Abstract

A method of coherent spatial filtering of optical sound records is proposed. Theoretical analysis shows that these methods provide suppression of scratch images and of worn sound track noise by 10–14 dB, i.e., to the level of a new sound record. It is shown that linear processing of a corrected image is inefficient, and only its nonlinear processing leads to an improved SNR. Three methods of realizing nonlinear transformation are suggested. Results of the experiment are in good agreement with theory.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967).
    [CrossRef]
  2. D. G. Falconer, Appl. OPt. 5, 1365 (1966).
    [CrossRef] [PubMed]
  3. P. L. Jackson, Appl. Opt. 4, 419 (1965).
    [CrossRef]
  4. M. B. Dobrin, A. L. Ingalls, I. A. Long, Geophysics 30, 1144 (1965).
    [CrossRef]
  5. A. VanderLugt, Opt. Acta 15, 1 (1968).
  6. L. R. Rabiner, B. Gold, Theory and Application of Digitial Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

1968 (1)

A. VanderLugt, Opt. Acta 15, 1 (1968).

1967 (1)

1966 (1)

1965 (2)

P. L. Jackson, Appl. Opt. 4, 419 (1965).
[CrossRef]

M. B. Dobrin, A. L. Ingalls, I. A. Long, Geophysics 30, 1144 (1965).
[CrossRef]

Dobrin, M. B.

M. B. Dobrin, A. L. Ingalls, I. A. Long, Geophysics 30, 1144 (1965).
[CrossRef]

Falconer, D. G.

Gold, B.

L. R. Rabiner, B. Gold, Theory and Application of Digitial Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Helstrom, C. W.

Ingalls, A. L.

M. B. Dobrin, A. L. Ingalls, I. A. Long, Geophysics 30, 1144 (1965).
[CrossRef]

Jackson, P. L.

Long, I. A.

M. B. Dobrin, A. L. Ingalls, I. A. Long, Geophysics 30, 1144 (1965).
[CrossRef]

Rabiner, L. R.

L. R. Rabiner, B. Gold, Theory and Application of Digitial Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

VanderLugt, A.

A. VanderLugt, Opt. Acta 15, 1 (1968).

Appl. OPt. (1)

Geophysics (1)

M. B. Dobrin, A. L. Ingalls, I. A. Long, Geophysics 30, 1144 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

A. VanderLugt, Opt. Acta 15, 1 (1968).

Other (1)

L. R. Rabiner, B. Gold, Theory and Application of Digitial Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Coherent spatial filtering of sound tracks.

Fig. 2
Fig. 2

Dependence from y (at a constant x) of functions θ,θ′,θ2,θ′2 corresponding to distribution of light amplitudes (θ and θ′) and illumination (θ2 and θ′2) in input and corrected sound track images.

Fig. 3
Fig. 3

Harmonic signal spectrum.

Fig. 4
Fig. 4

Correction with a slit filter.

Fig. 5
Fig. 5

Correction with a bandpass filter.

Fig. 6
Fig. 6

Sound track of a 2-kHz signal with a 100-μm wide scratch (top) and the same corrected with a bandpass filter with X = 0.86 mm and Y = 0.1 mm.

Fig. 7
Fig. 7

Sound track of a 4-kHz signal with a 100-μm wide scratch (top) and the same corrected with a bandpass filter (Y = 0.2 mm and X = 0.2 mm, 0.38 mm top to bottom).

Fig. 8
Fig. 8

Sound track of a 8-kHz signal with a 100-μm wide scratch (top) and the same corrected with a bandpass filter (X = 0.86 mm and Y = 0.6,0.3,0.1 mm, top to bottom).

Fig. 9
Fig. 9

Spatial spectra of sound recordings of 1-, 2-, 4-, and 8-kHz signals prior to filtering (left column, top to bottom, respectively) and after filtering out the scratch noise spectrum (right column).

Equations (47)

Equations on this page are rendered with MathJax. Learn more.

