Exploring Distance-Doppler Effects: Innovations in Locating, Isolating, and Signal Synthesis

1. “distance-Doppler” effectand applications v. guruprasad inspired research

2. discovery applications locating isolating synthesis sample calculation realizability premise empirical support status contents

3. discovery ω r = 0 r

4. discovery ω r = 0 r

5. discovery ω ω1 r = 0 r1 r

6. ω ω1 ω2 r = 0 r1 r2 r discovery • frequency scaling effect • generic ~ Doppler • but asymmetric • α ~ at receiver • r ~ source distance • application classes • locating • isolating • synthesis (& analysis)

7. ω ω1 ω2 r = 0 r1 r2 r discovery • frequency scaling effect • generic ~ Doppler • but asymmetric • α ~ at receiver • r ~ source distance • application classes • locating • isolating • synthesis (& analysis) z3 z2 z1

8. ω ω1 ω2 r = 0 r1 r2 r discovery • frequency scaling effect • generic ~ Doppler • but asymmetric • α ~ at receiver • r ~ source distance • application classes • locating • isolating • synthesis (& analysis) z

9. ω ω2 r = 0 r2 r locating α3 α2 α1

10. ω ω1 r = 0 r1 r locating α3 α2 α1

11. ω ω1 ω2 r = 0 r1 r2 r locating • α:temporal parallax • in frequency domain • receiver-controlled • atan(α)∈ (- π/2, π/2) • ∆ω/ω ≡ z = α r • complementary: • spatial freq. • directional antennae α3 α2 α1

12. ω ω1 ω2 α3 α2 α1 -α1 r1 r2 location verification • special case α < 0 • narrows the spectrum • notch filter to verify r

13. locating applications • fast, precise, monostatic triangulation • half the round-trip delay • simpler, faster computation • infinite range of “parallax angles” • “true stealth radar” • where no phones go! • seeing = ranging • infinite range ~ P ∝ R-2 • “reverse-engineered” from astrophysics

14. received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances your mission, should you accept it, is… F1 F2 F3 F

15. received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances separate the signals without involving content or modulation! F1 F2 F3 F

16. received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances H α 1. spread α α F1 F2 F3 F

17. received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances H α G2 α α 2. filter F1 F2 F3 F

18. received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances H α G2 α α H-1 3. down-scale F1 F2 F3 F

19. extracted signal: received signal: F = F1 + F2 + F3 H-1 G2 H F ≈ F2 isolating “co-channel” sources at different distances H α G2 α α H-1 F1 F2 F3 F receiver processing

20. isolating applications • distance-based selectivity • ~ directional antennae, polarizations • orthogonal to modulation • by physics of space • obviates TDM, FDM, CDMA • raises channel capacity to Rayleigh criterion • universal anti-jamming • even noise sources can be isolated out

21. α3 α2 α1 -α1 r1 r2 synthesis α1 optional signal ~ F1 μwave H(α) F3 F2 F0 F1 r r1

22. α3 α2 α1 -α1 r1 r2 synthesis α2 optional signal ~ F2 μwave H(α) F3 F2 F0 F1 r r1

23. F3 α3 F2 α2 α1 F1 -α1 r1 r2 synthesis α2 optional signal ~ F3 μwave H(α) F0 r r2

24. ω ω1 ω2 α3 α2 α1 -α1 r1 r2 synthesis optional signal tune α optical μwave H(α) F3 F2 F0 μwave source F1 r RF tune r

25. synthesis • precise control ~ r • infinite range ~ α • scales up or down • +α– up • - α – down • and generic • almost any waves • no nonlinear media • no b/w, freq. constraints optional signal tune α μwave H(α) r tune r

26. analysis • hi-fi down-scaling • even gamma rays • to μ-waves or RF • nifty analytical tool • if realizable tune α UV RF H(-α)

27. synthesis applications • universal wave sources • say using GW microwave sources • to yield THz, visible, UV or even gamma rays • modulation & coherence with power • without lasing • COTS-realizable • main constraint: source phase spectrum • expect better with non lasing photonic sources • e.g. z = 10 with r = 1 m easily using Terfenol-D

28. corrected: 2005-11-09 sample calculation • For z = 1 at r = 100 m, we need α = z / r = 1 / 100 m = 0.01 / m • From theory in paper, α≡ β / c , whereβ= normalized rate of change of grating or sampling intervals • We need β ≡ α c = 0.01 / m * 3x108 m / s = 3x106 / s, i.e. must vary the intervals by a factor of 3x106 every second! • But (a) variation is exponential, and (b) can be repeated over smaller intervals. • Same effective βpossible over intervals of 1 ns ≡ 1x10-9 s using e3E6 *1E-9≈ 1.0030045 • Max. change possible with Terfenol-D : 1.008 – 1.012

