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Mathematical method used in optics and acoustics
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified
Transfer-matrix method (optics)
Transfer-matrix_method_(optics)
Topics referred to by the same term
Transfer-matrix method (optics), a method to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. Ray transfer matrix
Transfer-matrix_method
Ray tracing technique
Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple
Ray_transfer_matrix_analysis
Topics referred to by the same term
dictionary. TMM may refer to: Transfer-matrix method, a statistical mechanics method Transfer-matrix method (optics), a method to describe wave propagation
TMM
Matrix relating system inputs and outputs
various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output
Transfer_function_matrix
Technique for computing light scattering by nonspherical particles
The transition matrix method (T-matrix method or TMM) is a computational technique of light scattering by nonspherical particles originally formulated
T-matrix_method
Idealized model of light
require methods such as physical optics or wave theory. Collimated beam Optical path Optical path length Paraxial approximation Pencil beam Ray transfer matrix
Ray_(optics)
Optical phenomenon
interference spectroscopy Thin-film optics Transfer-matrix method (optics) Stavenga, D. G. (2014). "Thin Film and Multilayer Optics Cause Structural Colors of
Thin-film_interference
Matrix-valued random variable
counterparts exhibit chaotic behaviour are described by random matrix theory. In quantum optics, transformations described by random unitary matrices are crucial
Random_matrix
American atmospheric scientist (1959–2020)
contributions to the T-matrix method for the computation of light scattering by complex particles and clusters, and atmospheric radiative transfer theory. Mishchenko
Michael_I._Mishchenko
Scientific journal
and Radiative Transfer is a peer-reviewed scientific journal published by Elsevier. Established in 1961, it covers research in optics and spectroscopy
Journal of Quantitative Spectroscopy and Radiative Transfer
Journal_of_Quantitative_Spectroscopy_and_Radiative_Transfer
Array of numbers
vibrations, and oscillations in electrical circuits. Geometrical optics provides further matrix applications. In this approximative theory, the wave nature
Matrix_(mathematics)
Study of classical optics using Fourier transforms
Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination
Fourier_optics
electromagnetics, the scattering-matrix method (SMM) is a numerical method used to solve Maxwell's equations, related to the transfer-matrix method. SMM can, for example
Scattering-matrix_method
French engineer
a French physicist who specialized in optics. In his 1949 doctoral thesis, Abelès developed a transfer-matrix formalism to compute the transmission and
Florin_Abelès
Branch of physics
finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments); using
Computational electromagnetics
Computational_electromagnetics
Optical filter
Domain Method in Electromagnetics, Artech House, Bibcode:1989ah...bookQ....S, ISBN 0-89006-349-4 Scott, Craig (1997), Introduction to Optics and Optical
Frequency_selective_surface
Small angle approximation in geometric optics
paraxial approximation is used in Gaussian optics and first-order ray tracing. Ray transfer matrix analysis is one method that uses the approximation. In some
Paraxial_approximation
Electric circuit with two pairs of terminals
parameters Transfer-matrix method (optics) for reflection/transmission calculation of light waves in transparent layers Ray transfer matrix for calculation
Two-port_network
Ionization technique
spectrometry, matrix-assisted laser desorption/ionization (MALDI) is an ionization technique that uses a laser energy-absorbing matrix to create ions
Matrix-assisted laser desorption/ionization
Matrix-assisted_laser_desorption/ionization
Numerical analysis technique
S2CID 25120679. A. Deinega; S. Belousov; I. Valuev (2009). "Hybrid transfer-matrix FDTD method for layered periodic structures". Opt. Lett. 34 (6): 860–2. Bibcode:2009OptL
Finite-difference time-domain method
Finite-difference_time-domain_method
Thin layer of material
Thin-film interference Thin-film optics Thin-film solar cell Thin-film bulk acoustic resonator Transfer-matrix method (optics) "IEC 60050 – International Electrotechnical
Thin_film
Field of depth extension
In optics and signal processing, wavefront coding refers to the use of a phase modulating element in conjunction with deconvolution to extend the depth
Wavefront_coding
Method for computing radiation
fields such as nanophotonics, radar scattering, aerosol physics, biomedical optics, and astrophysics. The basic idea of the DDA was introduced in 1964 by DeVoe
Discrete_dipole_approximation
Atmospheric optics ray tracing codes - this article list codes for light scattering using ray-tracing technique to study atmospheric optics phenomena such
Atmospheric optics ray-tracing codes
Atmospheric_optics_ray-tracing_codes
Method in natural language processing
of real numbers. Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models
Word_embedding
Algorithms for matrix decomposition
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra
Non-negative matrix factorization
Non-negative_matrix_factorization
Transduction (biophysics) Transfer-matrix method Transfer-matrix method (optics) Transfer operator Transfermium Wars Transformation optics Transformation theory
Index_of_physics_articles_(T)
Overview of and topical guide to machine learning
clustering Hierarchical clustering k-means clustering k-medians Mean-shift OPTICS algorithm Anomaly detection k-nearest neighbors algorithm (k-NN) Local outlier
Outline_of_machine_learning
Process by which dust, particulates, etc. scatter light
evolved. The technique is also known as null field method and extended boundary technique method (EBCM). Matrix elements are obtained by matching boundary conditions
Light_scattering_by_particles
Radiative Transfer, Volume 273, p. 107846 (2021) DOI Beutel, Dominik; Fernandez-Corbaton, Ivan; Rockstuhl, Carsten (2024). "treams – a T-matrix-based scattering
Codes for electromagnetic scattering by spheres
Codes_for_electromagnetic_scattering_by_spheres
Book by Max Born and Emil Wolf
Principles of Optics, colloquially known as Born and Wolf, is an optics textbook written by Max Born and Emil Wolf that was initially published in 1959
Principles_of_Optics
Scattering of an electromagnetic plane wave by a sphere
that allows a treatment of more generally shaped particles is the T-matrix method, which also relies on a series approximation to solutions of Maxwell's
Mie_scattering
Algorithm for finding density based clusters in spatial data
Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented in 1999
OPTICS_algorithm
Class of algorithms for pattern analysis
processes, then the Gram matrix K {\displaystyle \mathbf {K} } can also be called a covariance matrix. Application areas of kernel methods are diverse and include
Kernel_method
Specifies the properties of a Gaussian beam
imaginary unit. The complex beam parameter is usually used in ray transfer matrix analysis, which allows the calculation of the beam properties at any
Complex_beam_parameter
Wigner distribution function in physics as opposed to in signal processing
density matrix, so the realization of that operator in phase space. It has applications in statistical mechanics, quantum chemistry, quantum optics, and
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Calculation technique
distortion, arising mainly from atmosphere, optics and detector are taken into account. While this method of simulating images is inherently slow, advances
Ray_tracing_(physics)
Binary operation
ordinary matrix inverse and J {\displaystyle J} is as defined above. Observe that a scattering matrix can be rewritten as a transfer matrix, T {\displaystyle
Redheffer_star_product
Imaging technique based on fluorescence
}{T}}\\\end{matrix}}} and n is the harmonic number and T is the total time range of detection. FLIM has primarily been used in biology as a method to detect
Fluorescence-lifetime imaging microscopy
Fluorescence-lifetime_imaging_microscopy
Theorem in physics
with negligible error. In optics, this is equivalent to summing over many fringes of the diffraction pattern. By the method of stationary phase, we can
Optical_theorem
Signal processing computational method
the orthogonal matrix V {\displaystyle V} . This matrix can be computed using optimization techniques via projection pursuit methods (see Projection
Independent component analysis
Independent_component_analysis
Optical device which splits a beam of light in two
where the 2×2 element τ {\displaystyle \tau } is the beam-splitter transfer matrix and r and t are the reflectance and transmittance along a particular
Beam_splitter
Numerical method that reduces the complexity of computationally intensive simulations
The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational
Proper orthogonal decomposition
Proper_orthogonal_decomposition
Extracting features from raw data for machine learning
the feature coefficients. These include Non-Negative Matrix Factorization (NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor
Feature_engineering
Mechanism of light transport
In optics, subsurface scattering or subsurface light transport is the traveling of light through the surface of translucent object, the subsequent scattering
Subsurface_scattering
American mathematician and physicist (1928–2012)
scattering in electromagnetics, optics and acoustics. He has introduced the extended boundary condition and T-matrix methods, widely used in the analysis
Peter_C._Waterman
Reverse-engineering neural networks
as a description of his work in circuit analysis as opposed to usual methods in interpretable AI. Circuit analysis attempted to completely characterize
Mechanistic_interpretability
Density-based data clustering algorithm
also includes implementations of DBSCAN*, HDBSCAN*, OPTICS, OPTICSXi, and other related methods. scikit-learn includes a Python implementation of DBSCAN
DBSCAN
Optimization algorithm
iteration is higher. An example is the BFGS method which consists in calculating on every step a matrix by which the gradient vector is multiplied to
Gradient_descent
Statistical method in psychology
retain (Velicer, 1976). By this method, components are maintained as long as the variance in the correlation matrix represents systematic variance, as
Exploratory_factor_analysis
