Abstract

We have analyzed the principal sources of noise in a commercially available 2-D scanning microdensitometer which we use to estimate the noise power spectra of radiographic films. Two kinds of noise have been observed. One source, associated with the glass platen of the instrument, is correlated from scan to scan. This source of noise limits our ability to measure the NPS of film samples at low sample optical densities. The other major noise source is uncorrelated from scan to scan and increases exponentially with sample optical density. We have measured both of these component noise sources as well as the total instrument noise as a function of instrument density and spatial frequency. A method for minimizing the effects of instrument noise on estimates of the noise power of film samples is described and demonstrated.

© 1988 Optical Society of America

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References

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  1. R. Shaw, “The Equivalent Quantum Efficiency of the Photographic Process,” J. Photogr. Sci. 11, 199 (1963).
  2. P. Fellgett, “Concerning Photographic Grain, Signal-to-Noise Ratio, and Information,” J. Opt. Soc. Am. 43, 271 (1953).
    [CrossRef]
  3. R. C. Jones, “New Method of Describing and Measuring the Granularity of Photographic Materials,” J. Opt. Soc. Am. 45, 799 (1955).
    [CrossRef]
  4. H. J. Zweig, “Autocorrelation and Granularity. Part I. Theory,” J. Opt. Soc. Am. 46, 805 (1956); H. J. Zweig, “Autocorrelation and Granularity. Part II. Results on Flashed Black and White Emulsions,” J. Opt. Soc. Am. 46, 812 (1956); H. J. Zweig, “Autocorrelation and Granularity. III. Spatial Frequency Response of the Scanning System and Granularity Correlation Effects Beyond the Aperture,” J. Opt. Soc. Am. 49, 238 (1959).
    [CrossRef]
  5. C. E. Shannon, W. Weaver, The Mathematical Theory of Communication (Illinois U. P., Urbana, 1949).
  6. E. C. Doerner, “Wiener-Spectrum Analysis of Photographic Granularity,” J. Opt. Soc. Am. 52, 669 (1962).
    [CrossRef]
  7. E. Klein, G. Langner, “Relations between Granularity, Graininess and the Wiener-Spectrum of the Density Deviations,” J. Photogr. Sci. 11, 177 (1963).
  8. F. J. B. Wall, B. G. Steel, “Implications of the Methods Chosen for the Measurement of the Statistical Properties of Photographic Images,” J. Photogr. Sci. 12, 34 (1964).
  9. M. DeBelder, J. DeKerf, “The Determination of the Wiener Spectrum of Photographic Emulsion Layers with Digital Methods,” Photogr. Sci. Eng. 11, 371 (1967).
  10. H. Frieser, “Noise Spectrum of Developed Photographic Layers Exposed by Light, X-rays, and Electrons,” Photogr. Sci. Eng. 3, 164 (1959).
  11. R. F. Wagner, “Fast Fourier Digital Quantum Mottle Analysis with Application to Rare Earth Intensifying Screen Systems,” Med. Phys. 4, 157 (1977).
    [CrossRef] [PubMed]
  12. J. C. Dainty, R. Shaw, Image Science, Principles, Analysis and Evaluation of Photographic-Type Imaging Processes (Academic, New York, 1974), pp. 276–314.
  13. J. Vranckx, P. Breesch, M. DeBelder, “Two-Dimensional Noise Power Spectra of Radiographic Systems,” Photogr. Sci. eng. 28, 134 (1984).
  14. J. M. Sandrik, R. F. Wagner, K. M. Hanson, “Radiographic Screen-Film Noise Power Spectrum: Calibration and Inter-comparison,” Appl. Opt. 21, 3597 (1982).
    [CrossRef] [PubMed]
  15. G. M. Jenkins, D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, Oakland, CA, 1968), pp. 321–362.
  16. J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986), pp. 291–317.
  17. G. C. Carter, C. H. Knapp, A. H. Nuttall, “Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing,” IEEE Trans. Audio Electroacoust. AU-21, 337 (1973).
    [CrossRef]
  18. Y. Lee, P. L. P. Dillon, “A Cross-Power Spectral Method for Improved Measurement of Film Noise Power Spectra,” Proc. Soc. Photo-Opt. Instrum. Eng. 767, 250 (1987).
  19. J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980), pp. 273–275.
  20. K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).
  21. P. C. Bunch, R. Shaw, R. L. Van Metter, “Signal-to-Noise Measurements for a Screen–Film System,” Proc. Soc. Photo-Opt. Instrum Eng. 454, 154 (1984).
  22. P. D. Welch, “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms,” IEEE Trans. Audio Electroacoust. AU-15, 70 (1967).
    [CrossRef]
  23. R. K. Otnes, L. Enochson, Digital Time Series Analysis (Wiley, New York, 1972).
  24. J. M. Sandrik, R. F. Wagner, “Radiographic Screen-Film Noise Power Spectrum: Variation with Microdensitometer Slit Length,” Appl. Opt. 20, 2795 (1981); K. Koedooder, J. Strackee, H. W. Venemax, “A New Method for Microdensitometer Slit Length Correction of Radiographic Noise Power Spectra,” Med. Phys. 13, 469 (1986).
    [CrossRef] [PubMed]

