Abstract: Systems and methods of reproducing images onto surfaces are disclosed. In one embodiment, the system includes an image file that digitally produces a planar surface normal to a surface of a master model. The planar surfaces are referenced to a coordinate system of the master model through a series of points. A tracker surfacing system, comprising a tracking instrument, generates and emits a signal as the tracking instrument crosses the planar surface. An output device is actuated by the tracking device as it crosses the planar surface, reproducing the series of points as an image onto a surface, including a flat, curved or compound surface. Both the spatial position and orientation of the output device are detected and adjustments are made so that the image is precisely applied to intended locations on the surface being imaged.

Abstract: Computer-implemented methods, computer-readable media, and systems for determining one or more characteristics of a wafer are provided.

Abstract: Systems and methods of reproducing images onto surfaces are disclosed. In one embodiment, the system includes an image file that digitally produces a planar surface normal to a surface of a master model. The planar surfaces are referenced to a coordinate system of the master model through a series of points. A tracker surfacing system, comprising a tracking instrument, generates and emits a signal as the tracking instrument crosses the planar surface. An output device is actuated by the tracking device as it crosses the planar surface, reproducing the series of points as an image onto a surface, including a flat, curved or compound surface. Both the spatial position and orientation of the output device are detected and adjustments are made so that the image is precisely applied to intended locations on the surface being imaged.

Abstract: Methods and systems for use in detecting an air pocket in a single crystal material are described. One example method includes providing a matrix including a plurality of data units, the plurality of data units including image data related to a region of interest of the single crystal material; defining a first half and a second half of the matrix based on a first axis passing through the center of the matrix; determining, by a processor, a difference between each data unit of the first half and a corresponding data unit of the second half; calculating, by the processor, a first index value based on the determined differences; and identifying an air pocket within the single crystal material based on the first index value and a predetermined threshold.

Abstract: A solution for evaluating a vehicle using infrared data is provided. In particular, evaluation data for the vehicle is obtained, which includes infrared data for a plurality of sides of the vehicle as well as vehicle identification data for distinguishing the vehicle from another vehicle. The infrared data is processed to enhance a set of signal features. Additional non-infrared based data also can be obtained for evaluating the vehicle. The evaluation data is analyzed to determine whether one or more anomalies are present. The anomaly(ies) can be correlated with a possible problem with a component of the vehicle. Data on the anomaly, problem, and/or vehicle identification can be provided for use on another system, such as a remote inspection station, maintenance system, and/or the like.

Abstract: A system includes a scope for obtaining images of an end face of an optical fiber in a fiber optic connector. The system also includes a computing device. The computing device is configured to obtain images of the end face of the optical fiber via the scope, identify surface defects on the end face of the optical fiber based on the images, and determine insertion loss of the fiber optic connector due to the surface defects.

Abstract: A method of determining a parameter of an object using penetrating radiation such as X-rays. The parameter of the object could be weight or mass or volume. The method comprises the step of passing the penetrating radiation through the object; determining a first value derived from the total energy of penetrating radiation absorbed by the object; determining a second value related to the mean energy per unit area of penetrating radiation absorbed by the object and determining the parameter from the first and second values. An algorithm representing a proportionality relationship is derived from the first and second value. The parameter is determined by establishing an exponential relationship to an amount derived from the algorithm.

Abstract: An inspection system (9) includes an idler wheel (61) that is coupled to a fabrication system (8) and is in contact with a backing layer (65) of an applied material (64), A rotation sensor (63) monitors the idler wheel (61) and generates a rotational signal. A controller (24) is coupled to the rotation sensor (63) and determines a characteristic of one or more flaws and FOD (19) on a composite structure (12) in response to the rotation signal.

Abstract: By using powerful data analysis techniques, such as PCR, PLS, CLS and the like, in combination with measurement techniques providing structural information, gradually varying material characteristics may be determined during semiconductor fabrication, thereby also enabling the monitoring of complex manufacturing sequences. For instance, the material characteristics of sensitive dielectric materials, such as ULK material, may be detected, for instance with respect to an extension of a damage zone, in order to monitor the quality of metallization systems of sophisticated semiconductor devices. The inline measurement data may be obtained on the basis of infrared spectroscopy, for instance using FTIR and the like, which may even allow directly obtaining the measurement data at process chambers, substantially without affecting the overall process throughput.

