foueier optics课件c7 wavefront modula.ppt

Chapter 7 Wavefront Modulation,Attention is focused on methods for spatially modulating optical wavefields, especially coherent fields,Analysis and synthesis,In Fourier analysis a signal is decomposed into its constituent frequency spectrum In inverse Fourier transform a signal can be synthesised by adding up its constituent frequencies The tools of linear systems and frequency analysis are useful in the analysis of optical systems The theory becomes much more significant if it can be applied to synthesis problems as well,Synthesis and modulation,In order to synthesize linear optical systems with desired properties, the ability to manipulate light waves is needed (1)Introduce information into an optical system amplitude in coherent systems intensity in incoherent systems (2)Modify and manipulate the complex optical fields transmitted through the focal plane of a lens,Modulation methods,Attention is focused on methods for spatially modulating optical wavefields, especially coherent fields The traditional means of modulation has been through the use of photographic materials The much more powerful is spatial light modulator (SLM) capable of changing transmitted light in real time in response to optical or electrical control signals,7.1 WAVEFRONT MODULATION WITH PHOTOGRAPHIC FILM,Film can play three very fundamental roles in optics a detector of optical radiation a storage medium for images a spatial modulator of transmitted or reflected light,7.1.1 The Physical Processes of Exposure, Development, and Fixing,Structure of a photographic film or plate,Certain sensitizing agents are added to the gelatin These agents introduce dislocation centers within the silver halide crystals,Light incident on the emulsion initiates a complex physical process,If a photon is absorbed, an electron-hole pair is released within the grain The resulting electron becomes trapped at a crystal dislocation The trapped electron electrostatically attracts a silver ion The electron and the silver ion combine to form a single atom of metallic silver at the dislocation site. The lifetime of this combination is rather short More combinationstability of the combination The combinationthe silver speck in order for it ultimately to be developable,Latent image,The speck of silver formed as above is referred to as a development speck The collection of development specks present in an exposed emulsion is called the latent image The film is now ready for the development and fixing processes,Development and fixing,The developer causes the crystal to be entirely reduced to metallic silver Two types of grains: one has been turned to silver, and the another did not absorb enough light to form a development center. Without further processing, the latter will eventually turn to metallic silver themselves simply through thermal processes Fixing to remove the undeveloped silver halide grains,Pictorial representation of the photographic process,(d),Exposure latent image (c) after development, and (d) after fixing Only the emulsion is shown,7.1.2 Definition of Terms,Exposure The energy incident per unit area on a photographic emulsion during the exposure process is called the exposure Represented by the symbol E(x,y) E(x,y) is equal to the product of incident intensity I(x,y) at each point and the exposure time T:,Intensity transmittance,The ratio of intensity transmitted by a developed transparency to the intensity incident on that transparency Represented by the symbol (x,y),Photographic density,The logarithm of the reciprocal of the intensity transmittance of a photographic transparency should be proportional to the silver mass per unit area of that transparency Represented by the symbol D,Hurter-Driffield (H&D) curve,A plot of photographic density D vs. the exposure E that gave rise to that density contrast, contrast,Major factors influencing ,The type of emulsion in question The particular developer used The development time,7.1.3 Film in an Incoherent Optical System,Film may be regarded as an element that maps an intensity distribution I incident during exposure into an intensity distribution I transmitted after development This is particularly appropriate in incoherent optical system,Nonlinear intensity mapping,In the linear region of the H&D curve,Positive intensity mapping,First step: the negative transparency is made in the usual fashion,Second step: this transparency is placed in contact with a second unexposed emulsion and illuminated with intensity I0,p=-n1n2 is a negative number, making -p a positive number,Linear intensity mapping,The general relation between intensity incident during exposure and intensity transmitted after development is a nonlinear one In the specific case of an overall gamma equal to unity, the process becomes a linear one Film can be shown to provide a linear mapping of incremental changes of intensity under a much wider class of conditions,7.1.4 Film in a Coherent Optical System,Film is used as providing a mapping of intensity incident during exposure into complex field transmitted after development a mapping of complex amplitude incident during exposure into complex amplitude transmitted after development,Complex amplitude transmittance tA,Modulating both amplitude and phase,Variations of the film thickness random thickness variations across the base of the film thickness of the emulsion often varies with the density of the silver,Liquid gate,The thickness variations are entirely undesired,Complex amplitude transmittance with liquid gate,Proper choice of fluid makes the optical path length through the liquid gate nearly constant,where U is the complex amplitude of the field incident during exposure, is a constant, and is a positive number for a negative transparency and a negative number for a positive transparency,tA-E curve,A direct plot of amplitude transmittance vs. exposure is often desirable,This equation represents linear region of tA-E curve, where