Holographic Interferometry Strain Mapping

Load & Optics

Load intensity q 3.0 N/m

Laser wavelength λ 633 nm

Sensitivity angle θ 20°

Panel thickness t 1.2 mm

Panel material

Live Readouts

Max out-of-plane disp.

0.0 µm

Fringe order (tip)

0.0

Fringe spacing near tip

— mm

How it works

Double-exposure holographic interferometry records the object's wavefront twice on the same photographic plate — once unloaded, once deformed — and reconstructs both together. Where the two wavefronts are out of phase, destructive interference darkens the image; where in phase, it brightens. The result is a fringe pattern that is a full-field contour map of surface displacement.

Optical path difference:  Δ = K · d(x,y)
Sensitivity vector:       |K| = (4π/λ) cos(θ/2)
Fringe order:             N(x,y) = Δ / (2π) = 2·d(x,y)·cos(θ/2) / λ

d(x,y) is the out-of-plane displacement, λ the laser wavelength, and θ the angle between the illumination and observation directions. Each bright-to-bright fringe marks a displacement step of λ / (2 cos(θ/2)) — for a HeNe laser near-normal, roughly 0.3 µm per fringe, which is why holographic/ESPI interferometry resolves sub-micron strain that strain gauges and vision systems cannot see.

The panel itself deflects like a cantilever beam fixed at the left edge under a distributed load q, using the closed-form solution of the Euler–Bernoulli equation:

w(x) = q·x²·(6L² − 4Lx + x²) / (24·D),   D = E·t³ / (12·(1−ν²))

D is the flexural rigidity (from Young's modulus E, thickness t, Poisson's ratio ν = 0.3), and L the panel length. Increase the load or thinner/softer material and D drops, w(x) grows, and more fringes crowd into the same length — exactly what a real inspector reads as higher local strain concentration.

Real-world use: aerospace panels, turbine blades, pressure vessels and PCBs are tested this way because it is non-contact, whole-field, and sensitive to displacements far below what strain gauges can register.

Deformed panel (exaggerated ×250 for visibility) Fixed edge (cantilever support)

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