Abstract: A first generating unit generates a plurality of blood vessel image data sets at the plurality of imaging angles by performing subtraction processing for the plurality of mask image data sets and the plurality of contrast image data sets. A second generating unit generates a blood vessel volume data set including an artery region, a vein region, and a capillary vessel region by performing reconstruction processing for the plurality of blood vessel image data sets. A third generating unit generates a capillary vessel volume data set associated with the capillary vessel region by removing the artery region and the vein region from the blood vessel volume data set. A fourth generating unit generates a capillary vessel image data set by performing three-dimensional image processing for the capillary vessel volume data set.

Abstract: A dual-technology motion sensor with an ultrasonic sensor element (transducer) and a PIR sensor element is disclosed. The dual-technology motion sensor is configured to modulate ultrasonic radiation emitted from the ultrasonic sensor element when the motion sensor detects a condition under which other wireless devices, especially ultrasound-based wireless devices, are in operation, thereby eliminating problems associated with interference.

Abstract: Methods and systems for determining a characteristic of a wafer are provided. One method includes generating output responsive to light from the wafer using an inspection system. The output includes first output corresponding to defects on the wafer and second output that does not correspond to the defects. The method also includes determining the characteristic of the wafer using the second output. One system includes an inspection subsystem configured to illuminate the wafer and to generate output responsive to light from the wafer. The output includes first output corresponding to defects on the wafer and second output that does not correspond to the defects. The system also includes a processor configured to determine the characteristic of the wafer using the second output.

Abstract: Methods and systems for detecting defects on a wafer are provided.

Abstract: Disclosed are a detection method and a detection system for an array substrate. The method comprises: supplying power to data lines and/or gate lines of the array substrate continuously in a setting time; proceeding temperature sensing to the data line and/or the gate line of the array substrate and recording results of the temperature sensing; find defect points on the data lines and/or the gate lines according to the results of the temperature sensing. The skill solution provided by the present invention is capable of detecting the inner defects of the data lines and/or the gate lines of the array substrate for preventing defect products entering the follow-up processes to promote the production quality and avoid the waste.

Abstract: The present invention relates to a defect inspection device which includes: irradiating means for simultaneously irradiating different regions on a sample with illumination light under different optical conditions, the sample being predesigned to include patterns repeatedly formed thereupon, wherein the patterns are to be formed in the same shape; detection means for detecting, for each of the different regions, a beam of light reflected from each region irradiated with the illumination light; defect candidate extraction means for extracting defect candidates under the different optical conditions for each of the different regions, by processing detection signals corresponding to the reflected light which is detected; defect extraction means for extracting defects by integrating the defect candidates extracted under the different optical conditions; and defect classifying means for calculating feature quantities of the extracted defects and classifies the defects according to the calculated feature quantities

Abstract: A system is provided for improving the damage tolerance of a rotor assembly. The system includes one or more measurement subsystems for measuring the stresses in respective parts of the rotor assembly and issuing respective measurement signals. The system also includes a control subsystem for receiving the measurement signals from the measurement subsystems, determining a response to measured stresses indicative of crack growth, and issuing response signals. The system also includes one or more release subsystems for receiving respective response signals, and activating controlled release of material from respective parts of the rotor assembly to mitigate the effect of the crack growth.

Abstract: An inspection method of an SOI wafer in which profiles P1 and P2 are calculated in the SOI wafer to be inspected and in an SOI wafer having a film thickness of the SOI layer thicker or thinner than that of the SOI wafer to be inspected, respectively; a profile P3 of a difference between P1 and P2, or a profile P4 of a change ratio of P1 and P2 is calculated; light having the wavelength band selected on the basis of a maximum peak wavelength within the calculated profiles P3 or P4 is irradiated to the surface of the SOI wafer to be inspected, to detect the reflected-light from the SOI wafer; and a place of a peak generated by an increase in reflection intensity of the detected reflected-light is found, as the defect caused by the change in the film thickness of the SOI layer.

Abstract: An apparatus for identifying the position of defects (100) in bodies (2), comprises feed means (3) for moving the body (3) along a feed direction (A), an emitter (5) designed to direct towards the body (2) a plurality of beams (6?, 6?, 6??) of electromagnetic radiation lying in lying planes (P1, P2, P3) set at different angles to each other, and transversal to the feed direction (A), and a plurality of sensors (8?, 8?, 8??) each facing the emitter (5) for receiving a respective beam (6?, 6?, 6??) after the beam (6?, 6?, 6??) has passed through the body (2). The lying planes (P1, P2, P3) are positioned one after another along the feed direction (A), allowing each portion of the body (2) to be struck by successive beams (6?, 6?, 6??) as the body (2) is fed forward. A corresponding method is also claimed.

