NOTE 1: You have arrived at the INVESTIGATION: ANALYSIS SECTION of this website.
This section is Under-Edit or Analysis Addition if necessary: Construction began on November 4, 2009 and was finished on January 11, 2010.
NOTE 2: This section contains the relevant facts and associated ideas that have been derived from each reference that is used in this investigation. They are presented in Summary form using the following SECTION GUIDE:
Item Number. Reference Description: Derived Fact (s) from the Reference Document [Reference No.] Derived Ideas.
NOTE 3: GTD: Geometrical Theory of Diffraction; PTD: Physical Theory of Diffraction
Beginning of RESULTS PAPER derived from RESEARCH on PROBLEMS of DIFFRACTION, SCATTERING, and PROPAGATION of WAVES.
25. Proceedings of the IEEE: Special Issue on Rays and Beams, 1974:
Wave processes that can be regarded as “localized” are considered here.
Characteristics of high frequency
As of 1974, 'GTD “now ranks as the major tool for the analytical determination of diffracted fields.”'
Asymptotic methods: U.S. & USSR
Leopold B. Felsen attended September 1967 & 1971 symposiums in USSR.26. Knott and Senior's November 1974 paper on Comparison of High-Frequency Diffraction Techniques:
University of Michigan Radiation Laboratory: perform very important work in US on Diffraction and EM phenomenon including radar
Critique of Ufimtsev PTD work
Key criticisms raised (page 1474):
PTD is based on an approximation to the surface field for the problem of diffraction
No expressions for non-uniform currents (edge currents)
Virtual sources of scattering
Application of “ad hoc" matching functions
Method of Equivalent Currents
Very important paper: this paper demonstrates that U.S had its own expertise in Scattering and Diffraction Theory
Knott & Senior extensive expertise in diffraction theory27. Borovikov and Kinber's November 1974 paper on Asymptotic Theory of Diffraction:
Extensive review of Soviet contribution to theory of diffraction
Different schools of Diffraction theory exist & there are many Soviet contributors to the theory.
Ufimtsev is only one of many workers in this field: V.M. Babitch, V.A. Fock, B.Z. Katsenelenbaum, L.A. Wainstein, etc.
Methods of Physical Optics
Method of Successive diffraction (page 1422)
Integral Equations of Theory of Open Resonators (page 1426)
7 of 199 References correspond to Ufimtsev’s papers (175-181)
There are other Soviets doing diffraction work28. P.C. Clemmow’s 1956 paper on Edge Currents and Diffraction:
“Very early in the history of the diffraction problem both experimental and theoretical work suggested that in some respects the diffracted field could be regarded as emanating from a source located on the diffracting edge.”
“The proposed method, then, may be stated briefly as follows: by using the known half-plane results, edge currents are derived from which the scattered field at certain points may be calculated.”
English Diffraction worker29. R.G. Kouyoumjian and P. H. Pathak’s 1974 paper on Uniform Theory of Diffraction (UTD):
Asymptotic high-frequency solution for Diffraction due to Curved Wedge: Curved edge diffraction
Method is based on J.B. Keller's method of the canonical problem and Keller's law of edge diffraction
Wedge Edge and Higher Order Edges:
Surface Normal discontinuous at edge
Straight edge for a wedge, Curved edge
General edge problem: curved edges & curved surfaces
Approximate an edge geometry by a wedge whose surfaces are tangent to the surfaces forming the edge at the point of diffraction
Proper ray-fixed coordinate system
Dyadic diffraction coefficient for wedge: a sum of 2 dyads
Dyadic Diffraction coefficients are valid in the transition regions of the shadow & reflection boundaries where the diffraction coefficients of Keller's original theory (Geometric Theory of Diffraction) fail
Diffraction coefficients contain simple correction factors or transition functions for the diffracted field
The expressions for wedge diffraction coefficients contain Fresnel integrals: ensures that the total field is continuous at shadow and reflection boundaries
Properties of Incident field Assumption:
Slowly varying vs. rapidly varying (sum of slowly varying) at point of diffraction (page 1459)
UTD approach cannot be used to calculate the field at a caustic of the diffracted ray.
Total diffracted field is formed by superposition:
UTD solution is consistent with the reciprocity principle
Key American Diffraction workers (Ohio State University)
A very important paper: based on research that was partially funded by the Air Force Cambridge Research Laboratory and NASA.
