Abstract: A spectroscopic sensor includes a wiring substrate having a main surface, a light detector disposed on the main surface of the wiring substrate, a Fabry-Perot interference filter, a spacer which is provided on the main surface of the wiring substrate and supports the Fabry-Perot interference filter so that the Fabry-Perot interference filter and the light detector are separated from each other, and a stem connected to a ground potential. A second current path which has a smaller electric resistance than that of an arbitrary first current path which extends from the Fabry-Perot interference filter to the light detector via the spacer and the wiring substrate is formed between the Fabry-Perot interference filter and the stem.

Abstract: An illumination system for a STED optical microscope includes an illumination light path consisting of an illumination light source and an optical elements. The illumination light path includes a first light filter, a second light filter, a polarizing light splitter, a first quarter wave plate, a first dichroic element, a light path delay unit, a phase plate, a second dichroic element, and a second quarter wave plate arranged in sequence along the transmission direction of the light path. The light beam emitted from the illumination light source is divided into two coaxial light beams after transmitted by the illumination light path. A first light beam is incident to a microscope objective to form a first light spot, a second light beam is incident to the microscope objective to form a second light spot, and the center of the first light spot coincides with that of the second light spot.

Abstract: An optical filter system includes a Fabry-Perot interference filter, and a controller that controls the Fabry-Perot interference filter. The Fabry-Perot interference filter includes a first mirror portion, a second mirror portion, a first driving electrode and a first monitor electrode provided with the first mirror portion, and a second driving electrode and a second monitor electrode provided with the second mirror portion. The controller includes a control unit that calculates an electrostatic capacitance between the first mirror portion and the second mirror portion based on an alternating voltage generated between the first monitor electrode and the second monitor electrode while an alternating current is applied between the first monitor electrode and the second monitor electrode.

Abstract: An electrically-tunable optical filter has an optical cavity that forms an absorption peak in light that is incident on the filter. The optical cavity includes a layer composed of a material with a high electro-optic coefficient so that the index of refraction of the layer changes in response to a voltage applied by a controller. By adjusting the voltage, the controller can control the index of refraction so that an absorption peak of the filter can be tuned as may be desired without having to alter the physical structure of the filter.

Abstract: An optical system including at least one liquid crystal lens and an imaging lens module is provided. The optical system is configured to form an image of an object. The at least one liquid crystal lens and the imaging lens module is disposed on a path of light from the object. The at least one liquid crystal lens includes a first substrate, a second substrate, and a liquid crystal layer. The second substrate is opposite to the first substrate. The liquid crystal layer is disposed between the first substrate and the second substrate. An effective refractive index of each position on the liquid crystal layer is related to an voltage applied, and the at least one liquid crystal lens is configured to change an optical axis of the at least one liquid crystal lens by changing distribution of orientations of liquid crystal molecules of the liquid crystal layer.

Abstract: A variable spectrum element includes: first and third sensors which are placed at positions at which the first and third sensors are symmetrical with respect to a line connecting the centers of mass of the surfaces of a pair of optical substrates opposite to each other, respectively; second and fourth sensors which are placed at positions at which the second and fourth sensors are symmetrical with respect to the line connecting the centers of mass, respectively; and first to fourth actuators which are placed on lines running from the center of mass of the surface of each of the pair of the optical substrates opposite to each other to the centers of the first to fourth sensors respectively, respectively.

Abstract: A micro movable device includes: a micro movable substrate in which a micro movable unit is formed, the micro movable unit including a frame, a movable part, and a coupling part for coupling the frame and the movable part to define an axial center of rotation of the movable part; a supporting substrate; and a reinforced fixed part provided between the frame and the supporting substrate, and including a first spacer that joins the frame to the supporting substrate and an adhesive part that covers the first spacer and joins the frame to the supporting substrate, wherein the frame includes a first area facing the movable part in a direction of extent of the axial center, and a second area different from the first area, and the reinforced fixed part is bonded to the second area of the frame.

Abstract: An optical module (colorimetry sensor) includes an interference filter, and a transparent substrate to which a first substrate of the interference filter is fixed, having a second thermal expansion coefficient which has a value different from a first thermal expansion coefficient. The interference filter is fixed to the transparent substrate through an adhesive layer made of gel-like resin, and the adhesive layer alleviates stress generated due to a difference in the thermal expansion coefficients between the interference filter and the transparent substrate.

