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We investigate the expression of non-Kolmogorov turbulence in terms of Zernike polynomials. Increasing the power-law exponent of the three-dimensional phase power spectrum from 2 to 4 results in a higher proportion of wave-front energy being contained in the tilt components. Closed-form expressions are given for the variances of the Zernike coefficients in this range. For exponents greater than 4 a von Kármán spectrum is used to compute the variances numerically as a function of exponent fordoi:10.1364/josaa.13.000517 fatcat:2u4idnwmr5h7zpwma7rnvlajnm