30. P.L. Christiansen’s 1974 paper on Edge Diffraction Processes:
Diffraction processes at a wedge in GTD
Ray systems – Computer aid
Diffraction processes occur at neighboring points where different diffraction processes take place at same point
Presence of more than one mode of propagation
Plasma-based Wedge Diffraction for two modes of propagation
2-D & 3-D Edge
Danish Diffraction investigator:
No mention of Ufimtsev31. T.B.A. Senior’s 1975 University of Michigan report RL-610 on the Equivalent Current Method:
1950s, Braunbek & R.F. Millar working with concept of Equivalent edge currents
Practical cross-section estimation tool – computer programs – scattering
Non-specular generating bodies
Advanced radars – phase & polarization
Diffraction: de-polarization"Unfortunately, GTD is not very convenient for computation.":
Problem of locating specular points (flash points);
Ray divergence factors; &
Need new scattering-diffraction effects estimation computer program
GTD & Equivalent current method
Compare this new approach with Ufimtsev PTD
Ufimtsev second order formula revision
Senior claims in practice, both approaches are similar
Conceptual flaw: angle parameter specification in currents, undefined
Equivalent Current Method: common ground between GTD & Ufimtsev theory32. T.B.A. Senior's 1977 University of Michigan Final Report to the AIR FORCE OFFICE OF SCIENTIFIC RESEARCH:
"Studies in Diffraction"
Work Duration: January 1, 1972 through December 31, 1976
High frequency Scattering Determination for Edged Bodies, 3 Methods:
Geometrical Theory of Diffraction (GTD), extension of Geometrical Optics with the inclusion of diffracted rays;
PTD, extension of Physical Optics, "no systematic procedure for obtaining higher order effects"; and
Application of Equivalent (edge) currents may be able to combine GTD with caustic-correction advantage of PTD.
Curved edge: support a creeping wave
Material effects in scattering: behavior of absorbers
"Non-specular" sources of scattering: edge & traveling waves
Imperfect half-planes: Resistive & conductive sheets
Volume distribution of Polarization Currents
Wavelength >> all dimensions of a body:
Induced electric & magnetic dipoles
Low frequency scattering: Plasma sheath of space objects
Cone of diffracted rays experimentally generated by application of laser beam to edge of razor blade:
Confirmation of GTD predictions
Material properties on edge diffraction: half-planes
Impedance sheets: Leontovich boundary conditions & resistive and/or conductive sheets characterized by a jump condition
"Scattering by a thin disk of large radius":
Electrically large, perfectly conducting thin disk;
Experimental measurements of surface current on this disk,
=> Creeping waves can exist on the disk surface (under certain conditions);
Theoretical verification using mathematical treatment of the problem of surface field
on a soft thin disk of large radius due to presence of a point source far from the
=> Complex disk edge field(dependent on angle of incident).
Professor Senior & University of Michigan Radiation Laboratory were intimately involved with the U.S. Air Force (funded with Air Force Office of Scientific Research Grant No. 72-2262)USAF key decision-makers (scientific/policy) had to be aware of Professor Senior's expert opinion on Ufimtsev's work (PTD & its associated issues)
.33. Ufimtsev’s December 1975 Comments on Diffraction Techniques and Dr. Senior’s Reply: 
Learn that Professor Ufimtsev’s widely used formulas were not correct
Interesting that Ufimtsev was corresponding with Senior prior to this paper. (page 1737)
Senior refers to the 1971 translated paper of Ufimtsev 1962 Russian monograph
Very complex formulas & Senior found errors. This fact implies that Senior understood the derivations in Ufimtsev’s 1962 workMisunderstanding of method is very different than erroneous formulas??34. Ufimtsev’s December 1996 paper on Radar Cross Section Reduction:
In this paper, he says Diffraction is another word for Scattering.
He starts the paper by claiming that PTD was one of the keys to the successful development of the B-2, F-117 and stealth ships that are military weapon systems.
We learn from this paper how much Ufimtsev is knowledgeable about radar cross section reduction techniques and diffraction principles.
Ufimtsev appears to be quite an expert
in this field, much more than a theoretical mathematical physicist. There are 214 references: Soviet as well as non-Soviet contributors.
Here we learn that he left Soviet Union in 1990, went to UCLA, and then became affiliated with Northrop-Grumman, the developer of the B-2 Stealth bomber, a highly classified project.35. Ufimtsev's 1997 comments on correction for Ufimtsev's December 1996 paper:
Yu. I. Orlov, Moscow, Virtual ray concept
1976 Paper on application of virtual rays (L.A. Vainshtein & Tishchenko)
1982 Paper on Virtual rays (L.A. Vainshtein & Ufimtsev)
1994 Paper on Virtual rays (N.G. Alexopoulos,...,P.Y. Ufimtsev)36. L.A. Vainshtein Personalia 60th Birthday:
As of 1980, L.A. Vainshtein's work consists of more than 100 titles.