Abstract: An apparatus for performing spectroscopy incorporates, between an EM source and a detector, an optical filter comprising a pair of mirrors opposed along the optical axis and shaped to provide an optical cavity with stable resonance and having a cavity length of at most 50 ?m and a mode at a wavelength within said band of wavelengths for bandpass filtering EM radiation passing therethrough. The actuator system is arranged to move the mirrors relative to each other along the length of the optical cavity for tuning the wavelength of said mode.

Abstract: A tunable optical filter is formed in the structure of an etalon. A thin electro-optic ceramic substrate is fixed between two end substrates. Each end substrate has an inner parallel surface toward said electro-optic ceramic substrate covered by an electrode layer and a reflecting layer. An adhesive which attaches the electro-optic ceramic substrate to each first and second end substrates has a consistency so as to avoid stress on the electro-optic ceramic substrate. A voltage imposed on the electro-optic ceramic substrate by the electrode layers on the inner parallel surfaces of the first and second end substrates effectively controls an optical distance between the reflective coating layers on the inner parallel surfaces of the first and second end substrates of the etalon structure. The electro-optic ceramic substrate is preferably PMN-PT ((1-x)Pb (Mg? Nb?) O3?x—Pb Ti O3) and no more than 160 ?m thick.

Abstract: An optical element (21) with a substrate (30) and a reflective coating (31). The coating (31) has, in particular for the reflection of EUV radiation, a plurality of layer pairs having alternate layers (33a, 33b) composed of a high refractive index material and a low refractive index material At least one active layer (34) composed of a magnetostrictive material is formed within the reflective coating (31). Also disclosed is an optical element (21) having a substrate (30) and a reflective coating (31). The optical element (21) has at least one first active layer with a material having positive magnetostriction and at least one second active layer with a material having negative magnetostriction. The layer thicknesses and the layer materials of the active layers are such that mechanical stress changes or changes in length of the active layers that are produced by a magnetic field mutually compensate for one another.

Abstract: Methods, systems, and apparatus for optical fiber communications. One tunable optical filter includes a light inputting assembly and a light receiving assembly; an adjustable cavity length assembly arranged between the light inputting assembly and the light receiving assembly, wherein the adjustable cavity length assembly includes an adjustable length device, a first substrate, and a second substrate, wherein the first substrate and the second substrate are positioned parallel to each other and are fixed at respective ends of the adjustable length device; and a Fabry-Perot filter arranged in the adjustable cavity length assembly, the Fabry-Perot filter including a first component which is fixed on the first substrate, and a second component which is fixed on the second substrate, the first component includes a reflecting surface facing the second substrate and the second component includes a reflecting surface facing the first substrate.

Abstract: An optical resonator by which reflectivity of ring-down cavity mirrors can be altered and enhanced by adding external optical cavities that recycle light to the main cavity. A coupled-cavity ring-down spectroscopy (CC-RDS) is used for controlling the finesse of an optical resonator. Applications include extending the sensitivity and dynamic range of a cavity-enhanced spectrometer as well as widening the useful spectral region of high-reflectivity mirrors. CC-RDS uses controlled feedback of the probe laser beam to a ring-down cavity, which leads to interference between the internally circulating light and that which is fed back through a cavity mirror port.

Abstract: An optical device with a deformable membrane including an anchor zone on a support contributing to trapping fluid, a central zone reversibly deforming from a rest position, and an actuating mechanism to displace fluid acting on the membrane in an intermediate zone between the anchor and central zones. The actuating mechanism includes a principal actuation mechanism and supplementary actuation mechanism each arranged in at least one ring mounted around the central zone, each ring including one or plural piezoelectric actuators, and being anchored on the intermediate zone, only the supplementary actuation mechanism may be anchored to the support, these actuation mechanisms and the membrane to which they are anchored forming at least one piezoelectric bimorph, such that they contract or expand in the radial direction during actuation such that when the fluid moves, it deforms the central zone.

