Photometric stereo light distance: avoid shadows that flatten detail

Photometric stereo fires four lights at a part in sequence and combines the frames into one image where embossing, engraving and texture stand out regardless of surface reflectance — plus a surface normal map for depth-sensitive checks. Whether that composite comes out sharp or smeared is decided before the first exposure, by the lights' distance and angle to the part. Sit them too close and the shadows harden, the solver loses the pixels behind every tall edge, and the depth map over-smooths. This guide gives the geometry rules with the arithmetic shown: how elevation sets shadow length, how distance sets falloff and direction spread, a worked station design, and the point at which four bar lights beat a quadrant ring.

Why light-to-part distance decides the result

Photometric stereo holds the camera still and changes only the light direction between exposures. Software compares the frames pixel by pixel, separates reflectance from shading, and returns two things: a composite in which surface detail reads at even contrast, and a normal map of the local surface tilt. The classical method assumes each light acts as a distant point source — one illumination direction for the whole field, no brightness gradient across it.

Real quadrant hardware rarely meets that assumption. A ring or bar sitting tens of millimetres from the part is a near-field light: intensity at each pixel depends on that pixel's 3D position, the effective direction swings across the field, and any feature taller than its neighbours casts a hard shadow into at least one frame. The documented failure mode follows: when many strongly shadowed frames are processed, the solver discards occluded pixels, the smoothness term fills the gaps, and the depth map comes out over-smoothed with a lower-contrast composite.

Distance is therefore a trade to set on purpose. Pull the lights back and the falloff flattens, the direction spread narrows, and the occluded fraction shrinks — at the cost of intensity, which falls with the square of distance. Push them in and every pulse carries more signal, but more of the field sits in shadow in more frames. The numbers below bound both sides; for the wider question of how angle sets contrast, see lighting geometry for image contrast: camera, light and part positions.

The four numbers that set the geometry

Four quantities decide the geometry, and all of them are yours to choose:

• θ — beam elevation: the angle of the light direction above the part surface.
• h — the height of the tallest feature you must keep unshadowed.
• r — field radius: half the camera's field of view at the part plane.
• L — slant distance from emitter to part centre.
• a — emitter size along the beam direction: the arc of a quadrant, the width of a bar.

The spread and falloff are small-angle estimates: a field point at radius r sees the light direction tilted by about r/L, at a distance shorter by about r. The penumbra is the emitter's angular size a/L projected over the feature height.

The shadow budget sets elevation. Keep s under half the finest pitch you must read:

The distance budget sets L. Stay at or above three field radii for a contrast composite, and five or more when you also want usable normals:

Worked example: embossed code on a 30 mm cap

The part is a moulded cap with raised date characters 0.5 mm tall on a 1.0 mm pitch. The camera fields 40 mm at the part, so r = 20 mm. Plan: a four-quadrant ring with quadrant centres 35 mm off axis and the emitter plane 60 mm above the cap top.

Elevation and slant distance:

θ = atan(60 / 35) ≈ 60° L = √(35² + 60²) = √(1225 + 3600) = √4825 ≈ 69.5 mm

That is 3.5 field radii — just past the composite floor. Check each budget:

• Spread: Δφ ≈ 20 / 69.5 = 0.29 rad ≈ 16°, inside the 19° three-radius limit, so one direction per quadrant stays a fair description of each frame.
• Falloff: F ≈ (69.5 / 49.5)² ≈ 2.0× from the near edge to the centre of each frame. Opposing quadrants mirror the gradient, so the composite evens it out, and a flat-field correction removes the rest.
• Shadow: s = 0.5 / tan 60° = 0.5 / 1.732 = 0.29 mm, which is 29% of the 1.0 mm pitch. Most of every character survives unshadowed in each frame, and the opposite quadrant lights whatever the active one hides.
• Penumbra: with a ≈ 25 mm of emitter arc, p ≈ 25 × 0.5 / 69.5 = 0.18 mm — comparable to the umbra, so the shadow edges arrive soft, which the solver handles cleanly.

Decision: the geometry passes for the flattened code image, and at 3.5 radii the normal map is usable though not metrology-grade.

Now drop the same ring to 20 mm above the cap — the tempting move in a tight cell or a dim image:

θ = atan(20 / 35) ≈ 30°, and L = √(35² + 20²) = √1625 ≈ 40.3 mm.

• Spread: 20 / 40.3 = 0.50 rad ≈ 28°.
• Falloff: (40.3 / 20.3)² ≈ 3.9×.
• Shadow: 0.5 / tan 30° = 0.87 mm — 87% of the pitch, so a character facing away from the active quadrant is mostly shadow in that frame.

Decision: the composite still forms, but the depth map over-smooths, the documented near-light failure. Raise the ring and buy intensity back with pulse current instead of proximity: doubling L costs (2)² = 4× the light, which a strobe driver recovers from its duty-cycle headroom — see LED overdrive and current control: stable machine vision lighting.