Learn of his major contributions to Soviet Diffraction theory:
1947 – 1950: diffraction, theory of open cavities & open waveguides
1947: problem of wave diffraction at the open waveguide end reduced to an integral equation for the current flowing on the waveguide wall.
"Radiation from large openings"
"Limits of validity of the Huygens' principle"
Theory of Wave Diffraction by metal gratings & Theory of Thin Vibrators
Associate of P.L. Kapitsa, V.A. Fock, G.D. Malyuzhinets, & M.G. Belkina
Derived a nonlinear theory of traveling-wave tube (1956-1957)
High-power magnetron devices: Stability of oscillation
Theory of Signals
Theory of Microwave plasma diagnostics
USSR Diffraction Workshops & Microwave-electronics lecturer
No mention of Ufimtsev37. L.A. Vainshtein's Obituary:
Principal scientist of USSR Academy of Sciences, Institute of Physical Problems
Lev Al'bertovich Vainstein died 8 September 1989 (born 6 December 1920)
Continued the Tradition of the school of Theoretical Physics of V.A. Fock & M.A. Leontovich
Moscow State University1946 – 1957: he worked at a defense institute1957 – 1989: he worked at Institute of Physics Problems1947: Theory of diffraction
, the problem of radiation from the open end of a waveguide
Properties & theory of open resonators
Ultra-High frequency electronics:
Non-linear theory of traveling-wave tubes
"Calculation of powerful continuous magnetron type generators" (P.L. Kapitsa's proposal & development)
No mention of Ufimtsev38. Pyotr Kapitsa, Online Nobel Prize Biography:
Extremely important scientist of USSR, Institute of Physical Problems in Moscow
Student of A.F. Ioffe, also of Rutherford
Nobel Prize in Physics, 1978
Strong magnetic fields, low temperature physics, & cryogenics39. P.L. Kapitsa’s Obituary:
Famous and Great physicist of USSR & World
Created Institute of Physics (Physical) Problems in Moscow in 1934
Co-authored a paper with Dirac in 1933 "on the reflection of electrons from a standing light wave"
Discovery of Superfluidity of liquid Helium
Collaboration with L.D. Landau: theory of superfluidity
Birth of Physics of quantum liquids
M.V. Lomonosov gold metal
Electronics of high power40. First Soviet Radar Development Study:
Pulsed L-band radar, “Zenit”, 1938 (before West's development of radar)
1920-30s L-band Magnetron Development: world's highest level in achieved output power and frequency
1937 – 1938 Kharkov, Ukraine, UIPT
1920s Academian A. Ioffe, number-one Soviet physicist, director of Leningrad Institute of Physics & Technology
Soviet celebrities involved (1932 – 1937): V.A. Fok, P.L. Kapitsa, Lev Landau
WWII radar used in USSR, not Soviet made, Backward Engineering
Connection between Landau, microwave and radar
Landau went to P.L. Kapitsa’s institute in 1937
Atmospheric-duct effect discovery
Necessity of large-scale radio-wave propagation research
41. Lev D. Landau’s group in Moscow 1956:
L.A. Vainshtein, I.E. Dzyaloshinskii, and L.D. Landau are shown in this 1956 photograph.
Others shown: S.S. Gershtein, L.P. Pitaevskii, R.G. Arkhipov, L.A. Prozorova, A.A. Abrikosov, I.M. Khalatnikov, and E.M. Lifshitz.
Ufimtsev is not in the photograph.
42. Springer Overview of Diffraction:
Contributor to Soviet/Russian work: V.M. Babich
Shorter the wave, the poorer the convergence of the series & integrals
Asymptotic methods, wavelength small
“Asymptotic methods are certain methods yielding the approximate value of the unknown functions. They are based on physical ideas and formal transformations, mostly without a rigorous foundation.”
Method of canonical problems
Development of parabolic-equation method
No mention of Ufimtsev
43. Joseph B. Keller’s 1962 paper on Geometric Theory of Diffraction (GTD):
GTD: an extension of Geometric Optics
Usual rays of Geometric Optics: straight or curved lines of light travel
Introduces a new form of rays called Diffracted rays:
Caused by edges, corners, or vertices of boundary surfaces;
Modified form of the Fermat’s principle;
Huygens' wavelet construction.