1987 (1)

Y. Lee, P. L. P. Dillon, “A Cross-Power Spectral Method for Improved Measurement of Film Noise Power Spectra,” Proc. Soc. Photo-Opt. Instrum. Eng. 767, 250 (1987).

1984 (2)

P. C. Bunch, R. Shaw, R. L. Van Metter, “Signal-to-Noise Measurements for a Screen–Film System,” Proc. Soc. Photo-Opt. Instrum Eng. 454, 154 (1984).

J. Vranckx, P. Breesch, M. DeBelder, “Two-Dimensional Noise Power Spectra of Radiographic Systems,” Photogr. Sci. eng. 28, 134 (1984).

1982 (1)

1981 (1)

1977 (1)

R. F. Wagner, “Fast Fourier Digital Quantum Mottle Analysis with Application to Rare Earth Intensifying Screen Systems,” Med. Phys. 4, 157 (1977).
[CrossRef] [PubMed]

1973 (1)

G. C. Carter, C. H. Knapp, A. H. Nuttall, “Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing,” IEEE Trans. Audio Electroacoust. AU-21, 337 (1973).
[CrossRef]

1967 (2)

M. DeBelder, J. DeKerf, “The Determination of the Wiener Spectrum of Photographic Emulsion Layers with Digital Methods,” Photogr. Sci. Eng. 11, 371 (1967).

P. D. Welch, “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms,” IEEE Trans. Audio Electroacoust. AU-15, 70 (1967).
[CrossRef]

1964 (1)

F. J. B. Wall, B. G. Steel, “Implications of the Methods Chosen for the Measurement of the Statistical Properties of Photographic Images,” J. Photogr. Sci. 12, 34 (1964).

1963 (2)

R. Shaw, “The Equivalent Quantum Efficiency of the Photographic Process,” J. Photogr. Sci. 11, 199 (1963).

E. Klein, G. Langner, “Relations between Granularity, Graininess and the Wiener-Spectrum of the Density Deviations,” J. Photogr. Sci. 11, 177 (1963).

1962 (1)

1959 (1)

H. Frieser, “Noise Spectrum of Developed Photographic Layers Exposed by Light, X-rays, and Electrons,” Photogr. Sci. Eng. 3, 164 (1959).

1956 (1)

1955 (1)

1953 (1)

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986), pp. 291–317.

J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980), pp. 273–275.

Breesch, P.

J. Vranckx, P. Breesch, M. DeBelder, “Two-Dimensional Noise Power Spectra of Radiographic Systems,” Photogr. Sci. eng. 28, 134 (1984).