When four bar lights beat a quadrant ring

Scale the cap station up and the ring body grows with it. At 60° elevation the emitters stand H = 0.87 × L high and R = 0.5 × L out, so a 360 mm slant distance wants a ring about 360 mm across, mounted 312 mm over the part — bulky to bridge over the field and awkward to service. Four discrete bars reach the same geometry on brackets, and each keeps its own channel, aim and pulse.

Take a 240 mm field (r = 120 mm) and hold the distance floor, L = 3 r = 360 mm, at θ = 60°:

R = L cos θ = 360 × 0.5 = 180 mm lateral radius H = L sin θ = 360 × 0.866 = 312 mm mounting height

Four bar lights of about 290 mm lit length, set on a 360 mm square around the part, cover the field with margin, and a 3 mm tall boss casts s = 3 / 1.732 = 1.7 mm of shadow — short against any realistic spacing between features. Bars also bring a long emitter, and in the penumbra formula a longer a softens the shadow edge at the same L, which is friendlier solver input than a compact quadrant of the same output.

For a station in this class, three catalog bars cover the usual choices:

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

All three are 24 V standard-type bars in the 200-400 mm size class. Choose by lit width for the penumbra you want and by luminance class for short strobe pulses. If the part needs two elevations from one station, angle-switching rings are the ring-side route — see stacked ring lights: switching angles to catch more defect types. For a smaller field, stay with the quadrant route from the ring lights range; its build is laid out in photometric stereo ring lighting for surface inspection.

Driving the four channels

Each quadrant needs its own channel, fired once per exposure: quadrant 1 flashes during exposure 1, quadrant 2 during exposure 2, and so on through the set. A four-channel strobe controller with independent pulse width and delay per channel does this directly — the event patterns are laid out in multi-channel light controller sequencing for photometric stereo. If an image comes back black while the light visibly flashes, the pulse is landing outside the exposure; the timing checks are in strobe light on but camera image is black: fix the timing.

Keep the channels matched. A dim quadrant biases every surface normal it illuminates, and mismatched pulse widths show up as brightness steps between frames. Constant-current output holds the balance as the LEDs warm and age; if you trim brightness per channel, trim against a measured grey part, not by eye. One four-channel digital control box with strobe and RS232 covers the sequence:

Wavelength can ride the same sequence: give opposing quadrants different colours and a monochrome sensor separates four directions and two wavelengths from one frame set — the pattern is in multi wavelength light: sequence colours to get more from one camera.

On a moving line, add a fifth, full-illumination frame: all quadrants together, or one diffuse ring, gives the registration image that locates the part in every strobe frame — moving part photometric stereo: synchronize image capture walks through the synchronization. A diffuse full ring covers that role in one unit:

Checks before you order

Run the arithmetic, then confirm it on a first article before the cell is built:

• Measure h and the finest pitch p on a real part. Require s = h / tan θ ≤ p / 2 at the elevation you plan to mount.
• Compute R = L cos θ and H = L sin θ at the chosen L, and check the frame has H of headroom plus the camera's own working distance above the part.
• Confirm the controller: four channels minimum, strobe output, independent width and delay per channel — the light controllers category filters by channel count, strobe and constant-current output directly.
• Capture the four single-quadrant frames and check three numbers: edge-to-centre ratio ≤ 2× within each frame, shadow length ≤ half the feature pitch, and clearly different shading between frames. Two frames that look alike mean the directions have collapsed, and no distance will fix a weak solve.
• On a moving line, confirm dwell: the four pulse widths plus gaps must fit the time the part spends inside the field at belt speed.

When the usual answer is wrong

• Grazing is the goal. For dents and pits on otherwise flat metal, mount below 30° on purpose and let the long shadows draw the defect — the shadow budget above is for keeping shadows off features, not for shadow-based inspection. The low-angle dents and pits guide covers that case.
• Mirror finishes break the shading model. Photometric stereo assumes diffuse reflectance; on polished metal the composite can still ghost. Add cross-polarization or a dome before blaming distance — see cross polarization machine vision: reduce surface glare and lighting shiny metal pins without glare: dome, diffuse and polarizer.
• Traceable depth needs a calibrated sensor. Normals from a near-field ring are relative, not metrology. Use photometric stereo for the contrast image and a 3D sensor for dimensions.
• One angle would do. If a matte part's defect already reads in a single frame, a single low-angle light is the cheaper station — and robust machine vision lighting: why adequate contrast is not enough explains why contrast quality still decides the result.

The decisions, in one line each: low-relief marked part in a field up to about 60 mm — quadrant ring or four compact lights at θ = 45° to 60° and L ≥ 3 r. Large field or features 3 mm and taller — four bar lights at the corners, θ = 60° to 75°, L ≥ 3 r, extended to 5 r when the normal map matters. Moving belt — sequenced flashes plus a full-illumination registration frame. Size the field first with the lens focal length calculator, then take θ and L to the lights finder or start at the light configurator step; more illumination patterns sit on the lighting topic page, and we will check a station geometry against a part drawing through the contact page.