Abstract

The effect of noise on the modulation transfer function was studied by means of threshold measurements. White noise and 1/f noise of various levels and different cutoff frequencies were displayed on a television screen together with a sinusoidally modulated bar pattern. The signal-to-noise threshold necessary for perception was measured as a function of the spatial frequency of the bar pattern. This signal-to-noise threshold, in addition to being strongly dependent on the bar-pattern frequency is also dependent on the rms value and the frequency distribution of the noise as well as the difference between the bar-pattern frequency and medium frequency of the noise. An attempt was made to explain the results by visual observation of the bar pattern in the presence of narrow-bandwidth noise.

© 1970 Optical Society of America

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References

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  1. J. Nachmias, J. Opt. Soc. Am. 57, 421 (1967).
    [Crossref]
  2. F. L. van Nes and M. A. Bouman, J. Opt. Soc. Am. 57, 401 (1967).
    [Crossref]
  3. H. A. W. Schober and R. Hilz, J. Opt. Soc. Am. 55, 1086 (1965).
    [Crossref]
  4. J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).
    [Crossref]
  5. R. Roehler, Vision Res. 2, 391 (1962).
    [Crossref]
  6. R. W. Gubisch, J. Opt. Soc. Am. 57, 407 (1967).
    [Crossref]
  7. J. W. Coltman and A. E. Anderson, Proc. IRE 48, 858 (1960).
    [Crossref]
  8. A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
    [Crossref] [PubMed]

1967 (3)

1966 (1)

1965 (1)

1962 (2)

1960 (1)

J. W. Coltman and A. E. Anderson, Proc. IRE 48, 858 (1960).
[Crossref]

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Figures (15)

Fig. 1
Fig. 1

Roll-off characteristic of 1/f filter for three different low cutoff frequencies. The solid line represents the function G ( f ) = 1 / [ f ( MHz ) ] 1 2. The spatial frequency scale is for 1.8-m viewing distance.

Fig. 2
Fig. 2

Signal-to-noise threshold as a function of spatial frequency, for four different subjects. White noise 0–5 MHz ~0–32.5 cycles/deg for 1.8-m observing distance; 1 Vrms.

Fig. 3
Fig. 3

Signal-to-noise threshold as a function of spatial frequency. 1 Vrms white noise 0–5 MHz ~0–32.5 cycles/deg for 1.8-m observing distance. – – – Measured in August 1967, — measured in December 1967, □□□ measured with method 2.

Fig. 4
Fig. 4

Signal-to-noise threshold as a function of the cathode voltage, which is inversely proportional to the TV-screen luminance. 1 Vrms white noise 0–5 MHz ~0–32.5 cycles/deg, for 15, 0.4, and 1.9 cycles/deg.

Fig. 5
Fig. 5

Threshold contrast ΔL/L as a function of spatial frequency. — Measured by the authors, 1.8-m distance; ●●● measured by Patel, 1.1-m distance, 2-mm artificial pupil, 1000 td. □□□ DePalma, 3-m distance. △△△ DePalma, 0.9-m distance.

Fig. 6
Fig. 6

Signal threshold as a function of spatial frequency for different kinds of noise. — No noise; ××× White noise, 1 Vrms, 0–5 MHz ~0–32.5 cycles/deg; –●–●– 1/f noise, 1 Vrms, low cutoff 25 kHz ~0.14 cycles/deg, high cutoff 5 MHz ~32.5 cycles/deg; ●●● 1/f noise, 1 Vrms, low cutoff 80 kHz ~0.5 cycles/deg, high cutoff 5 MHz ~32.5 cycles/deg; – – – 1/f noise, 1 Vrms, low cutoff 150 kHz ~0.85 cycles/deg, high cutoff 5 MHz ~32.5 cycles/deg.

Fig. 7
Fig. 7

Signal threshold as a function of spatial frequency for white noise (0–5 MHz ~0 32.5 cycles/deg) of different levels. — 0 Vrms, ●●● 0.6 Vrms, —●—●— 1.8 Vrms, – – – – 0.3 Vrms, +++ 1.2 Vrms.

Fig. 8
Fig. 8

Signal-to-noise threshold as a function of spatial frequency, for different observing distances; 1 Vrms white noise. ●●● 0.9 m, — — — 1.8 m, —— 3.6 m.

Fig. 9
Fig. 9

Signal-to-noise threshold as a function of the number of bars/picture for a constant spatial frequency of 6 cycles/deg. Comparison of results reported by different authors. 1 Vrms white noise 0–5 MHz. — Measured by Coltman, ○○○ measured by the authors in August 1967, ××× measured by the authors in February 1968.

Fig. 10
Fig. 10

Signal-to-noise threshold as a function of the number of bars/picture for 2 cycles/deg (– – –) and 15 cycles/deg (——) ○○○ Measured in August 1967, ××× measured in February 1968.

Fig. 11
Fig. 11

Signal threshold as a function of observing distance for 15, 2, and 6 cycles/deg. Comparison of results reported by different authors. ○○○ Measured by the authors, ××× measured by DePalma, □□□ measured by Schober.

Fig. 12
Fig. 12

Signal threshold as a function of noise level for different spatial frequencies. △△△ 0.4 cycles/deg, ××× 2.0 cycles/deg, ○○○ 10 cycles/deg, +++ 20 cycles/deg, —— fitted by S t h = a ( R 2 + N 2 ) 1 2.

Fig. 13
Fig. 13

Ratio of the threshold signal with noise to the threshold signal without noise as a function of the median frequency of narrow noise bands of ≃200-kHz bandwidth.— △—△— 96 kHz ~0.64 cycles/deg, — — — 500 kHz ~3.3 cycles/deg, —×—×— 1.5 MHz ~10 cycles/deg, —□—□— 2.5 MHz ~16.7 cycles/deg.

Fig. 14
Fig. 14

Signal-to-noise threshold as a function of the bandwidth of the noise for 3.3 and 10 cycles/deg. Comparison between measured (——) and calculated (– – –) curves.

Fig. 15
Fig. 15

Signal-to-noise threshold as a function of spatial frequency of white and 1/f noise, 1 Vrms. Comparison between measured and calculated curves. ××× Calculated for 1/f noise, ○○○ calculated for white noise, – – – measured with 1/f noise, —— measured with white noise.

Equations (3)

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Δ L / L ~ 0.6 S ( V rms ) ,
( S / N ) t h S 1 = [ μ S μ 2 ( Δ f 2 ) μ ] 1 2 / [ μ ( Δ f 2 ) μ ] 1 2 .
( S / N ) t h S 1 = [ μ N μ 2 S μ 2 ( Δ f 2 ) μ ] 1 2 / [ μ N μ 2 ( Δ f 2 ) μ ] 1 2 .