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OCR for page 31
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY 31 APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY The dependent variable that is the basis of the contrast sensitivity function is the contrast of the sinusoidal test grating. The most commonly used definition of contrast is: where Lmax is the maximum luminance at the peak and Lmin is the minimum luminance at the trough of the sine wave. Contrast may vary from 0.0 (a field of uniform luminance) to 1.0 (where Lmin = 0.0 and Lmax = 2.0 * Lmean since Lmean = (Lmax + Lmin)/2). It is not possible to have a real sinusoidal grating of contrast greater than 1.0, because luminance cannot be less than 0.0. At this time there are no standards for the measurement of the contrast sensitivity function, although there is general understanding of the factors that influence its shape. These factors are discussed below. MEAN LUMINANCE The mean luminance of the sinusoidal gratings has a profound effect on the contrast sensitivity function. At high photopic levels of mean luminance, the normal contrast sensitvity function has a peak sensitivity at about 5 cpd and a high frequency cutoff at about 60 cpd. As mean luminance is lowered, not only do the frequencies of the peak sensitivity and the high frequency cutoff become lower, but also the height of the peak is reduced (Figure 10). At mesopic levels of mean luminance the peak in the contrast sensitivity function has practically disappeared. This peak, which is so prominent at high luminances, is generally believed to reflect the dynamic interaction between excitatory and inhibitory influences in the visual system. RETINAL LOCUS use the print version of this publication as the authoritative version for attribution. Compared with the contrast sensitivity function measured at the fovea, the contrast sensitivity function measured for eccentric retinal loci shows a progressive shift to lower spatial frequencies for both the high frequency cutoff and the frequency of peak sensitivity (Figure 11). In addition there is a progressive lowering of overall contrast sensitivity. This change is believed to reflect the unequal way in which the retinal visual field is projected onto the visual cortex (Daniel and Whitteridge, 1961; Schwartz, 1980). When measured at different retinal eccentricities using sinusoidal gratings whose size and spatial frequency have been adjusted to stimulate equal amounts of visual cortex, the contrast sensitivity function is approximately the same at all retinal loci (Virsu and Rovamo, 1979; Rovamo and Virsu, 1979) as is shown in Figure 12.

OCR for page 31
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY 32 FIGURE 10 Contrast sensitivity functions for different levels of mean luminance. The upper curves were measured with gratings having a mean luminance of 500 cd/m2. The lower curves were measured at 0.05 cd/m2. SOURCE: Campbell and Robson, 1968. Reprinted with permission from F. W. Campbell and J. G. Robson. Copyright 1968 by The Physiological Society. FIELD SIZE Visual sensitivity at a particular spatial frequency depends on how many cycles of the sine wave grating are included in the pattern. Sensitivity increases as more cycles are included up to about 10 complete cycles (Figure 13). Usually the low frequency limit of testing is limited by the largest possible field. For example, in use the print version of this publication as the authoritative version for attribution. order to measure maximum sensitivity at 0.5 cpd, one would need a test field 20 deg square to have 10 complete cycles. TEMPORAL CHARACTERISTICS Both the exposure duration of the grating target and the time course of its onset influence the contrast sensitivity function, especially at the lower spatial frequencies. Figure 14 shows the contrast sensitivity function measured with two different stimulus duration characteristics. Notice that with brief exposure duration or with rapid onset of the grating stimulus, sensitivity to low spatial frequencies is enhanced

OCR for page 31
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY 33 compared with longer duration, more gradual onset stimuli. If gratings are modulated sinusoidally in time, the temporal frequency influences the measured contrast sensitivity function. The interaction between temporal frequency and spatial frequency are represented by a contrast sensitivity surface, as shown in Figure 15 (Kelly, 1979). Notice that contrast sensitivity at low spatial frequencies is higher when the grating is flickered at a relatively high temporal modulation compared with a low temporal modulation. FIGURE 11 A comparison of contrast sensitivity functions for the nasal visual-field half-meridian of the right eye (open symbols and continuous lines) and for the temporal half-meridian of the left eye (filled-in symbols and dashed lines). The values of eccentricity were measured as the angular distance of the fixation point from the middle of the gratings that subtended 10 deg. The nasal eccentricities were 0 deg (half-filled circles), 10 deg (triangles), 20 deg (diamonds), and 30 deg (squares). The temporal eccentricities were 0 deg (half-filled circles), 30 deg (filled squares), 50 deg (filled triangles), and 60 deg (filled circles). The foveal functions were similar for both eyes and are not drawn separately. use the print version of this publication as the authoritative version for attribution. SOURCE: Rovamo and Virsu, 1979. Reprinted with permission from J. Rovamo and V. Virsu. Copyright 1979 by Springer-Verlag.

OCR for page 31
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY 34 FIGURE 12 The photopic contrast sensitivity functions for 25 locations of the visual field. The eccentricities were measured along the various half-meridians of the visual field as indicated on the graphs and in A for the different symbols. The retinal dimensions of the gratings were scaled for equivalent calculated cortical representations. Contrast sensitivity is shown as a function of spatial frequency in the calculated cortical projection images (cycles per millimeter of cortex). In contrast to the data in Figure 12, the contrast sensitivity functions at the different retinal eccentricities are almost identical. SOURCE: Rovamo and Virsu, 1979. Reprinted with permission from J. Rovamo and V. Virsu. Copyright 1979 by Springer-Verlag. use the print version of this publication as the authoritative version for attribution. ORIENTATION The visual system is more sensitive to horizontal and vertical gratings than to other orientations, an example of the oblique effect (Appelle, 1972) wherein horizontal and vertical orientations are more important in vision than are obliques. Figure 16 shows the contrast sensitivity function measured with vertical gratings and for 45 deg orientation gratings. The contrast sensitivity, especially for the high spatial frequencies, is reduced for oblique orientations relative to horizontal and vertical orientations. This orientation anisotropy may be important for calculations of the “effective” visual stimulus.

OCR for page 31
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY 35 FIGURE 13 Contrast sensitivity as a function of the test field size in degrees of visual angle. The number of cycles in each stimulus is the product of the field size and the spatial frequency. Based on data reported by McCann, Savoy and Hall. SOURCE: McCann et al. (1978). use the print version of this publication as the authoritative version for attribution. FIGURE 14 Contrast sensitivity functions for long exposure time with gradual onset and offset (sustained presentation) and for short exposure time with rapid onset and offset (transient presentation). Note that low frequency sensitivity is enhanced and high frequency sensitivity is reduced with transient presentation. Based on data reported by McCann, Savoy, and Hall.

OCR for page 31
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please APPENDIX A: BASIC FACTORS IN SPATIAL CONTRAST SENSITIVITY 36 FIGURE 15 Contrast sensitivity as a function of both spatial and temporal frequency. Each individual curve represents the spatial frequency response at a fixed temporal frequency. SOURCE: Kelly, 1979. Reprinted with permission from D. H. Kelly. Copyright 1979 by the American Institute of Physics in the Journal of the Optical Society of America 69. use the print version of this publication as the authoritative version for attribution. FIGURE 16 Contrast sensitivity function for vertical and oblique orientations. Note the lower sensitivity at oblique orientation. SOURCE: Campbell et al., 1966. Reprinted with permission from F. W. Campbell. Copyright 1966 by The Physiological Society.