Optical cross section (OCS) is an important metric for optical systems in which unintended back reflections that propagate towards object space are of concern. This paper discusses the derivation and implementation of a first-order optical cross section (OCS) calculation. The Lagrange invariant is invoked to derive an expression for OCS based solely on a paraxial ray trace and is applicable for any optical surface within the system. It is shown that an explicit reverse ray trace is not required to complete the calculation. This approach enables rapid calculation of OCS for all surfaces within a lens system and is suitable for use during lens design optimization. The validity of the OCS expression relative to far-field diffraction calculations is examined in terms of the Fresnel number of the near field (exiting) beam. For this purpose, it is shown that the Lagrange invariant can be employed to perform an “effective” reverse ray trace so that the Fresnel number of the exiting beam can be calculated. The validity of the paraxial calculations in the presence of lens aberrations is also explored using real ray tracing.
We discuss a white-light processing system that produces a dynamic, achromatic Fourier transformation over the visible spectrum. The system includes an achromatic Fourier transform lens system and a low-dispersion spatial light modulator. A programmable phase mask can only write patterns with a spatial frequency appropriate for one wavelength. However, this problem is resolved by scaling broadband light from a point source to a common spatial frequency using an achromatic Fourier transformer. Then, the programmable phase mask must produce the same phase profile for all wavelengths. Using a chiral smectic liquid crystal (CSLC) spatial light modulator can minimize the wavelength dependence of the phase shifting elements. Phase modulation is accomplished by re-orientation of the optic axis in a plane transverse to the direction of propagation in a manner similar to mechanical rotation of a waveplate. The position of the optic axis is the same for all wavelengths and ideally so is the induced phase shift. We present experimental far field diffraction patterns due to a CSLC spatial light modulator that produces a binary broadband phase mask and an achromatic Fourier transform lens system. An analog modulator is also introduced. Applications for this technology include optical process, beam steering and adaptive optics.
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