In the Age of 8K Line-Scan Cameras, the Lens Still Sets the Ceiling on Inspection Resolution

OPTICS

Look at a 200 mm view with an 8K line-scan and a 50 μm solder bridge spans 2.05 pixels; whether its contrast survives is decided by the MTF the lens delivers at 34.9 lp/mm.

Starting from the pixel count, I chained the lens MTF, the diffraction limit of the aperture and the depth of field needed to cover board warp into one line, and calculated why f/8 holds for both visible and near-infrared light.

About 11 min read

This is full inspection of surface-mount PCBs on an SMT line. Even on one panel, solder joints are glossy metal dominated by specular reflection, solder mask is a matte face dominated by diffuse reflection, and plated connector pins combine curvature with a mirror finish, so their reflections head in every direction. When solder bridges from a particular lot slip past the inspection machine on such boards and flow downstream, the talk often turns first to swapping the camera for an 8K line-scan.

If leakage does not drop after the pixel count goes up, the bottleneck lies outside the sensor. A defect missed at inspection costs more to handle at each later process step, and once it is found after shipping, rework is joined by returns and lost trust. While the equipment is being chosen again, the line keeps sending out the same bridges.

The pixel count only decides how many pixels a defect lands on; whether contrast remains in those pixels is decided by the lens MTF and the aperture. Before looking at a camera quote, I calculate how much contrast the current lens keeps at the spatial frequency of the defect. That calculation takes one MTF curve from the lens spec sheet and a few numbers.

A 50 μm bridge spans 2.05 pixels on 8K

First, the pixel-side numbers. Looking at a 200 mm view with an 8,192 px line-scan, the length one pixel covers on the panel, the GSD¹, is 24.4 μm. A 50 μm wide solder bridge spans 2.05 pixels, which clears the two pixels of the Nyquist² criterion but falls short of my rule of putting the smallest defect on three pixels or more. At this view, the smallest defect that the three-pixel rule guarantees is 73 μm.

There are two ways to fill three pixels. Either shrink the view of one camera to 136.5 mm, or split it between two cameras at 100 mm each, where the bridge spans 4.1 pixels at a GSD of 12.2 μm. If a scratch on a plated pin of the same panel is 30 μm wide, it spans only 1.23 pixels at a 200 mm view, and filling three pixels requires splitting the view to 81.9 mm or less. Either way, the pixel count is a question of how many samples are taken, and whether the contrast of the defect remains in those samples has to be worked out separately.

The figure is a concept diagram that places an 8K line-scan, coaxial lighting and dark-field lighting at 15 to 20° on one page. The dimension line under the panel marks the 200 mm view and a GSD of 24.4 μm/px, and the vertical line on the right marks the WD. The bi-telecentric lens and the 150 mm WD written at the lens are example values that show the layout, and whether that choice holds at a 200 mm view has to be checked separately against the lens size.

Contrast splits at the spatial frequency of the defect

A 50 μm wide defect can be treated roughly as a pattern whose half period is 50 μm. That is a spatial frequency³ of 10 lp/mm on the object side, and assuming a sensor with 7 μm pixels, it becomes 34.9 lp/mm on the sensor after a magnification of 0.287. The value that says how much contrast the lens keeps at this frequency is the MTF⁴, and the apparent contrast of a defect is roughly its original contrast multiplied by the MTF.

Now overlay the judgment rule. Assuming an intrinsic defect contrast of ΔGV 40 in 8 bits and a noise σ of 4 GV, the 3σ judgment line is ΔGV 12, and the MTF of the whole system has to be 12 ÷ 40 = 0.30 or more at 34.9 lp/mm. The pixel itself also eats contrast: the aperture MTF⁵ of a 7 μm wide pixel is 0.905 at this frequency and 0.637 at the sensor Nyquist of 71.4 lp/mm. So what is left for the lens is 0.30 ÷ 0.905 = 0.33 or more.

Find 34.9 lp/mm on the MTF curve of the spec sheet and check whether it exceeds 0.33. If the curve sags before that point, swapping the sensor will not make the bridge any sharper. With the same lens and the same magnification, the frequency of the defect on the sensor stays the same, and slicing the pixels finer only adds pixels while the contrast left in each one has already been set by the lens. Software contrast correction does not revive spatial frequencies the lens never delivered either.

The aperture is chosen between depth of field and diffraction

The ceiling on the MTF a lens can deliver is set by diffraction⁶. Even an ideal lens without aberrations loses cutoff frequency as the aperture closes, and calculated with the effective F-number that includes magnification, the cutoff at f/8 in visible light at 550 nm is 177 lp/mm and the MTF ceiling at 34.9 lp/mm is 0.75. At f/16 it falls to 0.51, and at f/22 to 0.34.