τ ( x , y ) = { 1 , if | y | B + C f ( x / υ ) ; 0 , if | y | > B + C f ( x / υ )
θ = τ + η 1 + η 2 ,
η 1 = rect [ ( y y 1 ) / b ] ,
η 2 = rect [ ( y y 2 ) / b ] ,
T ( f x , f y ) = a i λ F B C f ( x / υ ) B + C f ( x / υ ) exp [ 2 π i ( f x x + f y y ) ] dydx ,
T ( f x , f y ) = a i λ F sin { 2 π f y [ B + C f ( x / υ ) ] } π f y exp ( 2 π i f x x ) d x .
f ( x / υ ) = A C cos ( 2 π x / Λ ) .
T ( f x , f y ) = a i λ F π | f y | { sin ( 2 π | f y | B ) J 0 ( 2 π | f y | A ) + sin ( 2 π | f y | B ) × n = 0 n = ( 1 ) n J 2 n ( 2 π | f y | A ) [ δ ( f x 2 n Λ ) + δ ( f x + 2 n Λ ) ] + cos ( 2 π | f y | B ) n = 0 n = ( 1 ) n J 2 n + 1 ( 2 π | f y | A ) × [ δ ( f x 2 n + 1 Λ ) + δ ( f x + 2 n + 1 Λ ) ] } ,
θ = ( τ + η 1 + η 2 ) * sin ( π y Y / λ F ) π y ,
θ = τ + η 1 + η 2 ,
λ F C f ( x / υ ) + B Y ,
Y / ( 2 λ F ) 1 / b .
η 1 = b sin [ π ( y y 1 ) Y / λ F ] π ( y y 1 ) ,
η 2 = b sin [ π ( y y 2 ) Y / λ F ] π ( y y 2 ) .
θ = τ b sin [ π ( y y 1 ) Y / λ F ] π ( y y 1 ) + b sin [ π ( y y 2 ) Y / λ F ] π ( y y 2 ) .
I l θ 2 d y .
I l τ 2 d y + l η 2 2 d y .
I l θ 2 d y
I l τ 2 d y + l η 2 2 d y .
b 2 sin 2 ( π y Y / λ F ) ( π y ) 2 d y .
I l θ d y ,
I l τ d y + l η 1 d y .
I l τ 2 d y + l ( 2 τ η 1 + η 1 2 ) d y .
θ ( y 2 ) < θ ( y 1 ) .
b Y / λ F < 1 b Y / λ F .
Y < λ F / 2 b ,
P b 2 sin 2 [ π ( y y 2 ) Y / λ F ] [ π ( y y 2 ) ] 2
J 0 P b 2 sin 2 [ π ( y y 2 ) Y / λ F ] E 0 [ π ( y y 2 ) ]
J 0 Δ E 0 l P b 2 sin 2 [ π ( y y 2 ) Y / λ F ] [ π ( y y 2 ) ] 2 d y ,
J 0 P Δ b 2 Y E 0 λ F .
2 J 0 [ C f ( x / υ ) + B ] J 0 P b 2 Y / E 0 λ F ,
P ( 1 b Y / λ F ) 2 = E O .
λ F b Y ( 1 b Y / λ F ) 2 ,
I = I * + k ( E E 0 ) ,
P [ 1 b sin ( π y Y / λ F ) π y ] 2
2 [ I * + k ( P E 0 ) ] [ C f ( x / y ) + B ] 2 kbP
I * + k ( P E 0 ) 2 k P .
I * + k ( P E 0 ) 2 k P = 5 .
k E 0 / I * = 1 / 40 .
I = k E .
4 E 0 { b sin [ π ( y y 2 ) / λ F ] π ( y y 2 ) } 2
4 k E 0 λ F b 2 Y
2 [ C f ( x / υ ) + B ] I * λ F 4 E 0 k b 2 Y .
I * λ F 4 k E 0 b Y .
k E 0 J 0 = ( 1 b Y / λ F ) 2 9 + ( 1 b Y / λ F ) 2 .
X υ / 2 λ F < f .
I 1 = I 0 ( 0.127 ) 2 j = j 0 j = ( 2.5 ) 2 ( j + 0.5 ) 2 ,

Metrics