7.3 Wavelength Separators

Transcription

1 7.3 Wavelength Separators colored glass filters are used to separate large regions of wavelengths interference filters are used to isolate intermediate-sized bands of wavelengths gratings separate wavelengths by angular dispersion P the grating equation P grating resolution P grating efficiency grating monochromators are used to isolate narrow bands of wavelengths monochromator throughput is determined by its f/# 7.3 : 1/15

2 Colored Filters (1) The figure shows the transmission curve for three bandpass filters passes everything except the deep UV. It would be used to reject the mercury nm line passes a band from the near UV to the green, while passes a band from ~280 to 400 nm. These would be used with fluorescence excitation : 2/15

3 Colored Filters (2) The figure shows the transmission curve for two high pass filters rejects wavelengths below 500 nm and passes those above performs the same function with a cutoff wavelength of ~580 nm. Note that it is nearly impossible to make a low pass colored glass filter : 3/15

4 Interference Filter (1) Center wavelengths can be from the UV to the infrared. Pass bands are narrower than colored filters, but broader than grating monochromators. The filter above is centered at 415 nm with a 10 nm FWHM and a transmission ~33%. As the bandwidth narrows the transmission drops. 7.3 : 4/15

5 Interference Filter (2) 7.3 : 5/15 An interference filter is created when light is multiply reflected between two parallel surfaces. The beams exiting the filter must be in phase. This means that the sum of x and d must equal an integral number of wavelengths. x+ d = mλ n ( θ) ( θ ) x+ xcos 2 = mλ n ( 1 cos 2 ) x + = mλ n 2 x2cos θ = mλ n 2cos t θ = mλ n mλ = 2ntcosθ air R 2θ θ transparent material with refractive index of n Note that the equation in your text on page 156 is incorrect. The pass band varies with the order, m. To restrict transmission to only one order, the exit surface is most often a colored glass filter. t R air

6 Prisms Because of a complicated mathematical relationship between wavelength and bend angle, prisms are seldom used in modern instruments For maximum dispersion (angular resolution), visible light is separated with a glass prism and ultraviolet is separated with a quartz prism One common design is the constant deviation, or Pellen-Broca, prism shown in the figure. Constructed from one piece of material, it can be viewed as three separate prisms. For a given orientation, only one wavelength exits at a 90 deviation. To select a different wavelength the prism is rotated about the juncture of the dotted lines, P. P : 6/15

7 Diffraction Grating A diffraction grating is created by a spatial modulation in phase or amplitude of an incoming plane wave m = 0 When exiting the grating, the input is separated into several plane waves traveling at angle to the original direction of propagation - these are called diffraction orders. The number and intensity of the orders depends upon the functional form of the modulation. a θ The figure at the top is a transmission grating, while that at the bottom is a reflection grating. The diffraction angle depends upon order, m, wavelength, λ, and spatial modulation period, a. a 8 9 θ θ r θ i sinθ m = mλ a 7.3 : 7/15

8 Blazed Gratings By forming the bottom of the grooves into a saw tooth shape, the angle of reflection can be made to correspond to one of the diffraction orders. One order then blazes, that is, it has most of the incoming optical power. Show below are three gratings blazed at 300, 400 and 500 nm. Note how the efficiency drops on either side of the blaze wavelength. a θ θ i +1 θ r 7.3 : 8/15

9 Grating Resolution The angular distribution of a monochromatic beam of light reflecting off a diffraction grating is a sinc 2 function (sinx/x) 2. The node spacing of the sinc function is called the angular resolution, Δθ, 2λ dθ m Δ θ = = Na cosθ m dλ acosθ m where N is the number of grating grooves and a is the groove spacing. The goal is to minimize Δθ, which is accomplished by maximizing the grating width, Na. You can also increase the order, which increases θ m. Grating spectral resolution is defined as, R λ = Δλ where Δλ is the range of wavelengths occurring over Δθ, and λ is the center wavelength. High resolution means small Δλ. The angle at which light leaves a grating leads to an ambiguous wavelength, e.g. 600 nm, m = 1; 300 nm, m = 2; 200 nm, m = 3. mn 7.3 : 9/15

