How Strongly Cross-Polarization Suppresses Glare Depends on the Lighting Angle

LIGHTING

Cross-polarization presses highlights down to 1/500 under coaxial light, but only to 1/36.5 on curved pins under a 15° ring.

For a connector with nickel-plated pins and a matte housing in one image, I used the optical constants of nickel to calculate the light two polarizers leave and the extinction at each angle of incidence.

About 12 min read

Shoot a connector whose nickel-plated pins stand beside a matte molded housing under one light, and the trouble usually starts on the pin side. The target is a connector whose black matte housing and nickel-plated pins share one field of view. The housing is assumed to have a diffuse reflectance of 5 %, and the normal-incidence reflectance calculated from the optical constants of nickel (Johnson and Christy 1974, n = 1.92 and k = 3.61 at 549 nm) is 64 %, so the plating bounces light back almost like a mirror. The defects to find are scratches 25 μm wide and foreign particles on the pin tops.

When specular reflection from the plating saturates the sensor, the scratches and particles on it vanish into the highlight. Defects buried in highlights slip through as misses, and forcing the sensitivity up makes the highlight edges read as defects, rejecting good parts. Changing only the intensity and angle of the light rarely avoids all the specular reflection from a near-mirror surface, and the knob left to turn is the polarization state of the light.

Cross-polarization¹ places a polarizer² in front of the light and an analyzer in front of the lens, with their polarization axes crossed at right angles. I judge this setup by three calculations: how much light the two polarizers leave, how strongly specular reflection is suppressed, and how much leaks when light comes in at an angle. The camera is assumed to be 2,448 × 2,048 px with 3.45 μm pixels at 0.5 magnification, so with a 6.9 μm pixel on the part, a 25 μm scratch spans 3.6 pixels.

Information lost to a highlight does not come back

Under a coaxial light³, the brightness ratio of plating to matte housing is approximately specular reflectance × π ÷ (diffuse reflectance × source solid angle). Plugging in 60 % specular reflectance (assumed below 64 % to allow for plating roughness), 5 % diffuse reflectance and a 10° source half-angle gives about 400 to 1. Expose for the housing and the pins overshoot the sensor’s saturation level by hundreds of times, and saturated pixels cannot hold the brightness difference of the scratch that was there.

An error that only shifts positions, such as distortion, can be undone in software, but saturation means the information was never recorded by the sensor, so no post-processing restores it. That is why I hold that specular reflection has to be suppressed before the light reaches the sensor, and polarization is a way of doing that on the optical side.

Two polarizers leave 18 % of the light

The principle is written into old patents too. US3812374A (Computer Identics), granted on May 21, 1974, covers an apparatus that illuminates with polarized light and blocks specular reflection with a polarizing element orthogonal to that polarization, explaining that specular reflection keeps the incident polarization and is blocked, while about half of the randomly polarized diffuse light passes. CN103743758A (Tangshan Yinglai Science & Technology), published on April 23, 2014, applied the same cross-polarization to a visual inspection system for highly reflective metal surfaces.

As in the figure, crossing the polarizer and analyzer at right angles blocks specular reflection, which keeps its polarization direction, and lets only diffuse light, whose polarization the surface microstructure has scrambled, into the lens. The price is light. An ideal polarizer passes 50 % of unpolarized light, and if the diffuse light is fully scrambled, the analyzer passes 50 % again, leaving 25 %. Assuming each polarizer passes 85 % of the component along its own axis, one sheet leaves 42.5 % and two leave 18 %, a loss of 2.5 stops, so matching the old brightness takes 5.5 times more exposure or light.

On the suppression side, the number is set by the extinction ratio⁴. Assuming an extinction ratio of 1,000 to 1, only 0.085 % of the specular reflection survives the analyzer while 42.5 % of the diffuse light does, so the highlight drops to 1/500 of its original ratio. The 400-to-1 brightness ratio of pins to housing becomes 0.8 to 1, so the flat pin surfaces actually sink darker than the housing, and only scratches and particles that scramble polarization stay bright.

More oblique light, more polarization leakage

The 1/500 holds only under coaxial light, where light comes in straight. In oblique reflection, the component parallel to the plane of incidence (p) and the component perpendicular to it (s) differ in reflectance and phase, so when the polarization axis sits at 45° to the plane of incidence, the reflected polarization rotates and turns elliptical. Calculating Fresnel reflection⁵ with the optical constants of nickel, the share escaping through the analyzer is 0.09 % of the reflected light at a local incidence angle⁶ of 20°, 0.49 % at 30°, 1.27 % at 37.5° and 2.86 % at 45°. The range where it exceeds the 0.1 % that the polarizer itself leaks begins around 30°.

