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Transcript
OPTICS | LIGHT TOUCH Chromatic Dispersion Stephen R. Wilk O ne of the more interesting optical phenomena is the Christiansen effect, discovered by the euphoniously named Christian Christiansen of Denmark in 1884. He found that, if he placed small fragments of glass into a liquid that had the same refractive index but a different dispersion (that is, a different dn/dl), the combination would transmit light at the wavelength where the indices coincide, but scatter at other wavelengths. The effect is rather dramatic, with the colorless liquid and solid collaborating to create a brilliantly colored composite that has a single spectral hue. Christiansen used glass in a mixture of benzene and carbon disulfide, but many other combinations have been discovered, including solid-in-solid mixtures. Christiansen filters generally take advantage of the considerably larger dispersion that is often found in liquids. The larger the difference in dispersion, the narrower the bandwidth. One can make a very serviceable Christiansen filter by using methyl salicylate, which has a high dispersion and is still available as a liniment at specialty drug stores, mixed with ethanol to vary the refractive index, and combining the mixture with most common glasses (microscope slides are very useful and readily available). 12 | OPN November 2006 Because liquids tend to have dispersion values that are one or two orders of magnitude greater than solids, you can “tune” the filter by heating or cooling it, changing the color of the passband. Because liquids also tend to have dispersion values that are one or two orders of magnitude greater than solids, you can “tune” the filter by heating or cooling it, changing the color of the passband. You can also tailor a Chrisitiansen filter by obtaining samples of specialty glass from a supplier such as Corning or Ohara and using indexmatching fluid from a firm such as Cargill Specialty Liquids. The basic relationships have been derived several times. Some researchers claim that the scattering is due to multiple passes through grains causing phase shifts to accumulate. However, it seems clear to me from studying grains of glass surrounded by index-matching fluid that the coloration occurs in regions where you have close to grazing incidence. This is particularly apparent when you look at glass microspheres in fluid—the central region is quite clear and there is no observable deviation of the rays, or coloring. The index match is extremely good at most angles. It’s only when you approach grazing incidence that all wavelengths encounter an index mismatch that causes scattering. Unless the indices match perfectly, near-grazing incidence, all wavelengths but that one will scatter, and you have a ring of transmitted light corresponding to the wavelength at which the indices coincide. Inevitably, there will be some surface of a grain of any shape for which you will have such near-grazing incidence. This is why no great care is needed to make a Christiansen filter. No matter what shape you grind your particles into, there will be enough grazing-incidence surfaces to guarantee satisfactory discrimination between index-matched and non-indexmatched rays. The use of Christansen filters as passband filters was common before the second World War. It’s easy to see why, if you look at a broad-area Christiansen filter made in a parallel-sided container. No matter how well-matched the indices are, in almost all cases a cell filled with a mixture of solid-phase and liquidphase materials will only be effectively transparent for an object held right against it. The farther removed an object is, the more translucent the filter becomes. Over any significant distance, the filter does a poor job of transmitting coherent images. However, it works very well as a method of removing unwanted wavelengths by scattering. The recommended method of using such filters is to place them in a system where a broad collimated beam is passed through the cell. Given that the filters www.osa-opn.org OPN Optics-Nov07.qxd 10/4/06 Optics Chromatic dispersions are made of two immiscible liquids with the same index at one wavelength, but different dispersions. need a liquid-tight seal (especially with changing volumes) and that the passband is temperature sensitive, Christiansen filters are far less desirable than thin film stacks. My experience with Christiansen constructions has been that very small differences can cause enormous scattering changes. Packages of glass microspheres immersed in index-matching fluid invariably reveal index variations. I have had the same experience with plastic pellets (intended for injection-molding input feeds) immersed in index-matching fluid. In small quantities, or in round bottles, the pellets look like excellent cases of index matching, with the individual beads losing their identity to the fluid. (Plastics closely resemble liquids in their optical properties, and it’s possible to find combinations with very nearly identical dispersion, so there is no obvious coloring.) However, when the pellets are placed in bulk in a flat-sided cell, it is immediately clear that there is more than one phase present. Variations in refractive index due to conditions of production or to stressinduced birefringence play a part in this imperfect index-matching—so does scattering due to surface contamination, fractures and the like. Rayleigh minimized this problem by grinding his glass with an iron mortar and pestle, boiling the resulting fragments in hydrochloric acid to dissolve any iron contamination, and then drying and annealing the glass. Even with such treatment, however, it’s hard to avoid the problems that can plague Christiansen filters. There is one method, however, that avoids the pitfalls of surface contamination, fractures, stress birefringence and index variation from piece to piece. It’s the only method that I’ve been able to use to produce filters that are truly transparent. Chromatic dispersions are made of two immiscible liquids with the same index at one wavelength, but different dispersions. The individual particles of the phase consist of spherical droplets of one phase in the other. In fact, one will have droplets of each phase within the other. Because it’s unlikely that two liquids suited to this purpose will have the same density, one will typically sit atop the other. There will be an effective dispersion only near the interface unless the phases are vigorously mixed, or if the lighter phase is continually pumped to the bottom of the heavier phase. Despite these difficulties, the dispersions thus created allow transparent viewing. A simple chromatic dispersion can be made from turpentine and glycerine. At room temperature, the passband is blue, but changing the temperature with a water bath will shift it to green. This should be done carefully, since turpentine is flammable. t [ Stephen R. Wilk ([email protected]) is an optical scientist at Textron Systems and a visiting scientist at MIT. ] 11:04 AM A Full Range of Optics • Spherical, Achromatic Doublets, Cylindrical & Aspheric Lenses • Mirrors • Windows & Diffusers • Prisms • Gratings • Diffractive Optics • Polarization Optics • Beamsplitters • Filters & Attenuators hungry for your thoughts… [ References and Resources ] >> W.G. Driscoll and W. Vaughan (eds.). Handbook of Optics (1978), pp. 8-103—8-106. >> L. Auerbach. Am. J. Phys. 25(7), 440-2 (1957). >> L. Auerbach. Am. J. Phys. 28(8), 743 (1960). >> C.V. Raman. Proc. Indian Acad. Sci. A29, 381 (1949). >> C.V. Raman and K.S. Viswanathan. Proc. Indian Acad. Sci. A41, 55 (1955). >> R.H. Clarke. Appl. Opt. 7, 861 (1968). >> John Strong. Procedures in Experimental Physics 373 (1938). >> E.D. McAlister. Smithsonian Misc. Coll. 33(7) (1935). >> U. Wojak et al. Appl. Opt. 26, 4788 (1987). >> Lord Rayleigh. Phil. Mag. 35, 373 (1918). >> L. Auerbach. Am. J. Phys. 25(7), 440-2 (1957). >> R.W. Wood, Physical Optics, 3rd ed., 115-7 (1934). >> Kento Okoshi et al. J. Colloid and Interface Sci. 263, 473-7 (2003). Share your product ideas www.thorlabs.com visit us on the web www.thorlabs.com Call a sales representative at: 973-579-7227 Request Your FREE Tools of the Trade Catalog With Over 10,000 Products. Order Online at www.thorlabs.com Over 700 New Products! OPN November 2006 | 13