Max von Laue quotes:

For both reasons, owing to the thermal motion and to the working together of various wavelengths, factors arise which, in a similar manner to the structural factor, exert some influence upon the brightness of the interference points but not upon their location.

For in 1900 all electromagnetic radiation of longer wavelengths was already known at least to the extent that one could not seek in it the more striking characteristics of X-rays such as, for example, the strong penetrating power.

For as long as one has no further point of reference, apart from the position of the maximum, the wavelength thus remains uncertain by an integral factor.

If diffraction or interference phenomena were to be sought it was therefore necessary, in accordance with the basic principles of wave theory, to select for the test arrangement far smaller decisive dimensions than those employed in corresponding tests with visible light.

There is no doubt that I, also, had long been aware of the problem, i.e. producing X-ray interferences, before the inherent difficulties had finally been surmounted.

Notwithstanding these major arguments the wave theory initially did not meet with complete acceptance.

With crystals we are in a situation similar to an attempt to investigate an optical grating merely from the spectra it produces... But a knowledge of the positions and intensities of the spectra does not suffice for the determination of the structure. The phases with which the diffracted waves vibrate relative to one another enter in an essential way. To determine a crystal structure on the atomic scale, one must know the phase differences between the different interference spots on the photographic plate, and this task may certainly prove to be rather difficult.