Under a ring light, the highlight on a cylindrical pin forms on the facet that faces midway between the light direction and the camera direction, so the local incidence angle is half the angle the ring light makes with vertical. With a ring at 15° above horizontal, the local incidence angle of the pin highlight is 37.5°, and by my calculation the highlight is suppressed only to 1/36.5, leaving the 400 to 1 at 11 to 1. Compared with 0.8 to 1 under coaxial light, the same polarizers become more than ten times weaker. Glossy resin is worse still: assuming a refractive index of 1.58, 9.3 % leaks at 37.5°.

The half mirror in a coaxial light rotates polarization too

Coaxial light has a trap of its own. The half mirror⁷ that bends the light downward sits at 45°, which makes it an oblique reflector in its own right, with different s and p reflectance. An uncoated glass plate (refractive index 1.52) at 45° reflects 9.7 % for s and 0.94 % for p, so with the polarization axis at 45° between s and p, the polarization rotates 27° after the reflection and transmission. With the analyzer crossed to the original polarizer, 21 % of the specular reflection leaks straight through. Aligning the polarization axis with the mirror’s s direction stops the rotation and also sends ten times more light down than the p direction, so s alignment is my default. Real half mirrors differ by coating, so these numbers are an example, but the principle of aligning the axis holds.

The figure shows the light lost passing through the polarizers together with a structure that switches polarization states with a wave plate⁸. Setups that do not fix the polarization state to one setting have long been used in wafer inspection patents. US8400629B2 (Hitachi High-Technologies), granted on March 19, 2013, sets the illumination to S, P or circular polarization with wave plates, and US10228331B2 (KLA), granted on March 12, 2019, uses a rotatable wave plate and analyzer to separate defect scattering from surface scattering and raise the defect signal-to-noise ratio. Depending on material and defect, one polarization angle may not be enough.

The setup for pin-top inspection fits in one table. The lens is assumed to have a 25 mm focal length, putting the WD at about 75 mm by thin-lens approximation, and subtracting the analyzer filter on the lens front (5 mm thick, assumed) leaves about 70 mm of height for the coaxial light.

Inspection item	① Minimum defect size	② Optical setup · WD	③ Algorithm parameters · in plain words
Scratches and particles on nickel-plated pin tops	25 μm = 3.6 pixels (6.9 μm on the object)	5 MP with 3.45 μm pixels, magnification 0.5, 25 mm lens, WD about 75 mm (thin-lens approximation, 5 mm analyzer filter assumed), coaxial light + cross-polarization (axis aligned with the half mirror’s s direction)	Highlights suppressed to 1/500 (1,000-to-1 extinction assumed), exposure ×5.5 (85 % polarizer transmission assumed), scratches and particles detected as bright spots or lines
When a ring light is added	25 μm	With a 15° ring, the local incidence angle of pin highlights is 37.5°	1.27 % leakage on nickel limits suppression to 1/36.5 (400 to 1 → 11 to 1); exclude highlight areas from judgment in the ring frame
Matte housing	To be confirmed (fixed by sample test)	Same setup	Cross-polarization gains little and costs 2.5 stops of light, so the housing is judged in a frame without polarization

Reading the three rows together, the effect of cross-polarization depends on the angle at which light arrives as much as on the grade of the polarizers, and the 2.5 stops of light it costs have to be provided in advance through lighting and exposure. The difference between 1/500 under coaxial light and 1/36.5 under a 15° ring, with the same polarizers, becomes the basis for choosing the lighting layout.

Surfaces where polarization costs more than it gives

On surfaces where diffuse reflection dominates from the start, such as a matte housing, cross-polarization gains almost nothing. There is little specular reflection to suppress, yet 2.5 stops of light are lost, so contrast can actually drop. The same goes for lines where the target is dark to begin with and has no exposure margin, or where moving parts rule out longer exposures. In my judgment, splitting the lighting into dark field and coaxial frames to avoid specular reflection may work better in those cases. Which approach wins depends on the gloss of the plating, the curvature of the pins and the type of defect, so it cannot be guaranteed before a sample test.

As the figure shows, suppressing specular reflection means designing lighting, lens and algorithm together. Polarizing film and filters cost less than lights or cameras, but the real cost appears only after adding the lighting output to support 5.5 times the exposure, the WD clearance, and the setup time for aligning polarization axes. This article explains technology and is not investment advice. See our Disclaimer.

Field Note

With nickel-plated pins and a matte housing in one image, I would measure the saturated area of the pin highlights before fitting any polarizer. Next, I fix the polarizer on the light side, turn only the analyzer in 10° steps while recording the brightness of the highlights and the housing together, and check whether the darkest angle falls at exactly 90°. If it is off 90°, that signals the half mirror rotating the polarization, so I align the polarizer axis with the tilt direction of the mirror and turn the analyzer again. Once the effect is confirmed, I reset the exposure around the 5.5-times baseline and measure contrast on pin scratch samples.

