Capabilities of diffractive optical elements for real ... - ResearchGate

110.90.90.80.8Diffraction efficiency η0.70.60.50.40.30.2q = 7q = m = 6q = 5Diffraction efficiency η0.70.60.50.40.30.2q = 7q = m = 6q = 50.10.10400 450 500 550 600 650 700Illumination wavelength λ [nm]0400 450 500 550 600 650 700Illumination wavelength λ [nm](a) Mirror-type(b) Lens-type (acrylate)Figure 3. Diffraction efficiency over the wavelength for a multi-order DOE with m = 6 for λ 0 = 525 nm. The marginalshift of the sinc-functions for blue and red wavelengths in (b) is due to material dispersion n(λ). The blaze depth isassumed to be ideal (µ = 1).Optical performance. The optical performance of diffractive optical elements strongly depends on how accuratethe operation corresponds to the ideal situation which the DOE is designed for. This applies to bothvariations in the optical setup (operation wavelength, alignment), as well as minor fabrication inaccuracies (profiledepth, pattern distortion) of the DOE itself. Apart from alignment errors, which can be avoided by a carefuladjustment, a wavelength change will have an impact on the diffraction efficiency and the phase reconstruction.To address these influences a parameter α was established 11α = λ [ ]0 n(λ) − 1. (6)λ n(λ 0 ) − 1Profile depth scaling errors will also influence the diffraction efficiency. In case of a constant profile depth errorthis can be addressed by introducing a parameter 6 µ = t′t , (7)with t as the nominal and t ′ as the actual profile depth. With the parameters α and µ the scalar diffractionefficiency of a multi-order DOE for the qth diffraction order is then given byη q = sinc 2 (αµm − q) . (8)If the argument of the sinc-function equals to zero, the diffraction efficiency will have a maximum. Fig. 3shows the diffraction efficiency vs. wavelength of a ’5/6/7’ multi-order DOE designed for λ 0 = 525 nm and m = 6.As it can be seen in Fig. 3(a) besides the green efficiency peak there are further maxima at the blaze-matchedwavelengths of 450 nm (q = 7) and 630 nm (q = 5). To illustrate the minor influence of material dispersion wehave distinguished between (a) reflective and (b) transmissive multi-order DOE. Figure 4 indicates the efficiencydependence on blaze depth scaling errors for different blaze orders. In contrast to a standard first-order blazedDOE, the multi-order DOE’s efficiency is much more sensitive to potential fabrication inaccuracies. For theabove mentioned ’5/6/7’-design for example, a variation in the blaze depth of only 5% will result in an efficiencydrop to 65% (blue) or 81% (red), respectively.On the other hand, the aberrations of multi-order DOE are highly wavelength-sensitive too. Unaberratedwavefronts for all wavelengths will be generated only if the operation wavelengths exactly match the design69124