A frequency analysis has shown that the formation for wood free paper by visual ranking is determined by the power ratio of wavelength of 6.2 mm to the sum of the powers. That wavelength might be derived from the flocs in the specimens. While that for the wood contained paper is determined by the distribution of light transmission, not by any particular wavelength or waveband.<BR>A group of 183 panelists who had been familiar to paper products compared specimens of wood free-and wood contained-papers along Scheffe's method (modified by Nakaya) in a previous work. The results of this visual qualification of the formation for the specimens by this method have been named observed M-values.<BR>While an image scanner coupled with an IBM-PC/AT compatible computer captured the light transmission images of the specimens. Where the resolution of the images is 50 dpi and the depth of 256 gray levels with the dimension of A 4 area (i.e. 210 mm horizontally and 297 mm vertically).<BR>A frequency analysis of 2-dimensional fast Fourier transform has been applied onto the specimens of 256×256 pixels of area (130 mm each). The transformation produces a 2-dimensional power spectrum. Where each of the peaks shows the direction of repetition of the wave and its wavelength or its frequency. The powers of the peaks on concentric circles in the spectrum (i.e. the peaks have the identical pixel distances from the center of the spectrum) were integrated, subsequently. That makes 1-dimensional spectrum of 127 elements proportional to the inverse of the wavelength.<BR>The linear regressions for all the combinations of the wavelengths (wavebands) of 127×126/ 2 patterns have been conducted with the visual qualifications by the panelists for the wood free paper specimens. The existence ratio of the power of 6.2 mm wavelength only has shown a fair agreement. On the other hand, the case for the wood contained paper found nearly every waveband except for the longer waves approximately than 7 mm wavelength to explain the M-value. That means the distribution of gray levels of transmitted light except the longer waves determines the visual qualification.