Multi Wavelength Methods in Holographic Interferometry

Techniques are presented which take advantage of the wavelength dependence of various phenomena in holographic interferometry. Image-plane interferograms illuminated with light containing multiple wavelengths exhibit color dispersion of the fringes. We extract from this dispersion, fullfield information concerning displacement components which are not disclosed by monochromatic illumination. Theoretical background: wavelength dependent effects during reconstruction Consider a holographic interferogram formed with light of wavelength λ. If the interferogram is illuminated with light of the same wavelength, the fringe order n of a given object point is given by[1] D = nλ = u.( k h ). (1) in which D is the optical path difference, u is the displacement vector of the object point, k is the observation unit vector from the object to the eye and h is the object illumination unit vector from the source to the object. If, however, the interferogram is reconstructed by light of a different wavelength λ', the optical path difference [2] is given by D' = [λ'/λ]u.( k h ) . (2) When a fringe of given order is viewed by light of wavelength λ', the observation direction becomes k', not k. The relation between these vectors has been given recently [2], for a hologram which experiences no deformation, N{[1/λ'](k' c' ) -[1/λ](k c )} = 0, (3) in which N is a projection operator, c is the unit vector from the reference source to the hologram, and c' is the unit vector from the reconstruction source to the hologram. The operator N acts upon a vector v, to give the normal projection of that vector on the hologram plane: Nv = v n[v.n], in which n is a unit vector normal to the hologram. Applications [2] of such theoretical developments have centered principally upon the problem of reconstruction using a gas laser, eg. helium neon at 633 nm, of holograms made with high power pulsed lasers, eg. ruby at 694 nm, a different wavelength. Wavelength dependence of fringe order in image-plane holograms In this article we consider applications in which multiple wavelengths are deliberately introduced at the reconstruction to display additional information about the object displacement field. The hologram itself is not deformed. To that end, let Eq. 3 be satisfied by setting the vector in the {} brackets equal to zero. We obtain the following from Eqs. 2 and 3. n'λ' = D ' = u. (k' h ) + u. (c h )[(λ'/ λ) -1 ] + u. (c c' ) (4)