Abstract: The present invention relates to a finger-motion detecting apparatus and method and includes a sensing unit to be disposed on a wrist of a subject person, said sensing unit being configured to output a measurement signal into the wrist of the subject person and to receive a reflected signal of the measurement signal according to the motion of tendons in the wrist of the subject person, a signal control unit configured to control whether the measurement signal is outputted and to adjust the measurement signal on the basis of the reflected signal, and a finger-motion recognizing unit configured to detect finger motion of the subject person from the reflected signal. According to the present invention, since a sensor capable of detecting finger motion is worn on a wrist, the problem of inconvenience in existing methods is resolved.

Abstract: A system and method for determining correction factors used to determine energy of an event detected by a gamma ray detector having nonlinear photosensors arranged over a scintillation array of crystal elements, the gamma ray detector using optical multiplexing or analog electronic multiplexing. The method includes acquiring, for each nonlinear photosensor, a signal value generated by the nonlinear photosensor in response to receiving scintillation light emitted by a crystal in the array of crystal elements in response to arrival of a gamma ray; and determining a relative position of the event, the relative position being one of a predetermined number of cell locations, the predetermined number of cell locations being greater than a number of crystal elements in the array of crystal elements; and determining, for each cell location, a correction factor based on an average total signal value and a predetermined energy value of the gamma ray.

Abstract: Systems and methods are provided for calibrating emission data or other information signals collected during a polymerase chain reaction (PCR), amplification reaction, assay, process, or other reaction. Calibration of multiple detectable materials can be achieved during a single cycle or run, or during a plurality of runs of the reaction. A reading from every well, container, or other support region of a sample support does not have to be taken. Interpolation can be used to determine values for emission data or other information signals that were not taken, or are unknown, using detected emission data, or other detected information signals. By calibrating the detected emission data and the interpolated data, a more accurate reading of emission data or information signal can be obtained.

Abstract: Disclosed are apparatus and methods for the generation of a stage speed profile and/or the selection of care areas for automated wafer inspection. The stage speed profile generated corresponds to a fastest speed the inspection machine is able to inspect provided a set of care areas. The set of care areas selected correspond to specific regions on the wafer which are to be imaged in detail by the inspection machine. The apparatus and methods herein may also calculate speed of inspection and coverage (and possibly other characteristics of the inspection) for a quantity of cases, and select the best trade-off of coverage versus inspection time using a cost function. Other aspects, features, and embodiments of the invention are also disclosed.

Abstract: A non-contact, far-field radar nondestructive testing (NDT) method is disclosed that is capable of detecting at least one of defects, damages, and reinforcement conditions in near-surface region of multi-layer systems using monostatic inverse synthetic aperture radar (ISAR) measurements and applicable to various types of structural elements. The method includes the steps of conducting far-field monostatic ISAR measurements, executing an imaging algorithm, and executing a progressive image focusing algorithm.

Abstract: A system measures the strain of an object. The system includes a laser source for generating an output radiation, a strainable optical fiber having first and second facets, and means for calculating a measure of a strain of the optical fiber. The first facet is coupled to the laser source to receive the output radiation and transmit a guided radiation over the optical fiber towards the second facet. The second facet is adapted to receive the guided radiation and to reflect a corresponding reflected radiation towards the first facet. The laser source is a self-mixing type adapted to receive at least part of the reflected radiation and to mix the output radiation with the received radiation. The calculating means calculate the measure of the strain of the optical fiber based on a self-mixing effect in the laser source that is caused by the linear displacement of the second section.

Abstract: A mask inspecting apparatus and method of inspecting a mask having a plurality of openings used in deposition in a desired pattern, the mask inspecting apparatus capable of detecting a defect of the mask through the openings of the mask.

Abstract: A test system for testing a projective mask is provided to make an analysis based on the defect figures of the projective mask obtained by a figure capture unit and thus determine whether the quality of the projective mask meets a requirement. The test system comprises a figure analysis unit for comparing the defect figure and the target design figure corresponding to the projective mask and obtaining a bias proportion between the defect figure and the target design figure, and a test determine unit for comparing the bias proportion outputted by the figure analysis unit with a maximum permitted bias proportion. If the outputted bias proportion does not exceed the maximum permitted bias proportion, a determination that the quality of the projective mask meets the requirement is made by the test determine unit; otherwise, the test determine unit determines that the quality of the projective mask does not meets the requirement.