Method of machine learning
In computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update
Online_machine_learning
Representation learning method
the directional gradient of a rasterized matrix. Once a matrix or a high-dimensional vector is transferred to a sparse space, different recovery algorithms
Sparse_dictionary_learning
Storage with three-dimensional resolution for information
as a method to read data written into a poled polymer matrix. Optical coherence tomography has also been demonstrated as a parallel reading method. Masahiro
3D_optical_data_storage
Machine learning model for vision processing
each patch into a vector, and maps it to a smaller dimension with a single matrix multiplication. These vector embeddings are then processed by a transformer
Vision_transformer
Tuning parameter (hyperparameter) in optimization
case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is
Learning_rate
Technique in machine learning
method assumes that a model trained for an easier version of the problem can generalize to harder versions, so it can be seen as a form of transfer learning
Curriculum_learning
Type of large language model
impact of large AI systems have led to calls for more efficient training methods and more transparency in reporting resource usage. Vision transformer Haddad
Generative pre-trained transformer
Generative_pre-trained_transformer
Electrostatic digital printing process
policies). Inspired by the Xerox 9700's commercial success, Japanese camera and optics company Canon developed in 1979 the Canon LBP-10, a low-cost desktop laser
Laser_printing
Scattering of light by tiny particles in a colloidal suspension
Light scattering by particles of complex shape are described by the T-matrix method. Fog scattering traffic light The colloid on the right shows Tyndall
Tyndall_effect
Machine learning calibration technique
distribution over classes. The method was invented by John Platt in the context of support vector machines, replacing an earlier method by Vapnik, but can be applied
Platt_scaling
Integral transform
S.A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Amer. 60, 1168–1177 (1970). M. Moshinsky and C. Quesne
Linear canonical transformation
Linear_canonical_transformation
waves in plasma, oscillations in electrical circuits and in non-linear optics. They are a set of three completely integrable nonlinear partial differential
Three-wave_equation
Model-free reinforcement learning algorithm
the trust region method to limit the KL divergence between the old and new policies. However, TRPO uses the Hessian matrix (a matrix of second derivatives)
Proximal_policy_optimization
Adjusting input/output impedances of an electrical circuit for some purpose
energy, not necessarily electrical, is transferred between a source and a load, such as in acoustics or optics. Impedance characterizes the ratio of energy
Impedance_matching
and testing (optical components) Ray transfer matrix analysis Photographic lens design Surface imperfections (optics) Stray light Fischer, Robert E.; Tadic-Galeb
Optical_lens_design
structured interfaces. The method is versatile as interface structures of different optical regimes, e.g. geometrical and wave optics, can be included. It is
OPTOS_formalism
Similarity measure for number sequences
distance can be applied to words as well). For calculating soft cosine, the matrix s is used to indicate similarity between features. It can be calculated
Cosine_similarity
Pattern of color filters over an image sensor
some CVD silicon oxide processes are low temperature processes. Ocean Optics has indicated that their patented dichroic filter CFA process (alternating
Color_filter_array
Machine learning technique
Often, a correlation-style matrix of dot products provides the re-weighting coefficients. In the figures below, W is the matrix of context attention weights
Attention_(machine_learning)
Method of a dimension reduction
with an array of m counters (making the counter set into a two-dimensional matrix C i , j {\displaystyle C_{i,j}} ), with index j of a particular counter
Count_sketch
Method of data analysis
explicitly calculating and storing the covariance matrix XTX, instead utilizing one of matrix-free methods, for example, based on the function evaluating
Principal_component_analysis
Technique for the generative modeling of a continuous probability distribution
zero and variance one. To find the second one, we complete the rotational matrix: [ z ″ z ‴ ] = [ α t − α ¯ t σ t β t σ t ? ? ] [ z z ′ ] {\displaystyle
Diffusion_model
Optimization algorithm
approximation Hessian matrix is replacing it with the Fisher information matrix, which transforms usual gradient to natural. These methods not requiring direct
Stochastic_gradient_descent
dense matter Waveguide (optics) Wavelength-division multiplexing Weapon effects simulation Wideband materials Wireless energy transfer X-ray X-ray laser Xenon
List_of_laser_articles
Type of machine learning model
Chenfei; Song, Ting; Wu, Wenshan; Xia, Yan; Liu, Yu; et al. (2024). "TaskMatrix.AI: Completing Tasks by Connecting Foundation Models with Millions of APIs"
Large_language_model
Property of waves that can oscillate with more than one orientation