The reason to stop down is depth of field⁷. With one 7 μm pixel as the allowed blur, depth of field is 0.88 mm at f/4, 1.75 mm at f/8 and 3.51 mm at f/16. IPC-6012 allows 0.75 % bow and twist⁸ for surface-mount boards, so a 200 mm panel can warp by up to 1.5 mm, and covering that takes an F-number of 6.85 or more, which means f/8 on a real aperture scale.

A setup that adds a near-infrared channel changes the calculation. A wavelength of 850 nm is 1.55 times longer than 550 nm, so at the same F-number the diffraction limit arrives that much earlier. The MTF ceiling at f/8 is 0.62, which leaves room, but at f/16 it is 0.27, below the 0.33 requirement. Not even an aberration-free lens can cross that line, so on a line that uses near-infrared I hold the aperture at f/11 or wider.

The bi-telecentric lens in the figure deserves a look in numbers too. In an object-side telecentric lens⁹ the chief rays run parallel to the optical axis, so the front lens has to be larger than the view, and a 200 mm view needs a lens more than 200 mm across. Light starting at the edge of the view also has to travel parallel to the axis straight into the front of the lens. For an inspection that only judges whether defects are present, a regular lens is enough. Assuming a regular lens with a 60 mm focal length, the panel sits about 269 mm from the lens center, and when the panel rises by 1 mm the image at the edge of the view shifts by 0.37 mm, or 15 pixels, which has little effect on whether a defect is present or how much contrast it has. For an inspection that measures dimensions, those 15 pixels become measurement error as they are, and that is when I consider a telecentric lens.

More pixels restart the aperture calculation

Three setups go side by side on the same bridge. Splitting the view adds pixels but raises the magnification and shrinks the depth of field, and adding near-infrared pulls the diffraction limit closer. The judgment lines in the algorithm column only mean something after the optics are settled.

Setup	① Minimum defect size	② Optics · lighting · WD	③ Algorithm parameters
One 8K camera, 200 mm view	Bridge 50 μm = 2.05 px (24.4 μm/px), short of the three-pixel rule	Coaxial lighting, 7 μm pixels, 0.287 magnification, f/8 (depth of field 1.75 mm), lens MTF of 0.33 or more at 34.9 lp/mm, WD confirmed against the reference plane in the lens spec	Candidates at ΔGV 12 (3σ, σ 4 GV assumed) or more, minimum blob 2 px. It wobbles with pixel position, so record the re-inspection ratio
Two 8K cameras, 100 mm view each	Bridge 50 μm = 4.10 px (12.2 μm/px)	Coaxial lighting, 0.573 magnification, even f/22 gives only 1.47 mm of depth of field, barely reaching 1.5 mm of warp, lens MTF of 0.31 or more at 17.4 lp/mm (diffraction ceiling 0.59), check the seam overlap of the two cameras and the WD	Candidates at ΔGV 12 or more, minimum blob 3 px × 3 px, defects in the overlap counted once
One 8K camera with 850 nm near-infrared	Bridge 50 μm = 2.05 px	Same lens, aperture at f/11 or wider (diffraction ceiling 0.48, depth of field 2.41 mm), check that the near-infrared light fits within the WD	Judge the visible and near-infrared images separately, or set the blend ratio from specimen measurements

Row against row, the table shows that the choice to add pixels changes the lens requirement by way of depth of field and aperture. Splitting the view raises the bridge to 4.1 pixels, but even at f/22 the 1.47 mm depth of field barely reaches 1.5 mm of warp, while staying with one camera keeps the count at 2.05 pixels with plenty of diffraction margin at f/8. Conversely, on a line where panel warp is held to 0.5 mm or less, the two-camera setup also works at f/8 and the calculation gets simpler. Whether the contrast comes out as these numbers say on strongly reflective spots such as mirror-finished connector pins cannot be guaranteed before a sample test.

Lines where the sensor upgrade comes first

The principle that the lens sets the ceiling does not always make a sensor investment pointless. When the view itself cannot shrink, as with large panels, or when the line is too fast to split the view across more cameras, an 8K-class sensor brings a real gain. On a line where the lens MTF already clears 0.33 comfortably and only the pixel count falls short, the sensor comes first.

Then the data volume gets calculated too. Assuming a conveying speed of 500 mm/s, stacking lines at 24.4 μm spacing takes 20,483 lines per second, and with 8,192 px in 8 bits that is 168 MB per second. That exceeds the 125 MB/s theoretical ceiling of 1 GigE, so an interface such as the 10GigE written in the figure becomes a prerequisite. The line spacing has to match the GSD along the travel direction for pixels to come out square, so on a line whose speed changes, I let the line rate follow the encoder signal. A quote worked out this far also gives the person approving the purchase something to stand on, and where to spend, lens or sensor, gets decided in numbers. This article explains technology and is not investment advice. See our Disclaimer.