Abstract: A method for manufacturing a multi-dimensional target waveguide grating and volume grating with micro-structure quasi-phase-matching. An ordinary waveguide grating is used as a seed grating, and on this basis, a two-dimensional or three-dimensional sampling structure modulated with a refractive index, that is, a sampling grating, is formed. The sampling grating comprises multiple shadow gratings, and one of the shadow gratings is selected as a target equivalent grating. A sampled grating comprises Fourier components in many orders, that is, shadow gratings, a corresponding grating wave vector is [Formula 1], and the grating profile of all the shadow gratings changes with the sampling structure [Formula 2]. In a case where a seed grating wave vector [Formula 3] and a required two-dimensional or three-dimensional grating wave vector do not match, a certain Fourier periodic structure component of the Fourier components of the sampling structure is used to compensate for the wave vector mismatch.

Abstract: An etalon has a pair of transparent components; a ring-shaped piezoelectric member which is provided between the pair of transparent components, which is bonded to the pair of transparent components, and which is provided with metal films on the surfaces which face the transparent component sides; and the external connecting terminals which are provided on the transparent components and which are connected to the metal films.

Abstract: An optical module (colorimetry sensor) includes an interference filter, and a transparent substrate to which a first substrate of the interference filter is fixed, having a second thermal expansion coefficient which has a value different from a first thermal expansion coefficient. The interference filter is fixed to the transparent substrate through an adhesive layer made of gel-like resin, and the adhesive layer alleviates stress generated due to a difference in the thermal expansion coefficients between the interference filter and the transparent substrate.

Abstract: A wavelength-variable interference filter includes first and second electrodes provided at first and second substrates, respectively, the second substrate including a movable section, first and second electrode wires that extend from the first and second electrodes toward outer circumferential edges of the first and second substrates, respectively, a first opposite electrode wire disposed so as to be isolated from the second electrode, and a first conductive section that connects the first electrode wire with the first opposite electrode wire. The second electrode wire and the first opposite electrode wire extend passing through a center point of an imaginary circle of the movable section in respective directions and dividing the imaginary circle at regular angular intervals.

Abstract: Described is a method of controlling the absorption of light in a cavity, a system in which absorption is so controlled, and an interferometer embodying the underlying physical concept. Materials can be made to completely absorb incident light when the light is imposed in a specific pattern of illumination. Coherent perfect absorption, as the process is referred to, is achieved when a cavity is illuminated coherently and monochromatically by the time-reverse of the output of a lasing mode. Varying the parameters of the incident light and/or of the cavity allows the absorption of the incident light by the cavity to be controlled; enhanced or even reduced.

Abstract: In an optical assembly having a light source which provides two optically different light components with essentially planar wavefronts on an optical axis, wherein the light components differ at least in their wavelength; in the case of an objective lens which projects the two optically different light components into a projection space; and in the case of an optical component which is arranged on the optical axis and has an plane through which the wavefronts of the two light components pass and in which at least two different areas of the optical component with different dispersion behaviors n(?) abut against one another in the lateral direction with respect to the optical axis; the optical component causes phase shifts of the wavefronts of the two light components, wherein the phase shift of the wavefronts of the one light component differs by at least one quarter of the wavelength of that light component between the two different areas, and wherein the phase shift of the wavefronts of the other light compo

Abstract: An optical module (colorimetry sensor) includes an interference filter, and a transparent substrate to which a first substrate of the interference filter is fixed, having a second thermal expansion coefficient which has a value different from a first thermal expansion coefficient. The interference filter is fixed to the transparent substrate through an adhesive layer made of gel-like resin, and the adhesive layer alleviates stress generated due to a difference in the thermal expansion coefficients between the interference filter and the transparent substrate.

Abstract: Fabry-Perot tunable filters is provided with a first fixed semitransparent mirror and a second movable semitransparent mirror arranged against each other, and piezoelectric elements more than three arranged at an equi-interval on the second movable semitransparent mirror to change a space between the first and second semitransparent mirrors. The second movable semitransparent mirror is adapted to be rotated by using as a pivot an imaginary axis toward which each length of perpendiculars let fall from each of the piezoelectric elements on a plane parallel to the second movable semitransparent mirror and including the imaginary axis connected between arbitrary two points of each middle point between the adjacent piezoelectric elements is equal each other.

Abstract: The present invention discloses a unique and novel combination light source and active light filtering system for microscopes that eliminates the need for individual color filters, fluorescence filters, and many other filter types. The present invention provides variable light wavelength generating capabilities, and all of the benefits of most commercially available light sources in a compact package that can be mounted on a microscope or used at a distance from a microscope, but be coupled to it through a fiber optic cable or other light transmission means. Additionally, the present invention eliminates the need for a filter wheel turret in a microscope's optical path, as well as eliminates the need for multiple fluorescent filter blocks in a fluorescent microscope optical path. The present invention can improve microscope filter systems to enable effective imaging of live cells without staining.