Bunch, P. C.

P. C. Bunch, R. Shaw, R. L. Van Metter, “Signal-to-Noise Measurements for a Screen–Film System,” Proc. Soc. Photo-Opt. Instrum Eng. 454, 154 (1984).

Carter, G. C.

G. C. Carter, C. H. Knapp, A. H. Nuttall, “Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing,” IEEE Trans. Audio Electroacoust. AU-21, 337 (1973).
[CrossRef]

Chan, H-P.

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

Dainty, J. C.

J. C. Dainty, R. Shaw, Image Science, Principles, Analysis and Evaluation of Photographic-Type Imaging Processes (Academic, New York, 1974), pp. 276–314.

DeBelder, M.

J. Vranckx, P. Breesch, M. DeBelder, “Two-Dimensional Noise Power Spectra of Radiographic Systems,” Photogr. Sci. eng. 28, 134 (1984).

M. DeBelder, J. DeKerf, “The Determination of the Wiener Spectrum of Photographic Emulsion Layers with Digital Methods,” Photogr. Sci. Eng. 11, 371 (1967).

DeKerf, J.

M. DeBelder, J. DeKerf, “The Determination of the Wiener Spectrum of Photographic Emulsion Layers with Digital Methods,” Photogr. Sci. Eng. 11, 371 (1967).

Dillon, P. L. P.

Y. Lee, P. L. P. Dillon, “A Cross-Power Spectral Method for Improved Measurement of Film Noise Power Spectra,” Proc. Soc. Photo-Opt. Instrum. Eng. 767, 250 (1987).

Doerner, E. C.

Doi, K.

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

Enochson, L.

R. K. Otnes, L. Enochson, Digital Time Series Analysis (Wiley, New York, 1972).

Fellgett, P.

Frieser, H.

H. Frieser, “Noise Spectrum of Developed Photographic Layers Exposed by Light, X-rays, and Electrons,” Photogr. Sci. Eng. 3, 164 (1959).

Hanson, K. M.

Holje, G.

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

Jenkins, G. M.

G. M. Jenkins, D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, Oakland, CA, 1968), pp. 321–362.

Jennings, R. J.

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

Jones, R. C.

Klein, E.

E. Klein, G. Langner, “Relations between Granularity, Graininess and the Wiener-Spectrum of the Density Deviations,” J. Photogr. Sci. 11, 177 (1963).

Knapp, C. H.

G. C. Carter, C. H. Knapp, A. H. Nuttall, “Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing,” IEEE Trans. Audio Electroacoust. AU-21, 337 (1973).
[CrossRef]

Langner, G.

E. Klein, G. Langner, “Relations between Granularity, Graininess and the Wiener-Spectrum of the Density Deviations,” J. Photogr. Sci. 11, 177 (1963).

Lee, Y.

Y. Lee, P. L. P. Dillon, “A Cross-Power Spectral Method for Improved Measurement of Film Noise Power Spectra,” Proc. Soc. Photo-Opt. Instrum. Eng. 767, 250 (1987).

Loo, L-N.

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

Nuttall, A. H.

G. C. Carter, C. H. Knapp, A. H. Nuttall, “Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing,” IEEE Trans. Audio Electroacoust. AU-21, 337 (1973).
[CrossRef]

Otnes, R. K.

R. K. Otnes, L. Enochson, Digital Time Series Analysis (Wiley, New York, 1972).

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980), pp. 273–275.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986), pp. 291–317.

Sandrik, J. M.

Shannon, C. E.

C. E. Shannon, W. Weaver, The Mathematical Theory of Communication (Illinois U. P., Urbana, 1949).

Shaw, R.

P. C. Bunch, R. Shaw, R. L. Van Metter, “Signal-to-Noise Measurements for a Screen–Film System,” Proc. Soc. Photo-Opt. Instrum Eng. 454, 154 (1984).