Field Checkpoints

Once the analyzer rotation log and the pin scratch samples have confirmed the assumptions behind the calculations, work down the list below.

• At a WD of about 75 mm, is there still height for the coaxial light (about 70 mm) after subtracting the analyzer filter thickness?
• Is there lighting output or exposure margin to make up for the light lost through two polarizers (25 % left if ideal, 18 % with 85 % transmission assumed)?
• When the analyzer is turned, does the darkest angle fall at exactly 90° to the polarizer?
• Is the polarization axis of the coaxial light aligned with the s or p direction of the half mirror?
• If a ring or dome is added, have you calculated the leakage at the local incidence angle of the highlights? (37.5° for a 15° ring)
• Have you measured contrast before and after polarization on pin scratch samples?

Frequently Asked Questions

What changes with circular polarizers?

A circular polarizer, a linear polarizer stacked with a quarter-wave plate, can block specular reflection by using the way near-normal specular reflection reverses the handedness of circular polarization. US3812374A also covers a circular-polarization arrangement with an orthogonal linear polarizer behind a quarter-wave plate. It is less sensitive to axis orientation, but the wave plate is tuned to a particular wavelength, so the lighting wavelength and the wave plate spec have to match.

Is a polarizer on the light side alone enough?

With a polarizer only on the light side, the light is polarized, but with no analyzer to block the specular reflection, the highlight comes straight in. With only an analyzer on the lens side, near-normal specular reflection of unpolarized light comes back almost unpolarized and simply dims at the same rate as the diffuse light. The effect appears only when the two sheets pair up at right angles, and checking that the pair is at the right angle is the first step of the setup.

Glossary

• [1] Cross-polarization crossed polarizers
  A setup that blocks specular reflection by crossing the axes of a light-side polarizer and a lens-side analyzer at right angles. ↩
• [2] Polarizer linear polarizer
  A sheet that passes only light vibrating in one direction. The one in front of the lens is called the analyzer. ↩
• [3] Coaxial light on-axis light
  Lighting sent along the lens axis through a half mirror. The light reaches the part almost straight on. ↩
• [4] Extinction ratio contrast ratio
  The ratio of light passing two polarizers with parallel axes to light passing with crossed axes. The text assumes 1,000 to 1. ↩
• [5] Fresnel reflection Fresnel reflection
  Equations giving the share of light reflected at a boundary between different refractive indices, separately for s and p components. Metals are calculated with a complex index n + ik. ↩
• [6] Local incidence angle facet incidence
  The angle between the incoming light and the normal of the small facet it strikes. On curved surfaces, it differs from spot to spot. ↩
• [7] Half mirror half mirror
  A mirror that reflects part of the light and passes the rest. In a coaxial light, it sits at 45° to bend the light downward. ↩
• [8] Wave plate retarder
  A plate that adds a set phase difference between two polarization components. A quarter-wave plate turns linear polarization into circular. ↩

References

• Computer Identics, US3812374A, Specular reflection suppression apparatus (1974-05-21, specular reflection blocked by a crossed polarizing element, about half of diffuse light passes, circular arrangement with a quarter-wave plate)
• Tangshan Yinglai Science & Technology, CN103743758A, Visual inspection system for high-reflective metal surface based on cross-polarization (published 2014-04-23)
• Hitachi High-Technologies, US8400629B2, Surface defect inspection method and apparatus (2013-03-19, wave plates set the illumination to S, P or circular polarization)
• KLA, US10228331B2, Methods and apparatus for polarized wafer inspection (2019-03-12, rotatable wave plate and analyzer separate defect scattering from surface scattering)
• refractiveindex.info, Optical constants of Ni (Johnson and Christy 1974) (n = 1.92 and k = 3.61 at 0.549 μm)
• Formulas: normal reflectance = ((n − 1)² + k²) ÷ ((n + 1)² + k²), brightness ratio = specular reflectance × π ÷ (diffuse reflectance × π sin²(half-angle)), two-polarizer transmission = (0.5 × axial transmission)², highlight suppression = (leakage × axial transmission + axial transmission ÷ extinction ratio) ÷ (0.5 × axial transmission), rs = (cos θ − √(N² − sin²θ)) ÷ (cos θ + √(N² − sin²θ)), rp = (N² cos θ − √(N² − sin²θ)) ÷ (N² cos θ + √(N² − sin²θ)), leakage at 45° polarization = |rs + rp|² ÷ (2(|rs|² + |rp|²)), N = n + ik

Related reading — For Scratches on Highly Reflective Metal, Choose the Lighting First · What HDR Multi-Exposure Fusion Does When Specular and Matte Share One Frame · How to Handle Imaging on Highly Reflective Surfaces