Abstract: Various embodiments provide methods for testing a fuel cell interconnect including the steps of providing a fuel cell interconnect and performing a non-destructive test on the fuel cell interconnect comprising at least one of detecting a magnetic response of the interconnect, calculating a volume by optically illuminating the interconnect, detecting an acoustic response of the interconnect, and detecting a thermal response of the interconnect.

Abstract: A magnetic resonance apparatus is operated with continuous movement of an examination subject through a measurement volume of the apparatus. At each successively-occupied position of the examination subject within the measurement volume during the continuous movement, magnetic resonance data are acquired with system parameters, each having system parameter values. Contemporaneously with each data acquisition at each position, the acquired data are evaluated as to the effect produced by the system parameter values employed to acquire the data. The system parameter values are then adapted to cause the effect to correspond to a target value, and the adapted system parameters are then used to acquire data at the next-successive position occupied by the examination subject in the continuous movement.

Abstract: An object of the present invention is to quantitatively evaluate a distribution of defects which are generated within an inspection material.

Abstract: A measurement system that includes an industrial machine and an interferometer can detect when abnormality has occurred in measurement targeted at a reflector attached to a movable body, for example, in a case where the movable body has moved too close to the interferometer. A judging section of the interferometer judges that there is abnormality in measurement targeted at the reflector on the basis of a received-light signal. Upon such an abnormality judgment, a stop command outputting section of the interferometer outputs a stop command to the industrial machine. A stopping section of the industrial machine stops the driving operation of a moving mechanism upon receiving an input of the stop command, thereby stopping the movement of the movable body. The measurement system makes it possible to prevent the industrial machine, which includes the movable body and the moving mechanism, from colliding with the interferometer.

Abstract: Disclosed is a method to determine behavior characteristics of one or more modules of a laser system. The method includes applying inputs to the one or more modules of the laser system, measuring outputs resulting from the application of the inputs, and determining an equation-based mathematical relationship relating the inputs to the resultant outputs of the one or more modules of the laser system.

Abstract: An X-ray inspection apparatus includes a storage device, a setting device, a determining device, a calculating device and a display control device. The setting device is configured to set a hypothetical reference value that is different from an actual reference value that was used during the inspection of the articles. The determining device is configured to determine whether a contaminant exists inside each of the articles based on a result of a comparison between the hypothetical reference value and each of detection data stored in the storage device. The calculating device is configured to calculate a hypothetical contaminant existence rate as a ratio of a number of the articles in which the determining device has determined that a contaminant exists with respect to a total number of the articles. The display control device is configured to control a display section to indicate the hypothetical contaminant existence rate.

Abstract: Sensors and techniques for an automated data acquisition and notification system having a plurality of receptacles adapted to store items. In each of the plurality of receptacles, at least one sensor is operated to detect a presence of an item in that receptacle. Light is emitted from a planar surface within the receptacle to a space within the receptacle opposite the planar surface. While that light is emitted light incident on the planar surface is detected. A determination is made whether an amount of light that is detected is significant to indicate a presence of the item.

Abstract: The present invention provides an optical inspection method capable of detecting a finer defect in the surface of a substrate, including the steps of: irradiating a surface of a sample which is rotating and continuously moving in one direction with illumination light which is incident in a direction obliquely to the sample surface; detecting an image of light formed by a forward scattering light around an optical axis of regular-reflection light while excluding the regular-reflection light from the sample surface irradiated with the illumination light; condensing and detecting lateral scattering light which scatters laterally from the sample surface with respect to an incidence direction of the illumination light; and processing a signal obtained by detecting the image of light formed by the forward scattering light and a signal obtained by condensing and detecting the lateral scattering light to extract a defect including a scratch defect.

Abstract: While an illumination optical system 2 is irradiating the surface of a contaminated standard wafer 110 with illumination light, this illumination light is scanned over the surface of the contaminated standard wafer 110, then detectors 31 to 34 of a detection optical system 3 each detect the light scattered from the surface of the contaminated standard wafer 110, next a predefined reference value in addition to detection results on the scattered light is used to calculate a compensation parameter “Comp” for detection sensitivity correction of photomultiplier tubes 331 to 334 of the detectors 31 to 34, and the compensation parameter “Comp” is separated into a time-varying deterioration parameter “P”, an optical characteristics parameter “Opt”, and a sensor characteristics parameter “Lr”, and correspondingly managed. This makes it easy to calibrate the detection sensitivity.