Abstract: An optical module (colorimetry sensor) includes an interference filter, and a transparent substrate to which a first substrate of the interference filter is fixed, having a second thermal expansion coefficient which has a value different from a first thermal expansion coefficient. The interference filter is fixed to the transparent substrate through an adhesive layer made of gel-like resin, and the adhesive layer alleviates stress generated due to a difference in the thermal expansion coefficients between the interference filter and the transparent substrate.

Abstract: Embodiments herein are directed to a metamaterial transmission filters including a metamaterial component and a upper medium positioned within proximity of the metamaterial component such that movement of the upper medium changes the resonances and optical transmission, reflection or absorption spectra of the filter. The upper material may be a natural material or a second metamaterial identical or non-identical to the metamaterial component. Embodiments herein are designed to allow both continuous tuning of the optical spectra of the assembly and/or discrete spectral switching.

Abstract: Described is a method of controlling the absorption of light in a cavity, a system in which absorption is so controlled, and an interferometer embodying the underlying physical concept. Materials can be made to completely absorb incident light when the light is imposed in a specific pattern of illumination. Coherent perfect absorption, as the process is referred to, is achieved when a cavity is illuminated coherently and monochromatically by the time-reverse of the output of a lasing mode. Varying the parameters of the incident light and/or of the cavity allows the absorption of the incident light by the cavity to be controlled; enhanced or even reduced.

Abstract: An imaging system includes a platform for placement of a sample or an animal to be imaged, and at least one excitation light source for irradiating the sample or animal to stimulate an emission at a plurality of different center wavelengths. An acousto-optic tunable filter (AOTF) is provided that includes a piezoelectric transducer crystal for emitting an acoustic wave having a ground electrode disposed on one side of the piezoelectric crystal. A patterned electrode layer is disposed on a side of the piezoelectric crystal opposite the ground electrode. The patterned electrode layer includes a continuous region proximate to its center and a discontinuous region, a pattern in the discontinuous region comprising a plurality of spaced apart features electrically connected to the continuous region, and an AO interaction crystal receiving the acoustic wave attached to the ground electrode or the patterned electrode layer.

Abstract: A tunable filter is provided.

Abstract: A thermally tunable Fabry-Perot optical filter includes a single crystalline sheet resistance heater layer. A single crystalline semiconductor spacer layer is positioned proximate to and in thermal communication with the single crystalline sheet resistance heater layer. A first distributed Bragg reflector is positioned proximate to a first surface of the single crystalline semiconductor spacer layer. A second distributed Bragg reflector is positioned proximate to a second surface of the single crystalline semiconductor spacer layer.

Abstract: The present patent application provides an interference cavity for precisely controlling an optical path including a cavity formed by two equal distance arms, wherein a positive adjusting plate and a negative adjusting plate are disposed in the interference cavity for compensating the change of a cavity length with temperature and thereby ensuring that the interference cavity length is a constant. The present patent application utilizes the matching relationship between the change of the refractive index of the positive adjustment plate with the temperature and the change of the refractive index of the negative adjusting plates with the temperature to make the optical path difference OPL invariant with changes in the environment temperature and thereby to ensure the precision of the optical path.

Abstract: In one embodiment of the invention, a semiconductor optical amplifier (SOA) in a laser ring is chosen to provide low polarization-dependent gain (PDG) and a booster semiconductor optical amplifier, outside of the ring, is chosen to provide high polarization-dependent gain. The use of a semiconductor optical amplifier with low polarization-dependent gain nearly eliminates variations in the polarization state of the light at the output of the laser, but does not eliminate the intra-sweep variations in the polarization state at the output of the laser, which can degrade the performance of the SS-OCT system.

Abstract: A system and method for uniform light generation in projection display systems. An illumination source comprises a light source to produce colored light, and a scrolling optics unit optically coupled to the light source, the scrolling optics unit configured to create lines of colored light from the colored light, and to scroll the lines of colored light along a direction orthogonal to a light path of the illumination source. The scrolling optics unit comprises a single light shaping diffuser to transform the colored light into the lines of colored light, an optical filter positioned in the light path after the light shaping diffuser, and a scrolling optics element positioned in the light path after the optical filter. The single light shaping diffuser is capable of simultaneously transforming colored light into lines of colored light having substantially uniform intensity to provide uniform illumination.

