= Photoelastic fringe value
{title2=$f_\sigma=\lambda/|C|$}
The <photoelastic fringe value> $f_\sigma$ is the material-and-wavelength scale connecting <photoelastic fringe order> to principal-stress difference times specimen thickness in the linear <stress-optic law>. With vacuum wavelength $\lambda$ and <stress-optic coefficient> $C$, use the magnitude convention
$$
f_\sigma=\frac\lambda{|C|},\qquad |\sigma_1-\sigma_2|=\frac{Nf_\sigma}{t}.
$$
Here $N=|\delta|/(2\pi)$ counts full relative-phase cycles and $t$ is specimen thickness. Since $C$ has units $\mathrm{Pa^{-1}}$, $f_\sigma$ has units $\mathrm{Pa\,m}=\mathrm{N/m}$. A value expressed in $\mathrm{MPa\,mm}$ equals the same numerical value in $\mathrm{kN/m}$. The wavelength dependence of $C$ must be retained.<Experimental Strain Analysis by David Roylance>[Printed p.6, stress-optical law and wavelength-dependent coefficient; pp.7–8, fringe interpretation]{ref}
For an original example, take $\lambda=600\,\mathrm{nm}$ and $|C|=50\times10^{-12}\,\mathrm{Pa^{-1}}$. Then $f_\sigma=12000\,\mathrm{N/m}$. A3mm specimen at fringe order2.5 has stress-difference magnitude $2.5(12000)/0.003=10\,\mathrm{MPa}$. One additional complete phase cycle changes the inferred magnitude by4MPa for that thickness.
A uniaxial calibration supplies a known stress difference away from grips and other stress concentrations. For a rectangular strip of width10mm and thickness3mm, load300N gives stress10MPa. If the corresponding referenced fringe order is2.5, the measured fringe value is $10(3)/2.5=12\,\mathrm{MPa\,mm}$. Repeating at several loads tests the assumed linear regime; counting from a referenced unloaded state helps separate the applied-load change from pre-existing retardation.
A primary instructional apparatus uses a manual leadscrew, load-cell readout, monochromatic illumination, polarizing elements and a camera. Those components connect a known mechanical load to the observed optical pattern.<Polariscope and Photoelasticity by the University of Illinois Mechanical Testing Instructional Laboratory>[Specimen loading and load readout; monochromatic illumination, analyzer and camera]{ref} A single intensity value does not uniquely identify an absolute phase cycle, so fringe order requires continuity, reference information or another phase-resolving method.
The magnitude convention loses the sign of $C$ and does not separately determine the two principal stresses. It also assumes the stated through-thickness optical/stress model. A varying stress field along the light path requires the appropriate retardation model rather than inserting one arbitrary local stress into the uniform-specimen formula.
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