Field Note

On a line considering an 8K swap, I place one panel at the center and at the edge of the view, shoot a bridge specimen with the current lens, and write down first whether the ΔGV of the bridge pixels clears 12. If it clears at the center and drops at the edge, the MTF at the edge of the lens field is giving out first, so I put a lens change in the quote instead of a sensor; if both clear, I look at adding pixels. For a panel with heavy warp, I repeat the same shot once at f/8 and once at f/11.

Field Checkpoints

With the ΔGV at the center and edge of the view written down, confirm the items below one by one before ordering.

• Do the coaxial lighting unit and the dark-field lights at 15 to 20° fit within the lens WD, with room to place the lights at the intended angles? (Confirm the WD against the reference plane in the lens spec.)
• On the lens MTF curve, does the value at the defect frequency on the sensor exceed 0.33? (34.9 lp/mm for a 200 mm view, checked separately at the center and edge of the view)
• Has panel warp been measured, and was an aperture chosen whose depth of field covers it? (f/8 for a 200 mm panel with 1.5 mm of warp)
• If near-infrared is added, is the aperture inside the diffraction limit? (f/11 or wider at a 200 mm view)
• Does the data volume at line speed stay within the interface bandwidth? (168 MB per second at 500 mm/s)
• Has the ΔGV judgment line been re-measured against the noise σ of real lots?

Frequently Asked Questions

Aren’t two pixels by the Nyquist criterion enough?

Two pixels are the theoretical minimum for sampling a defect. When a defect straddles a pixel boundary, its contrast can split across two pixels and drop by half, so I use three pixels as the rule for stable judgment. For 8K at a 200 mm view, the smallest defect that rule guarantees is 73 μm.

Is a telecentric lens a must?

For an inspection that measures dimensions, the magnification change with height becomes measurement error, so a telecentric lens helps. For an inspection that only looks for the presence of defects, a regular lens is usually enough, and covering a 200 mm view with a telecentric lens needs a front lens more than 200 mm across, so its size and price have to be weighed together.

Glossary

• [1] GSD ground sample distance
  The length one pixel covers on the target. It is the view divided by the pixel count, written in μm/px. ↩
• [2] Nyquist Nyquist
  The sampling rule that a period shorter than twice the sample spacing cannot be captured properly. It is the basis for putting a defect on at least two pixels. ↩
• [3] Spatial frequency spatial frequency
  The fineness of a pattern, written as how many light and dark line pairs repeat within 1 mm. The unit is lp/mm. ↩
• [4] MTF modulation transfer function
  A value showing how much contrast a lens or system keeps at each spatial frequency. At 1 the contrast stays intact; at 0 it vanishes. ↩
• [5] Pixel aperture MTF pixel aperture MTF
  The contrast loss caused by a pixel collecting light over a finite width. It is about 0.64 at the Nyquist frequency. ↩
• [6] Diffraction limit diffraction limit
  The ceiling on resolving power that even an aberration-free lens cannot pass because light is a wave. It drops as the wavelength grows longer and the F-number larger. ↩
• [7] Depth of field depth of field
  The distance before and behind the focused plane within which the image stays inside the allowed blur. It deepens as the aperture closes. ↩
• [8] Bow and twist bow and twist
  How far a board departs from flat, written as a ratio to its length. IPC-6012 allows 0.75 % for surface-mount boards. ↩
• [9] Telecentric lens telecentric lens
  A lens whose object-side chief rays run parallel to the optical axis, so the image barely changes size or position when the target height changes slightly. ↩

References

• IPC-6012 bow and twist limits (0.75 % for surface-mount boards, 1.5 % for other boards): Eurocircuits, Bow and Twist on a PCB Read the page
• Diffraction-limited MTF: optical transfer function of a circular aperture, MTF(ν) = (2/π)(φ − cos φ sin φ), φ = arccos(ν ÷ νc), νc = 1 ÷ (λ × N × (1 + m)). J. W. Goodman, Introduction to Fourier Optics, 3rd ed., Roberts & Company, 2005
• Formulas: GSD = view ÷ pixel count; spatial frequency = 1 ÷ (2 × defect width); frequency on the sensor = object-side frequency ÷ magnification; pixel aperture MTF = |sin(πνp) ÷ (πνp)|; depth of field ≈ 2 × N × c × (1 + m) ÷ m²; perspective shift = distance from view center × height change ÷ object distance; data volume = pixel count × line rate
• Assumed values: a sensor with 7 μm pixels, intrinsic defect contrast of ΔGV 40, noise σ of 4 GV, allowed blur of one pixel, a regular lens with a 60 mm focal length and a conveying speed of 500 mm/s are assumptions for the worked example

Related reading — In PCB Inspection, the Lens Comes Before the AI · Why a Line-Scan Camera Chosen by Line Rate Alone Misses Defects · Can One Focus Plane Keep Parts of Every Height Sharp?