A field is associated with each ray.
A point's total field is the sum of the fields on all rays that pass through that point where a field is associated with each ray.
The Amplitude of the field on a ray varies per the principle of conservation of energy
in a narrow tube of rays.
The Phase of a ray's field is proportional to the optical length of the ray from some reference point.
They disappear as wavelength goes to zero;
The immediate neighborhood of the point of diffraction affects a coefficient's value;
"Canonical" problems used to determine these coefficients.
Complex or imaginary rays
Diffraction effects at a caustic or focus: requires the application of a caustic correction factor"Edge-Diffracted Rays":
GTD's fundamental premise: propagation of light is a "local phenomenon" because the light's wavelength is very small
Laws of propagation, reflection, and refraction:
Used to specify the behavior of "usual" rays;
These usual laws fail to specify what happens to a ray when its hits an edge or vertex, or grazes a boundary surface;
"Such rays must give rise to diffracted rays. We hypothesize that they do.";
This hypothesis: "diffraction is an edge effect" (Thomas Young's idea).
Mathematically testing of this hypothesis:
A.J.W. Sommerfeld's solution to the problem of diffraction of a plane wave by a semi-infinite screen with a straight edge (Optics
Incident, reflected, and diffracted waves (rays);
If Incident wave (ray) is propagating in a direction normal to the edge of the screen, the diffracted wave is cylindrical with the edge as its axis & the diffracted rays are produced that are normal to the edge and which leave it in all directions.
"When the incident rays in the direction of propagation of the incident wave are oblique to the edge of the screen, the diffracted wave in Sommerfeld's solution is conical.
This means that the diffracted wave fronts are parallel cones with the edge as their common axis. The straight lines orthogonal to these cones also appear to come from the edge, and can be identified with our diffracted rays."
Edge-diffracted rays defined by the Law of edge diffraction (proposal):
Cone of diffracted rays produced as incident ray hits an edge;
Fermat's principle for edge diffraction.
Kirchhoff method: method of physical optics
A. Rubinowicz’s contribution in 1924
W. Braunbek’s contribution in 1950
Indirect experimental verification of the existence of edge diffracted rays & of the law of edge diffraction: photograph of bright line in shadow, evolute of a disk edge
"Fields Diffracted by Straight Edges":
Keller's diffracted field derivation is compared to Sommerfeld's exact solution for diffraction of a plane scalar wave by a half plane (Optics
, 1954): agreement, determines edge diffraction coefficient D
Next, he compares his results for a wedge of angle (2 - n)pi with Sommerfeld's exact solution for a wedge. He claims agreement. For n = 2, the wedge becomes a half-plane.
"Fields Diffracted by Curved Edges":
Kirchhoff theory, Braunbek’s modification, Diffraction coefficient
u electromagnetic field and D edge diffraction coefficient
u, acoustic pressure
force ~ total scattering Cross-section
Incident pressure wave P amplitude
"Corner or Tip Diffraction":
Law of vertex diffraction & Fermat's principle for vertex diffraction
“Creeping waves”: discovered in oscillating measurements in radar back-scattering cross sections
V.A. Fock & C.L. Pekeris analysis
GTD Further Developments: any kind of Wave propagation: water waves, elastic waves, quantum-mechanical waves, surface waves, etc.
The mathematical framework of the GTD Field construction is the application of the leading part of the asymptotic expansion of the exact field for small values of wavelength (λ) or large values of the propagation constant (κ).
American Diffraction worker in 1962 (1960)
A very important paper: based on research that was funded by the Air Force Cambridge Research Laboratory, Office of Aerospace Research.
