D. H. Kelly, "Visual nonlinearity measurement," J. Opt. Soc. Am. 71, 368A (1981).

V. Virsu and P. Laurinen, "Long-lasting afterimages caused by neural adaptation," Vision Res. 17, 853–860 (1977).

C. W. Tyler, "Observations on spatial frequency doubling," Perception 3, 81–86 (1974).

B. G. Cleland, W. R. Levick, and K. J. Sanderson, "Properties of sustained and transient ganglion cells in the cat retine," J. Physiol. (London) 228, 649–680 (1973); see also C. Enroth-Cugell and J. G. Robson, "The contrast sensitivity of retinal ganglion cells," J. Physiol. (London) 187, 517–552 (1966).

W. Richards and T. B. Felton, "Spatial frequency doubling: retinal or central?" Vision Res. 13, 2129–2137 (1973).

C. Rashbass, "The visibility of transient changes of luminance," J. Physiol. (London) 210, 165–186 (1970).

C. A. Burbeck and D. H. Kelly, "Retinal mechanisms inferred from measurements of threshold sensitivity versus suprathreshold orthogonal mask contrast," in Proceedings of Topical Meeting on Recent Advances in Vision (Optical Society of America, Washington, D.C., 1980), paper ThB4.

B. G. Cleland, W. R. Levick, and K. J. Sanderson, "Properties of sustained and transient ganglion cells in the cat retine," J. Physiol. (London) 228, 649–680 (1973); see also C. Enroth-Cugell and J. G. Robson, "The contrast sensitivity of retinal ganglion cells," J. Physiol. (London) 187, 517–552 (1966).

W. Richards and T. B. Felton, "Spatial frequency doubling: retinal or central?" Vision Res. 13, 2129–2137 (1973).

See, for example, I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965). This integral is evaluated on p. 372 (Formula 3.631-9) in terms of the beta function *B*, where *B*(*x, y*) = [Γ(*x*)Γ(*y*)]/Γ(*x* + *y*).

D. H. Kelly, "Visual nonlinearity measurement," J. Opt. Soc. Am. 71, 368A (1981).

D. H. Kelly and R. E. Savoie, "Theory of flicker and transient responses. III. An essential nonlinearity," J. Opt. Soc. Am. 68, 1481–1490 (1978).

D. H. Kelly, "Frequency doubling in visual responses," J. Opt. Soc. Am. 56, 1628–1633 (1966).

C. A. Burbeck and D. H. Kelly, "Retinal mechanisms inferred from measurements of threshold sensitivity versus suprathreshold orthogonal mask contrast," in Proceedings of Topical Meeting on Recent Advances in Vision (Optical Society of America, Washington, D.C., 1980), paper ThB4.

V. Virsu and P. Laurinen, "Long-lasting afterimages caused by neural adaptation," Vision Res. 17, 853–860 (1977).

B. G. Cleland, W. R. Levick, and K. J. Sanderson, "Properties of sustained and transient ganglion cells in the cat retine," J. Physiol. (London) 228, 649–680 (1973); see also C. Enroth-Cugell and J. G. Robson, "The contrast sensitivity of retinal ganglion cells," J. Physiol. (London) 187, 517–552 (1966).

K. I. Naka and W. A. H. Rushton, "S-potentials from luminosity units in the retina of fish (cyprinidae)," J. Physiol. (London) 185, 587–599 (1966).

C. Rashbass, "The visibility of transient changes of luminance," J. Physiol. (London) 210, 165–186 (1970).

W. Richards and T. B. Felton, "Spatial frequency doubling: retinal or central?" Vision Res. 13, 2129–2137 (1973).

K. I. Naka and W. A. H. Rushton, "S-potentials from luminosity units in the retina of fish (cyprinidae)," J. Physiol. (London) 185, 587–599 (1966).

See, for example, I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965). This integral is evaluated on p. 372 (Formula 3.631-9) in terms of the beta function *B*, where *B*(*x, y*) = [Γ(*x*)Γ(*y*)]/Γ(*x* + *y*).

B. G. Cleland, W. R. Levick, and K. J. Sanderson, "Properties of sustained and transient ganglion cells in the cat retine," J. Physiol. (London) 228, 649–680 (1973); see also C. Enroth-Cugell and J. G. Robson, "The contrast sensitivity of retinal ganglion cells," J. Physiol. (London) 187, 517–552 (1966).

C. W. Tyler, "Observations on spatial frequency doubling," Perception 3, 81–86 (1974).

V. Virsu and P. Laurinen, "Long-lasting afterimages caused by neural adaptation," Vision Res. 17, 853–860 (1977).

K. I. Naka and W. A. H. Rushton, "S-potentials from luminosity units in the retina of fish (cyprinidae)," J. Physiol. (London) 185, 587–599 (1966).

C. Rashbass, "The visibility of transient changes of luminance," J. Physiol. (London) 210, 165–186 (1970).

B. G. Cleland, W. R. Levick, and K. J. Sanderson, "Properties of sustained and transient ganglion cells in the cat retine," J. Physiol. (London) 228, 649–680 (1973); see also C. Enroth-Cugell and J. G. Robson, "The contrast sensitivity of retinal ganglion cells," J. Physiol. (London) 187, 517–552 (1966).

C. W. Tyler, "Observations on spatial frequency doubling," Perception 3, 81–86 (1974).

V. Virsu and P. Laurinen, "Long-lasting afterimages caused by neural adaptation," Vision Res. 17, 853–860 (1977).

W. Richards and T. B. Felton, "Spatial frequency doubling: retinal or central?" Vision Res. 13, 2129–2137 (1973).

C. A. Burbeck and D. H. Kelly, "Retinal mechanisms inferred from measurements of threshold sensitivity versus suprathreshold orthogonal mask contrast," in Proceedings of Topical Meeting on Recent Advances in Vision (Optical Society of America, Washington, D.C., 1980), paper ThB4.

See, for example, I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965). This integral is evaluated on p. 372 (Formula 3.631-9) in terms of the beta function *B*, where *B*(*x, y*) = [Γ(*x*)Γ(*y*)]/Γ(*x* + *y*).

Regardless of the form of the nonlinearity, its odd part can create only odd harmonics and therefore can have no effect on the second harmonic. Conversely, the even part of the nonlinearity can create only even harmonics and therefore can have no effect on the fundamental. Thus, even if these two frequency components are responses of the same nonlinear transducer, they represent separate, independent, additive aspects of its behavior. This is true for any transducer function that can he expanded in a Taylor series, and it does not depend on the phase of the stimulus. It follows from the fact that odd powers of a sinusoidal input (sin^{2n-1} θ and cos^{2n-l} θ) can always be expressed as a (finite) sum of odd harmonic terms, sin(2*n* - 2*k* - 1)θ and cos(2*n* - 2*k* - 1)θ, while even powers (sin^{2n} θ and cos^{2n} θ) can be expressed as a sum of even harmonic terms, in the latter case always of the form cos 2(*n* - *k*)θ, where *K* ranges from 0 to *n* - 1. See Ref. 10, pp. 25, 26.