U is the incremental amplitude changes and are negative numbers for a negative transparency,Gamma of film,A high-gamma film has a steeper slope than does a low gamma film A high-gamma film is more efficient in transferring small changes of exposure into changes of amplitude transmittance This increased efficiency is often accompanied by a smaller dynamic range of exposure,7.1.5 The Modulation Transfer Function,We have tacitly assumed that any variations of exposure, however fine on a spatial scale, will be transferred into corresponding variations of silver density In practice, each given type of film has a limited spatial frequency response,Limited spatial frequency response of an emulsion,Light scattering within the emulsion during exposure Chemical diffusion during the development process Both of these phenomena are linear ones,The Kelley model of the photographic process,Simplified model,Measurement of the linear filter,Input a cosinusoidal exposure pattern,The “modulation“ associated with the exposure is defined as,Effective modulation Meff can be inferred through H&D curve (assumed known),Modulation transfer function of the film,Typical MTF of an Emulsion,Eeffective exposure pattern spatial frequency,Explanation of M() curve,The small hump rising above unity at low frequencies is caused by chemical diffusion Plus-X film has a significant response to about 50 line-pairs (cycles)/mm Kodak 649F spectroscopic plate extends to beyond 2000 line-pairs/mm,7.1.6 Bleaching of Photographic Emulsions,In conventional photography emulsions modulate light primarily through absorption caused by the metallic silver Significant amounts of light are lost Phase modulation rather than absorption is more efficient Such structures can be realized with chemical bleaching,Two kinds of Bleaching,The bleaching process is one that removes metallic silver from the emulsion and leaves in its place either an emulsion thickness variation or a refractive index variation within the emulsion,Tanning bleach,The chemical agents used in this type of bleach release certain chemical byproducts as they remove the metallic silver These byproducts cause a cross-linking of the gelatin molecules within the emulsion in regions where the silver concentration was high As the transparency is dried, the hardened areas shrink less than do the unhardened areas, with the result that a relief image is formed,Relief image,A relief image produced by a tanning bleach,Effect of Tanning Bleach,This phenomenon depends strongly on the spatial frequency content of the density pattern Act as a bandpass filter, with no relief induced at very low spatial frequencies and at very high spatial frequencies For a 15-m-thick emulsion, the peak thickness variations are found to occur at a spatial frequency of about 10 cycles/mm, with a maximum relief height in the 1 to 2m range,Nontanning bleach,The metallic silver within the developed transparency is changed back by the chemical bleach to a transparent silver halide crystal, with a refractive index considerably larger than that of the surrounding gelatin The resulting refractive index structures constitute a pure phase image,Effect of Nontanning Bleach,The bleach must remove the sensitizing agents in unexposed silver halide crystals to prevent them from turning to metallic silver due to thermal effects Very high-frequency phase structures can be recorded using this method Phase shifts of the order of 2 radians can be induced,Comparison of two bleaches,Tanning bleach relief image bandpass filter with no relief induced at very low spatial frequencies and at very high spatial frequencies Nontanning bleach refractive index modulation spatial frequency response is similar to that of the original silver image,7.2 Spatial Light Modulator (SLM),If information is being rapidly gathered, one would prefer a more direct interface between the electronic information and the data processing system A spatial light modulator is an object that imposes some form of spatially varying modulation on a beam of light in electronic or light form,Types of SLM,Electrically written (addressing) SLMs electrical signals directly control spatial distribution of light absorption or phase shift Optically written (addressing) SLMs information may be input to the SLM in the form of an optical image,Advantages of optically addressing SLMs,Fast temporal response They can convert incoherent images into coherent images They can provide image amplification They can provide wavelength conversion,Applications of SLM,Data input Information processing Spatial filters Wavefront modulation Most important SLM technologies liquid crystal, magneto-optic, deformable mirror, multiple-quantum-well, acousto-optic Bragg cells,7.2.1 Properties of Liquid Crystals,In liquid crystals displayers voltages applied to pixelated electrodes cause a change in the intensity of the light transmitted Similar principles can be used to construct a spatial light modulator,Molecules of liquid crystals,Liquid crystal materials share some of the properties of both solids and liquids The molecules composing such materials can be visualized as ellipsoids, with a single long axis about which there is circular symmetry in any transverse plane These ellipsoidal molecules can stack next to one another in various ways Different geometrical configurations define different general types of liquid crystals,Mechanical properties of liquid crystals,Nematic(向列的) Smectic(近晶的) Cholesteric(胆甾醇的),Our focus,Spatial light modulators are based primarily on nematic liquid crystals a special class of smectic liquid crystals (smectic-C* phase) called ferroelectric liquid crystals (FLC),Alignment of LC molecules on boundary,The nematic liquid crystal molecules are contained between two glass plates Alignment of LC molecules is possible by polishing soft alignment layers coated on those plates with strokes in the desired alignment direction The small scratches associated with the polishing