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# ENGR OPTICS MED APP BmE 136

UCI

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This 2 page Class Notes was uploaded by Patrick Cormier on Saturday September 12, 2015. The Class Notes belongs to BmE 136 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/201898/bme-136-university-of-california-irvine in Biomedical Engineering at University of California - Irvine.

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Date Created: 09/12/15

HIEL GRA TING PHYSICS INSTRUMENTS HISTORY Diffraction gratings are used to disperse light that is to spatially separate light of different wavelengths They have replaced prisms in most fields of spectral analysis The manufacture of diffraction gratings dates back to the late 18th century Extensive use was limited by the difficulties in ruling gratings of adequate quality until Henry Rowland built ruling engines in the latter part of the 19th century Subsequent production of high quality gratings led to significant advances in analytical spectroscopy Today most diffraction gratings are replicated from masters Masters can be ruled with interferometric control generated holographically with possible enhancement through ion etching or made with newer techniques derived from semiconductor lithography THE GRATING EQUATION A typical diffraction grating consists of a substrate usually of an optical material with large number of parallel grooves ruled or replicated in its surface and overcoated with a reflecting material such as aluminum The quality and spacing of the grooves are crucial to the performance of the grating but the basic grating equation may be derived by supposing a section through the grating surface normal to the ruling direction as a sawtooth pattern shown below Fig 1 The sawtooth pattern of a grating section Light rays A and B of wavelength 7 incident on adjacent grooves at angle l to the grating normal are shown Consider light at angle D to the grating normal this light originates from the A and B rays as they strike the grating The path difference between the Al and BI rays can be seen to be a sin I a sin D Summing of the rays Al and BI results in constructive interference if the path difference is equal to any integer multiple of the wavelength 7 asin l sin D m Where m an integer and is the order of diffraction This is the basic grating equation Note that if D is on the opposite side of the grating normal from I it is of the opposite sign We have considered only two grooves Including all the other grooves does not change the basic equation but sharpens the peak in the plot of diffracted intensity against angle D THE GRATING EQUATION N PRACTICE When a parallel beam of monochromatic light is incident on a grating the light is diffracted from the grating in directions corresponding to m 2 0 3 etc This is shown below and discussed further under Grating Order on the following page MONOCH ROMATIC LIGHT Fig 2 The Grating Equation satisfied for a parallel beam of monochromatic light When a parallel beam of polychromatic light is incident on a grating then the light is dispersed so that each wavelength satisfies the grating equation This is shown in Fig 3 WHITE LIGHT 0 SHORTEST WAVELENGTH TRANSMITTED180 rim m1 FOR MOST SYSTEMS INCREASING WAVELENGTHS m2 360 rim 1st OR 180 rim 2nd ORDER ORDERS OVERLAP UNLESS A SHORTWAVE CUTOFF FILTER iS iNSERTED IN BEAM Fig 3 Polychromatic light diffracted from a grating Positive orders have been omitted for clarity n most monochromators the input slit and collimating mirror fix the direction of the input beam which strikes the grating The focusing mirror and exit slit fix the output direction Only wavelengths which satisfy the grating equation pass through the exit slit The remainder of the light is scattered and absorbed inside the monochromator As the grating is rotated the angles l and D change although the difference between them remains constant and is fixed by the geometry of the monochromator more convenient form of the grating equation for use with monochromators is m7v2gtlt a gtltcos gtltsin9 Where cl Half the included angle between the incident ray and the diffracted ray at the grating 9 Grating angle relative to the zero order pOSItion These terms are related to the incident angle l and diffracted angle D by l9 andD9 Contact us for further information on any of the products in this catalog GRATING ORDER It is important to note the sign of m is given by either form of the grating equation and can be positive or negative In a monochromator the angles I and D are determined by the rotational position of the grating We use the sign convention that all angles which are counter clockwise from the grating normal are positive and all angles which are clockwise to the grating are negative See Fig 4 The incident light diffracted light and grating rotation can be at positive or negative angles depending on which side of the grating normal they are The half angle is always regarded as positive If the angle D is equal to I and of opposite sign then the grating angle and order are zero and the light is simply being reflected If the grating angle is positive then the order is positive m1 if the grating angle is negative then the order is negative m 1 Table 1 lists the half angles and the sign of the orders passed by our monochromators The grating equation is also satisfied for wavelengths in higher orders when lml is gt1 Therefore M MZ for m 2 A3 MS for m 3 etc The wavelength M is in the second order and A3 is in the third order etc Again this concept is illustrated in Fig 3 Usually only the first order positive or negative is desired The other wavelengths in higher orders may need to be blocked The input spectrum and detector sensitivity determine whether order sorting or blocking filters are needed BLAZE WAVELENGTH If monochromatic light strikes a grating then a fraction of it is diffracted into each order The fraction diffracted into any order can be termed the efficiency of the grating in that order All Oriel Gratings are designed for efficient diffraction into the first order Gratings are not equally efficient at all wavelengths for a variety of detailed reasons The efficiency can be tuned by changing the groove facet angles or shape and depth The optimization of efficiency by appropriate groove shaping has become known as blazing The Blaze Wavelength is the wavelength for which the grating is most efficient Fig 5 shows a typical efficiency vs wavelength curve for a ruled and a blazed holographic grating POSITION OF GRATING I AND LIGHT IS REFLECTED T IN ZERO ORDER 0 LIGHT emyo POSITIVE 40 ANGLES 4 NEGATIVE ANGLES THE GRATING ANGLE 9 IS POSITIVE THE ANGLE OF INCIDENCE I IS 9 I AND IS POSITIVE THE ANGLE OF DIFFRACTION D IS 9 I AND IS POSITIVE THE ORDER ISLx sin 9 x cos AND IS POSITIVE EFFICIENCY HOLOGRAPH IC 250 nm BLAZE I l I 1000 12 0 Fig 4 The sign convention for the angle ofincidence angle of diffraction and grating angle 0 WAVELENGTH nm Fig 5 The ef ciency of a ruled and a blazed holographic grating both have 1200 llmm HOLOGRAPch GRATINGS Holographic gratings are created using a sinusoidal interferometric pattern and sometimes an etching process Sinusoidally grooved gratings produce very little scattered light but have low flat efficiency curves although they are generally quite broad Blazed holographic gratings use etching during the interferometric process or an ion gun to form a blaze angle in a secondary process The former does not produce strong blazing and while the latter produces high efficiencies at the blaze wavelengths light scatter is increased due to the formation of micro structure along the edges of the grooves Oriel offers both ruled and holographic gratings to provide the best combination of blaze efficiency and low light scatter for different wavelength ranges Table 1 Half Angles and Orders for Oriel Monochromators Monochromator Half Angle Model No degrees Orders 77250 51 Positive 77400 125 Positive 77200 1304 Negative 77700 1183 Positive 74000 51 Positive 74100 1183 Positive Photoithography Light Sources Lasers USU A SE gs 93 5 UL 3 50 Ear Instruments Detection F TIR E qurpment Spectrometers Fiber Optics 3 w

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