R. Shaw, “The Equivalent Quantum Efficiency of the Photographic Process,” J. Photogr. Sci. 11, 199 (1963).

J. C. Dainty, R. Shaw, Image Science, Principles, Analysis and Evaluation of Photographic-Type Imaging Processes (Academic, New York, 1974), pp. 276–314.

Steel, B. G.

F. J. B. Wall, B. G. Steel, “Implications of the Methods Chosen for the Measurement of the Statistical Properties of Photographic Images,” J. Photogr. Sci. 12, 34 (1964).

Van Metter, R. L.

P. C. Bunch, R. Shaw, R. L. Van Metter, “Signal-to-Noise Measurements for a Screen–Film System,” Proc. Soc. Photo-Opt. Instrum Eng. 454, 154 (1984).

Vranckx, J.

J. Vranckx, P. Breesch, M. DeBelder, “Two-Dimensional Noise Power Spectra of Radiographic Systems,” Photogr. Sci. eng. 28, 134 (1984).

Wagner, R. F.

J. M. Sandrik, R. F. Wagner, K. M. Hanson, “Radiographic Screen-Film Noise Power Spectrum: Calibration and Inter-comparison,” Appl. Opt. 21, 3597 (1982).
[CrossRef] [PubMed]

J. M. Sandrik, R. F. Wagner, “Radiographic Screen-Film Noise Power Spectrum: Variation with Microdensitometer Slit Length,” Appl. Opt. 20, 2795 (1981); K. Koedooder, J. Strackee, H. W. Venemax, “A New Method for Microdensitometer Slit Length Correction of Radiographic Noise Power Spectra,” Med. Phys. 13, 469 (1986).
[CrossRef] [PubMed]

R. F. Wagner, “Fast Fourier Digital Quantum Mottle Analysis with Application to Rare Earth Intensifying Screen Systems,” Med. Phys. 4, 157 (1977).
[CrossRef] [PubMed]

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

Wall, F. J. B.

F. J. B. Wall, B. G. Steel, “Implications of the Methods Chosen for the Measurement of the Statistical Properties of Photographic Images,” J. Photogr. Sci. 12, 34 (1964).

Watts, D. G.

G. M. Jenkins, D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, Oakland, CA, 1968), pp. 321–362.

Weaver, W.

C. E. Shannon, W. Weaver, The Mathematical Theory of Communication (Illinois U. P., Urbana, 1949).

Welch, P. D.

P. D. Welch, “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms,” IEEE Trans. Audio Electroacoust. AU-15, 70 (1967).
[CrossRef]

Zweig, H. J.

Appl. Opt. (2)

IEEE Trans. Audio Electroacoust. (2)

G. C. Carter, C. H. Knapp, A. H. Nuttall, “Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing,” IEEE Trans. Audio Electroacoust. AU-21, 337 (1973).
[CrossRef]

P. D. Welch, “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms,” IEEE Trans. Audio Electroacoust. AU-15, 70 (1967).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Photogr. Sci. (3)

R. Shaw, “The Equivalent Quantum Efficiency of the Photographic Process,” J. Photogr. Sci. 11, 199 (1963).

E. Klein, G. Langner, “Relations between Granularity, Graininess and the Wiener-Spectrum of the Density Deviations,” J. Photogr. Sci. 11, 177 (1963).

F. J. B. Wall, B. G. Steel, “Implications of the Methods Chosen for the Measurement of the Statistical Properties of Photographic Images,” J. Photogr. Sci. 12, 34 (1964).

Med. Phys. (1)

R. F. Wagner, “Fast Fourier Digital Quantum Mottle Analysis with Application to Rare Earth Intensifying Screen Systems,” Med. Phys. 4, 157 (1977).
[CrossRef] [PubMed]

Photogr. Sci. eng. (1)

J. Vranckx, P. Breesch, M. DeBelder, “Two-Dimensional Noise Power Spectra of Radiographic Systems,” Photogr. Sci. eng. 28, 134 (1984).