Abstract: An inspection method of an SOI wafer in which profiles P1 and P2 are calculated in the SOI wafer to be inspected and in an SOI wafer having a film thickness of the SOI layer thicker or thinner than that of the SOI wafer to be inspected, respectively; a profile P3 of a difference between P1 and P2, or a profile P4 of a change ratio of P1 and P2 is calculated; light having the wavelength band selected on the basis of a maximum peak wavelength within the calculated profiles P3 or P4 is irradiated to the surface of the SOI wafer to be inspected, to detect the reflected-light from the SOI wafer; and a place of a peak generated by an increase in reflection intensity of the detected reflected-light is found, as the defect caused by the change in the film thickness of the SOI layer.

Abstract: This present specification provides, amongst other things, an electro-optical monitoring system for obtaining a once-per-revolution signal based on the surface reflection of a rotating device that mandates non-contacting sensor input in potentially hostile environments. The system can use optical and electronic sections to illuminate and detect surface reflections from the rotating surface using existing mounting locations on the periphery of the machine to be measured. The electronic portion is configured to determine a unique mark as the once-per-revolution marker or allow an attending operator to assign a specific marker based on the observed reflected pattern. The optical portion consists of a light source, receiver, and optics that allow for focused and directed light paths.

Abstract: A first wafer is fabricated using a first value for a process parameter specifying a process condition in fabricating the structure. A first value of a dispersion is measured from the first wafer. A second wafer is fabricated using a second value for the process parameter. A second value of the dispersion is measured from the second wafer. A third wafer is fabricated using a third value for the process parameter. The first, second, and third values for the process parameter are different from each other. A third value of the dispersion is measured from the third wafer. A dispersion function is defined to relate the process parameter to the dispersion using the first, second, and third values for the process parameter and the measured first, second, and third values of the dispersion. The simulated diffraction signal is generated using the defined dispersion function. The simulated diffraction signal is stored.

Abstract: Method of determining an edge of a first anomaly in a wall of a pipeline from a first set of data elements representing measurements of the wall of the pipeline. An element of the first set comprises a first coordinate, a second coordinate, and a parameter being indicative for the presence and/or severity of the first anomaly a position along the wall indicated by the first and second coordinate. The method comprises determining a data element that is associated with a maximum in the severity of the first anomaly; evaluating a value of the parameter by comparing with a predetermined threshold; determining an initial edge data element for which the parameter has reached the threshold; determining a next edge data element; determining further edge data elements; and determining the edge of the first anomaly by combining the first and second coordinates of the determined edge data elements.

Abstract: A defect detection system identifies defects in weld seams. An exemplary system includes a scanner device, mounted on a displacement device of a processing unit and which can be displaced by the unit over at least one weld seam that is to be examined. The scanner unit scans the weld seam using a predefinable frequency, each scanning sweep being correlated with a time signal. The time signal is used to record the point in time when at least one location containing defects is scanned. An analysis module determines the co-ordinates of the defects from the signals that are obtained by the scanning sweeps and stores the co-ordinates of the defects and transmits them to a localisation module. The localisation module determines the spatial arrangement of the defects of the weld seam by evaluating a speed profile of the displacement device during the scanning sweeps, the time signal and the co-ordinates.

Abstract: A detection method and apparatus is provided. The detection apparatus includes at least two angular mounted lasers, a surface for receiving laser lines emitted by the angular mounted lasers, a camera for detecting a laser pattern formed by the laser lines on the surface, and a processor for analyzing the laser pattern. The lasers emit orthogonal laser lines on a surface of the device. The camera detects a laser pattern on the surface of the device and the processor analyzes the laser pattern to determine whether the position of the device is in pocket based on the analysis and position algorithms.