Abstract: A wavelength-specific optical switch combines one or more tunable filters and bandblock reflectors such that the absorption or reflection of selected wavelength bands in the optical spectrum (visible, near infrared, or near ultraviolet) can be switched on and off. The wavelength switch is programmable, multifunctional, general-purpose, solid-state optical filter. The wavelength switch may serve as a tunable notch or bandblock filter, a tunable bandpass filter, a tunable highpass or lowpass filter, or a tunable band reflector. The wavelength switch has particular, but not exclusive, application in optics as a filter, band reflector, and as a means of isolating particular wavelengths or wavelength bands from a collimated light stream for transmission to, or rejection from, a sensor.

Abstract: Light in a desired wavelength band is accurately separated by changing the distance between optical substrates while minimizing deformation thereof. A variable spectroscopic element (1) includes: a plurality of optical substrates (3, 4) opposed to each other with a space therebetween, the optical substrates being provided with coating layers (2a, 2b) on opposed surfaces; actuators (5) arranged circumferentially at intervals around a central axis of the optical substrates (3, 4), the actuators being capable of expansion and contraction in a direction of the gap between the optical substrates (3, 4); and connecting members (10) connecting the actuators (5) and the optical substrates (3, 4) at several locations at intervals in the circumferential direction.

Abstract: Fabry-Perot tunable filters is provided with a first fixed semitransparent mirror and a second movable semitransparent mirror arranged against each other, and piezoelectric elements more than three arranged at an equi-interval on the second movable semitransparent mirror to change a space between the first and second semitransparent mirrors. The second movable semitransparent mirror is adapted to be rotated by using as a pivot an imaginary axis toward which each length of perpendiculars let fall from each of the piezoelectric elements on a plane parallel to the second movable semitransparent mirror and including the imaginary axis connected between arbitrary two points of each middle point between the adjacent piezoelectric elements is equal each other.

Abstract: A color-mixing laser module is disclosed, which is comprised of a laser unit capable of emitting red, blue and green laser beams; a beam combiner, for receiving and converging the laser beams emitted from the laser unit and then directing the converged laser light to illuminate on a light pattern adjusting unit; and the light pattern adjusting unit, capable of receiving the converged laser light from the beam combiner for adjusting the pattern of the same.

Abstract: In an optical assembly having a light source which provides two optically different light components with essentially planar wavefronts on an optical axis, wherein the light components differ at least in their wavelength; in the case of an objective lens which projects the two optically different light components into a projection space; and in the case of an optical component which is arranged on the optical axis and has an plane through which the wavefronts of the two light components pass and in which at least two different areas of the optical component with different dispersion behaviors n(?) abut against one another in the lateral direction with respect to the optical axis; the optical component causes phase shifts of the wavefronts of the two light components, wherein the phase shift of the wavefronts of the one light component differs by at least one quarter of the wavelength of that light component between the two different areas, and wherein the phase shift of the wavefronts of the other light compo

Abstract: Actuator assemblies are formed by at least one cylinder where each cylinder is formed by at least one piezoelectric fiber composite actuator adapted to have actuation energy applied thereto.

Abstract: In various embodiments described herein, a display device comprising a light collection film and a photovoltaic device disposed on an edge of the collection film. The collection film has a plurality of light-turning features for redirecting light between the front and back surface of the collection film and the photovoltaic device. In some embodiments, a light source is also disposed on an edge of the collection film and emits light which is turned by the light-turning features toward the display.

Abstract: Methods, systems, and devices are provided for an electrooptical modulator. One method embodiment includes receiving an optical input signal to an electrooptical modulator. A first voltage input is applied to a first drive electrode associated with a first optical path in the electrooptical modulator. A second voltage input is applied to a second drive electrode associated with a second optical path in the electrooptical modulator at times alternative to applying the first voltage input to the first drive electrode.

Abstract: Disclosed is a microelectromechanically tunable Fabry-Perot device and method of manufacturing tunable Fabry-Perot device and method of manufacturing. The F-P device comprises a first and second substrate which has partially reflective planar surfaces, and the partially reflective planar surfaces are separated by a predetermined separation distance and aligned to provide a F-P cavity, where one or more piezoelectric members are adapted to displace the first and second substrates when an electric field is applied.

