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.

**[25]****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

**[26]**Very important paper: this paper demonstrates that U.S had its own expertise in Scattering and Diffraction Theory

Knott & Senior extensive expertise in diffraction theory

**27. 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)

**[27]**There are other Soviets doing diffraction work

**28. 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.”

**[28]**English Diffraction worker

**29. 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

**[29]**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

Complications:

Diffraction processes occur at neighboring points where different diffraction processes take place at same point

Presence of more than one mode of propagation

“Non-reflected contribution”
“Reflected contribution”

Plasma-based Wedge Diffraction for two modes of propagation

2-D & 3-D Edge

**[30]**Danish Diffraction investigator:

No mention of Ufimtsev

**31. 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; &
Caustic infinities.

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 theory

**[31]****32. 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:

Rayleigh scattering

Induced electric & magnetic dipoles

Polarizability tensors

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
disk,

=> Complex disk edge field(dependent on angle of incident).

**[32]**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: [33]**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 work

__Misunderstanding 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.

**[34]**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: **More references:

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)

**[35]****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

**[36]**No mention of Ufimtsev

**37. 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 University

__1946 – 1957: he worked at a defense institute____1957 – 1989: he worked at Institute of Physics Problems____1947: 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)

**[37]**No mention of Ufimtsev

**38. 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, & cryogenics

**[38]****39. P.L. Kapitsa’s Obituary: **
Famous and Great physicist of USSR & World
Remarkable man

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 power

**[39]****40. 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

**[40]**
**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.

**[41]**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

**[42]**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.

Diffraction coefficients:

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*, 1954);

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

Acoustic Diffraction:

u, acoustic pressure
force ~ total scattering Cross-section
Incident pressure wave P amplitude
Acoustic torque

"Corner or Tip Diffraction":

Law of vertex diffraction & Fermat's principle for vertex diffraction

"Surface-diffracted Rays":

“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).

**[43]**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 rays

__Keller 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:

Scattering centers
Canonical geometries
Total field is the sum of the individual field contributions

**[44]**
**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

**[45]**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 Eigenoscillations

**[46]****47. 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

**[47]**No mention of Ufimtsev

**48. B.Z. Katsenelenbaum’s 1994 paper on Electromagnetic field: **Property of Nonapproximability

Near field

**[48]**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 1978

**[49]****50. 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

Semi-empirical approach

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

**[50]**Another Russian diffraction worker

**51. L.A. Vainshtein and V.D. Zubakov’s 1962 book on Extraction of Signals from Noise: **Appendix V:

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”

Wandering inhomogeneities

**[51]**
**52. P.L. Kapitsa and L.A. Vainshtein‘s 1964 book on High-Power Microwave: [52]**Proof of joint expertise in High-Power Microwave Electronics

Radar Applications

**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

Non-gyrotropic media

Currents & electron waves

His work on Periodic waveguide began in 1953 (reference)

**[53]**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

**[54]**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

Practical problem:

Electrical radius parameter

No analytical solution available for material-coated wedge

Postulate

**[55]**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

Heuristic criteria

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 & remarks

**[56]****57. 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

Waveguide caustics:

Bound wave beams in waveguiding systems

**[57]**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:
Pulsed character

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.”

**[58]****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

**[59]**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.”

**[60]****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:

Hartree-Fock Method

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"

Great Mathematician:

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.

**[61]**No mention of Ufimtsev

**62. 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”

**[62]**California Institute of Technology investigator

Beginning of RESULTS PAPER derived from RESEARCH on PROBLEMS of DIFFRACTION, SCATTERING, and PROPAGATION of WAVES.