GTD: an asymptotic method of determining the diffracted field in terms of raysKeller provides no mathematical basis
to support his "Law of Edge Diffraction" other than saying that it is obtained from Sommerfeld's solution to the problem of diffraction of a plane wave by a semi-infinite screen with a straight edge:No mathematical structure is provided to describe the cone of diffracted rays.44. Uslenghi’s 1978 book on Electromagnetic Scattering:
Principle of local field:
Local geometrical & electrical properties of the scatter in the immediate neighborhood of a point of reflection and diffraction
High-frequency diffraction problems:
Total field is the sum of the individual field contributions
45. B.Z. Katsenelenbaum’s review of Weinstein’s 1955 book on Diffraction and Super High Frequency Electronics:
Academic publication of an outstanding scientist's work of 40 years
Editorial board headed by S.M. Rytov
600 pages of one fourth of Weinstein's work
Learned more about L.A. Weinstein (Vainshtein)
Important book but it’s a Russian publication
46. Additional Soviet Diffraction Works (List):
Online List of Soviet Works: Generalized Method of Eigenoscillations47. Additional Soviet Workers in Diffraction Theory, 1976 paper:
Generalized Natural-oscillation method & Diffraction Theory
N.N. Voitovich, B.Z. Katsenelbaum, and A.N. Sivov
Reference to L.A. Vainshtein
No mention of Ufimtsev
48. B.Z. Katsenelenbaum’s 1994 paper on Electromagnetic field:
Property of Nonapproximability
Moscow Diffraction worker
Very important paper: surface(s), current(s), and field (s)
49. A.N. Sivov passing in September 2007:
Chief Research at Institute of Radio Engineering & Electronics
Moscow State University & Doctoral degree in 197850. V.G. Niz’ev’s 2002 paper on Diffraction:
Most general & rigorous approach to diffraction problems:
Mentions Ufimtsev’s 1962 paper & Vainshtein’s 1988 book on Electromagnetic Waves
Poor convergence of series
This paper proposes a new approach for vector theory of diffraction:
Use of Hertz vector in the Kirchhoff integral
Diffraction patterns: vector approach, “presence of ‘poles’ – zero-field points against the usual diffraction pattern of bright and dark fringes.”
Solutions satisfy Reciprocity principle
Another Russian diffraction worker51. L.A. Vainshtein and V.D. Zubakov’s 1962 book on Extraction of Signals from Noise:
Specular points – patches, depends strongly on orientation of object (time variation)
Number of specular points increase as shape of object becomes more complicated.
Diffraction theory: scattered wave- sum of fields due to various “diffracted rays” from the object’s surface specular points
Radar problems, detection, “Scintillating object”
52. P.L. Kapitsa and L.A. Vainshtein‘s 1964 book on High-Power Microwave: 
Proof of joint expertise in High-Power Microwave Electronics
53. L.A. Vainshtein’s 1957 paper on Electron Waves:
Linear properties of tube with waves running in both directions
Theory of driving a waveguide & periodic structure
Currents & electron waves
His work on Periodic waveguide began in 1953 (reference)
No mention of Ufimtsev
54. L.A. Vainshtein and E.A. Tishchenko’s 1976 paper on Plasma Wave Diagnostics:
Plasma wave diagnostics based on Short wave probing
Asymptotic solution, wave probing, cylindrical plasma
Virtual rays – Diffraction – Profile
Interested in dielectric constant characteristics of plasma
Negative dielectric constant in plasma core
Curved ray segment – Circular rays
A very important paper: potential application to stealth technology
55. N.G. Alexopoulos, et al.’s 1994 paper on 'Method of Virtual Rays':
Acknowledge that Soviet/Russian scientist, Yu. I. Orlov created this approach
Claims Impedance boundary conditions on scatterer
Problems of diffraction by a perfectly or an imperfectly conducting wedge
Work of Orlov, Vainshtein & other Russians: not compared to Ufimtsev’s PTD
Electrical radius parameter
No analytical solution available for material-coated wedge
A very important paper: Linkage between Alexopoulos & Ufimtsev (UCLA)
No physical justification is presented for this approach.