10 Commercially Available Gratings The vast majority of commercially available gratings are plastic replicas. The master grating is coated with an epoxy resin to form a negative image. A thin layer of plastic coats the negative and cured. When removed from the negative, the replica is mounted on glass for rigidity and coated with aluminum. Ruled gratings are made with a spacing from 25 mm -1 to 1,800 mm -1. The upper size is cm, with 5 5 cm being typical. Concave ruled gratings can be manufactured with great difficulty. Ruled gratings have a scattered light figure of Holographic gratings are made by coating the surface of glass with a photoresist. Two laser beams irradiate the surface at an angle to each other creating interference fringes. Bright fringes polymerize the photoresist. The surface is washed with an organic solvent to dissolve remaining monomer, then coated with aluminum. Spacings up to 2,400 mm -1 are possible, as well as concave gratings. Holographic gratings have a scattered light figure of : 10/15

11 Czerny-Turner Monochromator the source is imaged onto the entrance slit using an f/# that matches the monochromator the first spherical mirror collects light from the slit (now the object), collimates it, and irradiates the grating the grating diffracts each wavelength at a different angle the second mirror focuses the diffracted parallel beam onto the exit slit - a narrow band, Δλ, passes through the slit light from the exit slit is focused by the lens into the sample cell sample (exit image) lens exit slit (entrance image) mirror variable λ monchromatic light white light grating source lens entrance slit (source image) mirror 7.3 : 11/15

12 Monochromator Resolution (1) The angular resolving power of a monochromator is given by the derivative of the grating equation. mλ m dθ m sinθm = cosθmdθ = dλ = a a dλ acosθ Angular dispersion can be converted to linear dispersion at the exit slit by using the diagram below, dl dθ dl dθ tan ( dθ) = f where f is the monochromator focal length. f dl = dλ Resolution is given as the reciprocal linear dispersion, dλ/dl, in units of nm mm -1. For a grating with 1,200 grooves mm -1, a = 833 nm. For 500 nm light and m = 1, θ = The angular dispersion is deg nm -1. For f = 250 mm, the linear dispersion is mm nm -1. The reciprocal is 2.66 nm mm -1. f dθ dλ m 7.3 : 12/15

13 Monochromator Resolution (2) High resolution can be achieved by either using small slits or large focal lengths. For the example on the last slide, a 0.1 mm slit will combine with the reciprocal linear dispersion of 2.66 nm mm -1, to produce a spectral resolution of Δλ = 0.27 nm. If a 1,200 groove mm -1 grating is put into a 1-meter monochromator, the reciprocal linear dispersion is 0.67 nm mm -1. With a 1 mm slit the resolution is 0.67 nm, while with a 0.1 mm slit the resolution is nm. For slits of 0.1 mm or larger width, the output of the monochromator will have a triangular shape when inputting a single wavelength. For slits 0.01 mm or less, diffraction from the slit will dominate grating dispersion. For this case the monochromator output has the shape of a sinc function squared. ( ) 2 sin πλ λ0 πλ λ0 7.3 : 13/15

14 Monochromator Throughput (1) To obtain the calculated resolution it is necessary that the grating be completely filled with light. This in turn requires that the entrance optics have the same f/# as the monochromator. With a "relay lens" arrangement, a lens with the same f/# as the monochromator is used to focus the image on the slit. The lens that gathers light from the source can have any desired f/#. The image of the source on the slit will be magnified by the ratio of the two lens focal lengths. 7.3 : 14/15

15 Monochromator Throughput (2) The two-lens scheme suffers from four reflections off lens surfaces, and the "real estate" required for implementation. A single lens can be used by doing appropriate calculations. Seldom will the lens diameter be exactly what is needed. To circumvent this problem, buy a larger lens and "stop it down" by using an aperture with the correct diameter. If a lens with too small an f/# is used, the grating will be overfilled. Much of the light is lost and shows up as scatter. If a lens with too large an f/# is used, the grating will be under filled. This reduces resolution, since fewer grooves are irradiated. 7.3 : 15/15