For 15 years, lensless microscopes have been constructed based on the use of holography, a digital CCD detector, and a computer for image reconstruction by use of, e.g., Fourier transformation. Thus, no lens is involved and therefore the conventional resolution limit of half the wavelength no longer applies. Instead of being limited by the wavelength, the resolution is in this case limited by how exact one can measure the phases of the light. It is remarkable that the interference-limited resolution is approximately 0.01X, whereas the diffraction-limited resolution is only of the order of 0.5X. It is my hope that by combining these two techniques it will be possible to increase the magnification in optical systems by at least an order of magnitude. The calculations at so indicate that information does not necessarily decrease with distance.