Resolution