Chandrasekhar, Subrahmanyan (2013). Radiative transfer. Courier. p. 30. Hecht, Eugene (2002). Optics (4th ed.). United States of America: Addison Wesley
Polarization_(waves)
Semiconductor light source
Different fields of light can be manipulated by the application of different optics or "lenses". LEDs cannot provide divergence below a few degrees. Shock resistance:
Light-emitting_diode
Type of feedforward neural network
not have a general method for training multiple layers. In 1965, Alexey Grigorevich Ivakhnenko and Valentin Lapa published Group Method of Data Handling
Multilayer_perceptron
Method used to normalize the range of independent variables
Feature scaling is a method used to normalize the range of independent variables or features of data. In data processing, it is also known as data normalization
Feature_scaling
Method of measuring prediction error
Out-of-bag (OOB) error, also called out-of-bag estimate, is a method of measuring the prediction error of random forests, boosted decision trees, and other
Out-of-bag_error
Algorithm for modelling sequential data
invariance, and generalization in high-order neural networks". Applied Optics. 26 (23): 4972–4978. doi:10.1364/AO.26.004972. PMID 20523475. Christoph
Transformer_(deep_learning)
Iterative method for finding maximum likelihood estimates in statistical models
statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates
Expectation–maximization algorithm
Expectation–maximization_algorithm
Class of artificial neural networks
own node-feature matrix and adjacency matrix. Pooling methods differ in how this coarsened graph is constructed: node-selection methods, such as top-k pooling
Graph_neural_network
Color motion picture process
The significance of this depended on the depth of focus of the projection optics. Much more serious was a problem with cupping. Films in general tended to
Technicolor
Diode that emits light from an organic compound
different mode of operation. An OLED display matrix can have various control schemes: A passive-matrix (PMOLED) where each row and line in the display
OLED
Computer that uses photons or light waves
equivalent optical transistor is required. This is achieved by crystal optics (using materials with a non-linear refractive index). In particular, materials
Optical_computing
Deep learning architecture
significantly more efficient in processing long sequences compared to previous methods. Additionally, Mamba simplifies its architecture by integrating the SSM
Mamba (deep learning architecture)
Mamba_(deep_learning_architecture)
Set of learning techniques in machine learning
Examples include dictionary learning, independent component analysis, matrix factorization, and various forms of clustering. In self-supervised feature
Representation_learning
Machine learning technique
models, and the development of video game bots. While RLHF is an effective method of training models to act better in accordance with human preferences, it
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Equations of light transmission and reflection
additional calculations to account for interference. The transfer-matrix method, or Rouard's recursive method can be used to solve multiple-surface problems. In
Fresnel_equations
Machine-learning and computational-neuroscience conference
Neuroscience (COSYNE) International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB) International Conference on
Conference on Neural Information Processing Systems
Conference_on_Neural_Information_Processing_Systems
Eleventh letter in the Greek alphabet
neighbourhood, satisfying the current definition of a planet. In crystal optics, lambda is used to represent a lattice period. In electrochemistry, lambda
Lambda
Scientific subjects
electromagnetism; relativity; quantum mechanics, atomic physics, and molecular physics; optics and acoustics; condensed matter physics; high-energy particle physics and
Branches_of_physics
Process of calculating the causal factors that produced a set of observations
Bleistein). Should geometrical optics techniques (i.e. rays) be used for the solving the wave equation, these methods turn out to be closely related to
Inverse_problem
Optimization algorithm for artificial neural networks
node counts for which other methods might not converge. The Hessian can be approximated by the Fisher information matrix. As an example, consider a simple
Backpropagation
tubing for liquid dosage forms ISO 11421:1997 Optics and optical instruments - Accuracy of optical transfer function (OTF) measurement ISO 11442:2006 Technical
List of ISO standards 10000–11999
List_of_ISO_standards_10000–11999
Physics related to the study, design, building and operation of particle accelerators
then be calculated using Ray transfer matrix analysis; e.g., a quadrupolar field is analogous to a lens in geometrical optics, having similar properties
Accelerator_physics
Mirror with a curved reflecting surface
McGraw-Hill Education. p. 6.4. ISBN 9781259006449. Hecht, Eugene (1987). "5.4.3". Optics (2nd ed.). Addison Wesley. pp. 160–1. ISBN 0-201-11609-X. Venice Botteghe:
Curved_mirror
integration beyond the limits of van der Waals forces using adhesive matrix transfer". Nature Electronics. 7: 17–28. doi:10.1038/s41928-023-01079-8. ISSN 2520-1131
Van_der_Waals_integration
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