Abstract: An optical tunable filter has a fixed substrate having a first recess formed therein and a movable substrate bonded to the fixed substrate. The movable substrate includes a movable portion having an opening formed at a location facing the first recess and a support portion for supporting the movable portion so that the movable portion can be displaced. The optical tunable filter also has a light-transmittable substrate bonded to the movable portion, a fixed reflection film formed on a bottom of the first recess, and a movable reflection film formed on a surface of the light-transmittable substrate. The optical tunable filter includes an interference gap formed between the fixed reflection film and the movable reflection film. The optical tunable filter also includes an actuator operable to displace the movable portion relative to the fixed substrate.

Abstract: Disclosed are a method for driving a piezoelectric element or an optical modulator including a piezoelectric element and a recorded medium recorded with a program for executing the same. In accordance with an embodiment of the present invention, the method for driving a piezoelectric element causing a displacement object to be displaced by being contracted or expanded according to a supplied driving voltage, including supplying a driving signal to the piezoelectric element during a first driving period in a first voltage range; supplying a control signal for controlling a polarization hysteresis of the piezoelectric element according to a driving, performed during the first driving period, to the piezoelectric element; and supplying the driving signal to the piezoelectric element during a second driving period in a second voltage range.

Abstract: Imaging techniques. The focus of an imaging device is varied while acquiring an image of an object. The resulting blurred image is deconvolved to generate, in one embodiment, a two-dimensional projection image of three dimensions of the object.

Abstract: A dual membrane, single cavity MEMS Fabry-Perot filter has a cavity that is defined between two mirror structures that are located on separate MEMS membranes. This configuration can yield a number of advantages. First, the membranes will be typically subject to the same mechanical vibrations, thus, will vibrate together. This vibration, however, will be rejected as common mode, however. Moreover, since the membranes will move in opposed directions in the gravitational field, the dual membrane device is insulated against passband shifts resulting from changes in orientation in the gravitational field. Finally, since each membrane can now be deflected separately, the scanning range is effectively doubled without increases in the size of the electrostatic cavities.

Abstract: A spectrally tunable optical detector and methods of manufacture therefore are provided. In one illustrative embodiment, the tunable optical detector includes a tunable bandpass filter, a detector and readout electronics, each supported by a different substrate. The substrates are secured relative to one another to form the spectrally tunable optical detector.

Abstract: A tunable Fabry-Perot filter that is less sensitive to angle of incidence is formed by replacing the cavity (air gap) with a partitioned cavity that has an effective refractive index greater than one. The partitioned cavity includes a pair of partitioned cavity dielectric layers formed on the reflectors on either side of the variable air gap. Each of the dielectric layers has an optical thickness that is less than one fourth the shortest wavelength in the tuning range of the filter. The resulting three-layer partitioned cavity has an effective optical thickness substantially equal to an integral multiple (m) of one half the transmitted wavelength within the tuning range of the filter.

Abstract: A CWDM filter having four channels of the present invention comprises a substrate and odd number of stack structures. Each stack structure includes a first multi-layer stack, a spacer layer, a second multi-layer stack and a coupling layer arranged in turn from the side thereof approaching the substrate. The rules of the coupling layer of the No. [(N+1)/2?1] stack structure and the coupling layer of the No. [(N+1)/2+1] stack structure both are (2n+1)L, among which, n being a positive whole number, L representing for a low refraction index layer with a thickness of ?0/4 and ?0 representing for the center wavelength thereof. While the coupling layers of the other stack structures can be expressed as L.

Abstract: An optical device including: a glass substrate; a crystalline silicon layer bonded to the glass substrate; and a thermally tunable thin-film optical filter fabricated on top of the crystalline silicon layer.

Abstract: A method and apparatus for stretching a pulse, shaping a stretched pulse, and modeling a stretched and/or shaped pulse are disclosed. An etalon has a port, a partially reflective surface, and a fully reflective surface. A base pulse is introduced into the etalon, and a plurality of portions of the base pulse propagating from the etalon are collected. The collected portions are then combined to generate a stretched pulse whose width is proportional to the width of the base pulse. This can be modeled by assigning a transmission factor value to each one of a plurality of tags and a reflection factor value to each one of the taps, excepting only one tap. A transport delay for is assigned to each tap to which a reflection factor value was assigned, wherein the transport delay is proportional to the width of a base pulse.