A comprehensive treatment is presented for the diffraction efficiencies of transmission holographic elements and cascade lenses when subject to broad spectral and field angle detunings. Experimental measurements are made in support of our theory on holographic optical elements fabricated in bleached silver-halide emulsions and in dichromated gelatin. The theory of holographic grating diffraction efficiency is studied through two approaches. A numerical treatment based on the theory of thin grating decomposition is implemented and shown to be in close agreement with other theories. Additionally, a more approximate approach is pursued in which the volume grating is treated as a phased array of scatterers. The latter approach leads to closed-form formulas in addition to a simple physical picture of volume effects. It is found that three-element cascades can exhibit spectral and field angle bandwidths essentially as broad as two-element cascades and that these bandwidths are in excess of 2300 Å and 7° respectively.
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