operation establish a preferred direction of alignment for the molecules,Alignment layers between two plates,If the two alignment layers are polished in different directions, then the molecules combine to create a twisted nematic liquid crystal,The structure of ferroelectric liquid crystals (FLC),Smectic type For smectic-C* materials there is a cone of possible orientations for any given layer The directions of orientation between layers form a helical spiral,Electrically controlled liquid crystal cell,The angular directions of the two layers at the interfaces with the glass plates can be stabilized by aligned polishing Cells are made sufficiently thin to eliminate the possibility that different layers will be in different allowed states,Electrical properties of liquid crystals,The applied electric field across such a device can induce an electric dipole in each liquid crystal molecule, and can interact with any permanent electric dipoles The torques exerted on these dipoles by the applied fields can cause the liquid crystal molecules to change their natural spatial orientation The dielectric constant of a molecule is larger in the direction of the long axis of the molecule than normal to that axis,Realignment of nematic LC molicules,A sufficiently large applied voltage will cause the molecules to rotate freely and to align their long axes with the applied field Vast majority of the molecules have their long axis aligned with the field,Driving voltage,DC voltage may cause permanent chemical changes to the NLC material Cells of this type are driven by AC voltages (1 kHz to 10 kHz and the order of 5 volts) The dipole moment of a nematic liquid crystal is an induced moment rather than a permanent moment The direction of the moment reverses when the applied field reverses in polarity,Ferroelectric liquid crystal cell,The molecules have a permanent electric dipole with an orientation normal to the long dimension of the molecules This permanent electric dipole enhances their interaction with the applied fields Only two allowable orientation states, one for each possible direction of the applied field,FLC Molecule and polarization,Molecule is shown by green ellipsoid Polarization is shown by the blue arrow In FLC the molecules have a permanent electric dipole (with an orientation normal to the long dimension of the molecules),Consistency of FLC molecular orientation,Clark and Lagerwall in 1980 proposed a way to suppress the helix and developed the surface stabilized ferroelectric liquid crystal (SSFLC) arrangement Interaction forces between the liquid crystal and the bounding plates unwind the intrinsic helix This boundary condition also causes the molecular orientation for each layer to be the same and the material exhibits ferroelectric behavior,Alignment of ferroelectric liquid crystal molecules,The current state is retained by the material even after the applied field is removed,Incident light,Properties of ferroelectric LC,FLC cell is bistable FLC cell has memory Unlike the case of nematic liquid crystals, DC fields of opposite polarity must be applied to the ferroelectric liquid crystal in order to switch between states,Temporal characteristics,Liquid crystals act primarily as an electrical dielectric material A liquid crystal cell is predominantly a simple RC circuit 100 s for the molecules to align with an applied field for NLC materials 20 ms for the molecules to relax back to their original state FLC has switching times of the order of 50 s,Optical properties of nematic LC,A quantitative understanding of the behavior of SLMs that operate by means of polarization effects requires the use of Jones calculus The state of polarization of a monochromatic wave with X and Y components of polarization Ux and Uy,Jones vector and matrix,The light passed through a linear polarization-sensitive device is described by a 2 X 2 Jones matrix,If we can characterize a given device by specifying its Jones matrix, we will then be able to understand completely the effect of that device on the state of polarization of an incident wave,Appendix C.3 Reflective polarization devices,Light passes through a polarization element with Jones matrix L, is normally incident on a lossless mirror, reflects from the mirror, and passes a second time through the same polarization element,Treatment of reflective device,We wish to specify the Jones matrix for an equivalent transmissive device that will function in the same way as this reflective device We will consider only reciprocal polarization elements before the mirror For a reciprocal element, the coupling from, say, the x component of polarization to the y component of polarization on the forward pass through the device must equal the coupling from the y component back to the x component on the reverse pass,Matrixes for forward and backwrd passage,For a reciprocal element, the Jones matrix for backward passage of light is exactly equal to the transpose of the Jones matrix for forward passage of light Most polarization elements are reciprocal, the most important exceptions being devices that operate by the Faraday effect in the presence of a magnetic field For nonreciprocal devices, the Jones matrix for reverse propagation is identical with the Jones matrix for forward propagation,Coordinates of polarization,Looking towards the source and using x and y axes that form a right-hand coordinate system, with the z axis pointing in the direction of propagation Reflection converts right-hand to left-hand in terms of x-y coordinates despite of z-axis inverse For a transmissive device, the coordinate system both before and after passage through the device is right-handed. We attempt to retain this convention even with the reflective device,Final form,Reversing the direction of the x axis converts the left-hand to right-hand by a Jones matrix of the form,Thus the transmission equivalent of the reflective device has a Jones matrix of the form,Example,Consider a polarizati