Spectral Dispersion Spectral resolution defined as R = Low 10-100 Medium 100-1000s High 1000s+ Broadband filters have resolutions of a few (e.g. J-band corresponds to R=4).
Anti-reflection Coatings Significant Fresnel reflection loss occurs at a refractive index interface (particularly for high-index materials like silicon or ZnSe). Reflection losses can be reduced by ''softening'' introduction to refractive medium with an intermediate refractive index layer A standard, simple coating is ¼ wavelength of material with index which is the square root of the index of the material being coated. This coating creates destructive interference between reflected wavefronts (which enhances transmission via conservation of energy).
Anti-reflection Analysis More generally, the intensity reflected is n 2 n 1 2 n 2 n 1 if the layer thickness is ¼ of a wavelength the reflected waves from the first and second surface will be 180 degrees out of phase the condition for cancellation is equal intensity from each reflection (note that this oversimplification is exactly true thanks to multiple reflections) the cancellation is perfect at only one exact wavelength. n 1 n 0 n 1 n 0 2 = n 2 n1 n 2 n1 n 1= n 0 n 2 2
Anti-reflection Analysis More generally, the intensity reflected is n 2 n1 2 n 2 n1 if the layer thickness is ¼ of a wavelength the reflected waves from the first and second surface will be 180 degrees out of phase the condition for cancellation is equal intensity from each reflection (note that this oversimplification is exactly true thanks to multiple reflections) the cancellation is perfect at only one exact wavelength. n 1 n 0 n 1 n 0 2 = n 2 n1 n 2 n1 n1= n0 n 2 2
Real-world Anti-reflection Coatings Multiple element systems require excellent coating performance across a broad spectral range.
Multi-layer Coatings Using a multi-layer approach yields custom anti-reflection coatings (and bandpass filters) with excellent transmission (and sharp cutoffs). http://infrared.als.lbl.gov/irwindows.html Concepts of Classical Optics (Strong) Blocking (opaque) elements are often employed to remove out of band leaks. For example, a sapphire substrate would yield a 4-5.5um filter using the coating above (with poor leakage performance shortward of 4 um, however which might be ok with an Si:As detector). 4 Typical out of band transmission is < 10
Interference Filters Multiple dielectric stacks create successive tuned cavities which, when cascaded, can be tailored for welldefined bandpasses. The physics/optics are well defined such that a coating recipe can be reliably engineered on paper. http://www.olympusfluoview.com/theory/interferencefilters.html
Interference Filter Manufacture Coatings are produced in a vacuum chamber an evaporator sprays the substrates with a stream of atoms which adhere, one monolayer at a time. The substrates usually point downward while the atoms spray upward. The vacuum is low enough that trajectories are purely ballistic. An optical monitor uses interference to monitor the thickness of a growing layer to great precision. http://www.olympusfluoview.com/theory/interferencefilters.html
Gradient Index Coatings Nature provides only a limited number of materials from which to design antireflection coatings. An alternative method consists of artificially manipulating the refractive index of a material to produce a custom index or gradient. For example, sputtering Ta x Si y O z films can produce just such a gradient. http://www.astro.virginia.edu/class/skrutskie/astr512/pdf/gradient.pdfc
Gradient Index Coatings Nature provides only a limited number of materials from which to design antireflection coatings. An alternative method consists of artificially manipulating the refractive index of a material to produce a custom index or gradient. For example, sputtering Ta x Si y O z films can produce just such a gradient. http://www.astro.virginia.edu/class/skrutskie/astr512/pdf/gradient.pdfc
Dependence on Temperature and Angle Since spacings and refractive indices change with temperature, bandpass changes with temperature as well. In general, filters shift to shorter wavelengths as the temperature decreases. The shift can be significant (completely out of band) for narrowband filters between room and cryogenic temperatures. Since the interference depends on differential pathlengths, tilting a filter changes the bandpass (to shorter wavelengths with increasing angle). Filters are often configured with a mild (few degree) tilt to avoid reflection ghosts. = 0 1 1 n 2 sin 2 where n is the effective refractive index of the filter 1 2
Generic Spectroscopy Collimated light (rays from each point source in the field restricted to a single direction) impinges on a disperser. The disperser sorts different wavelengths into different ray angles. Angles in collimated space translate to positions in image space. The final element is a focuser (camera) which converts the collimated light to an image. d dx f1 d d f2
Generic Spectroscopy The slit is located a distance f 1, the focal length of the first lens from the collimating lens. The image is formed one focal length from lens2 since collimated light represents an infinitely distant object The slit is magnified by the ratio f 2/ f 1 The reciprocal linear dispersion (microns/mm) decreases in proportion to f 2 d dx f1 d d f2
Prisms Refractive index is a function of wavelength Snell's Law then dictates that polychromatic incident light will be sorted by angle. sin 1= n sin 2 i The Infrared Handbook
Prisms Angular/Linear Dispersion Snell's law dictates angular sorting in collimated space. The focal length of the camera optics converts the angular dispersion to a linear dispersion Pixel scale on the detector then determines the resolution of the instrument
Prisms Dispersion vs. Geometry Maximum resolution is limited by diffraction and geometry. Geometrically, large apex angles can provide high dispersion, but throughput will suffer at high incidence angle. Conversely, a plane parallel slab produces no dispersion.
Prisms Optimal Geometries Optimal configuration for any apex angle is at ''minimum deviation'' At minimum deviation incident and emergent angles are identical and the angle of refraction inside the prism is ½ the apex angle. At minimum deviation optical aberrations are minimized minimize refractive angles maximize symmetry
Prisms Diffraction Limited Resolution The physical extent of the prism, via diffraction, defines the minimum angular spread of the emergent light = D Spectral resolution cannot exceed the wavelength range spanned by this angular spread - the Rayleigh limit. d = D d D is the ''diameter'' of the prism For a 10cm flint glass prism with an apex angle of 60 degrees the limiting resolution is 15,000.
Prism Spectrograph Configurations
Prism Spectrograph Configurations