Characterizing the Performance of Optical Filters
From time to time people are interested in optical filters whose response changes with position. Frequently the desire is for a filter that changes in one direction and remains constant in the perpendicular direction. The deliberate nonuniformity and anisotropy of these filters adds significant complications in the characterization of their spectral performance.
In the spectral measurement of real devices the size of area illuminated on the filter produces a measurement of the beam irradiance weighted average performance. In most commercial spectrophotometers this is an image of the entrance slit of the monochrometer and is typically around 2x7 mm. For optical interference filters, changes in the thickness and refractive index across the part result in changes in the spectral performance or in the uniformity. Among other things, the ability to control the uniformity determines the size of a filter that can be manufactured to a given tolerance. The narrower the filter, the tighter the control must be to fabricate a filter of the same size.
In Linear Variable Filters (LVF) our goal is to still control the thickness and index variation, but instead of targeting a constant value, we are after one that changes in a predetermined, usually linear, manner. We call this target the “filter dispersion” (FD) in order to offer the greatest likelihood of confusion with the material dispersion (MD) with which it is intrinsically linked. MD is the change in refractive index as a function of Wavelength. The FD of a LVF is the change in the filters central wavelength with position. In the visible region of the optical spectrum both the real and imaginary parts of the refractive index increase toward shorter wavelengths. MD is a materials-dependent parameter so that each material in a given design will have its own change in index with wavelength. FD is determined by the change in optical thickness of the filters constituent layers. The way Materion creates LVF, the relative thickness of the layers is fixed by the design and the total thickness changes as a function of position. In this manner, any filter type could be a LVF.
There are two types of LVF that dominate the market - Long wave pass (LWP) and Band pass (BP). A typical use of a LWP LVF is for order suppression in grating-based spectrophotometers. For these filters, the spectral response of interest is the transmission at two wavelengths that are widely separated, i.e. the measured wavelength and spurious signals from other grating orders that are spatially coincident, /2, /3 etc. A BP LVF, if used in conjunction with a pixilated detector, becomes a spectrometer on a chip. As an example of LVF BP, consider a narrow band filter with a 1% bandwidth designed to operate over the Visible and NIR wavelength range of 400 to 900 nm for use with a CCD Array that is 25 mm long. The FD of this filter is 500 nm/25mm or 20 nm/mm.
Click to view the full technical paper as a PDF: "Characterizing the Performance of Optical Interference Filters with Deliberate Large Variation in Spectral Response"