Reports 513 Wasielewski P. Establishment of lens epithelial cell 10. Dziedzic DC, Reddan JR, Hartzer MK, Misra IC. Estab- lines from Emory and cataract resistant mice and their lishment of cell lines from cryopreserved lens-capsule response to hydrogen peroxide. Lens Eye Tox Res. epithelial preparations and whole lenses. Invest Oph- 1989;6:687-701. thalmol Vis Sci. 1992; 33:1038. Masking Potency and Whiteness of have previously shown5'6 that when the spectral density of white image noise is constant, contrast sensitivity in Noise at Various Noise Check Sizes noise is independent of viewing distance, eccentricity, Heljd Kukkonen* Jyrki Rovamo,^ retinal illuminance, and exposure time as long as con- and Risto Nasanen% trast sensitivity is lower with spatial noise than without, that is, the effect of external noise exceeds the effect of Purpose. The masking effect of spatial noise can be in- internal noise. The spectral density of external spatial creased by increasing either the rms contrast or check noise equivalent to the internal neural noise2'4 is small- size of noise. In this study, the authors investigated the est at medium spatial frequencies and increases to- largest noise check size that still mimics the effect of ward low and high spatial frequencies.7 Therefore, white noise in grating detection and how it depends on only high spectral densities of external spatial noise the bandwidth and spatial frequency of a grating. will exceed the effect of internal noise at low and high Methods. The authors measured contrast energy thresh- spatial frequencies. olds, E, for vertical cosine gratings at various spatial frequencies and bandwidths. Gratings were embedded The effect of spatial noise on detection threshold in two-dimensional spatial noise. The side length of the is determined by its spectral density within the spatial square noise checks was varied in the experiments. The frequency range of the stimulus or, rather, the detec- 2 8 9 spectral density, N(0,0), of white spatial noise at zero tion filter used by the visual system. ' ' However, the frequency was calculated by multiplying the noise check spectral density of white noise has a constant value area by the rms contrast of noise squared. at all spatial frequencies, and its masking effect can 2 Results. The physical signal-to-noise ratio at threshold therefore be described by a single number. For spatial [E/N(0,0)]°l5 was initially constant but then started to noise, generated by adding a random number to each decrease. The largest noise check that still produced a noise check, spectral density is constant at low spatial constant physical signal-to-noise ratio at threshold was frequencies but dies out oscillating at high spatial fre- directly proportional to the spatial frequency. When quencies. Thus, such spatial noise always has a limited expressed as a fraction of grating cycle, the largest noise bandwidth, and there is a spatial frequency above check size depended only on stimulus bandwidth. The which noise is no more white. smallest number of noise checks per grating cycle To increase the spectral density of spatial noise needed to mimic the effect of white noise decreased consisting of checks, we can either increase the con- from 4.2 to 2.6 when the number of grating cycles in- creased from 1 to 64. trast of noise or the size of checks. When noise con- trast cannot be increased further, the only way to in- Conclusion. Spatial noise can be regarded as white in crease the spectral density is to enlarge noise checks. grating detection if there are at least four square noise However, an increase in noise check size also reduces checks per grating cycle at all spatial frequencies. Invest the bandwidth within which noise can be considered Ophthalmol Vis Sci. 1995;36:513-518. white. Therefore, it is important to know how large checks can be safely used without compromising the When external image noise is strong in comparison whiteness of noise within the detection filter used by to the internal neural noise of the visual system, it the visual system. A common estimate for the band- reduces human contrast detection performance.1"4 width of the detection filter is 1 to 2 octaves,2'9 but it The reduction is determined by the signal-to-noise ra- depends on both the bandwidth of the stimulus8 and tio, which is constant at the detection threshold.2'4 We the characteristics of the noise.2 These results imply that there is no single estimate for the bandwidth From the *Department of Communication and Neurosdence, University of Keek, within which noise is collected. Therefore, the largest Staffordshire, United Kingdom; the ^Department of Vision Sciences, University of noise check size that still mimics the effect of white Aston, Birmingham, United Kingdom; and the \Department of