56. Y.A. Kravtsov and Y.I. Orlov’s 1980 paper on Geometric Optics:
Soviet work on Diffraction
Concept of Fresnel volume of rays
L.A. Vainshtein footnote (page 753)
Non stationary Waves (pulses, wave packets) in dispersive media
Space-Time Geometric Optics
Analytical solution exist only for limited number of special cases
Develop a universal numerical program of analysis of high-frequency fields
Problem of scattering by a potential
L.A. Vainshtein provided valuable advice & remarks57. Y.A. Kravtsov and Y.I. Orlov’s 1983 paper on Caustics, Catastrophes, and Wave Fields:
“Modern view of caustics as the singularities of mappings performed by rays”
Theory of the singularities of differentiable mappings (catastrophe theory)
Asymptotic method for describing the field for penumbral caustics
Caustics: concentration of a wave field; types and characteristics of caustics
Acoustic, optical, electromagnetic, and seismic cases can be detected by physical instruments
Deterministic & random caustics
Review the present state of the problem of finding caustic fields as of 1983
This problem has two aspects: geometric and field aspects
V.I. Arnol'd, H. Whitney, and R. Thom contributions
Classification of structurally stable caustics has been created
Classification of standard integrals describing diffraction of fields near structurally stable caustics has been created, too
Uniform asymptotic expansion of the field in the presence of caustics of arbitrary complexity:
Actual construction procedure has serious difficulties:
Complicated rays identification & caustic type classification
Problem of corresponding standard integrals tabulation
Penumbral caustics and Penumbral fields:
Penumbral caustics of diffraction rays
Theory of edge singularities
Theory of edge catastrophes
Structurally unstable caustics (point foci & singular caustics) exist
Bound wave beams in waveguiding systems
A very important paper on Caustics & their analytical nature (standard integrals & standard functions)
No mention of Ufimtsev
Reference to L.A. Vainshtein's work on Open Resonators and Open Waveguides
58. L.A. Vainshtein’s 1976 paper on Pulsed Wave Field Propagation:
Narrow-band high-frequency pulse in homogeneous media
Linear Electromagnetic Wave
Problems pertaining to Diffraction and propagation of waves, waves cannot be regarded as monochromatic:
Key Principal part of a high-frequency pulse: the part governed by frequencies closest to the pulse carrier frequency
Radar, short pulses (nanoseconds) are strongly deformed even when propagation is over relatively short distances
“Even in recent years, most authors place unjustifiably large trust in the analytic formalism, and if numerical calculations are made the results are frequently not evaluated in the proper manner.”59. V.A. Fock’s 1965 book on Electromagnetic Diffraction and Wave Propagation:
Chapter 2: The distribution of currents induced by a plane wave on the surface of a conductor (Fock, 1948):
Magnetic Field Mapping, Universal function G()
Surface current density - surface current distribution
Amplitude of scattered wave derived
Chapter 3: Theory of diffraction by a paraboloid of revolution (Fock, 1957):
Introduction of parabolic potentials P and Q
Boundary conditions formulated without use of finite difference equations
Chapter 4: Diffraction of a plane electromagnetic wave by a perfectly conducting paraboloid of revolution (Fock and Fedorov, 1958)
Chapter 5: The field of a plane wave near the surface of a conducting body (Fock, 1946):
Method of parabolic equation
A very important work: New physical concepts
Generalization of physical theory but also inverse way: arise from approximate methods
Asymptotic diffraction theory
Parabolic wave equation (Leontovich): replacement of full wave equation
Transverse Diffusion model of Short Wave Diffraction (Malyughinetz)
Atmospheric Waveguide: stratified atmosphere
No mention of Ufimtsev
60. V.A Fock’s 1948 paper on New Methods in Diffraction Theory:
Key idea on page 154:
“Indeed, the field of the scattered wave is generated by the currents induced on the surface (in skin-layer) by the incident wave. These currents are given by our formulae. Thus, by applying well-known theorems on the vector potential due to a given current distribution, we may, in principle, calculate the field for arbitrary distances from the reflecting body.”61. V.A. Fock Personalia, 70th Birthday, 1968:
Academician Vladimir Aleksandrovich Fock is one the world's most eminent theoretical physicists
Authored ~ 200 articles and 5 monographs
Originator of the "Fock method," "Fock space," "Fock theory," "Fock's formulas", and "Fock's transform
Fock's ideas had a profound impact on the development of theory:
One of the founders of the Quantum Theory of Many-Particle Systems
General relavity: " the general principle of relativity is not feasible as a physical principle applying to arbitrary reference systems"
Solved the insoluble problem "the problem of the conformal mapping of a quadrange with zero angles onto a half plane
Studied the diffraction of radio waves around the earth's surface
Major contributor to the field of Diffraction theory
Worked on applied problems: the theory of luminosity of surfaces of arbitrary shape
Philosophic problems of Physics of great interest
The influence of the ideas of theoretical physics on philosophy
"He actively opposes vulgar materialism in the name of genuinely scientific materialism."
Fock's study of the fundamental significance of approximation methods (1936)
Fock's far reaching work on quantum mechanics, classical and quantum field theory or mathematical physics is found in many books.
No mention of Ufimtsev62. J.A. Cullen’s 1958 paper on Surface Currents and Diffraction:
Fock’s integral equation solved for induced surface current per application of diffraction by a paraboloid
“Behavior in the boundary zone is to a great extent independent of the precise shape of the object”
California Institute of Technology investigator
Beginning of RESULTS PAPER derived from RESEARCH on PROBLEMS of DIFFRACTION, SCATTERING, and PROPAGATION of WAVES.