Abstract: The present invention provides methods, devices, and systems for analyzing defects in an object such as a semiconductor wafer. In one embodiment, it provides a method of characterizing defects in semiconductor wafers during fabrication in a semiconductor fabrication facility. This method comprises the following actions. The semiconductor wafers are inspected to locate defects. Locations corresponding to the located defects are then stored in a defect file. A dual charged-particle beam system is automatically navigated to the vicinity defect location using information from the defect file. The defect is automatically identified and a charged particle beam image of the defect is then obtained. The charged particle beam image is then analyzed to characterize the defect. A recipe is then determined for further analysis of the defect. The recipe is then automatically executed to cut a portion of the defect using a charged particle beam.

Abstract: A consolidated RF switch includes a cell controller configured to process data packets received from an access port communicatively coupled to a plurality of mobile units via a wireless network, and an RFID network controller configured to process tag information received from an RFID reader communicatively coupled to a plurality of RFID tags. The cell controller and the RFID network controller are configured to transmit the tag information and the data packets to one or more enterprise applications.

Abstract: A system and method for detecting airborne agents. The system includes a semiconductor ultraviolet optical source configured to emit an ultraviolet light, a controller configured to generate a pseudo-random code for emission of the ultraviolet light modulated at the pseudo-random code, a telescope configured to focus the ultraviolet light to a distance from the source and to receive elastically backscattered signals and fluorescence signals from the distance, and a sensor configured to detect the elastically backscattered and fluorescence signals. The method generates a pseudo-random code and emits at least one wavelength of ultraviolet light modulated at the pseudo-random code, transmits the modulated ultraviolet light pulses to a distance from the source, receives elastically backscattered signals and fluorescence signals from the distance, and detects the elastically backscattered and fluorescence signals.

Abstract: Inspection of rolling stock (e.g., rail vehicles) traveling along a set of rails is performed using devices that are placed in a housing that is attached to the set of rails. The housing conforms to standard width, height, and load bearing requirements for a railroad tie. As such, the housing can be readily installed and allows for the continued use of standard railroad maintenance equipment. One or more sensing devices are attached to the housing and acquire evaluation data on component(s) of the rail vehicle, such as the wheels. A computing device can evaluate a condition of the component(s) using the evaluation data.

Abstract: Computer program products comprising tangible computer-readable media having instructions that are executable by a computer to generate a customized spectral profile, which can be used to generate a corresponding filter. The instructions can comprise: generating a trial source spectrum; determining an uncorrected lamp source spectrum; calculating one or more optical indices using the trial source spectrum or the uncorrected lamp source spectrum; and optimizing one or more of the optical indices by varying the trial source spectrum to generate the customized spectral profile.

Abstract: Electrical impedance tomography (EIT) data processing system, for acquiring and processing data from two-phase flows, comprising a dual-plane sensor, a plurality of digital signal processing modules configured in a data pipeline processing arrangement and a plurality of data acquisition subsystems in communication with a first one of said digital signal processing modules.

Abstract: A device to inspect a non-pattern wafer includes a light source to emit light that reflected from a wafer. A judgment unit converts the detected light into a quantitative measured value to determine whether the wafer is faulty. The wafer comprises a first region and a second region. The detection unit sequentially detects lights reflected from the first and second regions of the wafer, and a judgment unit converts the lights reflected from the first and second regions of the wafer into first and second quantitative measured values, respectively. The second region of the wafer is determined to be faulty by comparing the second measured value with a first reference value, wherein the first reference value is calculated using an average value between the first and second measured values, and a characteristic value that indicates distribution of the first and second measured values.

Abstract: A method includes supplying current to at least one photovoltaic device via a current source and detecting emitted photon radiations from the at least one photovoltaic device via a radiation detector. The method also includes outputting a signal corresponding to the detected emitted photon radiations from the radiation detector to a processor device, and processing the signal corresponding to the detected emitted photon radiations via the processor device to generate one or more two-dimensional photon images. The method further includes analyzing the one or more two-dimensional photon images to determine at least one defect in the at least one photovoltaic device.

Abstract: The exemplary embodiments of the method, system, software arrangement and computer-accessible medium according to the present invention facilitates an analysis of interactions between nonlinear absorbing materials and an incident electromagnetic wave based on material properties and characteristics of the incident beam of the electromagnetic energy. Using the exemplary embodiments of the present invention, it is possible to determine laser beam propagation in a variety of multiphoton absorbing materials. Energy levels associated with such materials, which may be associated with various electron absorption and/or relaxation phenomena, may be added to and/or removed from the analysis. Incident laser beams can vary from continuous wave to attoseconds in duration and a numerical solution can be obtained that is radially and/or temporally dependent.