Physiology, University of Helsinki, Helsinki, Finland. noise in grating detection has to be determined exper- Supported in part by The Finnish Ministry of Education, the Association of Finnish imentally. Ophthalmic Opticians, the Information Centre of Optics Business, the Finnish Culture Foundation, and the National Agency for Health and Welfare. RN is In this report, we used various noise check sizes, supported by The Academy of Finland. grating areas, and spatial frequencies, and we investi- Submitted far publication December 29, 1993; revised September 7, 1994; accepted September 9, 1994. gated at which square check sizes contrast energy Proprietary interest category: N. threshold in noise is maximal and still proportional Reprint requests: Jyrki Rovamo, Department of Vision Sciences, University of Aston, Aston Triangle, Birmingham B4 7ET, UK. to the spectral density of spatial noise, calculated by Downloaded from iovs.arvojournals.org on 09/30/2021 514 Investigative Ophthalmology & Visual Science, February 1995, Vol. 36, No. 2 multiplying check area by the square of the rms con- trast of noise. METHODS. Contrast, Check Size, and Spectrum of Spatial Noise. The two-dimensional spectral density function3 of spatial noise is given by sin (nfxnx) sin (nfyny) xnycj nfxn; irfyny where n^ and Vy are the horizontal and vertical noise check side lengths, c,, is the rms contrast of noise, and f* and fy are the horizontal and vertical spatial frequencies. At low spatial frequencies, where [sin (nfxnx)/ Spatial frequency (c/deg) 2 2 (itfxnx)] [sin (ftfyiiy)/(irfyTiy)] «* 1, the spectrum is flat and, according to equation (1), the spectral density FIGURE l. The spectral density of two-dimensional spatial of two-dimensional noise can be calculated by multi- noise plotted as a function of spatial frequency along the horizontal frequency axis. The broken line refers to a noise plying the square of the rms contrast of noise c^ by with the noise check side length of 0.1 deg and rms contrast the check area n^riy: of 0.3. The solid line refers to noise with the noise check side length of 0:2 deg and rms contrast of 0.3. The arrows N(0,0)= (2) indicate the cut-off frequency of noise equal to the inverse l of twice the noise check side length, fc = (2n)~ . Hence, noise contrast and noise check size both affect the spectral density of noise. Noise cut-off frequency, f , on the other hand, c noise contrast at each spatial frequency. This variance depends only on the size of the noise check n in the 2 is reflected in the response of the detection mecha- following way : nism, leading to an uncertainty of the presence of the signal and, therefore, a reduction in the human visual (3) performance. Apparatus. The apparatus is described in detail in an earlier study.6 Therefore, only its main features are Along the horizontal (fy = 0) and vertical (fx = provided here. 0) frequency axes of the Fourier space, the spectral Stimuli were generated under computer control density of two-dimensional noise, calculated by equa- on a 16-inch, high-resolution color monitor driven at tion (7), has decreased to 41 % of its maximum value 60 Hz by a VGA graphics board that generated 640 X at the theoretical cut-off frequency of noise. 480 pixels. The pixel size was 0.42 X 0.42 mm2. The Two examples of the spectrum of two-dimensional display was used in a white mode. The average phot- spatial noise, calculated by equation (i), are shown in opic luminance of the display was 50 cd/m2. The lumi- Figure 1. They demonstrate the effect of noise check nance response of the display was linearized by using size on the spectral density function. The side length the inverse function of its nonlinear luminance re- of noise check is doubled, whereas noise contrast is sponse when computing the stimulus images. kept constant. As expected, noise spectral density is To obtain a monochrome signal of 1,024 intensity increased fourfold at low spatial frequencies, and the levels selected from a monochrome palette of 65,536 cut-off frequency of noise, calculated according to intensity levels, we used a video summation device and equation (2), is halved due to the doubling of noise a periodic dithering signal. The contrasts of the grat- check side length. The same effect on the spectral ing stimuli displayed were found to be independent density of noise at low spatial frequencies can be ob- of spatial frequency and orientation up to 2 c/cm. At tained by doubling the noise contrast. This, of course, 4 c/cm contrast decreased by 0.12 log)0 units. does not affect the cut-off frequency of noise. Stimuli. Vertical cosine gratings were created, and The spectral density function of noise represents the experiments were run using a software developed the mean power spectrum of an infinite number of by one of the authors (RN).