Dependencies of Motion Assimilation and Motion Contrast on Spatial Properties of Stimuli: Spatial-frequency Nonselective and Selective Interactions Between Local Motion Detectors
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Two supra-threshold lateral interactions, the grating-induction effect, 1 and the contrast–contrast effect, 2,3 were compared regarding their dependence upon inducing grating spatial frequency, inducing and “victim” grating contrast, and inducing grating extent. Both effects cause “victim” gratings to be matched non-veridically. The respective magnitude of the effects was measured in common units which indexed the veridicality of contrast matches across a wide range (-0.9 to 0.9) of “victim” grating contrast. Grating induction had a low-pass, and contrast-contrast had a high-pass spatial frequency response, crossing over at ca. 1 c/d. Maximal grating induction strength exceeded that of contrast–contrast for 5 of 6 observers. Observers demonstrating strong grating induction tended to show weak contrast-contrast magnitudes, and vice versa. When inducing contrast was 0.75, the departures from veridical matching varied with “victim” grating contrast. For low frequencies (0.03125-0.125 c/d) grating induction produced a skewed unimodal departure from veridical matching, peaking at “victim” grating contrasts of 0.5. The pattern became bimodal at higher spatial frequencies (0.25-2.0 c/d) peaking at “victim” contrasts of ca. -0.3 and 0.5. Contrast–contrast caused symmetrical departures from veridicality which were consistent across spatial frequency, peaking at “victim” contrasts of ca. ±0.5. Both grating induction and contrast–contrast magnitudes decreased with reductions in inducing grating height, implying spatially extended mechanisms. With increasing inducing grating spatial frequency, however, the summation space-constant for grating induction decreased, whereas it increased for contrast–contrast.
Spatial frequency
High contrast
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Experiments were done to examine the minimum separation with respect to spatial frequency required for two superimposed gratings to be processed independently in the visual system. The contrasts of all stimuli were well above the detection threshold. The lack of independent processing was measured by the observers' failure to see both gratings as separate sinusoids; changes in the apparent contrast or spatial frequency of one grating when the other was present; and changes in the ability to discriminate small differences in the contrast or spatial frequency of one grating when the second grating was present. All measures point to a lack of independent processing when the gratings differ by less than 2 octaves. When they differ by more than 2 octaves, they are seen as separate, apparent spatial frequency is not altered systematically, and discrimination performance essentially is unaffected. However, the apparent contrast of the high-frequency grating varies, depending on whether its bars are seen against the bright bars or against the dark bars of the low-frequency grating.
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The off-axis pivot-point mounting for toroidal uniform line-space (TULS) gratings and spherical varied line-space (SVLS) is presented: One scans the spectrum by rotating the grating about the pivot point. The best choice for the location of the point is discussed: For a monochromator the location is chosen such that the grating is moved approximately along the bisector of the subtended angle; for a spectrometer, it is chosen such that the grating is moved approximately along the direction of the incident ray. Minimizing the spectral defocusing caused by the rotation of the grating determines the optimum length of the pivot arm. The pivot points for TULS and SVLS gratings are found to be located on opposite sides with respect to the normal to the grating. In a comparison of the optical performance, the spectral focusing is similar, but the spatial aberrations can be fewer for a SVLS grating.
Monochromator
Line (geometry)
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The properties of the moiré fringes in Talbot interferometry are analyzed for a small inclined angle beta between the two grating planes, which is produced by rotation of the beam splitter grating about the axis perpendicular to the lines of the grating. Theoretical analyses indicate that the tilt angle of the resultant moiré fringes is less sensitive to beta than when the small inclined angle is formed by rotation of the beam splitter grating about the axis parallel to the lines direction of the grating as described earlier [Appl. Opt. 38, 4111 (1999)] and that contrast of the moiré fringes decreases with an increase in beta or in the spatial frequency of the grating and may result in impaired measurement accuracy. The validity of the theoretical analyses is illustrated by experiments.
Moiré pattern
Talbot effect
Beam splitter
Ultrasonic grating
Spatial frequency
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A novel optical testing method termed the grating-slit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the grating-slit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometrical-optics model for the grating-slit test is presented and the fringe contrast ratio with respect to the slit width and object-grating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio.
Slit
Spatial filter
Image plane
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High contrast
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Spatial frequency
Transient (computer programming)
Square (algebra)
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Fringe formation in the two-grating interferometer is analyzed in the presence of a small parallelism error between the diffraction gratings assumed in the direction of grating shear. Our analysis shows that with partially coherent illumination, fringe contrast in the interference plane is reduced in the presence of nonzero grating tilt with the effect proportional to the grating tilt angle and the grating spatial frequencies. Our analysis also shows that for a given angle between the gratings there is an angle between the final grating and the interference plane that optimizes fringe contrast across the field.
Moiré pattern
Electromagnetically induced grating
Spatial frequency
Ultrasonic grating
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