29. premise • wave speed independent of frequency • exceptions: dispersive media • realm of current research with phase & group velocities • sources of nonzero spectral spread • likely exceptions: CW carriers, lasers • spectral decomposition is receiver’s choice • exposes: usual Fourier assumptions • notably in quantum mechanics

30. receiver’s choice • spectral analysis or selection requires summing • summing is macroscopic • receiver can change during summing • general case is NOT Fourier decomposition • Fourier <=> absolutely zero change • zero change cannot be verified except by distant sources • error is Hubble’s law frequency shifts • overlooked in • all signal processing, spectrometry, even wavelets • all of astronomy & quantum physics

31. diffractive summing detector element static grating corresponding to time = t1 focal plane grating lens

32. diffractive summing detector element static grating corresponding to time = t2 focal plane grating lens

33. diffractive summing detector element static grating corresponding to time = t3 focal plane grating lens

34. summing by unsteady receiver younger rays (from t3) detector element instantaneous sum θ focal plane older rays (from t1) grating lens

35. summing by unsteady receiver younger rays (from t3) detector element n λ = l sin θ θ focal plane older rays (from t1) grating lens

36. n dλ = dl sin θ --- --- dt dt summing by unsteady receiver younger rays (from t3) detector element n λ = l sin θ θ focal plane older rays (from t1) grating lens

37. n dλ = dl sin θ --- --- dt dt summing by unsteady receiver younger rays (from t3) detector element n λ = l sin θ θ focal plane 1 dλ = 1 dl = -β -- --- -- --- older rays (from t1) λ dt l dt grating lens

38. time-varying receiver states t1 t2 changing receiver selection state... t3 time ...stationary in an expanding or shrinking reference frame

39. traditional receiver basis applied states incoming signal receiver states spectral window • receiver ~ spectral window of representative states • a state = a Fourier component mode that can be excited • a state = mode observed if excited • observation by a dot-product with states • as if the states were flowing into the receiver (left) • dot-product ≡ instant-by-instant product (right)

40. traditional receiver basis applied states incoming signal receiver states spectral window (inverted) • receiver ~ spectral window of representative states • a state = a Fourier component mode that can be excited • a state = mode observed if excited • observation by a dot-product with states • as if the states were flowing into the receiver (left) • dot-product ≡ instant-by-instant product (right)

41. evolving receiver basis applied states incoming signal receiver states spectral window time • when receiver window itself slides • relative to world frequency frame • incoming sinusoids appear expanding • own states appear steady

42. evolving receiver basis applied states time applied states incoming signal incoming waves receiver states spectral window spectral window ? time • when receiver window itself slides • relative to world frequency frame • incoming sinusoids appear expanding • own states appear steady • receiver states shorten in world frame • all states ~ same function (exponential λ) ~ in world frame • position in window identifies state

43. evolving receiver basis spectral window received component • Dot-product selects time-varying world wave • receiver states ~ exponential-λin world frame • dot-product ≡ instant-by-instant product • vanishes for sinusoid (broken line) • maximum for similar wave of same starting λ

44. evolving receiver basis spectral window received component • Dot-product selects time-varying world wave • receiver states ~ exponential-λin world frame • dot-product ≡ instant-by-instant product • vanishes for sinusoid (broken line) • maximum for similar wave of same starting λ

45. evolving receiver basis spectral window received component • Dot-product selects time-varying world wave • receiver states ~ exponential-λin world frame • dot-product ≡ instant-by-instant product • vanishes for sinusoid (broken line) • maximum for similar wave of same starting λ

46. evolving receiver basis applied states time applied states incoming signal selected waves receiver states spectral window spectral window time • when receiver window itself slides • selects exponential-λ wave components from world • selected wave components bear distance • λ∝ r or λ∝ r -1 • already well known in cosmology, thanks to…

47. Leonard Parker • Ph.D. thesis, Yale, ca. 1966 • particle wavefunctions in an expanding universe • leonard @ uwm . edu • But what do these eigenfunctions REALLY represent? • in their present incarnation as receiver states ?

48. spectral phase gradients • Green’s function theory • source = collection of radiating points • each radiating point ~ delta function • delta ~ same starting phases • consider their wave-vectors slopes ∝ distance

49. spectral phase gradients space part signal part ∆φ = ∆(k r – ω t) = r ∆k+ k ∆r – ∆(ω t)

50. spectral phase gradients space part signal part ∆φ = ∆(k r – ω t) = r ∆k+ k ∆r – ∆(ω t) k ∆r ~ holography, SAR, interferometry