M. DeBelder, J. DeKerf, “The Determination of the Wiener Spectrum of Photographic Emulsion Layers with Digital Methods,” Photogr. Sci. Eng. 11, 371 (1967).

H. Frieser, “Noise Spectrum of Developed Photographic Layers Exposed by Light, X-rays, and Electrons,” Photogr. Sci. Eng. 3, 164 (1959).

Proc. Soc. Photo-Opt. Instrum Eng. (1)

P. C. Bunch, R. Shaw, R. L. Van Metter, “Signal-to-Noise Measurements for a Screen–Film System,” Proc. Soc. Photo-Opt. Instrum Eng. 454, 154 (1984).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

Y. Lee, P. L. P. Dillon, “A Cross-Power Spectral Method for Improved Measurement of Film Noise Power Spectra,” Proc. Soc. Photo-Opt. Instrum. Eng. 767, 250 (1987).

Other (7)

J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980), pp. 273–275.

K. Doi, G. Holje, L-N. Loo, H-P. Chan, J. M. Sandrik, R. J. Jennings, R. F. Wagner, MTF’s and Wiener Spectra of Radiographic Screen-Film Systems, FDA 82-8187 (U.S. Department of Health and Human Services, Rockville, MD, Apr.1982).

C. E. Shannon, W. Weaver, The Mathematical Theory of Communication (Illinois U. P., Urbana, 1949).

R. K. Otnes, L. Enochson, Digital Time Series Analysis (Wiley, New York, 1972).

G. M. Jenkins, D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, Oakland, CA, 1968), pp. 321–362.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986), pp. 291–317.

J. C. Dainty, R. Shaw, Image Science, Principles, Analysis and Evaluation of Photographic-Type Imaging Processes (Academic, New York, 1974), pp. 276–314.

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Figures (8)

Fig. 1
Fig. 1

Total microdensitometer NPS as a function of instrument density and spatial frequency. Instrument configured as used for noise power measurement of photographic materials.

Fig. 2
Fig. 2

Microdensitometer NPS measured with glass platen removed and illumination optics refocused to account for the associated change in optical path length.

Fig. 3
Fig. 3

Coherence function of two independent scans of the microdensitometer (glass platen in place).

Fig. 4
Fig. 4

Cross spectrum of two scans of the microdensitometer (glass platen in place) at zero instrument density.

Fig. 5
Fig. 5

Predicted total instrument NPS of the microdensitometer obtained by summing the platen and electronic noise components.

Fig. 6
Fig. 6

Measured NPS of the microdensitometer after applying the noise reduction methods described in the text.

Fig. 7
Fig. 7

Predicted NPS of the microdensitometer for the noise reduction method described in the text.

Fig. 8
Fig. 8

High density noise reduction. Spectra measured at an instrument density of 5.35 are: (— —) film NPS without instrument noise reduction; (——) film NPS with instrument noise reduction; (- - - - - -) true film NPS; (– – –) instrument NPS; and (— · —) film NPS without noise reduction less the instrument NPS.

Equations (5)

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r x y 2 = G x y 2 G x x G y y ,
b [ G x y ] ( 1 - γ x y 2 ) G x x G y y n ,
W k ( f l ) = L Δ x N | j = 1 N T j exp [ - 2 π i N ( j - 1 ) ( l - 1 ) ] | 2 ,
W ( f l ) = ( log 10 e ) 2 T D 2 Q ˙ 2 · 1 MTF ap 2 ( f l ) · 1 MTF el 2 ( f l ) · 1 M k = 1 M W k ( f l ) ,
G k ( f l ) = L Δ x N j = 1 N T 1 j exp [ + 2 π i N ( j - 1 ) ( l - 1 ) ] × m = 1 N T 2 , m exp [ - 2 π i N ( m - 1 ) ( l - 1 ) ] ,

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