18. Laser Speckle Metrology — Non-Contact Surface Roughness¶
Module
Practical Applications
Try it live
Explore this on the interactive simulator with real-time sliders and graphs: 🔬 Launch in Simulator
Aim¶
To study how the grain size and contrast of a laser speckle pattern depend on the illumination geometry and on the roughness of the scattering surface, and to see how this forms the basis of a non-contact surface-finish inspection technique.
Theoretical Background¶
When coherent laser light illuminates an optically rough surface — one whose height variations are comparable to or larger than the wavelength of light — each illuminated point scatters light with a random phase determined by its exact height. Downstream, these many randomly-phased spherical wavelets interfere with one another, producing a grainy, random intensity pattern known as laser speckle, rather than a smooth, uniform reflection.
Two statistical properties of this speckle pattern are of practical interest. The grain size (the characteristic size of the bright/dark blobs) is set purely by the illumination geometry — the beam diameter D and the distance z to the observation screen — independent of the surface roughness itself, following a diffraction-limited relation analogous to the resolution limit of an aperture. The speckle contrast, on the other hand, depends strongly on the surface roughness relative to the wavelength: a surface much smoother than the wavelength (σ ≪ λ) reflects almost specularly, producing low-contrast (nearly uniform) speckle, while a surface with roughness comparable to or greater than the wavelength (σ ≳ λ) produces fully-developed, high-contrast speckle.
This roughness-dependence of speckle contrast is exploited directly in industrial laser speckle profilometers, which grade the surface finish of machined parts, semiconductor wafers, and rolled sheet metal on a production line by measuring speckle statistics — entirely without touching the part, unlike a stylus profilometer, which must physically drag a fine needle across the surface and risks scratching delicate finishes.
Governing Formulas¶
Objective speckle grain size, for a beam of diameter D observed at distance z:
Approximate speckle contrast as a function of RMS surface roughness σ (relative to wavelength λ):
where λ is the laser wavelength, D the illuminated beam/aperture diameter, z the distance to the observation screen, and σ the RMS height variation of the scattering surface.
Simulator Controls¶
| Control | Symbol | Range | Unit |
|---|---|---|---|
| RMS surface roughness | σ | 5 – 2000 | nm |
| Illuminated beam diameter | D | 0.5 – 5 | mm |
| Screen distance | z | 10 – 100 | cm |
Readouts:
| Quantity | Symbol | Unit |
|---|---|---|
| Speckle grain size | s | µm |
| Speckle contrast | C | (0–1) |
| Surface regime | — | (qualitative) |
Procedure¶
- Launch the Laser Speckle Metrology panel; set the beam diameter D and screen distance z to fixed values.
- Vary the RMS surface roughness σ and record the resulting speckle contrast C at each value.
- Repeat for at least six different values of σ spanning from well below to well above the laser wavelength (632.8 nm), tabulating C each time.
- Fix σ, then vary the beam diameter D and record the speckle grain size s at each value, verifying the inverse relationship between s and D.
- Plot both C vs σ and s vs D as separate graphs.
Observation Table¶
Table: Variation of speckle contrast with surface roughness, at fixed beam diameter and screen distance
| S. No. | D (mm) | z (cm) | σ (nm) | σ/λ | Contrast, C |
|---|---|---|---|---|---|
| 1 | |||||
| 2 | |||||
| 3 | |||||
| 4 | |||||
| 5 | |||||
| 6 |
Graph¶
Plot Speckle contrast, C (y-axis) against Roughness ratio, σ/λ (x-axis).
Expected trend: a sharply rising curve from near zero (optically smooth, specular) to close to 1 (fully-developed speckle) once σ/λ exceeds roughly 0.1–0.2.
C vs σ/λ, showing the transition from specular to fully-developed speckle
Calculation¶
- For each trial, compute the roughness ratio σ/λ using λ = 632.8 nm.
- Compute the predicted speckle contrast C ≈ 1−exp[−(2πσ/λ)²] and compare it with the simulator's readout.
- Separately, compute the speckle grain size s = 1.22λz/D for your D-sweep trials and verify the inverse dependence on D.
Result¶
Table: Speckle-pattern behaviour for the simulated rough surface
| Quantity | Mean value | Unit |
|---|---|---|
| 1 | ||
| 2 |
Maximum Permissible Error¶
The speckle grain size s = 1.22λz/D is a product/quotient of measured quantities (λ taken as exact for a stabilized laser source), so the fractional errors in the screen distance z and beam diameter D simply add.
Precautions¶
- Use a genuinely coherent, single-frequency laser source; a source with poor spatial or temporal coherence will wash out the speckle pattern regardless of the surface roughness.
- Keep the beam diameter D and screen distance z fixed while varying only σ (and vice versa), so the two dependences are not confounded in your data.
- Avoid stray ambient light on the observation screen, since it reduces the apparent contrast of the genuine speckle pattern.
Self-Check Quiz¶
1. A surface with RMS roughness much smaller than the laser wavelength (σ ≪ λ) will produce:
- A) High-contrast, fully-developed speckle
- B) Low-contrast, nearly specular reflection
- C) No reflected light at all
- D) A speckle pattern with zero grain size
Answer: B — When the surface is optically smooth compared to the wavelength, it reflects almost like a mirror, so scattered wavelets stay nearly in phase and produce little of the random interference that characterizes fully-developed speckle.
2. Doubling the beam diameter D, with the screen distance z fixed, will make the speckle grain size:
- A) Double
- B) Halve
- C) Stay the same
- D) Quadruple
Answer: B — Since s ≈ 1.22λz/D, s is inversely proportional to D, so doubling D halves the grain size.
3. Why can a laser speckle instrument grade surface roughness without ever touching the part?
- A) Because speckle contrast is set by surface roughness relative to the wavelength, and can be measured purely optically
- B) Because lasers physically polish the surface as they scan it
- C) Because speckle patterns only occur on rough surfaces, never on smooth ones
- D) It cannot; a stylus is always still required
Answer: A — The contrast (and other statistics) of the purely optical speckle pattern already encode the σ/λ ratio, so no physical contact with the surface is ever needed.
Viva-Voce Questions¶
- Why does speckle contrast depend on surface roughness while speckle grain size does not?
- Explain physically why illuminating a rougher surface produces a higher-contrast speckle pattern.
- How would using a shorter-wavelength laser (e.g., a blue laser instead of a red He-Ne) change the sensitivity of this technique to a given surface's roughness?
- Why is a genuinely coherent source essential for observing speckle, and what would happen with an ordinary incoherent lamp instead?
- Give one advantage of a laser-speckle-based surface inspection method over a traditional contact stylus profilometer, beyond simply avoiding scratches.
- What practical factors (other than roughness) might also affect the measured speckle contrast in a real industrial setting?